PURSUE ULTIMATE FACTS

2025-09-26
A Revelation of the Apocalypse

A Revelation of the Apocalypse

The Apocalypse of St. John, illustrated with an analysis and scholia, in which the meaning is explained by Scripture and the predicted events are shown by histories. A general overview is prefixed hereunto; and at the end of the seventeenth chapter is inserted a refutation of Robert Bellarmine concerning Antichrist, in his third book on the Bishop of Rome. By Thomas Brightman.

CHAPTER 2. (BOOK 2)
1 To the Angel of the Church of Ephesus write, these things says he, that holds those seven stars in his right hand, which walk in the midst of the seven candlesticks;
2 I know your works and your labor, and your patience, and that you cannot suffer the wicked: and have tried them, which say that they are apostles and are not, and have found them liars.
3 And you were burdened, and do endure, and for my name have labored and were not weary.
4 But I have something against you, that you have left your first love.
5 Be mindful therefore from whence you are fallen, and do the first works; or else I will come against you shortly, and remove your candlestick from its place, unless you do repent.
6 But this you have, that you hate the works of the Nicolaitans, which I also hate.
7 Let him that has an ear hear what the spirit says to the Churches, to him that overcomes I will give to eat of that tree of life, which is in the midst of the Paradise of God.
8 To the Angel of the Church of Smyrna write, these things says he that is the first and last, who was dead, and is alive.
9 I know your works and your affliction, and poverty (but you are rich) and the blasphemy of those who say they are Jews and are not, but the synagogue of Satan.
10 Fear none of those things which you will suffer: Behold it shall come to pass, that Satan shall cast some of you into prison, that you may be tried; and you shall have affliction ten days: Be faithful unto death, and I will give you the crown of life.
11 Let him that has an ear, hear what the spirit says to the Churches. He that shall overcome, shall not be hurt by the second death.
12 And to the Angel of the Church of Pergamus write, these things says he, that has that sharp two‑edged sword.
13 I know your works, and where you dwell, to wit, where Satan’s throne is, and that you keep my name, and have not denied my faith, yea even in those days in which Antipas that my faithful martyr was slain among you, where Satan dwells:
14 But I have a few things against you, that you have there those who hold the doctrine of Balaam, who taught Balak to lay a stumbling block before the children of Israel, that they should eat of those things, which were offered to idols, and that they should commit fornication,
15 So also have you them, which hold the doctrine of the Nicolaitans, which I hate.
16 Repent: or else I will come against you quickly and fight with them, with that sword of my mouth.
17 Let him that has an ear, hear what the spirit says to the Churches: I will give to him that overcomes, to eat of the hidden manna, and I will give him a white stone, and a new name written in the stone, which no man knows, but he that receives it.
18 And to the Angel of the Church of Thyatira, write, these things says the Son of God, which has eyes as a flame of fire, and whose feet are like fine brass.
19 I know your works, and love, and service, and faith, and patience, and your works, and your last are more than the first.
20 But I have a few things against you, that you suffer the woman Jezebel, which says she is a prophetess, to teach and deceive my servants, that they should commit fornication and eat of things which are offered to idols.
21 And I gave her time to repent of her fornication: but she has not repented.
22 Behold I will cast her into a bed and them that commit adultery with her into very great affliction, unless they repent of their works.
23 And I will kill her children with death, and all the Churches shall know that I am the searcher of the reins and of hearts, and I will give to every one of you according to your works.
24 And to you I say, and the rest of the Thyatirians, whosoever holds not this doctrine and who have not known the depths of Satan, as they say: I will lay no other burden upon you;
25 Yet that which you have, keep till I shall come:
26 For if any shall overcome, and observe my works unto the end, I will give him power over nations.
27 And he shall rule them with a rod of iron, and they shall be broken in pieces as earthen vessels, as I also have received of my father.
28 And I will give him the morning star.
29 Let him that has an ear, hear what the spirit says to the Churches.

The Resolution. Until now, in common, that which pertains to all the seven churches: that which is proper to each one follows, an epistle being inscribed to each one separately. In each of them there is an inscription, narration, and conclusion. The first three concern churches falling into a worse state: Ephesus, Smyrna, and Pergamum. The other four return to the same, and as the next three are opposed to the first three and are answerable to each other: the Thiatiris to the Ephesians, the Sardis to the Smyrna, the Philippi to the Pergamon. Only Laodicea has no equal to which it may be compared.

Regarding the Ephesian, which holds the first place, the inscription is addressed to the angel by name, describing him as the one who gave the epistle: he holds the seven stars in his right hand and walks amid the candlesticks, verse 1.
The narration, partly respectful praise, commends their labor, patience, and discipline, verse 2.
Then their unwearied desire, verse 3.
Partly reproach, which shows their sin, their first love lost, verse 4.
And the remedy, which he first proposes, teaches what it consists of, in care of their first works; afterward he urges them to use it, partly by denouncing the removal of the candlestick unless it is done in time, verse 5.
Partly by a rehearsal of the cause for which they had been spared hitherto, verse 6.
The conclusion is both epiphonetic, requiring attention, and also rewarding: where the reward is the power to eat from the tree of life, verse 7.
The other analyses shall follow in each of their places.

Scholions.
1 TO the Angel: Every one of the Epistles is inscribed to the pastors, not so that they should keep them private to themselves, but so that they should communicate them with the rest of the church, as has been said before in ch. 1.11. Send them to the seven churches in Asia—Ephesus, Smyrna, etc.—and at the end of each let the reader hear what the Spirit says, not only to the angel but to the churches. They are sent to him by name, partly because he is the dispenser of doctrine, exhortation, reproof, etc., as the use of the church requires. Partly because the safety of the whole congregation rests chiefly upon the integrity of the pastors. Neither are they sent to any one angel, but to the whole, that I may so say, the college of pastors, who are all encompassed by this common term. For there was not one angel of Ephesus, but many, and no prince among them, as is evident from Paul, who sent to Miletus for the elders or bishops of Ephesus (Acts 20:17–28). He would have spared the multitude if anyone had been over them in authority, or at least, wise among his admonitions, he would have spoken one word of obedience to the chief bishop. But this preeminence and principality had not yet been established; it began first after the apostles were removed from human affairs, except that Diotrephes gave some indication thereof.

Therefore, under the name of one Angel, he writes to the whole order of Pastors, for whose praise or disparagement the chief purpose of every epistle is intended. For this is, for the most part, the condition of particular congregations, as their faithfulness and diligence shall be. From this, it follows that at the end the admonition is given to the whole congregation, fitted for the administration by the teachers.

Neither is it to be thought that these epistles were sent separately, and asunder one from another, but that all were written together in a common epistle, such as we have said this whole prophecy is, and that each church obtained from there that which belongs to them separately. And these things are common to all the seven angels, to be applied to every one apart.

¶ To the Church of Ephesus: Of the city Ephesus we have spoken briefly in the eleventh verse of the first chapter: to which are to be added the reason of the order, the force of the name, and the antitype of it, that the counsel of the spirit may be better understood. There may be a double reason for the order: one is that this city settles before our eyes as the Church of the Gentiles, like the Prodigal son who spent his patrimony in a far country (Luke 15:11). And when he returns, we see Christ as an image of the conversion and calling of the Gentiles.

For this city, besides the horrible idolatry of which she was a leader of other cities, it was also subject to great riot, casting out of the city a certain man called Hermodorus, not for any other crime than that he was a thrifty man. Moreover, it is added: Let no one of us excel, but if there be any such, let him be in another place among other men. Tusc. quest. book 5. leaf 125. a voice indeed of beasts, and even in the sentence of Ethnics, worthy of a halter.

For thus says Strabo: All the Ephesians are to be punished by death. Behold, therefore, the prodigal son, coming again to his father, running to meet him, falling to his neck, and kissing him. How is the grace of God to be praised, who has converted us Gentiles, being a gulf of wickedness, the disposition of all which we see in this city, into a most glorious palace of salvation.

We were once princes of naughtiness; now we have become the head of holiness, as among the seven churches: no less excelling in godliness than we did in all wickedness of late. For the Father has commanded the best robe to be brought forth and has killed the fattened calf for our sake.

Another reason for the order is that this city was foremost in embracing faith among all that country, from which it spread to neighboring places. For Paul, coming to Ephesus, was daily disputed in the school of one Tyrannus, and over the space of two years, so that all who dwelt in Asia—both Jews and Gentiles—heard the word of the Lord Jesus (Acts 19:9–10). Therefore it is well made in the same place, the beginning of cities, from which faith began.

Now the force of the name is to be declared. For it shall be clear to everyone that the Holy Ghost has chosen those churches, which even by their very names, as it were by certain marks written on the forehead, should manifest their whole condition. We let pass that Amazon, from whom they report that it took the name, that which follows beneath verse 4, that thou hast left thy first love, teaches sufficiently what the Spirit regarded in this city: namely that Ephesus was, as it were, an omission, whereupon we call her languishing, whose godliness wavered cold in such a sort that at length it is utterly extinguished. How is it to be feared that in this thing also it carries a type of the Gentiles!

Regarding the antitype, we observe that these seven cities embody the universal condition of the churches of the Gentiles. As is clearly stated in the first chapter, each city is not only to be considered on its own, but also the neighboring church that may be directly related to it. What kind of antitypes are these? Were these seven churches meant to be patterns for all churches of that time, or for churches of different times? If we say the former, then in all ages the church spread throughout the world, it agreed with those seven; that is, one should be Ephesus, one Smyrna, one Pergamum, and so on. The same form should have existed in the first times and should exist today, as the teaching of all times dictates. Therefore it is necessary to treat each of them as separate types, in the order in which they are listed. The antitypes are those churches that, whether divided by time or by place, agree with each other in order. The convenience of the matter will become clear within the limits of these conclusions. According to this rule, we make the first Christian church the antitype of the city of Ephesus, which, drawing from the preaching of the apostles, continued even until Constantine the Great, as will be made manifest in what follows. This is the chief of all the following churches, as Ephesus is the first of the seven cities.

¶ These things say he that holds the seven stars: A description of him that sent the Epistles, which is diverse in every part, yet drawn from the former vision, diverse members of it being applied according to the diverse conditions of things. Which teaches abundantly, both the whole former figure to have shadowed out only the administration of things, and also to be proper in a manner and peculiar to the seven Churches. The seven stars in his right hand declare that the power of Christ is notable in defending the Ministers of this Church. He is even as mighty a keeper and faithful maintainer of all his faithful servants, in whatever place of the earth, or whatever timesoever they have been or shall be; yet in some certain places and times, he manifests himself more clearly to the world as an avenger, than everywhere else, as appears both in this city and antitype. As touching the city, Paul, who planted the faith there first, how many adversaries did he find there? I will abide, says he, at Ephesus till Pentecost, for a great door and effectual is opened to me, and the adversaries many: 1 Cor. 16:9. Yet we read not that any calamity came unto him. He was beaten elsewhere and stoned and left for dead: but here Demetrius stirring up the workmen against him, he that holds the stars in his right hand, not only kept Paul free from all evil, but also Caius and Aristarchus and Alexander, pacifying the tumult by the prudence of the town clerk; Acts 19. The same hand shielded Tychicus and Timotheus, the Angels thereafter of the same Church: Ephes. 6:21. 1 Tim. 1:3. And no less the Elders, the ordinary Bishops of the Church, whom Paul called to Miletus to give them his last farewell. At length John came to the same place, and there abode many years, establishing all the neighboring Churches. Neither did the rage of the tyrant proceed to his death: but at length returning from banishment, he died quietly in this city. The power of the mighty and star‑bearing hand gave such safety to his servants. The same power also shone forth in preserving the Pastors through the whole time of the first Church. A huge number indeed of the faithful were slain daily, but this is marvelous, that in the opinion of men it being necessary that the name of Christ should be extinguished utterly, much more the Pastors, against whom the Tyrants raged most of all, there was a daily great increase, that it was spoken then commonly and truly: That the blood of the Martyrs is the seed of the Church. But Christ walks among the candlesticks, as often as he gives a manifest proof of himself being present and regarding diligently all things which pertain to the salvation of the faithful. In what city did he give a show of more plentiful grace and favour, than in Ephesus, to whom for teachers he gave Paul, Apollos, Tychicus, Timotheus, John the Apostle, besides many other Apostolic men? And where or when was Christ more manifestly conversant in the earth since his ascension into Heaven, than in those first times, until about Constantine? He did enrich so abundantly the Church with all gifts, he pricked forward their sluggishness, corrected their negligence, rewarded their virtue, so as he might seem by himself to compass every one, and view their labour with his own eyes. In one and the same manner he is always among the candlesticks, neither does he sit idly, but walks about continually, and comes to visit everything, so that he has no need of a vicar: yet because by outward arguments, this is not often manifested to the world, therefore that which is properly and singularly belonging as it were to one city and time, is alleged.

¶ I know thy works: A narration, and first of praise. And it is common to all the Epistles, in the beginning of the narration, to profess that he knows certainly and tries every angel’s works. Therefore neither shall reward be wanting at any time to virtue, nor just punishment to naughtiness. And as even now I have put in mind of a Vicar, how wickedly serviceable are they, who arrogate to themselves, as an absolute lord, the power over their fellow servants, seeing he thoroughly knows all things, and is not in vain conversant among the candlesticks? The praise of the Ephesians Angel respects either his office, in this verse, or his virtue against outward evils, ver. 3. His office consists, either in administering the word and those things which are wont to accompany it usually, the Sacraments and prayers, or in exercising of discipline. As he says, I know thy labor and thy patience: For the pains which are bestowed in preaching the word, because it is laborious, and full of troubles and grief, is wont to be called labor in the scriptures, as, we pray you brethren that ye as know them that labor among you; &c. 1 Thessalonians 5:12. And they are worthy of double honor: especially they that labor in the word and doctrine: 1 Timothy 5:17. But patience as a necessary companion must be added to the labor of teaching: which the Spirit shows, saying, and your patience. As also Paul, the servant of God must not fight, but must be gentle toward all men, apt to teach, suffering from evil men: teaching them with meekness that is contrary-minded: 2 Timothy 2:23-24. Therefore this church was famous in the faithfulness and diligence of teaching. Behold the example of Paul, who by the span of three years, day and night, ceased not to admonish everyone with tears: Acts 20:31. Do thou also consult from those godly bishops, who loved Paul so greatly, whom also he again loved no less: Acts 20:37-38. Afterwards mind John and the rest. But a matter that is clear need not many words.

As touching her Antitype, the matter is even evident; they never more faithfully gave themselves to teaching. That monster was not yet born, that any should be a pastor, that does not feed at all; or that one should sit in the chair of the teacher, who, being dumb, should be sleepy and distracted with other businesses. There was then no bishop who had the office of teaching and who did not teach most diligently. Even in Rome, where it was fitting that the mystery of iniquity should spring up early, they had not yet ceased from this office. The pastor, at least on every Lord’s Day, plainly and clearly expounded those things that were read from the books of the apostles and prophets. He also admonished and exhorted them to follow those things, which, being holy and good, they had heard rehearsed: Justin, Apolog. 2. The same thing is testified by Clemens, Origen, Tertullian, and Cyprian. But the matter is so clear and manifest that it should be done contrary to this at this day.

¶ And that you cannot bear the wicked: Such was the care of teaching, the manner of their discipline was no less pure and sound: Which first is universally set down, of what sort it was toward all the wicked: afterward specially, what it was toward the clergy, that I may so speak, in the next words, and has tried them which say they are apostles, etc. The general discipline did not tolerate men in any sort living wickedly, and with the offense of others, but according to the manner of their fault, rebuked either privately or before many, if private admonition was unprofitable; then finally it debarred them from holy things if they would not obey those who counseled them well. Regarding Ephesus, it cannot be uncertain, but that this holy rule held there, since Paul taught there for three years, who gave a command to Timothy regarding this matter so diligently and exactly. The observation thereof was famous in the primitive church, as even Pliny testifies in an epistle to Trajan: The Christians are wont, he says, to rise early in the morning to praise Christ as God, for the preservation of their religion, to prohibit murders, adulteries, avarice, cozenage, and the like unto those: Eusebius, book 3, chap. 33, of the Ecclesiastical History from Tertullian. They not only prohibited in word by teaching but also restrained them by holy discipline. They rightly determined that religion could not be preserved otherwise, unless vices be cut off by this spiritual sword. Justin testifies that no man was admitted to the sacrament of the supper except he whose life should answer and accord with his profession, Apoll. 2. But more plainly Tertullian writes thus: There are also exhortations, corrections, and divine censure: it is shown with great gravity that if anyone has offended, he may be sent away from communicating in prayer, both of the assembly and all holy society, where all most approved elders have authority, having obtained that honour not by money but by good report: Apologetics, ch. 39. Origen in his 35th treatise on Matthew. In the churches of Christ, he says, such a custom has held that those who are manifest in great sins, of whom they are convicted, should be cast out from common prayer lest a little leaven of those who pray not from their heart corrupt the whole sprinkling and consent of truth. So in Homily 7 on Joshua: He who, being admonished a third time, refuses to repent, is commanded to be cut off from the body of the church by its rulers. He also shows that priests, sparing one, and neglecting their priestly severity, do work the ruin of the whole church. The epistles of Cyprian are clear witnesses of how holy and religiously he kept it in his church; they also prove how purely the discipline abided hitherto in Rome, as is clear from the epistles of Cyprian to the clergy of Rome, and to Cornelius, and again from them to Cyprian. It is therefore an excellent testament of that time, which, combined with purity of doctrine and sanctity of manners, demonstrates the most wholesome discipline.

¶ And have tried them who say they are apostles. The other part of discipline is toward ecclesiastical men, who were reproved not only for sins in life, but also punished for their ungodliness if they introduced any new ideas and deviated from the truth, which, after proper examination, were found not to agree with the rules of the sanctuary. And great was the courage of the angel in this matter; he was not deterred by great names, but brought them back to a thorough examination, where they boasted they were apostles. It is clear that there were men in Ephesus, as is evident from the instruction given to Timothy: “You should remain in Ephesus so that you may warn some, that they teach no other doctrine, nor listen to endless fables and genealogies that raise questions rather than godly edification, which is by faith.” (1 Timothy 1:3). And Paul also warned the bishops of Ephesus to take care of themselves and the whole flock: “I know that after my departure, fierce wolves will come among you, and some of your own will arise, speaking perverse things, so that they may lead disciples after them.” (Acts 20:29‑30). But the diligence of the pastors removed the deceivers from the hypocrites and did not allow their craft to spread to the destruction of the flock, so the church remained uncorrupted even up to the time of John, who ruled for many years: who eventually, for a time, withdrew, and the care slackened somewhat, as we shall show later. Likewise, in the early church there was such a group of heretics as rare as in all other times. There arose Simonians, Menanderists, Ebionites, Cerinthians, Pseudoapostles, Gnostics, Sabellians, Samosatenians, Manichees, etc. Some of these the apostles themselves pierced with the dart of truth. Paul taught Titus to shun a heretical man after one or two admonitions: Titus 3:10. But after they turned to Christ, many other bright lights rose up, diligently dispelling all heretical darkness. Among them were Agrippa Castor, as Eusebius reports, Justin Martyr, Irenaeus, Tertullian, Cyprian, etc., all of whom fought eagerly for truth against counterfeit apostles. Therefore, as both the city and that former age were perilous due to the impudence of those who, with false titles, claimed to be apostles, they were not less happy thanks to the faithfulness and diligence of such defenders, who were not deceived by a vain show, but brought the matter to the touchstone and showed the whole church that they were most filthy fellows, who would be counted as principal masters.

¶ And thou wast burdened: Hitherto his faithfulness in executing his office, now he rehearsed his virtue against external evils: which were many and great, both of that city and of all the Christian world. The battles of Paul against beasts at Ephesus are famous: 1 Cor. 15:32. But what tranquility could be to the following angels, who should have to do with grievous wolves not sparing the flock: Acts 20:29‑30. It was therefore the commendation of this angel, that he did sustain and endure calamity stoutly, which is declared in a triple degree: that he bear the burden; that he laboured under the burden, and yet was not tired; as though he should say, a great weight indeed of trouble did lie upon thee, under the burden whereof thou groaned, yet thou wast not discouraged that thou shouldst pluck thy neck from the yoke, and betray the truth. It is a manly fortitude to bear troubles and torment. Many bear the yoke cheerfully as long as they feel but a little grief, but to go on constantly among the stings of grief and sorrow is a point of great courage and of heavenly fortitude.

Such was this angel, such also was the whole primitive church. Nero and Domitian had greatly persecuted the church before John wrote these things. And besides Nero and Domitian, it abode patiently under Trajan, Adrian, Antoninus, Severus, Diocletian. The times were never more miserable when the emperors let their labor be hired by the devil to shed Christian blood, which he always thirsts after. Yet the faithful revolted not but continued constantly to the end, becoming at length conquerors, setting up the sign of victory against the devil and all foes.

For what other thing were so many scars and prints, with which many Bishops were marked, who after the tempest of tyrannical persecution driven away, did meet in the Nicene Council, than so many triumphant bows of the victory gotten against the enemies? Paulus Neocesariensis was bereft of the use of both his hands, the sinews being shrunk and cut by the persecutors with a hot iron. Others had both their eyes put out. Others their right hands cut off by the elbow, among which was Paphnutius Aegyptius. In sum a man might have seen a company of famous and picked Martyrs gathered together: Theod. book 1. chap. 7. He was an Angel of an invincible courage, whom so many calamities could not break, yea not bow never so little. Now therefore if we shall gather all these things into one sum, we shall see a most beautiful image of any excellent Church. For behold an Angel sparing no trouble of his own in the labour of teaching, administering the discipline most religiously: suffering none that should offend the Church with his naughtiness: either keeping far away the leaven of heretics, or taking it away most carefully at the very first. And last of all for all these things undergoing boldly whatsoever the wicked enemies were able to inflict upon him. Doth he in any thing need amending? In nothing indeed, if only he had continued in his integrity: but godliness fainteth by little and little unless it be kindled continually: and oftentimes a certain naked profession remain, where all his power is utterly dead & lieth quenched: as we shall see by & by to have happened here.

Referring to the words, Montanus and the vulgar translation distinguish this verse differently, and they also omit and change some words: And have borne a burden and have patience for my name, and have not fainted: So, Aretas, but the first words are set out of order: And have patience and have borne a burden. But these readings lack expressive meaning, which our books have, that conjoin together burden, trouble, and perseverance. The sentence becomes much weaker where the word “trouble” is omitted.

4 But I have somewhat against them Hitherto was the praise: The reprimand is for the leaving of their first love: Of which even a light slacking had not wanted great fault: But to put off the same wholly, how great wickedness: For so the word thou hast left, soundeth: as if the Ephesians angels were like to those widows given to riot, which Paul says, are to be condemned, because they have cast away their first faith, 1 Tim. 5.12. Although this loss of love was nothing to the heinous offence of the widows, For their Apostasy was manifest, his only a faint, or rather no care, and a very great negligence of godly duties, the profession of the truth being kept. But the Spirit speaketh of divers times, as it appeareth from this that he says, that thou hast left thy first love, and in the verse following biddeth them to do the first works. From which it is perceived easily, of what sort was this coldness, to it that the Angel who in the first times of the Gospel received, faithfully executed the office of teaching, and observed diligently everyone’s manners, to which forthwith he applied a remedy by ecclesiastical discipline: afterward in the latter years did so languish, that he was negligently occupied in the first labour, permitted some of his flock to perish through ignorance, some through the infirmity of the flesh to be carried headlong into destruction, no lawful curing undertaken. This is that love, which Christ takes grievously to be laid aside so shamefully. For he shows that he is then truly loved, when his sheep are fed faithfully and with a sincere mind. Whereto pertains that thrice repeated commandment to Peter, If thou lovest me, feed my sheep, John 16:17. But in process of time in this Church this fervency waxed cold or rather altogether vanished away, as is manifest by the reprimand. Such is our infirmity rushing apace no less to the loss and destruction of spiritual life, than our bodies has continually to the graves. Wherefore then is there too much cure of this, and none of that? The Ephesians retained an outward profession, neither were any calamities able to take it from them, as the former verse even now taught, yet in the mean time they decayed by little and little, neglecting those things, without which true godliness cannot consist. And this leaving of love seems to have come to pass then, when John had been sent away into Patmos. Doubtless while he abode at Ephesus he suffered not either doctrine or discipline to decay, but being at length bereft of so vigilant a watchman, they fell into this detested drowsiness. The bishop may serve as an example, although not of that city, yet of a neighbour place, who through the negligence of holy discipline suffered a certain young man delivered to him by John to be kept, to become a thief and a robber. Wherefore John did worthily hit and cast in his teeth his good keeping: Eusebius Histories book 3.23. But however the history is silent in this matter, it is certain that the Ephesians angels fell together into shameful negligence about these times. Of which sort also we find the carelessness of the Church growing in use by little and little.

In the first times, while the Apostles served as presidents and eyewitnesses of all things, the diligence of the Elders was fervent; they both preached the word of God faithfully and furthered the godliness of their flock carefully by discipline, but after two hundred years from Christ’s birth they suffered as all things worsened, by a manifest decline. How did discipline begin to be loosened and corrupted when the Martyrs and Confessors gave rest to those who had fallen, not only without the Bishops’ counsel but also against their will? How this outrageous disturbance of the heavenly rule troubled Cyprian, we may see from his epistles: among other causes of the incumbent persecution many of which he rehearsed, at length he descends to this, and what plagues and what stripes do we not deserve when not even the Confessors keep discipline, who ought to have been an example to others in good manners? Epist. book 4, §4. And not many years later, Eusebius relating the condition of the Church a little before Diocletian began his persecution says: “They, who were thought to be our Pastors, rejecting the bond of godliness, were busily occupied in mutual contentions among themselves.” These things only increased beyond measure—contentions, threatening, emulations, mutual grudges and hatred—following with all their might the preeminence and dominion, as it were kingdoms. Book 8 of History, chapter 1. It must need be that the edge of holy discipline was made blunt in a wonderful manner, which had no force to cut off such noxious herbs. But Ambrose, who rehearsed that the divine rule had vanished quite away before his times, speaking of the Elders, at length infers most clearly: “Whereupon he says both the Synagogue and afterwards the Church had Elders, without whose counsel nothing was done in the Church.” I do not know by what negligence it has grown out of use unless perhaps by the slothfulness or rather pride of the teachers. He was not long after that time, which we call the Primitive Church. Yet he speaks as though some ages before his time this wholesome custom had been abolished. These things clearly show how in later times the first love waxed cold altogether and at length went to nothing.

5 Remember from where you have fallen; such was their sin: the remedy consists of three parts—a just consideration of their fall, repentance, and redressing of the discipline.
All of these together are required for amendment, in the same order in which they are presented.
Because we fall little by little, we hardly perceive how deep the pit into which we fall: but let us look back to the high point from which we fell, and we shall marvel at the gulf in which we lie.
Whereupon he warns that he knows from where he fell.
It is not enough simply to perceive that we have fallen; we must quickly get out of the gulf through repentance.
He therefore joins repentance: but many deceive themselves, thinking they have repented well when in fact they have done nothing.
Therefore, lastly, he requires that the first works be done.
Then you will prove your repentance just if it brings forth true holiness of works, and either return to the first love if it is sincere, or increase it by adding a greater one.
But why does he require the first works immediately, especially in the Antitype, which covers about three hundred years?
Would he want the Church, which spread far and increased with an innumerable multitude of people, to return again to its cradle?
Or does he want there to be the same reason and respect for the whole earth, which is one city?
Now also it was near when the Church was to have a Christian magistrate, with Constantine about to come straight to the empire and government of the world:
What need would they then have for that former ancient discipline?
It may have been fitting that Christ had waited a little time, and had not urged so earnestly the first beginnings, which would not be useful in the short term.
But these are the dreams of those who are sick with a fever.
He who knows what is most fit for his spouse earnestly requires the first works after so many years, and after the dispersion of his church in many places:
he wishes that she labor again in the word, and that she punish wicked men with ecclesiastical discipline.
He knew that the order appointed by him should fit both provinces and cities: it should not hinder civil administration, but further enhance and adorn it above all.
From hence let us learn that this first government is common to all times and places:
It should not be permitted for men to follow whatever they wish, but in reforming the church we must always have recourse to the first beginnings:
This rule must be recalled whenever something errs from the right way, and it should not be framed according to the corruption of following churches.

¶ Or else I will come against you quickly: The threat spurs and stirs up the feeble strength of the remedy. Often the fear of peril prevails more with men than the hatred of wickedness. He threatens that he will come quickly and remove the candlestick from its place. But what need is there for him to come, who walks in the midst of the candlesticks? He does not dwell among them as an avenger, but as a brother and defender; from whence, as often as he must take punishment, he puts on a new person and form, in which he had not appeared before: and it is said he comes from another place, and seems now another, from him whom they had known before. In Greek it is, “I will come to you,” against you. Now, to remove the candlestick from its place is to take away the truth and dignity of the Church. Which, though not noted expressly by historians, is that according to this combination, Ephesus lost its form and honour as a church for a time. I contend not about the name of a church, which I know she has retained for many ages, but for the first purity, by which alone God measures a holy church, and not by coloured and naked names. Much less is the candlestick to be understood as the episcopal dignity, as the Jesuit would have it, which we read to have continued from those times, at least eight hundred years. Therefore this candlestick was not quickly removed: Did the angel perhaps repent? It is not likely, seeing that in the Antitype it is certain, that something followed in a short time, which is threatened here to come to pass. For the angels proceeding in negligence, as we have learned from those things previously spoken, Christ took the first golden candlestick from men’s sight by taking away his most holy ordinances, of which the world was most unworthy, on which the primitive church was founded by himself and his apostles. For there was a new face of things when Constantine came: there remained yet the desire of preaching among the bishops: but the doctrine was foully contaminated in many points: relics began to be counted, temples were adorned more magnificently, all kinds of superstition increased, besides the pride of the teachers, as Ambrose had taught, spoiling the church of a necessary help to rule their manners. Instead, ecclesiastical dignities increased, all things being sought out more for pomp than for truth. And while men gave themselves to such things, the golden candlestick, which among the candlesticks had obtained the chief praise, was removed from its place. This will be clearer than the light at noon in the rest of the book. In the meantime let men see how evil they provide for themselves and the truth, which they think is everything right, which they read to have been used in those times. Rather let them go to the entire age in which the candlestick stood in its place: after it was set in another place, it was overwhelmed with darkness, and it could not give light to others.

6 But this you have & c. This also avails to quicken their carefulness: they might have been proud of their present happiness, as though their own godliness had procured it for them: It is not so, says the Spirit: but in that the punishment is yet withheld, it does not come from your approved faithfulness and diligence, but from the only mercy of God whereby He spares that little good, which you have yet left. For as He would not have destroyed Sodom if ten good men had been found in it, so His wrath does not grow hot against Him, as long as any hope of good remains in them. It was but a small thing therefore, that let it be, that He should not by and by translate the candlestick, nor should suffer it to remain any longer among them. But what was this small thing? To wit, that He hated the works of the Nicolaitans, that is, of those whose chief author was Nicholas of Antioch, once one of the seven deacons, Act. 6. Who taught that wives ought to be common, and that it was an indifferent thing to commit adultery, as Irenaeus, Theodoret, and others declare. For as touching that Clemens Alexandrinus Strom. book 3. does attribute this heresy rather to the wickedness of His followers, who drew this foul licentiousness, the fact and saying of Nicholas, which had respect only to the removal of jealousy, it seems scarce credible. For John would have spared the credit of the man, and would have told the ringleader of so great filthiness, nor would have suffered his name to have been borne falsely by wicked men. The Ephesian Angel therefore was pure from the contagion of this sin. What were the Angels of the Primitive Church? They were no less free from this blemish. This heresy was soon rejected, for His own foulness. But after we shall see, that the doctrine of the Nicolaitans did extend not only to the filthiness of the body, but also was transferred unto spiritual fornication: ver. 15. Were they also without fault in this part? In the first hundred years the Church remained a chaste virgin: in the next ages it began to wax wanton, defiling somewhat the marriage bed, partly with unprofitable opinions, partly with foolish ceremonies, but somewhat fearfully & privately at first: nothing according to that impudency which came together with Constantine, and afterward. In this respect therefore, Christ suffered it a long time, although He saw that their first love had waxed cold.

7 He that hath an ear &c. An Epiphonetic conclusion common to all the Epistles: wherein he shows that all whatsoever they be ought to hear these admonitions of the Spirit. Properly indeed they belong to the angels, but it concerns us all greatly, of what sort their condition shall be. They either offend or do their duty not for themselves alone, but their condition is joined either with the great good or evil of the whole flock. But what do these things that happened so long ago pertain to us? There is the same disposition of all churches, and of every one severally: whereupon it is very profitable for us, of whatever age, to beware of their evil. Although not everyone will obey these admonitions, but only those whose ears the Spirit opens. For they are called to hear, those who have ears. And therefore we ought not to marvel if we see many contemptibly secure these threats, and think that these praises and reprimands do not belong to them at all. But what is that which he wishes to be heard? That which follows by and by, says the Jesuit, “To him who overcomes, I will give to eat &c.” Forsooth, the Spirit would have the last clause to be heard of all churches, and of all the members of any church, but all that which was before the bishop shall have privately for himself: a witty indeed and trusty exposition. Are not the epistles pronounced universally and inscribed to the churches, Chap. 1.11? Would it not profit them very much to be instructed touching the state of their angels, and to understand what they might require of them by right? They are sent indeed by name to the angels, not that they should keep them close to themselves as mysteries, but that by their means, they might be communicated to the churches, whom the Lord uses as his ambassadors, to speak to his spouse. Which does yet more appear from those that follow. For it does not fit a bishop only which after is written to them from Smyrna, “Behold it shall come to pass that Satan shall cast some of you into prison &c. ver. 10,” or that to them from Thyatira, and to you, I say, and the rest of Thyatira, ver. 24. That I say nothing, that in some of the epistles, the exhortation to hear shuts up the whole matter, as to the church at Thyatira ver. 29. To the church at Sardis chap. 3.6., at Philadelphia, ver. 13., at Laodicea ver. 22. Whereupon if the church be reserved to the epiphonema, she ought to open and shut the ears all at one time. For there follows nothing to be heard.

¶ To him that overcometh, I will give to eat of the tree of life: The reward in every one is fitted to the times: and is one and the same everywhere, Jesus Christ alone. For what greater thing can he give to his elect? Or what thing shall we need, if we do enjoy him? But according to the diverse condition of times he is set before us in a diverse manner. In this Primitive Church he is the tree of life in the midst of the Paradise of God. Why? Because the first state of the spouse, was wholly like to the first happiness of Adam in Paradise: of which that was a certain visible image and figure, restored in the last times on earth, after our so long banishment from thence. For there was a tree of life in the midst of the garden like a shadow: here Jesus Christ born of a Virgin was conversant with us in the midst of mortal men: there all kinds of beautiful plants, most profitable both for sight and for meat: here a copious abundance of all gifts, which belong either to salvation, or to ornament: there one river, but dividing itself from the garden into four heads: here one voice of verity among all the Apostles, but which beginning at Jerusalem, was spread abroad into the four quarters of the world, watering all lands wherever it flows with peace and salvation. What pleasantness was wanting there, that the mind of man can think of? What is not here sufficiently furnished by him at whose administration the Angels themselves are amazed? To wit, that terrible Angel, with a shining sword keeping the way to the tree of life; it is now removed out of his place, and an entrance again is opened into the garden most full of true pleasure. Christ therefore promised that those who shall keep themselves pure from the corruptions of these times, neither shall forsake their first love, shall continue those true citizens of this holy Church, and that they shall have free leave to eat of Christ, that true tree of life in the midst of this new Eden. Many wicked men and heretics at that time, were thrust headlong (as once Adam) out of the Celestial garden, yet with unlike issue and condition. For Adam falling away from the shadow‑like Paradise, by faith in Christ he found an entrance into the true, but these heretics being driven from the heavenly and true, what return can ever be hoped for? Seeing therefore that this is the natural sense of the words, how foully do they err, who do count the Primitive Church an infant, rude and imperfect? and do attribute ripeness of age and perfection to the latter corrupt times? For they do prefer Tophet before Paradise: neither do mind that all pleasantness did belong to the first beginning: but thorns and thistles and all noisome herbs to the curse following. Far be it that we should think the water flowing by dirty channels, either purer or sweeter or fitter for our use, the further it shall be distant from the fountain. Further let the reprobate know that they do never eat of this tree. For there is the same meat both for way and for country: there is only a difference of a more full fruition, wherein we shall rejoice after the battle finished. Neither is the reward of them that overcome given to the slothful cowards. The Angel will keep them far from it with his glittering sword, that they may not pluck anything at any time from this tree.

The Analysis.
So it is the first epistle: the second is sent to the Church of Smyrna, but inscribed in the manner to the angel: afterward he describes the one who sends: that he is the first and last, then that he was recently dead, but now alive, verse 8. The narration partly commends their suffering of affliction, which the blasphemous Jews brought upon them, verse 9. Partly instructs against a new calamity, both showing the author, kind, end, continuance, and also promising a crown, verse 10. The conclusion has both the usual epiphoneme, and also immunity from the second death in verse eleven.

Scholions.
8 AND to the Angel of the Church of Smyrna: Smyrna was a colony of the Ephesians, as we have said. It was also called the Amazon of Smyrna, but the Spirit respects another name. For where it is a sweet‑smelling Smyrna, that is myrrh, far more pleasant than any spices, it is evident that he reproves no fault of this church, but shows that it is most dear to him, however nothing was more contemned and despised by the world. We should not think that it holds the second place after Ephesus. The Spirit does not list the cities by jumps, putting apart Sardis or Philadelphia, or any of the rest, but in the correct order in which they were situated. First, it goes forward to the north, where about three hundred and twentieth furlongs Smyrna is placed on the shore. From there it turns to Pergamum further into the north; from Pergamum the rest, in their order, turn to the south. This order demonstrates the same progress of the church. In our part of the world, the further we go north, the farther we are from the sun, the fountain of light. Therefore, after Ephesus, Smyrna shows that after the first purity the church will proceed each day toward greater darkness, while at length it will come to Pergamum, the final destination; from there it will go toward the south, each day becoming brighter. We will see in what follows that the event so agrees that no equal judge will condemn these things for vain subtleties, but rather, with me, will admire the greatness of the mystery. If we hold back our opinions while the whole matter is fully understood, we will judge far more uprightly, which will be best both for ourselves and for the truth: which I respect (God is witness) and not any desire for division or novelty. But you will say, how is Smyrna’s myrrh so delectable to God, when its condition is worse than that of Ephesus? In outward appearance it indeed is more deformed, shining with no ornament of lawful policy; in this respect the northern corner agrees with it. Yet the fervent desire of the godly, who fought most valiantly for the truth in this miserable deformity, raised to God a sweet savor. Furthermore, the greater the temptation upon them, the more God is inclined to deal favorably with them. He does not then show rigor in threats, but comforts as much as he can, so that he may confirm the languishing and not add affliction to affliction. The Primitive Church suffered the most grievous calamities at the hands of heathen men, which somewhat assuaged their sorrow. But Smyrna must suffer all extremes at the hands of its own. In these griefs, it should not faint or be overcome; he hears nothing but that which may add courage. Hereupon, reprimands are passed over, although it had more of the basest sort than former Ephesus. The Antitype is the next church after the first. Its colony, as of Ephesus Smyrna, sometimes also enjoyed one common name, as did those two cities, because of their great conjunction at first, as Strabo shows. This Antitype begins with Constantine, until which time the Primitive Church, the Ephesian Antitype continued, and proceeds even unto Gratian around the year of the Lord 382 according to Eusebius.

¶ These things he says that he is the first and last: The description of the sender of the Epistle is taken from verse 17 of the former chapter. In these words we have shown that Christ is praised as the maker and ruler of all things, by whose authority and command all things are done, and that to his glory: or rather that in this eulogy the marvelous joining together of his great majesty and his humility is praised. Which interpretation receives confirmation from here, that the condition of the Smyrneans was like: “Thou art afflicted,” he says, “and poor, but in very deed thou art rich.” What other thing is this than, although with the world thou art counted last, thou art nevertheless in truth the first? And together it shows that alteration, whereby the truth first flourished among the Smyrneans in great esteem, afterward despised and trampled under the feet of hypocrites: even as Christ in the beginning was in incomprehensible glory, God with God, but in later times, taking upon himself the form of a servant, made himself of no reputation, becoming like unto men. He takes to himself titles that may fit the present condition of things. Whereupon he spread a diverse beam of his glory in the several Epistles, according to the diverse condition in which the Churches are. Whereby he teaches that his infinite divine majesty is chiefly to be contemplated with the mind, which may be most available for the present matter. But that they should not think that they must always lie in this base estate, he adds another title: Who was, he says, dead, but is alive; as though he should say, “Although I was in the beginning the first, after the last, yet I did not remain long in this most base estate; but death being overcome within the space of three days, I obtained my former dignity, in which I now live forever.” These things then declare the notable change that came to pass at Smyrna, and no less in his Antitype. Where the first truth, which over the span of three hundred years was established by so much blood, became at last to be hated by the Christians themselves, and the last fortune stayed together with his professors: which Christ, having risen from the dead, should rise again from the dust and restore it to its former dignity. Why then should they be discouraged, who their captain has gone before in the same steps? Or why should they fear afflictions, whose outcome is so joyful and comfortable?

9 I know thy works and afflictions: The narration of the condition, which he says, is known to him, as in the rest, lest peradventure they should suppose that their miseries are not regarded by him, because of his long suffering. The state of this Church was afflicted, as at the present time in this verse, so afterward to be expected, in the next: Whereto the Antitype agrees altogether. For after the first age driven away, by and by a lamentable strife arose, when Constantine succeeded. The persecutions of open enemies ceased, but the strifes and contentions of the citizens forthwith waxed very hot. And not only of the whole Church in general, but also of this city: Theodosius Junior boiling with envy against one Cyrus, whom he saw to be very gracious with the people, sent to Smyrna under a color to make him Bishop of this city, but with a determinate purpose that he should be killed; For the Smyrneans had killed long ago four of their bishops; which barbarous cruelty shows how grievously this Angel was afflicted: Epitome chr. set out with Eusebius chr. by the famous Joseph Scaliger, pag. 293. But if we shall enlarge this Smyrna a little unto those contentions of the citizens, of which I spoke; by and by came Arius, who kindled that fire, whereby all things as well divine as human, were inflamed. The Bishops studied no other thing, than that one might spoil another of their seats and dignities. Eustathius Antiochus was banished with a great company of Elders and Deacons: Athanasius in his epistle to them that lead a solitary life. Athanasius himself, the only defender almost of the truth, was not only assailed, but also oppressed with all kinds of false accusations; neither did they cease from their wicked assailing him, before that he was banished to Treveres in France. Those were sorrowful times, when the Emperor, in the meantime, not minding sufficiently the drifts of the bishops, did not know the true original of those stirs.

¶ And thy poverty: That is, how thou art mocked and contemned, as a beggar: but be thou despised more than any of those hypocrites, thou art rich in mine account, that thou mayest regard the wicked’s scoffing of those men as less.
And that we may let pass the Smyrneans, the matter is clear in the Antitype. How few were there of the Orthodox that dared to profess the truth? How superstitiously were those few suppressed by the enemies? Certainly the Saints were constrained to run hither and thither in order that they might seek aid against tyranny. They, too, being turned out of their goods, could not maintain their life except by the liberality of others. Athanasius alone may serve as an example, from whose many perils—flight, hidden places, no hope of escape—anyone may easily see how the faithful could prevail, even with little wealth, against the injuries of their enemies. The Smyrnean angel was then poor indeed, if we measure riches by human defence.

¶ But you are rich: Not naked and forsaken, as men think, but by me, and in my account, abounding in all riches. These things are also together to show what defense and esteem Christ could prepare for him even in spite of the world. Authority increased together with affliction, as we know it came to pass concerning Athanasius, who, being vexed with all manner of contumelies in the East, was esteemed highly in the West. Constantius the son, Constans the brother, Julius Roman, the Bishop of Treveris, who gave him entertainment most kindly and liberally for the space of two years, reverenced him according to his worth. Moreover, Constantine the Great himself, having perceived the calumnies of his adversaries, honored his innocence and virtue, and determined to bring him back from banishment.

¶ And the blasphemy of those &c. Hitherto the kind of the present calamity: now he show the authors, arrogating to themselves, that which in no way was fitting them. But is it blasphemy for a Jew, to profess himself to be a Jew? A Jew is taken figuratively for one people of God, which alone among all men, knew the right way of worshipping him; as though he should say: They that boast that they worship God after the ancient rule of the law, in the manner their ancestors once worshipped, and all men ought always to worship. This was blasphemy, the retaining of the worship abolished, and the thrusting upon God the ancient ceremonies, by which the glory of his son sent at length into the world, should be overwhelmed: For which cause, although they were Jews by stock, they lied in affirming that they were Jews, being so far from that holy people, that in very truth they made a Synagogue of Satan. And it is known, with what bitter minds they persecuted Christians in all places, as we see in Paul & Barnabas at Antioch, Pisidia, Iconium, Lystra, and in other places, Act. 13.50. and 14.2.5.19. Which they did also at Smyrna about these times, as we learn from this place. Under Constantine these Jews were Arian bishops, namely, Eusebius Nicomediensis, Theognis of Chalcedon, Maris, Patrophilus, Ursatius, Valens, and the rest of this sort, men indeed not ethnics, nor wholly void of all knowledge of God, as neither were the Jews, but bearing the name of Christians, & such as were standard bearers in this war. Who notwithstanding did hold their errors with tooth & nail, no less than that stubborn nation of the Jews, striving to establish their Decrees only, to vex by all means such as were contrary minded, to boast that they alone had the true faith, to condemn all the rest of ungodliness and blasphemy. But whatsoever boastings that wicked company made, as though God dwelt in their congregations only, they gathered Churches not to God, but to the Devil, of whose Synagogue, they were the chief rulers.

¶ Fear none of those things which you shall suffer. Now he instructs them against the future evils, which appear to be more grievous than those that have passed. Those things with which the Jews troubled them in the present, and also those false accusations of the bishops while Constantine lived, were minor skirmishes of a sharper battle that followed. Therefore he describes diligently the manner of this combat, who should be its chief captain, how cruelly he should rage, to what end, and for how long. The Prince is the Devil, whom after we shall learn to denote as the heathen emperors, open enemies of the truth, as in chapter 12.9. This also includes the heretics, Christians in name but, in truth, wolves devouring the flock.

The kind of punishment is imprisonment, which, as history teaches, includes prohibitions, confiscation of goods, banishment, slaughter, fire, and torture. With all these measures, the devil would greatly torment people to draw them away from the truth. But this persecution should last only ten days. In this book, one day is taken to represent a year. The number ten sometimes signifies a definite quantity, and sometimes, by synecdoche, points to an uncertain number. I think both are used here: a certain number represents the type, and an uncertain number represents the antitype. Therefore, regarding Smyrna itself, this persecution occurred during the reign of Trajan, when the devil—an enemy of truth—reigned after this writing, was very fierce against Christians, sending men to prison and death, so that he could force them to renounce the profession of Christ.

Smyrna could not be free from the common calamity, especially when Bithynia, being near it, was altogether abounding in the murders of the Christians, as the epistle of Plinius Secundus to Trajan shows. From this, one may also gather a sense of the continuation of the persecution. For in the fourteenth year of Trajan, Pliny, relating to him the multitude of those who were slain, offered an occasion to halt that rage and to obtain some relief. The year it began is not plainly set down by the historians. Some suppose it was at the very beginning of his reign, but in the fourth year, after triumphing over the Dacians and Scythians, he seemed to have had his kingdom first hindered, so he could not afford the leisure to afflict the Christians. But it is certain that he exercised his cruelty for at least ten years. It is likely that the end of that war gave the beginning of the torment of Christians. Neither is it necessary that this affliction be referred to Smyrna only; rather, it was part of the general persecution mentioned in the Church of Philadelphia, which should affect the whole world (Ch. 3.10). As for the Antitype, Constantine and Valens, who were Christians by name, they were no less fierce against the orthodox and true godly people than the ethnic devils once were. In this account, the inferior ministers of that wickedness are also held: of the people, Syrianus, a captain, and Sebastianus, governor of the Manichean armies; of the bishops Eusebius, once of Nicomedia, then of Constantinople, Macedonius, George Alexandrinus, and others of that sort, not bishops but monsters: whose barbarous cruelty was scarcely matched by any tyrant. In old times, the matter was handled with brawls, chidings, and calumnies of all sorts. But after the death of Constantine, the devil came to the fore, and what turmoil was raised? It was a light thing to banish holy men, imprison many, and kill almost an infinite number; they tyrannized with torments and all manner of contumelious punishments. Some were beaten with stripes to death, some were marked on the forehead with prints of hot iron, some were tortured in other ways. Indeed, the breasts were cut off from holy women; some were burned off with a hot iron; many had eggs roasted in a fire at an excessive heat. Who would believe that any such thing could have been inflicted upon Christians by men of the Christian profession? It cannot be shown in a few words how full of calamity those times were; see Socrates, book 2 and 4; Theodoret, book 2 and 4; Sozomen, books 3, 4, and 6.

And although this tyranny continued for more than fourteen years, yet nevertheless it makes those ten days in the same manner that we have said.

¶ Be faithful unto death: He provokes fortitude, the reward being proposed to be eternal life. It is a profitable loss which is recompensed with such great gain. What should the godly not undergo most willingly, being sure of such a reward? It is fitting for the times, ministering comfort against the loss of this present life. To which purpose did he speak before, that he was alive who had been dead, that by his example they should learn not to fear death, which they should know to be a means between God and them to eternal happiness.

11 He who has an ear: the usual conclusion, warning all men, to hearken diligently to these instructions touching fortitude and courage of mind in afflictions. We were instructed before against the sluggishness which is inbred in us: here we are armed against outward violence. The reward which is added to the end, he who overcomes shall not be hurt by the second death, is common to the whole church. That which was before belonged properly to the angel, the knowledge of which, notwithstanding, was very necessary to the people, as has been said before. But seeing that this conflict was to be undergone as well by the people as by the pastors, comfort also is given them by name, to the same purpose that the former was, but in a different respect. For there are two things which are wont to kindle the desire toward every excellent act, hope of reward and contempt of peril: that first was proposed to the pastors, whose courage is wont to be more ready and valiant by looking into the reward. This second to the people, whom the fear of danger chiefly withdraws from their duty, and prevents them from undertaking anything worthy of commendation. He teaches therefore that they must not fear to spend their life, if need be, for the truth’s sake: for there shall be no fear of the second death, by which the body and soul perish forever, according to Christ. Fear not those who kill the body, but cannot kill the soul; fear instead him who can destroy both soul and body in hellfire, Matt. 10:28. This hellfire is the same that he calls the second death: by which the whole man shall be no less deprived of all solace in God, as the body is destitute of all help, being separated from the soul by the first death. This is that horrible death, to be feared indeed, from which he who has overcome death delivers his: from which he promised to free those that overcome. He does not promise to deliver them from the first, being too light a thing, either to be given by such a great price rewarder, or to be expected by those that are his. And what need is there to be defended from the first death, which the necessity of nature will bring at length; but to prevent it for the truth’s sake procure a far greater crown? He promises therefore what is best, and does not allure us with a vain show of some light thing.

Analysis.
So is the Epistle to the Smyrneans: That to the Church of Pergamus is inscribed likewise to the Angel: he that sends has a two‑edged sword. The narration commends his constancy, illustrated by the throne of Satan, and the common times, in which Antipas suffered ver. 13. Then he reproves the sin: which he shows what quality it is, consisting in suffering Balaamites ver. 14. and Nicolaitans ver. 15. and also the remedy for it, namely repentance, which he sets forth by the danger of refusing the same ver. 16. Lastly he concludes with a solemn Epiphoneme, and proposes a reward, the hidden Manna, the white stone, and an unknown name, written upon it, ver. 17.

Scholions.
12 And to the Angel of the Church of Pergamus;* 1.3 Pergamus so far as the Spirit seems to respect the notation of it in this place, is as it were 〈 in non-Latin alphabet 〉, that is, 〈 in non-Latin alphabet 〉 the tower of Troy, as Hesychius expounds it: that is, a towered city, high and superb, agreeable to that which follows in the next verse, where the throne of Satan is. It is distant from Smyrna to the north about five hundred and forty furlongs, with a greater distance than Smyrna is from Ephesus, in the last border of the North latitude as touching those seven cities. A great diminishing of light fell out in the Smyrnean corner under Constantine, Constans & Valens even at the first turning from Ephesus into first purity: But now he goes from Smyrna to Pergamus into the utmost darkness, the Church being about to suffer a greater defect of light than ever before this time since Christ was born. The Antitype of this Church is for longer time than the former, as also the distance of place is greater, containing a great part of the kingdom of darkness, from the three hundred and four score years, that is, from Gratian, where the former period ceased, unto about the year one thousand three hundred, as in the explication we shall see.

¶ These things says he who has etc. The furnishings of those who indict the Epistle are taken out of chapter 1.16. Which he now takes before the others, because he would demonstrate this in practice in this Church. For he would punish the rebels, as he says after verse 16, upon whom no mild punishment should be imposed by a double‑edged sword, for the sword is sharp. The sword is the word of God itself, whose force should now be manifested in subduing the sinful man. Although this sword in this period is shaken rather than inflicted. For he threatens a fight against those who do not repent, verse 16. He does not come immediately with swift blows.

13 I know thy works: A narration of his more approved condition, which is set forth two ways: that he neither denied the faith, although he dwelt in that place where Satan’s throne is: secondly that neither in those days, wherein Antipas was slain. It is not hard to know, why it is called the throne of Satan. For the city where the Ethnic Emperors had their seat made war professedly against the Lamb, is called the Throne of the Dragon, chap. 13.2. So of the foster & inferior cities, which come nearest to the disposition of this chief city, because they make a palace more garnished for the Devil, they are noted with the same name.

Now it was the mother city of the Roman Empire in Asia. For it is likely that this region, being brought into a province, after Attalus Philometor, king of Pergamon, had named the people of Rome his heir, the proconsul was sent to govern the same, placing there the seat of his jurisdiction. Pliny in his fifth book of Natural History, chapter 30, says that this city was by far the most famous in Asia, and its glory should not be less if the proconsuls had dwelt in any other place, seeing that honour is wont to come to cities or depart from them together with the chief rulers. Although before it pertained to the Roman power, it was the head city of the Kingdom of Asia. For so Livy spoke, urging of Seleucus, son of Antiochus; he led, says he, to the assailing of Pergamon, the head and tower of the Kingdom, Decal. 4, book 7. It was therefore a great thing to profess Christ in the hearing and sight of such a mighty city, spiteful against the truth. There may not be prophecy in Bethel, for it is the sanctuary of the king and the king’s house, Amos 7:13. Aretas reports of Antipas, that he gave testimony to the truth at Pergamon, and that his martyrdom was known even in his times: but I find no more in any author worthy of credit. From this place it is evident that he was a very famous martyr, by whose sufferings the rage of a most grievous persecution was signified. This is another praise that Pergamon had continued steadfastly in the faith, when a fierce tempest raged greatly.

It is an easy thing to profess Christ, when a man may do it either with honor, or without danger: but to retain the profession of him without fear, even with the danger of life, is an excellent commendation and a point of true courage. We have said that the Antitype was the Church from the four hundred years, to the three hundred above the thousand; when after Constantius, Julianus and Valens, Smyrna being left it went further toward the North unto Pergamum, that is, was hidden in thick darkness, being brought under the power of that city, where the throne of Satan is, namely Rome.

This is that Towering City, the Tower of Troy, whose daughter she boasted herself as, once the Mother City of almost the whole world, the proud lady and queen of the nations no less famous for the stately temples, theatres, high places, than for the ample and large dominion and empire.

It is plainly called the Throne of Satan in the chapter 13 of this book, both because it was once the Seat of the Ethnic Emperors, as at the place we will show, and also because they being taken away, it was made the Seat of the Popes, who during this time have most plainly shown that they reigned by the help of the Devil and not of God. Four and twenty Popes were all given to Devilish arts: some of which gave up themselves wholly to Satan by covenant to obtain the Popedom. Yea by the space of whole four score years from Sylvester II unto Gregory the seven, no Pope reigned but was greatly famous in this impiety. Can any doubt where the Devil hath his Throne placed, when he shall see so many Necromancers clothed in purple sit at Rome? Rome therefore is Pergamus, and not only the city of Rome, but the whole Roman dominion, as far as the Dominion of the Roman Bishop did extend. As long as this tyranny flourished, in all those places subject unto it, there was the Seat of the Pergamen Church. And they that keep the name of Christ, are the faithful dispersed at that time in every place, who not discouraged with the Roman tyranny, retained firmly in the meantime the sound doctrine, of which sort were many in the East, in Africa, in Britain, and in other places, yet rather apparent or manifest man by man, than notable in any whole assemblies. For now was the time of the Church lying hid, as after shall be showed more fully, chap. 7. and 11. and 12. Antipas was slain, when about the year eight hundred it began to be a matter worthy death, to resist the Roman Bishop. For behold what a most fit name the Spirit gives to the Pergamen Martyr: He is called Antipas not with a feigned, but true name; which yet by almost so many letters & syllables, should declare that the Martyrs of this time should be Antipopes: not that two-headed or three-headed Hydra, whose heads should contend one with another for the Papacy, but who should oppose themselves against these sacrilegious Popes, desiring that the wicked power should be brought into order. Of which sort were Leo Isaurus, killed after a sort by Gregory the 2. when he was by him spoiled of the Empire of the East. Frederick Barbarossa was vexed with all manner of injuries. The Bishop Florentine of less fame, was condemned, for teaching that Antichrist had come. A certain man called Arnulf, or as others write Arnoldus, was hanged at Rome, because he had spoken boldly against the Pope, Cardinals and Priests.

Gerardus and Dulcimus Navarenses were burnt alive with thirty others because they preached that the Pope was the Antichrist, and many others, of whom a catalogue would be too long, are not my purpose.
The godly reader may conjecture from the Decrees, which are found in the Right of Bishops, how many Antipopes, or rather the Antipopes, were killed in this Pergamon state.
The first is: He who goes about to take away the privilege of the Church of Rome, given by the very highest head of all churches, undoubtedly falls into heresy and is to be called a heretic, Dist. 22.
All or the Patriarchs again, let him become anathema with God, which violates the censure of the Roman Bishops, cause 25. q. 1. general decree.
To which add, they are not homicide, who through zeal of the mother Church are armed against excommunicates, cause 23. q. 5. Of the killers of excommunicates.
From this consider yourself, seeing the good will of the Roman Church has always been the same, even before these laws were made, how many Antipopes have been killed of the same, after she had obtained some power.
Yet many, even in those times, kept the truth faithfully, as far as it was revealed to them, for which cause a more glorious crown is laid up for them.

14 But I have a few objections to you: The other part of the narration, wherein the angel is reproved for his excessive gentleness toward the wicked. From where it came to pass that this Church was infected with the doctrine of Balaam in this verse, and the Nicolaitans in the next. There was but one plague of the Nicolaitans in the Church of Ephesus, to this is also added Balaam. Whose fornication (which he taught) had not respect so much to the defiling of the body as to the violating of godliness by idolatry. Which double corruption is so distinguished that the doctrine of Balaam is proper to the antype, although it be rehearsed in the former place, the doctrine of the Nicolaitans to the type, to wit of the very city Pergamus. As touching that, most fitly is the pope of Rome in those first times compared to Balaam of great authority with kings, ready for any thing for the sake of profit, uttering some true oracles, but as a diviner and man of ethnic superstition, persuading the worship of images to Constantine and Irene Augustes, as it may be seen in the synodical epistle sent unto them, as Balaam to the king Balak, that he would entice the Israelites, beautiful women being set before them, to offer sacrifices to Baal Peor, Num. 31.16. Now therefore we see why Balaam was reserved to this place, to wit, that he might signify his true offspring, the pope of Rome, as like his father, as one egg another. He in these times which we have spoken of should tread the church under feet. But this was the sin of the Pergamian angel, that he suffered too favourably men to draw of the dregs of this false prophet. It was his duty to have been instant in teaching, admonishing, reproving, correcting, if peradventure the contagion might have been stayed, that it should not spread further abroad. Of which when the godly were something too negligent, handling too gently this man of sin, and halting or somewhat failing, as comes to pass in a common corruption, gave occasion to the overseer of churches, both to contend with them, and also at length to punish that estate. And who knows not how tenderly and mildly they which embraced the truth in those times touched in speaking or writing the Roman tyranny? They should have thundered against it most vehemently, and spared no sharpness of words, but we shall find that the angel in this point performed not his duty. But how then had he but a few things against the angel, seeing the whole state of the church was so greatly corrupt? Wonderful is the gentle entreating of our God. He requires but a few things of them to whom he gives few. The greater their corruption was, so much the less he exacts. He requires not so great ability of him that lives in darkness as of them around whom the clear light shines.

¶ That they should eat of those things which were sacrificed to idols; that is, being present at the worship of idols, should give honour to them. Otherwise, if anything offered to idols were sold in the market, and the offence of some weak brother was not hindered, anyone might well eat of it, 1 Cor. 8. &c. But the spirit seems, with good advice, to have spoken rather of eating that which is offered to idols than of worshipping the idol, that he might show the crafty and subtle ways of this Balaam in provoking and alluring men to idolatry. It seems not so ungodly a thing for men to eat flesh sacrificed to idols as to fall down at their feet and give adoration to the image. Therefore this Balaam would endeavour to win men to his purpose by very small things and having a fair appearance. He would abhor idols in words as much as anyone else, and would cry out that the honour he commands to be given to images is far from this ungodliness, by such words deceiving the unskilled and bringing them into this offence, which the spirit speaks of.

15 So you have, etc. The reduction of the similarity, whose proposition has not spoken a word of. Thus it should be full. As once the Israelites had those who held the doctrine of Balaam: so you have those who hold the doctrine of the Nicolaitans. Instead of the proposition, he attributes the doctrine of Balaam to the Pergamon Church, because it was proper to his antitype: but from where may be gathered the first part of the similarity. But this poison of the Nicolaitans had infected undoubtedly Pergamon.

¶ Which I hate: as before, the common translation is, repent likewise. And so he begins the verse following in this sense, as I have warned the Ephesian Church, so do I admonish thee. But this is weaker than if he did command simply, repent.

16 I will come against you quickly, and fight against them; He threatens a double punishment, one against the Church itself against which he says that he will come quickly: The other against the corrupters, against whom he says he will fight with the sword of his mouth. For we may not think, that he will come against the Church, only to take away those plagues and destructions of men (for this could have no fear, but would be a thing to be chiefly wished) but she also must suffer the punishment of her negligence, as well as their wickedness. Therefore this violent breaking into the Church, was a certain chastisement by war, or some such calamity, as is manifest in the Antitype: whose times were very troublesome, partly by the overflowing of the Northern Barbarians, partly by the Saracens, whom the Devil armed against the seed of the woman, after she fled into the wilderness, as we shall show at the chap. 12. to which times these things pertain: but here generally and obscurely shown, because this place suffered not any ample light. The other punishment is against the Balaamites, against whom he will use the sword of his mouth. For we must observe, how he distinguishes these from the Church: of her he said, I will come against you, then turning his speech to the Balaamites, and I will fight, says he, against them. But what is it to fight with the sword of his mouth? Whether to inflict the punishments which he has threatened in his word? Certainly Paul says that he had in readiness, wherewith to punish all defiance, 2 Cor. 10.6. And Jeremiah is set of God over the nations and Kingdoms, to root out and destroy &c. chap. 1.10. For there is no weapon in the whole armory of the world so effectual on both parts. Wherefore seeing by the judgement hereof all fornications and idolatry are appointed to a just punishment, worthily may he say, that he will fight with that sword, according to the rule whereof the pronounced judgement is exercised. But now when in another place it is said of Antichrist, that Christ shall consume him with the spirit of his mouth, 2 Thes. 2.8. (which manner of speaking what force it hath, we have learned by experience, to wit, that his errors convinced, his lies detected, then his fraud and deceits set in the open light, he shall be brought to destruction) these words seem to have the same meaning. And certainly after that the Church was for a while scourged by those Northern & Southern barbarians, Christ began to vex those Pergamen impostors with the light of the truth: for about the year 1120, arose certain godly men, which preached openly that Antichrist was come: that the holy days, Ecclesiastical broken songs, prayers for the dead, pilgrimages, oil, extreme unction, & the rest of that sort, were superstitious things: Work Trip. & Henric. Mon. Thol. To these were added in a short time after the Waldenses, the Albigenses & Parisienses, who published a book of the perils of the Church, & many other private men. From thence began this fight, which was soft in the beginning, terrible rather in the shaking of the sword, than in wounding: but after coming to a just & full battle, as after we shall see, which hath fallen out prosperously to the godly hitherto by the grace of God: but most unhappily to them that dwell at Rome in the throne of Satan.

17 He that hath an ear; let every one drowned in the Roman superstitions give ear, let him attend and hearken, in what account with God is that unmarried vicar of Christ: of what price is that famous and much spoken of Rome, that Chair of Peter, the pillar of truth, mother of the faith and of all churches; to wit, that chief prelate, that wicked Balaam: the very city which is renowned for the vain praise of men, the gate of heaven, is the very palace and throne of the Devil. Neither let anyone think that hatred does wring these words from a man who is an adversary: but let him compare the prophecy and the event, which if he sees that they agree in all things, let him know that he is warned of danger, not so much by the words of men as by the Holy Spirit.

¶ To him that overcomes I will and so on. The reward is threefold: hidden Manna, a white stone, and an unknown name written upon it. Each fits the times in a wonderful manner. As for Manna, it is the meat of the wilderness ministered by God when there was no means to have other bread. In this Pergamen state, when the company of the Nicolaitans and Balaamite offspring, that is, Roman idolatrous, possessed all places, the Church was conversant in a waste, unpleasant, and terrible wilderness, whither we shall see the woman betake herself flying from the Dragon, ch. 12. But Christ feeds the same with the meat of the wilderness, as once the Israelites. For he will not be wanting to him in the most difficult times, but bestow abundantly the joy of the Spirit, whereby not only may they be preserved in life, but also be very glad for the greatest joys. Therefore this Manna is the same meat, with the fruit of the tree of life in Paradise, as has been observed afore, ver. 7. but the manner of ministering it is different; there, in a most chaste, pure, and flourishing church, it was the fruit of the tree in the midst of the Paradise of God: here the truth being despised, contemned, and trampled underfoot, and utterly oppressed with thick darkness, it is Manna the food of the wilderness: this meat should be hidden from the world, and they should suppose them famished, who had fled into this wilderness, as the Egyptians thought the Israelites for this cause would perish suddenly. But God did sustain him extraordinarily with this bread of Angels.

Yet there is this difference between the manna of the Pergamen people and that of the Israelites: for this every way was spread round about the tents, that was dispersed peculiarly to every one of the saints, who did not dwell so close together in such great numbers as the Israelites in their tents; but in certain remote dens, far from the eyes of the world. From where the manna of these is hidden, theirs is manifest, like that which was gathered from the common provision of the people and, by God’s command, laid up in a golden pot, which the people could not see afterwards (Exodus 16:33‑34; Hebrews 9:4). Which, in a more excellent figure, shadowed the heavenly food. For the other manna, kept for only one day, was full of worms; this abode is pure and incorrupt through all ages, a lively and expressive image of the immortal food. Therefore this manna does not lie openly about the tents, in the way that every one who will gather it up, but is given from the golden pot, as much as may be sufficient to sustain life. And certainly, unless Christ, by hidden means, had provided for them in those most corrupt times, they would have been utterly undone with respect to their salvation.

¶ And I will give him a white stone: The second reward. Aretas reports that such a stone was wont to be given to master wrestlers striving in the theater. But that custom is not here regarded: For that was only for the entering of the fight, and not for the rewarding of the overcomer. In the plays called Olympiques, that the champions should not run together rashly, they pulled stones out of a silver pot, and those on which they did fall being marked with the same letter (for they were two by two marked with the same characters) were committed in the fight by the judges: neither do I think that there was any other use of stones in plays. In judgments they were used to another end, to wit to give voices. In which thing they were diverse, according to the sundry laws of the peoples; sometimes hollow and bored through, by which they did condemn, sometimes full and solid, by which they did absolve. Sometimes also they were distinguished only by the colour, the black condemning, the white contrariwise absolving. So Ulpian on Demosthenes against Timocrate: The stones sometimes bored and not bored: sometimes black and white. To the same purpose the Scholiast of Aristophanes in 〈 in non-Latin alphabet 〉. But that of Alcibiades is famous, who in the judgment of life and death would not believe his mother, lest peradventure she unaware should put a black stone for a white, Plutarch in Apology of the King. He alludes therefore to that manner of absolving in judgments. But why now is there a second, yea a third reward, which in the former Churches was but one? The use of the godly did so require.

For, because those few and rare faithful, in so great a multitude of the ungodly, were hated by all, condemned for schism, error, heresy, and I know not what wickedness, an absolving stone is promised to them. Though they might be judged guilty by the votes of all men on earth, yet they may know most surely that they are judged innocent before the heavenly tribunal. How great a solace is this against the reproaches of the world? Be of good courage; if God justifies, who shall condemn? Rom. 8.33.

¶ And in the stone a new name written: A third reward. He persists in the same custom of judgments: in some of which their names were written in the stones, who came to be judged. Aristides being desired by an unlearned one who knew not who he was, that he would write to him the name of Aristides in his shell, he wrote his name into his own banishment: Plutarch in Apology of Aristides. Here the like custom is showed. But the new name to be written in the white stone is the child of God, such as the faithful perceive and acknowledge themselves to be by the testimony of the Spirit, Romans 8:16. Which also avails against the railings of the world, to whom they should be as the filth and offscouring of all. But why dost thou vex thyself with thought of so great contempt, seeing thou art with God in the honor of a son? This name also is unknown to all, except to him that receives it. For the world knows us not, 1 John 3:2. Therefore their testimony is of no account, on what side so ever. But besides behold the solitariness of those times, wherein the elect were no less unknown to the world, than the way of salvation signified now by the hidden Manna.

Analysis.
Such is the Epistle to the Church of Pergamus, 1.4. This to the Thyatirens is titled also to the Angel: then he declares that he who sends is the son of God, with fiery eyes, and feet like fine brass, v. 18. The narration praises the increase of godliness, v. 19, but reprimands for the suffering of Jezebel; whose immorality he describes first by the kind of sin v. 20, secondly by the hardening v. 21, and punishment, which is notable both for the nature of the punishment itself, which is diverse according to the manner of the delinquents: For Jezebel herself is punished by the bed: those that commit fornication with her, by great affliction v. 22, and her sons with death, as also by an excellent testimony of all churches, of the just and severe judgment of God v. 23. To whom finally he annexed counsel against this wickedness (the way where he shows by gentle entreaty, laying no other burden upon them v. 24.) requiring constancy, v. 25, & persuading thereto by the reward of power over the nations, v. 26‑27, & the morning star v. 28. The conclusion v. 29.

Scholions.
18 And to the Angel of the Church of Thyatira: Thyatira is so called as it were Thugatera, as we have shown at the first chapter. A name well concurrent with the thing. For the godliness of this Church is growing, as a newborn daughter, which always grows up, until she has attained full maturity. In which respect it is opposed to Ephesus: which being of full age the very first day, or shortly after, the further she proceeds, hastening to old age, became weaker every day, while finally the natural heat being extinguished, she fell into the cold of death. And here is the first bend from the North, to wit, Pergamus, toward the south, but further to the East, being distant, according to Ptolemy, about eighty English miles. The Antitype is the time from the year 1300 to 1520.

¶ These things say the son of God: Now Christ makes himself known by his name, eyes, & feet: every one of which do appear more clearly from the Antithesis of what sort they are.
Regarding the name, now first of all it offers itself, not expressed before either in the things seen or heard in the first chapter.
There was mention of the son of man, verse 13. but the whole vision did declare sufficiently that he was the son of God.
It seems here to be used, as though now he would return out of Egypt.
He had been exiled for a good while, but in the renewing of the Church he returns as it were home, beginning more familiarly to be known to his, from whom he had seemed before time to be far off.
The fiery eyes are those spoken of in the first chapter fourteen and fifteen verses: by whose clearness he shows to the Theatines, that now the time flourishes wherein the light of the truth should dispel darkness of errors and falsehood, as it flies at the sight of the fire: as came to pass about the year 1300. when a new company of Teachers arose, by the judgment of all which the Pope was strangled, and began to be spoiled of his estimation, which he had kept for a good while by fraud. For they did maintain earnestly, that the Imperial Majesty ought to be preferred above others, and that the Pope had no power over it. Among these were Ockham, Marsilius, Patavinus, Dante, John de Ganduno, and many other.

The feet like fine brass do teach, with what kind of torment the Roman Balaam should rage against the faithful feet of Christ, he should deliver them to be burned in the flame, endeavoring to quench one burning with another.

Which cruelty he has not exercised this first time, but has brought it to noble infamy, by more frequent burnings than ever before. The fires shone through all of Europe; many martyrs were burned every day. But notably before others were John Hus and Jerome of Prague, who, a noble pair of feet like fine brass, did shine in the furnace of Constance in the eyes of all our world. But Antichrist was deceived, thinking he had consumed those feet by fire. Finally, he had experience that these feet are not stubble, but fine brass, which shines more in the fire, and is not consumed.

19 I know your works: The works which are rehearsed, Charity, Ministry, Faith, and Patience pertain to private duty, rather than public office: as though this church were hidden among secret members, and was not renowned for excellent administration. Such was undoubtedly the state of the Thyatirian city: It is plainly related to the Antitype. For although there were everywhere many excellent men, who defended the truth by writings and lively voices, yet no public church companies were constituted or set in order. Or if any were, as about the end of this period men began to meet together somewhat boldly, they obtained no lawful reform.

The chief praise was of their love for one another, not feigned; whereby men promised much but performed nothing, while both by deed and work they helped where there was need, and whereupon they joined charity and ministry. Their mutual faith was also excellent, free from all feigning and treachery. This faith seems to be a fruit of that which is properly called faithfulness, whereby they regarded each other’s goods from the heart. When it signifies a trust in God for Christ’s sake, it tends to be set in the first place, as the fountain and wellspring of other virtues; which perhaps deceived the old interpreter, and caused him to set this word before the other, contrary to the truth of the Greek copies. For so he read: Faith, Love, Service, and Patience. Patience was seen in enduring the calamities that they faced continually due to the hatred and plotting of the Roman prelate.

The last praise is for their last works, which are greater than the former. For so does the Common translation, the Complutensian Edition, and the King’s Edition, which are also used by Robert Stephens in his edition, state: and your last works are more than the first, that is, by presenting the second and.

And so indeed the sentence runs better; especially seeing works are rehearsed at the beginning of the verse: which if they were set down again, and not read together, perhaps the repetition should be superfluous. As touching the matter, it is an excellent praise to grow in godliness, and to exceed the former times in the fruitfulness of good works: which thing indeed befalls them that are planted in the house of the Lord, which in old age are fat and green, Psalm 92:15. Whose way shines as the light, it shines more and more toward the perfect day, Proverbs 4:18. So this Church continues to increase and proceed further and further, growing stronger every day from small beginnings. About the year 1300, many strong, courageous men sprang up, faithful defenders of the truth, but about seventy years later, John Wycliffe added much to their work: he clarified the doctrine in many more points and provided more plentiful arguments, which they had barely found. And forty years later followed John Hus and Jerome of Prague: their preaching and martyrdom greatly increased their influence. The Bohemians followed these, who openly fell away from the Roman Church, and appointed a more reformed worship in their assemblies. And then the minds of all the godly became stouter across Europe, who more boldly professed the truth, however they knew, that they did so at the risk of their lives. Neither did Thyatira stand still here, but about the year 1500, she produced a great number of learned men: who gave no vain hope of a fuller and clearer light that would break forth later. And these are the last works more than the first. Worthily therefore she is Thugateira that is, a daughter growing so notably, even as the waters running from the Temple, which at first was small, then full of shallow places, and could not at last be surpassed by the depth, Ezekiel 47. And so in this first movement from the North created the first pair of contraries; Thyatira grows directly opposite Languishing Ephesus, which has become an omission, leaving, as we have shown, worse in recent times, due to the continual omission of labor and watchfulness, and also by piling up superstitions. Until at last all care of true godliness was abated, and so in the two following Churches it became always worse. Now at last it began to return and to oppose three other Churches, as we shall see in each of them.

20 But I have a few things against thee: The reprehension is, that the woman Jezebel was permitted to deceive the servants of God with her vain shows, Therefore either their negligence, or faint heart, or both are blamed; whereby it came to pass, that she dealt not with the wicked according to their deserts; but they were suffered to sleep securely in their sins. Who this Jezebel was in the Thyatira City, the old History shows not. From this place we understand, that in the same place there was a certain Chief and famous woman, an Idolatress, Sorceress & Harlot, like the ancient Jezebel, which was the wife of Ahab; yet by thus much more furnished to destroy, because this showed herself openly an enemy and adversary to the truth: that would be accounted for a Prophetess. From that which follows, appears that she was taught to the naughtiness in the school of the Nicolaitans, of which she became a school mistress, teaching others the same rules. For the Heretics abused the labour of women to spread abroad their poisons. Simon Magus has his Helena, Carpocrates his Marcellina, Apelles his Philumena, Montanus later in the latter times, in places near to this Thyatira, his Priscilla & Maximilla. In the Antitype the thing is clearer. For this Jezebel is Rome Queen, Idolatress, Sorceress, Whore, Killer of Martyrs, Prophetess, the head of all Churches, and the whole way of salvation, which never yielded to any heresies, and many such like, with which we shall see her adorned by the Holy Spirit partly in this book, partly she boastingly sets forth herself impudently. Lately we learned that the Pope was signified by Balaam, now we have the city shown by Jezebel. Both which pertain to the description of the same Synagogue of Satan, see in the Bishop and the City, are things very nearly conjoined. And how doth it fit the times, that the Spirit doth set before our eyes now such a city? How long did the Pope deceive under a show of godliness, as the Hypocritical Balaam in the former ages about the beginning of increasing honour and reputation? but after he was grown to an immeasurable greatness, lifted up above Kings & Emperors, so as now all men quaked at the very name of the Pope of Rome, his Rome became the Queen Jezebel, an impudent and painted whore. Balaam therefore and Jezebel declare the same kind of impiety: only they are distinguished by the increase and times. Rome in her infancy, as Balaam, handled her matters more warily and secretly: she pretended that she could not speak, but that which the Lord should put in her mouth: being grown to full age, as the Prophetess Jezebel preaches openly that she cannot err, and that she is the rule of faith and all godliness; That abuses the labour of Kings to bring in and set up Idolatry: This by her own authority commands to commit fornication and to eat things sacrificed to Idols, in worship of Idols & Images. Who can admire enough the singular art of the Spirit, who has so lively set forth this matter. This then is Jezebel: the holy men of this time shaking too softly & modestly this pest, have therein so much the less approved themselves to Christ our head, who would have no earnestness spared in repressing so great impudency. Learned men have dealt somewhat more boldly and freely, than they had done in former times: yet they used not that earnestness that met in a cause of this sort.

¶ And I gave her time to repent: In these words is shown the stubbornness of Jezebel. Christ dealt some while patiently with that impure Thyatira woman: so also with the city of Rome, the stormy trouble of Barbarians being quieted, and the Lombards being overthrown. Nevertheless this peace brought no amendment, but increased rather the apostasy, while they came to this height of impudent Jezebel. For we shall see that after those times all ungodliness did grow, the Papists striving to oppress the former dimness with infernal darkness.

22 Behold I will cast her in a bed: The punishment of Jezebel. The bed is sometimes to delights and riot, as in the Prophet, sitting down on beds of ivory, and abounding upon their heads: Amos 6.4. Sometime to sickness and weakness, as, The Lord will uphold him on the bed of feebleness, and turn all his bed in his sickness: Psal. 41.4. Of which in this place? Not of delights, although this be a great punishment, to be given up to the occasion of sinning: but of grief, as appears from this, that by and by after follows, where they that commit adultery with her, shall be cast into great affliction. Therefore the Thyatira woman hath languished. Rome also hath been sick since the year 1300 consuming more every day, as being sick of a consumption. For since that time paleness hath covered her face, her stomach is grown weaker, her soul has become heavy, & her flesh consumed: yea her infirmity hath grown so far, that if thou behold her at this day, thou wilt say that she is a dry carcass in respect of her former plight and good liking. O the infinite wisdom of God, which even in one word, hath given so lively image and picture of a time so far off. Could the languishing destruction of Rome be noted out more elegantly and evidently? God would not have her perish on a swift or speedy disease, that the peoples should not forget her, but with a wasting consumption to be corrupted and wax rotten, both to the end that her lingering punishment should be an image of the eternal pain, and also that she might be a spectacle to many ages, whom she had led in error so long a time. Certainly unless Rome does feel and acknowledge this her consumption, she must needs be sick, not only of a consumption, but also of a phrenia.

¶ And those that commit adultery with her: The punishment of the adulterers, who are the Kings and Princes of the earth, as is after in the 17th chapter 2. Unless these shall forsake the whore, they shall feel great affliction. Have not yet the Kings learned this sufficiently by experience, the most fierce and savage Turk on the one side vexing the Emperor, the Spaniard on the other side? Remember the ages past since the year 1300, in which Jezebel began to languish: Who can attain to declare the great evils which Transylvania, Poland, Bohemia, the House of Austria, the Emperor, the Venetians, the Spaniards, have suffered at the hands of this barbarous Turk? Did not this your affliction begin at the same time, wherein Jezebel in Rome was cast into this her sick bed? Why do ye not observe that your adultery, which this whore hath brought forth, and caused all these evils unto you? But this calamity hitherto, while Jezebel lies sick in bed, is nothing to that wherewith at length ye shall be punished, unless ye renounce betime her ungodly commerce and society, when she shall yield her last breathing, as we shall show afterward. Is it then now time of ye Princes and Peers, to fly like cowards from the true God unto the whore of Rome? They have no pardon or excuse, who bewitched with her beauty while she flourished, accompanied with her. What torment await your wretched lust, who do now embrace a stinking carcass? For the love of Christ provide for yourselves in forsaking with all speed this harlot, lest suddenly at length ye be overwhelmed (when your repentance shall be too late) both with the most grievous calamities of this life, and also those that shall be endless.

23 And I will kill her children by death: the third punishment is directed at her children. These are the Popes, Cardinals, Archbishops, Bishops, Priests, Jesuits, and the rest of the whole troop of this hierarchy. Christ will destroy all those by death, not only in this first punishment, but also unless they repent, in the second. This has yet to come, having begun a long time ago, but will now soon be accomplished, as will be declared.

And all the churches shall know; the churches’ testimony of the just and severe judgment of God. For at length the other multitude of Christians shall have experience that Christ is such a one, as he has declared himself always in his word. His long patience has almost taken away credit from his holy threatenings, but in very deed he shall show at length, that they were not vain terrors of words, but which shall bring most certain vengeance in their time: and this partly begun, partly is yet to come. What reformed churches does not see the long continued languishing of Rome, and praise the just God and celebrate him, crying out, O the depth of his judgments? But there shall be a more plentiful argument of his praise, in his last and full destruction.

And whereas he says that he searches the reins and hearts, in the same he shows to what end his eyes were like a flame of fire, ver. 18. To wit, because not only his servants should approve themselves to be sharp‑sighted in searching out the deceits of this whore, but also Christ should show himself such in administering of things, laying open the impiety of Rome, however coloured with many coverings.

24 And to you I say and the rest: Now he comes to the Council, as we have noted in the Analysis, teaching how they should defend themselves against this wickedness of Jezebel. And it is given to you and the rest of Thyatira, that is, to you the Angel with the company of your colleagues, and the rest of the Church which have abounded in sound doctrine, as Theod. Beza has expounded very well. The common translations, the Complutensian Edition, and others put out the particle and, but to you I say the rest of Thyatira: But Aretas does read the same, with whom other written copies agree. From which particle it is evident that not only the last clause pertains to the Church, but also the whole narration, although it respects chiefly the Angel and speaks to him by name. The same judgment is to be held of the rest, for there is the same reason for each one.

¶ And who have not known the depths of Satan, as they say: But who are they which say? As far as seems to me, the teachers of this heinous wickedness: as though they should brag that they alone did know the depths of Satan, to perceive all his cunning and subtleties, and together also to know the way whereby they may resist his mischievous devices, and therefore that they permitted confused lust and buggery, or at least whoredom, to avoid a greater evil: that the other teachers which the common sort hold true ministers are simple men and unskilled, altogether ignorant of Satan’s enterprises. The name of Satan seems not to be cast in their teeth by John in reproach, but to have been used of themselves willingly, in that sense which I have said. So ungodliness is wont to vaunt itself, challenging to herself alone the power to loose and deliver others, when herself is on every side bound with the snares of the Devil.

Wherefore the Greek word is more fittingly translated by the old interpreter, who have not known. For the Spirit does rather check the boasting of the wicked than praise the integrity of the faithful.

¶ I will lay no other burden upon you; that is, I will denounce no more grievous thing against you, as well as expound it, Theod Beza. A burdensome prophecy was wont to be called massa, that is a burden. These words then show that no notable calamity should invade this church, which ought to be believed to have fallen out in the city of Thyatira. We know that it has come to pass in our part of the world, there having happened no other notable mutation, besides that which was spoken, from the year 1300, in the span of 200 years after and somewhat more. For from that time the Turk waxed strong, but this pertained to the affliction of kings who committed adultery with the whore, as we have shown at verse 22. The true church gets no great loss thereby, but it is a grief to hear that men of Christian name should be trod underfoot so cruelly by a most wicked enemy. Otherwise, while the Turk vexed the Roman whore and her adulterers, the truth springing up again had the chance to grow.

25 Yet that which you have, hold till I come: He exhorts you to constancy, that you keep faithfully the things obtained. Neither is this exhortation only a precept of what you ought to do, but a prophecy of what should be done, as often elsewhere. Therefore you should go forward in the light of truth, neither should you allow yourself to be driven from the right way. And the coming of which he speaks is a fuller reformation, whereby Christ is banished from us while superstitions and errors reign, and when they are taken away, he comes to us, giving us the comfort of his presence. Therefore this glimmer of truth should continue alive, until at last it breaks out into a flame, for instance even in the times of Luther, as we shall see.

26 For if anyone shall overcome, and he who overcomes and keeps to the end, my works I will give to him, instead of “and to him who overcomes and keeps I will give, …”, an Hebraism such as is also in the following chapter, verse 12:21, where the nominative case is put absolutely by defect of the preposition “lamech”, as in Psalm 11:4. Jehovah, in heaven, is His seat: that is, of Jehovah, or as touching Jehovah, His seat is in heaven. So Psalm 18:31, God Himself, His way is upright, for Leel Deo, that is for God, or, as touching God: that of Paul is like, etc. Rom. 8:3, which doth so trouble the interpreters, not marking this Hebraism, whether to adunatum be the nominative absolute, the sense whereof is, for as touching the impossibility etc. But the end which he here mentions is not of this life, but of this period; which should then cease when a perfecter reformation should come.

¶ I will give him power over the nations: the reward is double—power over the nations and the morning star. We have said that rewards are applied to the times and signify those good things that the saints enjoy in this life, while also being pledges of future things. Power over the nations is power over the enemies of the Church. This name once shone upon all, as many were not the people of Israel but strangers to their laws and covenant; now, of the Gentiles themselves, all who profess Christ sincerely are counted among the Israelites. The other multitude, which openly despises the truth or embraces it only in name, remains stuck in their former mire and is called by the old name of Gentiles. There were therefore Gentiles among the Thyatirans, namely Jezebel with hers. Among us Rome with her adulterers and children. Neither must we doubt that the Thyatirans obtained victory against Jezebel, as ours against Rome and her followers. When Luther arose, some princes of Germany departed from the service of the Roman whore; after some struggle they cast her to the ground and trod her underfoot. The same happened by the grace of God in many other places. Therefore this promised power is the society of victory against Papists, which all reformed churches enjoy today. In short, there shall be a full triumph in its place; by God’s help we shall show it.

27 And he shall rule them etc. These are the attributes of the former power. To rule with a rod of iron is mightily to subdue and to compel obedience; they will not. Which was done by the Protestant Prince in Germany and elsewhere, who turned the Papists out of their monasteries, colleges, temples, grounds, and other goods, and bestowed them on former uses, to wit, to maintain godly teachers, widows, orphans, schools, or finally on whatever could be used to promote Christianity. But the Papist cries out that this is sacrilegious and tyrannical: Let him cry out as much as he will; the more he mourns, the more we do acknowledge the iron rod upon his back. Therefore as many of the Theatines as should preserve even to the end, the truth kindled among them, they should see this joyful day with their eyes and should be partakers of the victory. Not that it should be necessary for them to be alive at that time, which arose about the year 1300, but because that is wont to be attributed to all which are of the same condition, that happens to any of them, to wit, to them who should be alive at the end of this period. For so the communion of saints requires that those few should be all.

And as the potter, etc., it is without any hope of restoration, even as the fragments of earthen pots, which are for no use. Let then the Roman Pope sweat and move every stone, that he may recover his former authority: he strives in vain, his fall is unrecoverable: he shall find no glue, whereby his earthen vessels may again be joined together. That in the end, as I have received from my father, signifies that this power shall not be obtained without blood, for Christ first suffered and so entered into glory. So Christians after some dangers and battles, yes overthrown in war, as we know to have fallen out in Frederick Saxon, Philip the Landgrave, and their armies, shall obtain this dominion over the Papists, as we shall show more fully in his place.

28 And I will give him the morning star: another reward no less agreeing to the times. This star is Christ, as we shall see later in 22 ch., where he says, “I am the root and generation of David, that bright morning star”; so called, partly because in this life he imparts to the saints himself a pledge and first fruits of true glory, lest long desire discourage them in their minds. Partly he takes this name in respect of the diverse administration of things. When he shines fully, he is both the morning star, the Day, and the Sun; but when he gives a lesser light, yet still gives hope of the perfect day that follows in time, he is the morning star, the precursor of the Sun. And we must know (which will become clearer in the following exposition) that a bright light of truth, of all godliness and religion, will shine upon the earth when our Jewish brethren are converted to Christ. Seeing therefore that then will be the full day, that renewed Church which goes next before, is the day star, which in the morning, seen near the horizon, shows that the fountain and spring of light will soon appear. And this Church is the reformed one, which succeeds Thyatiren, taking its beginning after the year 1520. The full restoration of the Jews follows at its heels, as the Sun the morning star. What is presented here is only barely alluded to, but may be sufficient to illustrate this point; the subsequent treatise will add proofs. Therefore, in this place the promised morning star is that sweet communion of Christ, which one shall enjoy in the reformed Churches, in which he shall be enrolled as a citizen, and which communication will be followed by the full happiness of the saints, as great as it can be on earth, shortly thereafter.

29 Let him that has an ear. The usual epilogue, but to be observed by reason of his diverse placement. For what end in the three first epistles is the reward set after the conclusion? In the four last this epiphoneme holds always the last place. First, the spirit teaches that there is a certain difference between the three first and four last, which we have observed, distinguishing all the seven into the three first churches growing worse, and the four last waxing stronger after sickness and feeling themselves somewhat better. Secondly, there may be another reason, which I gather from the event, that the rewards in the three first, as to eat the fruit of the tree of life in Paradise, not to be hurt by the second death, to eat the hidden manna and so on, were not paid suddenly and in one moment, but pertained to a time far off and delayed.

Whence do we follow the epiphonemes, as though after the admonition they should take time to deliberate: but in the four last they go before the epiphoneme, as if the admonition once given there should be no place left to take counsel, but the thing forthwith should obtain an issue, beyond all expectation, together with the deeds and sayings. And so we know it came to pass in the reformation begun by Luther, which we have shown to be a reward in respect to the antitype of the Thyatiren state. Who would have believed that from such small beginnings that thing could have gone so far at length? Luther indeed thought nothing less than any alteration or deviation from Rome, or who could have expected in such a small space such a great change of things? But now was the time when there should be power over the nations; and therefore the matter once begun proceeded of its own accord, an alteration of those things being made in a moment, whereat the world then not without cause was astonished, and at this the enemies do at this day behold with such heavy eyes. It seems that there shall be the same swiftness of the following rewards, which a man shall see given before he hears that they were to be given: and therefore in place they go before the admonition, which also no less they shall go before in time. You therefore, O Papists, you again I speak to, if peradventure the Spirit has given any of you ears, that you may hear: attend diligently those things which have been spoken. See what a one is your Rome which you embrace with so great reverence, and where you ran last year to celebrate your wicked jubilees: she is not a holy virgin, as you are persuaded falsely, but a most impudent Jezebel, a most cruel murderess of the saints, from whom we ought rather to flee into any wilderness with Elijah than to run to her by sea, by land, leaving at home the most chaste spouse of Christ. Behold also that this sorceress had lain sick now many years ago: (can you otherwise deny it?) which calls the Turk to come upon the Christian world, exiles our brethren out of their places of abode, turns them out from their goods, spoils them of their children and wives, and constrains them to be carried away into most cruel servitude, and heaps many calamities upon us all, which are far from that burning hatred. And not only these things at this present, but which shall bring finally a horrible death upon you your children. Can it be doubtful to anyone who shall weigh diligently these things with himself; but that we ought to flee very soon and very far from this plague and mischief? The Spirit give you ears to hear; I will speak no more; to them of whom the truth is esteemed, a bare signification of the will of God shall be sufficient: let him be filthy still, who shall despise this.

I will turn myself to the unfolding of those things that remain.

CHAPTER 3. (BOOK 3)
1 AND to the Angel of the Church which is at Sardis write: These things say who has the seven Spirits of God, and the seven stars: I know your works, to wit, that you are said to live, but you are dead.
2 Be vigilant & strengthen the things that remain, ready to die: for I have not found your works perfect before God.
3 Remember therefore how you have received and heard; and observe, & repent. That if you do not watch, I will come against you as a thief, neither will you know what hour I will come against you.
4 Notwithstanding you have a few names even in Sardis, which have not defiled their garments, and therefore they shall walk with me in white: for they are worthy.
5 He who overcomes shall be clothed with white garments, neither will I ever put his name out of the book of life, but will profess his name before my father and before his Angels.
6 Let him who has an ear hear what the Spirit says to the Churches.
7 And to the Angel of the Church of Philadelphia write: These things say he who is holy and true, who has the key of David; who opens and no one shuts, shuts and no one opens.
8 I know your works: behold I have set before you an open door, neither is any man able to shut it: because you have a little strength, and have kept my word, and have not denied my name.
9 Behold I will give those who are the Synagogue of Satan, that is, of those who say they are Jews and are not: Behold, I say, I will cause them to come and worship at your feet and to know that I have loved you.
10 Because you have kept the word of my patience, I also will keep you from the time of temptation, which shall come upon the whole world, to try the inhabitants of the earth.
11 Behold I come quickly, hold what you have: that no man may take your crown.
12 He who overcomes, I will make him a pillar in the Temple of my God, neither shall he go forth any more: and I will write upon him the name of my God, and the name of the city of my God, that is, of the new Jerusalem, which comes down from heaven from my God, and my new name.
13 Let him who has an ear hear what the Spirit says to the Churches.
14 And to the Angel of the Church of the Laodiceans write: These things say Amen, that faithful and true witness, the beginning of the work of God:
15 I know your works, to wit, that you are neither cold nor hot; I wish you were either cold or hot.
16 Therefore because you are lukewarm, neither cold nor hot, it shall come to pass that I will spew you out of my mouth.
17 For you say, ‘I am rich, and increased with goods, and have need of nothing’; and do not know that you are wretched, and miserable, and poor, and blind, and naked.
18 I counsel you to buy from me Gold tried in the fire, that you may be rich: and white garments, that you may be clothed, and that the shame of your nakedness may not appear; and that you anoint your eyes with eye salve that you may see.
19 As many I love I rebuke and chasten.
20 Be hot therefore and repent. Behold I stand at the door and knock, if any shall hear my voice and open the door, I will come into him and sup with him and he with me.
21 He who shall overcome, I will give him that he may sit with me in my throne, as I have overcome, and sit with my father in his throne.
22 Let him who has an ear hear what the Spirit says to the Churches.

The Analysis.
There are three Epistles in this chapter: one to the Sardenses, another to the Philadelphians, the last to the Laodiceans. Neither are they without cause included in one chapter, seeing they are of a somewhat diverse nature from the former. For the former were further distant from one another, so they had antipodes of a longer time; but these are both separated from one another with lesser distances, and also we shall find the Churches directly answering unto them, to be of a more conjoined time. The Epistle to the Sardenses after the inscription to the Angel describes the Sender from the seven Spirits, and seven stars: after it adds the Narration. Which reproves him, that he carries the name and some show of life, when in very deed he was dead, verse 1, but together also he teaches the remedy, which is double: the first consists in confirming the other things that are ready to die. For it should come to pass, that by the just judgment of God many should die, who so should punish the neglect of lawful and just amendment, verse 2. The second, that he should remember what things he had received, and should repent. Which admonition, lest he should negligently regard, he is sharpened by threatening of his unexpected coming, verse 3. After he praises some for their pure garments. Which praise contains the reward, both proper to them, and also common to all conquerors verse 5. Which is threefold, white clothing, a permanent name in the book of life, and his professing of him before his father and the Angels. All which are concluded with the usual Epiphoneme verse 6.

Scholions.
1 To the Angel of the Church which is at Sardis:* 1.1 Sardis is the second of the Churches rising again, going yet further in the South, and growing in a more ample light of truth.
The Antitype is the first reformed Church, begun by God by Martin Luther of Wittenberg, a town of Saxony on the River Elbe, in the year 1517, when that holy man opposed himself against the Roman Catholics selling for money the forgiveness of sins to the people.
The truth began to be revived under the Thyatiran state, but no reformation followed; This was first undertaken at the time which I have said.
For which cause we shall find no mention in these three Churches of this Chapter, either of Balaam or Jezebel.
For they were pure from the fault of this whore, whose fellowship they renounced utterly.
But yet notwithstanding seeing the same should not be done of all after the same manner, but a threefold difference would be found in them, in like manner they are shadowed out by three cities according to the beginning and condition of every one.
The first, after the impudency of Jezebel restrained, is Sardis.
And the first after the Roman impudency weakened, is the German Church of that time, which even now I have set down.
Only the indifferent and good readers are to be entreated that they do not think me to descend to this or that interpretation by any ill will, but in good faithfulness to follow that sense, which the printed steps of the Spirit going before, seem to me not darkly to point at.
I know how fearful a thing it is even to hurt the estimation of any brother with wrongful suspicions, how much more heinous a sin it should be to cast any blot rashly upon any whole Church?
And certainly as in all my life I desire to put far away all virulence of tongue, so especially I have thought always that I must take heed that I make not the name of God a cloak for my lust.
Let not then the office of an Interpreter be any fraud to me, speaking either here or in other places of things present otherwise peradventure than many either would or expect.
It is an impious and detestable thing, to play the hucksters with the word of God, in speaking rather according to the pleasure of men, then the truth of the thing itself.
Therefore all as well hatred as favor set aside, if we shall see that that which is uttered agrees with the truth, let us quake rather at the threatening of the most just God, then be angry with him, who to the end that we may not be oppressed unawares with the evils hanging over our heads, hath endeavored to his utmost power to reveal the hidden truth.
Which I hope I shall obtain easily of all the godly, so far shall it be from them, to reprehend mine industry: with which hope supported, I will proceed to my purpose through God’s help.

¶ These things says he that has those seven Spirits of God, and those seven stars: In the description of the sender of the Epistle, of those Spirits which are recalled, there was no mention in the vision of the first chapter. They are fetched from the common inscription of the Epistle in the first chapter, verse 4. They are seven for the abundance of all gifts, which that number usually signifies. Christ has in his own power, that being the keeper of the storehouse of heavenly grace, he bestows the Spirit on whom he shall think good; whereupon he says that he will send the Comforter from the Father (John 15:26), who should receive from Christ, and show unto us (John 16:14).

The stars are in the right hand, chap. 1:16. Likewise in the Ephesian Church, where we have heard declared the safety of the ministers, whom Christ carries in his hand, chap. 2:1. To what end then is this repeated again? Was there now any other honour spent wholly on the former? In no way, but only because of the convenience of matters, and not any vain novelty, is sought. Because Sardis should find the same safeguard of Christ in defending its pastors, which he had shown in Ephesus; not without reason does he use the same similarity, wherein there is such great connection of matters.

But of Sardis the history speaks not a word, which thing in its antithesis is most clear. For he that gives the Spirit plentifully, to whom and when he will, sheds out in those times so great plenty of all gifts, as nowhere else in these last times. Good learning had already been buried, being driven away for many ages by the rusticity of the Scholastics. At length, after the wonderful art of printing was discovered, many excellent wits were raised up to search out the truth. Among them were John Picus Mirandulanus, Angelus Politianus, Platina, Trapezuntius, Gaza, Hermolaus Barbarus, Marsilius Ficinus, Pyrbachius, Joannes de Monte Regio, Aldus Manutius, Rodolphus Agricola, Joannes Jovianus Pontanus, Philippus Beroaldus, Joannes Reuchlinus, and many other most learned men; whose chief labour was in setting forth the tongues, arts, and other human learning. But how great an entrance was made from here to uncover the mysteries of salvation, the conjoined times have taught.

For by then, after came Martin Luther, Philip Melanchthon, Erasmus of Rotterdam, Zwingli, Oecolampadius, Capito, Blarer, Bucer, Musculus, Calvin, and many other most learned men—so many lights of the Christian world—who, being helped by the studies of those before, brought forth again the truth, covered with long filth and uncleanness, dissipated the Roman darkness, and dispelled utterly like smoke hither and thither all the subtleties of the enemies. Does Christ not rightly take upon himself this banner of the seven Spirits, enriching this time with such a great abundance of gifts?

Neither was his power and grace less famous for conserving safety to the pastors. Who would not have thought that Luther, in so great hatred and envy of all men, for whom almost the whole world laid wait—even he under whose feet the emperors once were compelled to subject their necks—that Luther, I say, should have died a thousand deaths? But perhaps troubles being raised he did scarce endure; yet by almost thirty years he abided in the battle safe, even from private assaults, with which the Pope is wont to make away those men whom he cannot conquer with open war and force: and at length, lying sick in his bed and giving up his soul to him that gave it, he slept quietly in Christ.

What should I speak of Melanchthon, Peter Martyr, John Calvin, and the rest of the valiant heralds? Bucer, buried a few years earlier, at last turned to dust, was dug out of his grave, or rather another buried there recently, so that they might show their cruelty even in the burning of his ashes, whom they could not, nor dared to, hurt while he lived. Who then has not seen the stars in the right hand of Christ, so wonderfully defending his servants against all adversaries? And should not the fresh memory of these things give constancy and courage to all, so that, relying on the same protection, they may boldly go to the defense of the truth, each according to his calling? There is indeed not the same explicit promise as in other times, yet there is always the same crown for those who fight lawfully.

¶ I know thy works, that thou art said to live, but art dead: A reprimension for their counterfeit life, of which the angel bears a shew, being void of truth: from whence Sardis may be called Hypocritical. The force of which notation is manifest from the name itself. For Sardis as Sardinian laughter, such rather in shew, then in very truth; so called of the city Sardis, even as the Sardonian laughter, of the Island Sardonia, as Erasmus notes from Plutarch.

For that kind of herb ranunculus in English trowfoot, by which the mind is taken away, may grow as well in Lydia as in the Island.

This Church was counted alive but was dead: like unto this laughing, which feigns joyfulness, in the mean time full of deadly sorrow. And from hence it is evident how Sardis is opposed to Smyrna; This found all outward things most troublesome, so as she was almost held of all for dead; yet in the mean time live a true life, and was most acceptable to God: That abroad in the judgement of men liveth and flourishes excellently, yet within, death reigns, true godlines being banished: From whence is made the second pair of contraries, as was observed in the common analysis of the seven Epistles.

But in what thing consisted this fawning, as far as concerns the city Sardis, it is not clear to us from the history: there flourished in the same place not very long after, the famous Melito, celebrated by Eusebius in his 4th book, chap. 26. But hence it appears that the matter was brought to that case when John wrote, that although the angel seemed to himself, and peradventure to some others, excellently well furnished with all things unto salvation; yet that he wanted many things necessary, and abounded in the contrary.

We know that those who are alive outwardly may be dead either in ignorance of doctrine and corruption, or through careless of Godly duties: as Christ calls them dead, which were void of faith and knowledge of salvation, John 5:25. And the Apostle calls the wanton widow dead when she is alive, however she had given her name to Christ, 1 Tim. 5:6. In which respect also works are called dead, Hebrews 6:2, as declaring that they are indeed dead that give themselves up to the study & love of them.

It may be that partly through neglect of godlines, partly by corruption of doctrine the angel of Sardis fell into this dead life. If the doctrine had been quite extinguished, which in deed is the soul of the Church, she could not have obtained even the name of any life.

We have said that the Antitype, because of the following order of things, was the first reformed Church, springing up in Saxony, when Luther began to teach. For the Thyatira Church have some blame for suffering the Roman Iezabell. This first, as Iehu, laboured that the painted & shameless whore should be cast out of the window, so as she did sprinkle the earth with her brain.

From whence it comes to pass, that she is not rebuked so much as in one word in respect of this. This Church then has the name that she is alive, for the truth restored, which in wonderful manner she has manifested; and also for the excellent courage, whereby she weakened and trod under foot the Romish tyranny, shaking of the same not only from her own neck, but also giving the same to be derided of the whole world: yet she is dead, having some errors and corruptions of no small importance, chiefly that consubstantiation of the body of Christ in the sacrament of the supper, which many other absurdities followed, which does spread like leprosy, and take away the life of the members living by themselves.

Notwithstanding these things are not to be understood of every man, but of the whole policy and form of the Church, which is apparent to the world: the image and proportion whereof, the Spirit portrays to us. Which also is to be observed in the rest.

2 Awake and strengthen the things that remain ready to die: The first remedy is diligence in confirming the rest; who, if it were not with all speed looked at, would rush into the destruction of death. By which it is taught that if the teachers would bestow faithful and diligent pains, in cleansing the whole doctrine and doctrines, they should take away from many the occasion of falling; but if they shall carry themselves over negligently in this matter, there would be a lamentable ruin of many. In the antitype the thing is so clear, that any man may be waylaid with tears, rather than to prosecute it in words. For how many excellent men hath that monster of ubiquity cast headlong into death? The seeds of which Luther sowed in the years 1526 and 1528 in a disputation against Zuinglius and Oecolampadius. But they ought to have been pulled out again from his books, at least after the controversy was brought to sleep, lest lurking as it were in the furrows, they should break forth at length into deadly hemlock. But Luther himself was careless thereof, providing after the manner of men rather for his own estimation then, as was meet, for the safety of the brethren. Moreover I find lack of your faithfulness and diligence, o holy Philip: because thou hast not thrust through so foul an error according to his due. Perhaps you thought it was to be handled more gently by you, partly in favour of thy friend, partly because you supposed it might be abolished by silence more easily than by sharp inveigling of words. But the errors which are not refuted seem to be allowed, and their estimation grows so much the more as they are dealt with more gently: for they are gangrenes, which gentle remedies do not heal but make worse. While therefore neither of you watches nor does his duty, many die: how many I pray, and how great men? An huge number in deed of all degrees: of which the principal as standard-bearers were Iohannes Brentius, Iacobus Andreas, Selnecerus, Kirchnerus, Chemnitius, and others of that sort, who have increased this monster of ubiquity, of itself horrible, with so many and notable errors, that there hath been scarce at my time any other more foul and deadly. Lamentable in deed is the fall of the famous men, whose labour was once courageous and no less profitable against the common enemies. And what a crown had they received, if they had continued in the same warfare, and had not as cruel elephants turned back the enemies, wasted their own friends. But my office is of an interpreter and not of a quereller: and therefore I leave these things. This death invaded not only some particular men, but also many whole cities and provinces, as may appear by the book of Concord published in the year 1580, which is not of so great force to establish the error with the consent of so many, as to testify this miserable calamity of the brethren. And to this error touching the supper of the Lord, and person of Christ, were many other also added, to wit of original sin, of free will, of justification, of good works, of the law and gospel, of indifferent things, and of predestination. Therefore death assaults with a manifold dart: how great must the slaughter be, seeing she cast to ground even with one, great troops of men?

¶ For I have not found your works perfect; the reason why so many fell into death. The Church of Sardis, as far as it seems, admitted not the sincere truth of God, but retained some ethnic superstition. The Church of Germany did indeed cast away many popish errors, yet in the sacrament of the supper, she stuck still as it were in the clay of bodily presence, not as Rome, dreaming of a changed substance of bread and wine into a true and real flesh and blood, but no less contrary to and disagreeing with the truth, conjoining the true flesh and blood together with the outward signs, affirming that he is present here on earth. This leaven Luther never cast out, but contended fiercely with Zuinglius & Oecolampadius, for to defend & retain the same. Neither would God, which afflicted so grievously the Corinthians for the profanation of this sacred mystery, so many were weak and sick, and many slept, 1 Cor. 11:30. have gone away unpunished the neglect of amending in this point. Of which punishment to come some proof was made, when Luther was constrained for the defense of an unjust cause, to fly for succor to Vbiquity and to confirm many other things touching the manhood of Christ, which are contrary to the truth. But for the heat of contention, he could not so well consider and mind, that from those beginnings and flourishes, he should understand God to be angry. How did he not beware of that error which did draw with it so great a multitude of wicked opinions? Why feared he not, what might have happened to others, having tried in himself, into what case he himself was brought in disputing? But his eyes were held, that he could not foresee for the time to come, and turn away this so grievous punishment from his people. Therefore their works were not perfect, because a full reformation was not used, but only one error changed into another not less grievous.

And God is wont often times to punish sin with sin.

3 Remember therefore etc. The second remedy is, to remember and repent; Theod. Beza translated thus: remember what thou hast received. And so indeed some time the word pos seemeth to be taken. For that of Mark take heed what thou hear, chap. 4.24. Luke hath it thus: take heed how you hear, chap. 8.18. But when he said even now, that their works were not full before God, he seemeth not so much to exhort, that they would retain those things which they had received (for so they should have continued in their former errors) as that they should remember the manner of receiving: So as pos in this place ought to remain in his own proper signification, denoting rather the quality, then the substance of the thing. He warns therefore the Sardenses, that they go back to the first institution, and amend things fallen into decay, after the rule of that alone: Even as also the German Church, that they mind what Luther propounded to himself at the beginning, and make their reformation according to that rule. But he regarded no other thing at first, then that all human inventions driven away, only the divine truth revealed in the scriptures inspired of God might prevail. For so in the preface of his assertion of the articles condemned by the Bull of Pope Leo X. First, he says, I will that they bear me witness, that I will not be compelled with the authority of any at all, how holy a fathersoever, unless as far as he shall be approved by the judgement of divine scripture: Again, let the first principles then of Christians be none other but the word of God: but all men’s conclusions be fetched from hence, and again reduced thither and tried thereby; Those first of all ought to be known to everyone, and not sought out by men, but men to be judged by them; Whereupon also he reiterates that Augustine’s third book of the Trinity is not bound to my Epistles as to the Canonical Scriptures, etc. Therefore we may not cling to Luther’s books, as the Vbiquitaries do, and those who corrupt the Sacrament by the late devised consubstantiation, but as he thought he must be wise only out of the scriptures, all his writings are to be brought back to these holy balances. Why do we give greater authority to his books, than to the books of others, or would he himself have to be given to his own? A matter indeed of great moment, and in which alone consists the turning away of the eminent evil. Unless men turn their eyes to these things, and have their ears bent to hear their voice, and also those things performed which they shall command, another scourge remains for Germany more bitter than that, which even hitherto has afflicted her not lightly. What godly man takes not great grief minding the destruction of so many brethren by a pernicious error, so long contentions of minds, so sharp battles both of words and weapons? But he must need be more vexed when he considers with himself that there is not yet an end to these evils, but some greater thing to hang over their heads, unless they repent in time. I could not but warn the brethren of the danger, lest I should hear with my great grief that they are afflicted and full of calamity, whom I desire in Christ Jesus to flourish. And I hope that however my judgement shall be troublesome, yet my good will shall not be ungrateful.

¶ If you do not watch, I will come, etc. The danger that He threatens is His coming like a thief, at an unexpected time. He does not expressly say what kind of evil will come, although part of it may be inferred from the simile, which is often used in Scripture to signify the invasion of the enemy. But seeing the following words have respect hitherto, you will not know at what hour I will come against you, perhaps He means something else, namely a certain force and violence, such as thieves use in robbing houses: who not only spoil the owners of their goods but also commit adultery with their wives, deflower virgins, and force confessions of where money is hidden; having obtained it, so that their wickedness may not be betrayed, they kill all without distinction of sex or age. Therefore, Christ appears here to threaten the same outrageous ferocity of some cruel enemy.

Of whose coming we may not define by the judgment of the flesh, seeing it shall not be known in what hour He shall come. Neither must we labor much to search out who this enemy should be. The Spirit, who has determined that his coming shall be sudden, would not have him known by name. It may be that it is the Turk, to whom the reins may be loosened awhile, until they be looked at that are to be punished. But whether it shall be he or some other, we may not sleep securely and neglect reformation, because we see no danger at hand; but we must think how it may come upon us in a moment. And it is to be feared that this which is threatened shall no more be avoided than that of removing the candlestick from the Ephesian Church (chap. 2.5). These things depend on the condition of repentance, to which the ears of men are deaf, even the greatest part.

4 Yet you have a few persons; in Greek it is a few names, that is, a few men, as Acts 1:15 and after in this book chapter 11:13. In these words he comes to the other part of the narrative, which pertains to commendation. Which always, at other times, tends to take the first place. But this new disposition and setting in order is not done rashly, teaching that in the latter times shall be some who refusing errors should embrace the truth. As we know, it was done when the Book of Concord began from this occasion, and so many visitations were undertaken, that the Calvinists, as they speak, might be rooted out utterly. For such men, followers of true godlines and judgement, were conversant in the deepest parts of this Sardinian state. Besides many free cities such as Strasbourg, Heidelberg, Marburg, Newstadt, Bremen, the people of Anhalt, etc., who opposed themselves against the forgeries of others. In every one of those places famous lights now and then did shine, which drove far away that darkness, gave a joyful day to their flocks.

¶ Which have not defiled their garments: The garment is Christ himself, the common clothing of all the faithful. Of which, in the parable, “Friend, how have you come hither,” not having on a wedding garment, Matt. 22:12. And Paul more plainly, “For all of you who have been baptized into Christ, you have put on Christ,” Gal. 3:27. But it has a diverse signification according to the diverse respects of things into which it is referred. In respect of God, it belongs to justification; in respect of other people, to sanctification and profession; in respect of ourselves, to honor, glory, triumph, joy, etc. Therefore these Sardinians kept their profession of Christ sincere and entire, free from the filth and pollution of those monstrous opinions. Although they too, by repentance, awoke from those errors, may be said to keep their garments also pure. For those who are in Christ are not judged by their former filth, but by their present apparel, with which all their former uncleanness is covered.

¶ And therefore they shall walk with me in white, to wit, garments. These are the same garments with the former, but a little differing in respect; for those were of profession, whereby the valiant soldiers of Christ did appear to others: these are of glory, triumph, and joy, which they shall enjoy both in themselves from the feeling of God’s love shed abroad in their hearts, and also which they should receive from the praising of others, who shall praise God in their name, who has bestowed on them fortitude & victory. A white and pure gown in a solemn mirth is commendable, both among the Gentiles and also the people of God. From whence the wise man alluding to this manner, Let, says he, thy garments be white always, Eccl. 9:8. But especially I think that of Mark is to be regarded, where some step of this celestial glory appeared in the shining garment, so white as snow, such as no fuller can make on earth, Ch. 9:3. At which sight Peter, being overwhelmed with unmeasurable joy, thought this one thing, which way he might have been able to enjoy it always. So this shall be a most ample reward for the saints in which they shall so heartily delight, that they shall desire no greater thing in this life.

And if any should ask the brethren themselves, whose these garments are, I doubt not but they would answer, that this joy is of more value, which they obtain by Christ in retaining his truth, than that they would change it with all the delight of this life. Certainly great is their glory among all the godly, which we pray with all our hearts to be perpetual to them.

¶ For they are worthy. The Papists are glad in their own behalf for this word, as an excellent patron of their merit of condign worthiness: but let them remember that this merit is attributed to the garment, not to the body, that is to the imputation of the righteousness of Christ, wherewith we are clothed as with a garment, not to our inherent holiness; For not to defile the garment cannot be more esteemed than the garment itself. And seeing there be sundry significances of the garments, as we have shown, the worthiness arises not either from the profession of good works, whereby the saints are seen by others, nor from the joy of the Spirit, which we ourselves feel within us, but from this alone: that the Father counts us righteous being clothed with His Son. He, therefore, is worthy to be clothed, though not in every use of garments, but only in that peculiar respect whereby we are presented blameless in the presence of God: even as a man sees, although not the whole man, but only that part to which the faculty belongs.

5 He that shall overcome &c. Some copies and the common translation read thus: He that shall overcome shall be so clothed. But the rendition of a similitude is unusual, where there is no question: unless peradventure they are referred to the former verse, as though he should say, as those who at all have not assented to errors, shall walk with me arrayed in white apparel, so that those who after some striving shall depart from the same, shall be clothed in white. As though the first reward were pertaining to those who fell not, this to those who repented and forsook their errors, with which they were possessed before time. Of this sort were many in Germany before the book of Concord was published, when in most universities the chief teachers understood the true doctrine of the supper of the Lord, and the opinions of ubiquity and corporal presence in the supper, everywhere were contemned, as witnesseth Georg. Sohnius in his exposition of the August Confessions, which appears more clearly from the Synod of Desdrense, in the year above 1571, where it was ordained by the common consent both of all the superintendents of the Duchy of Saxony, and also of the doctors of the universities of Leipzig and Wittenberg; that the ubiquity of the body of Christ was a horrible profanation of all the articles of the Creed, and a renewal of all heresies, Gallobel, in the year 1592. And since that time a fierce light breaking forth every day, many were roused up from their drowsiness, and opened their eyes to the truth. Whom also even as well as the other, he adorns with white garments, who gave a penny to those who were hired at the eleventh hour, Mat. 20.9. Such then is the first reward, though yet does remain.

¶ And I will never put his name out of the book of life; the second reward applied to the times. For because very many in these times should fall from the truth, and many cities, peoples, provinces, regions, should consent to error (as at this time it is evident how far and wide the contagion spread abroad, flying also over the sea and infecting those Northern regions Gothia and Suecia) by which their approving of error they should blot their names out of the register of the saints, and should cut off from themselves the hope of life, unless they should repent, lest I say, the falling away of so many should trouble the saints; he bids his conquerors to have good courage. Christ Himself would set them free from falling, however they might see infinite numbers rushing down violently on their right and left hand. For it is He alone, who first calleth us back from error, then sanctifies and confirms us in the truth, lest at any time we should revolt from it. Therefore, however this reward be full of comfort, yet it teaches that the time should be lamentable through the fall of many. For to betray and forsake the truth is not a light matter, as many suppose, who easily are carried away with every wind of doctrine, but it is an argument of a man of no reckoning with God. But how, wilt thou say, can they be blotted out, which once were written in the book of life? Especially seeing that this book is the book of the Lamb, as in chapter 13.8, that is, wherein those that are written, the Lamb acknowledges them for His, and counts them heirs of eternal life: neither is there any of those that are given to Christ, that can ever perish, John 6.37, 6.39, and 17.12. I answer that these things are spoken in respect of us. For there is a twofold book of life, one, as I may say, of vocation, another of election. Into the first are put all, who by the preaching of the Gospel are taken into the fellowship of the Church, who rightly do seem unto us to be partakers of life, and endowed with the hope of eternal salvation. For the scriptures are wont to speak so generally, giving thanks to the Father, who has made us meet to be partakers of the inheritance of the saints in light: who has delivered us from the power of darkness, and translated us into the kingdom of His dear Son, in whom we have redemption by His blood, the forgiveness of sins, etc. So the Apostle speaks of the multitude of the Colossians without difference, chapter 1.12. And after the same manner everywhere in other places. Yet men may be put out of this book. For many are called, but few chosen, Matthew 22.14. And it is declared later in the 7th chapter by an example, Dan and Ephraim being passed over in the rehearsing of the tribes, as soldiers put out of wages, and cast out of the register. For God of old, as in a certain visible shadow of this book, commanded the genealogies of each tribe among the people of Israel to be kept diligently. Whereto also pertained that of raising up seed to the dead, that his name should not be put out from his people: Deuteronomy 25.6. In which respect also the Psalmist wishes to certain reprobates, who held a place in the Church, like true citizens, that God at length would separate them from the congregation of the Saints and manifest them to be mere hypocrites, Psalm 69.29. Wherefore all are put out of this book of life, who forsake the fellowship of the holy Church, either through error and heresy, or wickedness, or other cause whatsoever: not that for this cause they are blotted out of the book of Election, but because by this way they make manifest that they were never written in this book; as John says, they went out from us, but they were not of us, 1 John 2.19. But the other book, to wit, of Election is never spotted with any blots, but the names once written remain constantly without being erased. Although these books are not so open and evident, that they can be read by all men without difference: but it is declared to every one separately by the Spirit that is found in this register, in what estimation and account he is.

¶ But I will confess his name: The third reward is of confessing their name. Which shows not only the falling away of many, but also that others shall be compelled by force: So as there is great need of the power of the Spirit, lest any weakened by the injuries and threats of adversaries, do forsake the truth. For the confession of their name before his father is for the comfort of confessing Christ and his truth boldly and without fear. So sending his Apostles to preach, furnishes and instructs them against the fear of affliction, Matt. 10.32. And who knows not to what inhumanity and cruelty proceeded the hatred of those who call themselves Lutherans, against the professors of the truth? In the year 1580 was imposed upon the Ministers of the Churches, and Schools the book of Concord, avouching the execrable error of Vbiquity. A subscription was commanded in the name of the Princes, the refusers were proclaimed Sacramentaries, or put out of their places. In the year 1591 Christian Duke of Saxony being dead, Paul Kreilius Chaunceler, suspected of Calvinism as they speak, was cast into prison: Vrbanus Pierius, Professor of Wittenberg, was led captive into prison: Gundermannus of Leipzig, committed prisoner. In the following year was appointed a new visitation, they went through all Saxony: those who would not subscribe to the articles were removed from their offices.

What should I rehearse the brawl of Leipzig the year following, when all the university men on every side assembled together to break open violently the houses of the Calvinists?
Or the savage cruelty of the Dressens against the dead body of Jac. Lassius, to which they denied a grave among the wicked, because being alive he was a lover of the purer truth?
I recite these few against my will, & I would be ashamed to mention them, but that the brethren were not ashamed to commit them.
But how much better is it for you to hear these things of your friends, then of your enemies?
These as much as they can do exaggerate with words your evil acts, unto your perpetual shame & of all religion: I do only show the congruence of the Prophecy, that seeing in what account you are with God, you may think earnestly of reforming the errors & making peace with the brethren.
God give you to see that way, whereby consenting to one truth, you may turn away the judgment from your heads, which otherwise will overtake you.
In the mean time if I shall prevail nothing with you (which estimation I pray may be far from you) yet I shall be glad to admonish the brethren, that they be of good courage, who do endure troubles and calamities among you.
Christ will not be ashamed of them before his Father, if they shall abide constantly in their profession.
Fear not therefore the stately look and countenance of men, but being grounded upon this hope, that which you have worshipped in darkness, profess now openly & in the eyes of all.

6 Let him that has an ear hear; Yet therefore brethren of Saxony, for Jesus Christ’s sake give ear and hearken, what action the Spirit charges you with. Your praise is great in respect of your first combat, and breaking off the yoke of Roman tyranny, yet you who in this were the first of all. But the Canaanites left in your land are come to be thorns in your sides and eyes. Those few errors neglected at first, by the just judgement of God, have brought forth new errors: by the contagion, where true godliness is driven away, and together with it true life is lost, there is left unto you a church defiled with horrible death. Neither is this the end of evils, but some new, great and sudden calamity shall come upon you unless you obey forthwith the Spirit, giving you warning. Therefore let that unhappy obstinacy depart and be packed away, and take those counsels which may promote the truth, recall again the banished life, and may procure the salvation and safety of every one of you. And do not only give ear, but let all hearken and learn from your evil, how great a danger it is to cherish the least error in the matter of religion.

Analysis.
So is the Epistle to the Sardians, this to the Philadelphians is inscribed likewise to the angel: He who sends is notable for holiness, truth and the key of David, which he carries not idle, but with the same opens and shuts, the supreme power being in himself, verse 7. The narration recounts first the good things, both present, of an open door, which is illustrated by his cause, a little strength and the constant observing of his word, verse 8, and also to come, both of subduing their enemies, verse 9, and also of ministering help in the common temptation; of which a reason is rendered, from their patience in the profession of the Gospel, verse 10. After he provokes them unto a care of preserving that which is good, because his coming is at hand, and there may be danger of their crown to be taken away, verse 11. Then there is a great reward, when he shall be made a pillar, and shall have written upon it the name both of God and of the new Jerusalem, and the new name of a son, verse 12. To all which is added in the end the common conclusion.

Scholions.
7 And to the Angel of the Church of Philadelphia; We have shown at the first chapter ver. 11 that Philadelphia is situated in a dangerous place, and therefore not so frequent of citizens, who did dwell scatteringly in the fields, fearing the often quaking of the city.
But she carries a sweet name, and which alone contains within it all virtues. Neither did the Apostle Peter find anything, when he would exhort to all godliness, which might commend more fitly the same unto us than brotherly unfeigned love, 1 Pet. 1.22. How well this name does fit this Church, which is reproved for no sin openly!
But as it was truly godly because of brotherly love, so is she lowly and not famous, both through a continual fear of danger, and also solitariness of the citizens, who dwelt here and there, and in waste places, where they could get safe dwelling.
Wherein she is altogether contrary to Pergamum, a towered and proud city, as before Sardis to Smyrna, and Thyatira to Ephesus.
And so there is made 3. pair of contraries. It lies from Sardis toward the South, having an increase of greater light, as becomes a reformed Church. She is set in the second place after Sardis (for this is the first after Iesabel overcome) whereby it is shown that her antitype is the second reformed Church, which should arise after the German, and this is the Church of the Helvetians, Suevia, Geneva, France, Holland Scotland. I join all these into one, because they live almost after one and the same kind of laws and ordinances, as touching the things that are of any moment.
Neither does the distance of place break that society which the conjunction of minds and will does couple. Yea this dispersion does agree chiefly to the Philadelphians, whom we have shown to dwell thicker and more frequent in the fields than in the city.
Whereby it comes to pass that this thinness of the citizens takes up much place, though the citizens are not so many. We shall find that this Church which I speak of arose a little while after the German; when Vlricus Zvinglius began to teach at Tigur in Helvetia, in the year 1519, and the reformation was begun the fourth year after, to wit, in the year 1523, at which time no Papist durst enter into combat against Zvinglius, who deferred the judgement of all controversies to the arbitration of the sacred scriptures. They of Constance, Basil, Strasbourg, Geneva and others, followed their steps. Where it is to be observed that the former antitypes were distinguished by longer intervals: these three last as they have types less distant one from another by space of place, so they are joined one with another with a nearer conjunction of times, neither are they divided so much by ages and limits of years, as by laws and customs. For after the first receiving, which happened to some later than to others: we shall see that they did all flourish together.

¶ These things say that holy one, that true one, who has, etc. A description of him who sent the Epistle: whose two first properties are taken from the nature of the sun of God, which yet are not rehearsed expressly in the vision of the first chapter: They do greatly help to declare the administration of this Church. Touching the city Philadelphia itself, we find no other thing, but that in the age following, there abodes in that place a famous congregation of the faithful, over which Demas had the charge, as is gathered from the Epistles of Ignatius. In the Antitype, a divine power specially shines forth sanctifying the Church, by kindling the desire of godliness, and in making it in Christ Jesus fit and cheerful to every good work. Let my words be without envy, the true doctrine sounds nowhere purer, the worship less corrupted, more flourishes the faithful diligence of the Pastors, is performed more willing obedience of the people, nor greater reverence for all religion among all degrees. But this holiness seems chiefly to respect manners. In which thing is not to be passed over that famous testimony of John Bodin, speaking of them of Geneva; Of whom that thing, says he, is praise worthy, if anything anywhere in the earth, and which makes a common wealth to flourish, if not in riches and greatness of Empire, yet certainly in virtues and godliness, namely that censure of the Pope, then which nothing greater and more divine could be devised to bridle men’s lusts, and to repress those vices, which by no means could be amended by any humane laws and judgments. How be it that this restraint is directed after the rules of Christ, first privately and friendly, after somewhat more sharply, then if you do not obey, there follows a heavy, grave and effectual prohibition from the holy things; after the interdiction, is the punishment of the Magistrate. And so it comes to pass, that those things which are punished nowhere by the laws, are there restrained without any force and stir or great ado. Therefore no whoredoms, no drunkennesses, no dancings, no beggars, no idle persons are found in that city, Those are his words in Method of History chap. 6. Worthily is the sanctifier of the Church to be prayed, who has wrought, that they should will and effect these things according to his free good will. There is the same care and fruit also of the rest, according to the measure, which Christ vouchsafes to every congregation of them. Neither is his truth less excellent, both in as much as he is a Prophet in teaching, and also a Surety in promising. We shall see this double truth in the following Church to be distinguished by their proper words; both which the Greek word true seems to contain, when it is put absolutely and by itself. And as touching truth of doctrine, where is it more pure and more sincere in the whole earth? The whole Papacy has here his throat cut. The Anabaptists, Antitrinitarians, Arians, and such like monsters raised again from hell, partly in Germany, partly in Transylvania, have found nowhere a fiercer enemy: What also has it not assayed, that she might pull away from the German Churches their errors? Neither does she keep only the doctrine of salvation uncorrupt, but also she both delivers and teaches in writings and exercises in practice a sincere manner of administering, whereby salvation is bestowed. Certainly the whole will of God is communicated with his saints, so as Christ takes to himself not undeservedly this praise of true in governing this Church: He also performs plenteously that which he promised, that he would keep safe and sound those that seek him with an upright heart. What have not endeavored the French man, the Spaniard, the Savoyan, the Pope, to root out them from Geneva, a small people, and surrounded on every side with enemies, and shut up from all aid of friends? Nevertheless it flourishes yet still thanks be to God, and shall flourish hereafter, while all her adversaries burst with envy: as long as she shall continue in this holy order. The French Church has been preserved hitherto, no other wise then the three children in the furnace. Who would have believed that the Low Countries had been able to resist and withstand the raging Philip, the cruel Duke d’Alve, and so many bloody tyrants? But true is he, who has promised this honour to his saints, that they should bind the Kings with chains, and their nobles with fetters of iron, Psalm 149:8-9. And that I may not speak of each one, they can be safe only by thy protection, O Most High God, who art constant in all thy promises, whom both enemies almost infinite do persecute with deadly hatred, and also to whom many of their friends through envy wish not very well.

¶ Who hath the key of David: The third property pertains also to the same administration. Christ opens and shuts, to whom he has thought it good, the entrance into the kingdom of Heaven, by his regal power. Which faculty in indeed he bestows upon all his who declares and preaches the word purely and sincerely, but which is principally to be seen in that part of government by which obstinate sinners who will not yield to admonitions are delivered to Satan by the ecclesiastical censure, and are cast out of the Church, which is the kingdom of Heaven: according to that, whatever ye shall bind on earth shall be bound in heaven, and whatever ye shall loose on earth shall be loosed in heaven: For where two or three are gathered together in my name, there am I in the midst of them: Mat. 18.18.20. By these therefore is shown that the power of opening and shutting, of binding and loosing is very effective in these congregations, and moreover also in the whole administration of the censures. And what godly man does not thank God from his heart, and does not exalt with worthy praises the holy pains of this Church, which restored discipline that had fallen into decay, and brought it back to the rule of truth and the use of the primitive Church?

But it is to be observed that this key was said before to be the key of Death and Hell, in the first Chapter 18th verse, by one part denoting the whole force of them. Therefore that key is to be feared, which locks up the gate upon the wicked being thrust into Hell, however they despise it with security: And yet notwithstanding it is less pleasant to them that fear God, because it unlocks to them the doors by which they may enter into life. But why is it called of David, seeing it is of Aaron rather, whose office was to keep away the leprous and uncleans from the holy things, and to shut the Temple against them? Certainly the Priest only could pronounce men uncleans: he was not wont by an ordinary & proper power to use force to compel the disobedient. Christ both King and Priest is very mighty in both faculties and powers, and joins together both in this Church: who not only raises up Pastors, that they should denounce men uncleans, but also together adjoins the civil Magistrate, that he should give his ready and diligent labour to the Pastors in this. So before Bod. the punishment of the Magistrate follows the debarring from holy things. Therefore both swords are drawn in this Church but separately by those to whom the one & the other belong. And indeed this society is most sweet, seeing all the industry of civil Magistrate ought to have respect there, that we may live with all godliness & honesty, 1 Tim. 2:2.

The words seem to be taken out of Isaiah chapter 22, verse 22: “I will lay, saith he, the key of the house of David upon his shoulder; when he openeth, no man shall shut, and when he shutteth, no man shall open.” But in this place the word house seems to have been omitted purposely; for he says not “who has the key of the house of David,” but “who has the key of David.” There is a difference, because the former seems to refer to an inferior minister in the family of David, whereas the latter refers to a supreme governor of a whole kingdom. So the omission of one word creates a difference between the type and the truth, between Eliakim and Christ. See also Isaiah 9:6–7. The Complutensian Edition and the King James Bible read somewhat otherwise: “Who openeth, and no man shall shut; who shutteth not, and no man shall open.” Arethas has “except him who opens.”

8 I know your works: behold, I have set before you an open door. He enters into the narration, and first of a present good thing. And it is an open door, which sometimes signifies the faculty of preaching the Gospel, for which Paul earnestly desired of God on his behalf, that the door of utterance might be opened to him, Col. 4:3, and that speech might be given unto him in opening his mouth, Eph. 6:19. And worthily is it so called, seeing by the word a door is opened to us into heaven, which being taken away and removed, the door is shut and locked, so that no one can enter in, Luke 13:25. And not only the faculty of the ministers is the door, but also the readiness of the hearers, as, “For a great door and effectual is opened unto me, and there be many adversaries,” as though he should say, although there are many who do resist and strive against the truth, yet there are many whose desire is prompt and ready, 1 Cor. 16:9. And again, coming to Troas to preach the Gospel, “and a door being opened to me in the Lord.” This door is opened when the hearts are opened to receive the truth, as Lydia, whose heart the Lord opened, that she might attend to those things which were spoken of Paul, Acts 16:14. But although the name of door be attributed to those apart, yet most of all the door is then opened when all these things meet jointly together: the word, discipline, the care of the magistrate and of the people. Then there is free leave to pierce into the consciences of men, unto which an entrance is shut up where any of these shall be wanting. This then is that open door whereby this Church was famous, which indeed no strength of wit has opened, which consists either in the virtue of speaking, or in the sharpness of wit and prudence in understanding, but only that chief key‑bearer, who has given freely that which no man could have obtained by human strength. How ungodly therefore are they who do check by reproachful words that which Christ has conferred for an excellent benefit? They whet their tongues against heaven, yea, against God himself; but they shall not escape unpunished, let them clatter as much as they will.

¶ Neither can anyone shut it; the endeavor of the adversaries has not been lacking; some have labored to bar these doors by slandering, reproaching, inveighing, with all manner of contempt; others by force and weapons, as it were by a rushing down violently to shoot this gate, but he has performed his promise, who has confirmed that none shall prevail. The enemies have lost their labor and have gained nothing but shame in the world, for their cruel minds against the truth, and punishment at God’s hand, deserved for their deserts. Let the experience of the time past be a confirmation against future fear.

¶ Because thou hast a little strength: The common translation has, because thou hast a little virtue, the sense, if I be not deceived, being well expressed which depends on that which follows, neither is it absolute of itself: as though he should say, because although thou hast but a little strength, yet thou hast kept my words. And in deed the fortitude in the greater danger is more famous. And this manner of speaking is frequent among the Hebrews, who use the copulative use, for the discrete particle: (the custom and manner of which is frequent with John) as, Neither shall any straw be given you, and ye shall deliver the whole tale of brick, for, yet shall ye deliver &c. Ex. 5.18. So, And behold an escaping remnant in her, for, yet shall some remain who shall escape, Ezekiel 14.22. Afterwards also John in the same manner, And men raged in heart, and blasphemed and repented not, for, and yet repented not, chapter 16.9. If he had prayed a part their small strength, how should there not be in the same thing much depravity. For this is wont to abound, where that which is opposed, is but little and small. Sardis had few names, upon death had possessed the greater part. Neither would the Spirit have passed over in silence the corruption, if he had found any worthy reprehension. Therefore the common translation ought here to hold in that sense which I have shown. This Church is of weak strength, which dwelleth here and there, and the greater part under a popular state, one only people enjoys a Monarch for their patron. But neither is this Church able to do much either by her own or by her friends’ riches. Therefore the greater is the praise of thy fortitude O Philadelphia: who hast not yielded to the threats of the adversaries, neither forsaken the truth, by being dismayed with the vain fear of men.

1 Behold I give of the Synagogue of Satan; Here is a defect of the word some, I will give some of the Synagogue of Satan, of those which say that they are Jews. This is the future good thing, as we have shown in the Analysis, and it may be manifest from the latter member of the verse, Behold I will make them come: unless perhaps this verb of the present tense diminished, respects the present time, wherein some of the Jews submitted themselves to this Church, for a token and pledge of a full submission afterward, which it may be the last words mean. We showed upon the ch. 2.9. how they which by nation are Jews, do lie saying they are Jews, to wit in bragging that they are the only people, when meanwhile they refuse Christ, in whom only we are counted children, and do continue and rest in the abolished ceremonies of the law. By which things they have made themselves to be the Synagogue of Satan, and not a congregation of saints, whatsoever they affirm to the contrary in words. In the Antitype are Jews as many as entangled in errors, challenge to themselves alone the truth, faith, salvation and promises of God, speaking of nothing, but the temple, the temple, of which sort were the Arian Bishops under Constantine, Constantine and Valence, and such as are at this day the Romanists, glorying no less in the Circle of Peter, then of old the Jews in their temple. These only will be Catholics: their Church to be the only spouse of Christ, that no salvation can be found, out of their congregations. But let them deceive themselves with as good words as they will, by their true name they are false Jews, in show only Christians, who gather congregations in the honour of the Devil: God acknowledges them not, which thrust upon him another worship, than that which he hath appointed from heaven. Some of these therefore are given to this holy Philadelphia, seeing there are many daily, whom God of his singular mercy plucketh out of the jaws of Antichrist, & enlighten their eyes, that they may acknowledge & embrace the truth. Among which are Peter Vergerius, Peter Martyr, Hier. Zanchus, Martinegus, & many other, both Italians & other nations: who first being papists were afterwards converted to the truth.

¶ Behold I say: Excellent undoubtedly was once the victory of the Philadelphians over the Jews, and no less famous shall be at length the triumph of this Church over the Papists. Hitherto we have fought with them by pen and ink: but the time shortly cometh when they shall be rooted out by weapons, chiefly by the labor of this Church, as will be shown more plainly. Rome shall be destroyed by some other means, but being overthrown, holy Philadelphia shall uproot the remnants of the Popish kingdom so that no name of it shall be left, as we shall show in chap. 19. For this worship of the false Jews pertains to that time when the Roman beast is cast into hell; all his hosts shall be killed with the sword that comes out of the mouth of him who sits upon the horse.

¶ And they shall know that I have loved you; For until now you are made a mocking stock, neither do unthankful men acknowledge any love of mine, by the singular gift of godliness, which I have bestowed on you: But then I will adorn you with those things also which are in account with the world: you shall set up a token of victory over your enemies, & shall enrich yourself with their spoils, that every one may be compelled to confess that you are dearly beloved, who, contrary to all hope, they shall see increase so wonderfully. O holy Philadelphia, cherish your hope with these things, neither be grieved in mind whatsoever the world says otherwise.

10 Because you have kept etc. My words and doctrine, which I have taught the world with great patience, and which is also to be preached always with the same patience: which I see you have used to your great peril, and yet you have remained constantly in your duty.

¶ I will keep thee also &c. But what is it to keep from the hour? Would not God suffer the temptation to touch the Philadelphians at all? It could scarce be done that they should be free altogether in the common calamity of all the world. To keep therefore is to deliver, as the Lord did keep them out of the hands of their enemies; that is, delivered, Jud. 2:18, as though he should say, I will not suffer thee to be overcome in that temptation, but I will give thee strength, by which thou mayest not only bear consciously the calamity, but also overcome & be victor. But what is this hour of temptation? In the type itself, that persecution doubts under Trajan, which Philadelphia together with all the other Churches sustained. Neither is it to be omitted why in the Epist. to the Ang. of Smyrna, he said that the same affliction was of x days, which in this place he included in one hour: in both places he respects the concurring of the type & antitype: there because under Constantine, Constantine & Valens (within which times we have shown that the antitype of the Smyrna Church is to be limited) there should be a long calamity, raging in the greatest part of that space, he defined that affliction by x days; in which he noted both the years, so many as Trajan should go on with rage, & also that long delay in the antitype under the Christian emperors; But seeing in the antitype of the Philad. Church there should be affliction far greater than all, yet short, he has joined the same trouble of times in one hour in the type. This temptation therefore yet to come, which shall come upon the whole world is the last fight of the Roman Antichrist in the west, & of the Mahometan Turks in the East; very terrible in the whole preparation; but on which the Church shall carry away the victory, to be preferred far before all the triumphs and the victories of all men. Of which is here given a taste the full declaration is reserved to his own place.

But seeing in this battle there shall be a common victory of the whole Church, and here seem to be promised something proper to this alone, perhaps this temptation shall be another, which shall go before that war. And before we have heard that in the Church of Germany some grievous thing doth hang over their head. For he threatens that he will come as a thief; then also in the Church following we shall see that some storm is to be expected. Wherefore it is to be feared that shortly this temptation will come upon us and shake the Christian Churches with a horrible tempest. Besides the conjecture of this place, the sins which reign everywhere, not without cause indeed may increase this fear. It shall be profitable for everyone to prepare himself so that he may stand firm in that day. And we may guess at the greatness of this tempest in some sort from the very words themselves. For they promise that this alone shall be kept pure, sound, and undefiled, to which also belong the reward of Pillars, verse 12. What then shall be done with the other Churches? The future disturbance of all things seems so miserable that there shall be no face of any Church anywhere besides. For it seems that those Churches at last shall by the just judgement of God come to nothing, which have not undergone full reformation.

11 Behold I will come quickly: Until now the good thing: the way to preserve is by constancy, unto which he exhorts, first by his quick coming. The Philadelphia Church felt the hour of temptation, later after this writing. For Trajan succeeded after Domitian: under whom John received this Revelation. Neither shall the newly restored Philadelphia find it to be long, before all these things be performed. Within two hundred years after she was born again, she shall see the issue and end of all these things, as the prophecy following shall declare with God his help.

¶ Hold that which you have, that no one may take away your crown: Go on courageously in the race in which you have begun; keep your sanctity of manners, purity of wholesome doctrine, severity of heavenly discipline, lest if you begin to relent in any matter another takes your crown from you. But what crown is this? The honor which she shall receive from the enemies brought under her and worshiping before her feet, ver. 9. These manners of rewards depend on the duties of godliness, to which they are proposed, and are sometimes taken away from the saints for a correction of their cowardice. Therefore they are unskillful who transfer these things to eternal life, as though that could be taken away from the elect, or at least, as though they should always waver as to an uncertain and doubtful thing, of which they could have no sure hope as long as they dwell on earth. It may come to pass, and it always comes to pass, that the wicked may deceive themselves with a false persuasion. But the elect have the Spirit, who witnesses that they are the children of God, neither can He, the author of all truth, either deceive or be deceived, Rom. 8:16. Although if any think that there is the same reason for the earthly and heavenly reward, and that they will have that to be at least a type, the same thing may be answered truly and rightly, which we have said before touching the book of life, ver. 5: that many are called, but few chosen. Now the crown may be taken away from those who are called but not persevering, who for a time did hope for it; in this respect it is called, not without cause, their crown. But how trifling is it that they wrest unto the elect that which pertains to the called only, because they envy that others should have the certainty or assurance of salvation which they themselves feel not! As to the words, “take it” is here the same as that of Matt. 5:40, “and take your coat,” that is, take away.

12 He that shall overcome, I will make a pillar; word‑for‑word in the Greek, “He that shall overcome, I will make him,” or, as touching the overcomer, “I will make him”; a Hebraism of the nominative case absolute, such as we have observed in chapter 2:26. The reward is that he shall be like a pillar in the Temple of God, that is, he shall abide firm and stable in the Church of God, neither shall he fear any ruin or fall, in whatever manner the rain shall fall, the floods shall come, and the winds shall blow, and all things at once shall fall upon it. He alludes to those two brass pillars, placed in the Temple by Solomon, which did illustrate the stability of the children of God, 1 Kings 7:15. And so is this Church, by the grace of God, not defiled with schism and foul apostasy, as lately we have seen in the Sardinian Church: which, taking no care of a full reformation, by the just judgment of God lost many citizens, losing them as a fig tree’s unripe figs, so far, they should be a pillar. Philadelphia should be free of this sorrow, not because she shall see some apostates, who shall feign godliness for a time, but because those few should more commend her faithfulness in trying and casting out hypocrites than cast upon her any blot of schism and defection.

¶ Neither shall he go out anymore: The pillar is declared by a double property, one of continuance, another of a name written upon. The first is signified in these words, “and he shall go out no more,” the force of which seems to be this, that they may meet with a secret doubt, which perchance might trouble somebody’s mind, because when the city was taken by Nebuchadnezzar, those pillars were broken and the brass of them was carried to Babylon, Jer. 52:17. Least any should fear that the same should befall him, namely that although for a time he shall be placed in the Temple, yet at length he should be banished away, he bids them to be of good courage. For he promises that this pillar shall be such, as no Nebuchadnezzar shall ever break in pieces, neither ever carry away by any force. The Son abides in the house forever, John 8:35. The bondwoman with her son is cast out, but the heir shall live always in the sight of his father, Gal. 4:30, etc.

¶ And I will write upon him the name of my God. The name written is threefold: of God, of the New Jerusalem, and a new name of the Son; all of which are spoken according to the manner of the pillars in the Temple, the figure of which the Spirit here declares, pointing at it as with the finger, teaching that nothing was ordained in vain, although it might seem to be of never so small moment. Solomon adorned the two erected pillars with two names: the one on the right hand he called Jachin, that is, “He shall establish”; the one on the left hand he called Boaz, that is, “In him is strength,” 1 Kings 7:21; not only does the matter of the pillars themselves, but also the names, show in what firm state the elect stand before God, both present and future. For the present, the children of God have strength in themselves; for the time to come, God will so establish them by his grace that they can never fall away from him altogether. Although I may also remind you of this further, that they seem to signify the two churches: the one on the right hand, Jachin, the Church of the Jews, which God at length in his time should establish, having not yet obtained stability because of their hardened hearts, whereby they should refuse Christ when he comes; the one on the left hand, Boaz, the Church of the Gentiles, because of the present strength which should be in it when it embraces Christ at first hearing. So Christ would write names upon those pillars, better than those Jachin and Boaz. For first, he will imprint the name of his God, so that it may be manifested to all men that they have been set at liberty to be God’s chief treasure and riches, as it comes to pass in things marked openly, which show by their titles to everyone that looks at them, which they are. In that sense it was said in verse 9, “and they shall know that I have loved you.” In this respect also, holiness to the Lord is written upon the bells of the horses, Zechariah 14:20.

The second name is that of the new Jerusalem, which in Chapter 21:2, to which this reward pertains: from whence it is clear that these seven epistles respect not only the present condition of the seven cities, but, by way of types, also contain a long following age, even as we have interpreted. But as it pertains to the new Jerusalem, we will show in this place that it is not that city which the saints shall enjoy in heaven after this life, but a Church to be expected on earth, the most pure and most noble of all that have ever been hitherto. The rewards in a peculiar manner serve the times, and if this felicity shall be after the resurrection, it shall be common to all the saints, not only to this Philadelphia. This therefore signifies both that the Philadelphians shall continue until that restoration in which the new Jerusalem shall come down from heaven and shall be conversant with men, and also shall be joined with the same in a league and fellowship, be endowed with that heavenly city, and enjoy the same law, privilege, and happiness. At that time all shall acknowledge their reformation not to be a thing devised of man, as contentious men affirm, when they shall see the same ordinances flourish in the new Jerusalem.

The third name is the new name of the Son: What can be new to him? Namely that which is not yet acknowledged by the world. Hitherto he has suffered the tyrants to bear rule and to tread upon the name of Christ, as though he were a King only in title, who should have the right to reign but lacked power. But at length he shall rise up, and shall take a club in his hand: he shall destroy all his enemies, he shall give the triumph to his spouse, and shall be celebrated King of Kings by all men throughout the whole span of the earth. To the society of whose glory he shall take his servants, he shall deliver them from the calamities with which they are now oppressed, he shall give them power over their enemies, and shall bestow on them the whole glory of his kingdom, as much as mortal men can receive. And there is some difference between a new name put absolutely, as in Chapter 2:17, and a new name of the Son. For that pertains to the certainty of adoption by Christ, which faith was very weak in the Pergamene state; this belongs to the society of the kingdom, which shall be communicated with him in the last times.

13 Let him who has an ear hear; hear Philadelphia and rejoice, you are low and unesteemed, but God will exalt you. Only go forward constantly and augment your care and diligence, slake and assuage it. Neither regard the scoffs of the wicked, who will bring upon themselves sorrow and a crown. Shortly there will be an end to your warfare. In the meantime we will pray for your peace. Do again join your prayers with ours, that Christ would bestow the same blessings upon the rest of your brethren, which he has so greatly approved of you. Farewell. The grace of our Lord Jesus Christ be with you, Amen.

Analysis.
So is the Epistle to the Philadelphians, the last remains for the Laodiceans, whose inscription is to the angel, like the former. The description of him, by whom it is sent, is fetched from a double property, first of Truth, partly in the promises, in that he is Amen, partly in the Doctrine, in that he is the faithful and true Witness; secondly of power, whereby he is the beginning of the creature of God, ver. 14. The narration first reproves and shows the greatness of sin, both secretly omitting any mention of good, as in former churches, and also openly, both by comparison of coldness, as a lesser evil, ver. 15. and also by the punishment to be inflicted, the vomiting from his mouth, ver. 16. After he teaches the way to heal them, both by opening the cause of the disease, which is a false persuasion of their own worthiness, and ignorance of their misery, ver. 17. and also in prescribing a remedy to be sought from Christ alone, ver. 18. And not this alone, but also by persuading its use, as well as by chastising sons if they neglect it, ver. 19. as also by his readiness to apply, ver. 20. and by the reward, ver. 21. The last end is the epilogue, to hear what the Spirit says to the churches, ver. 22.

Scholions.
14 And to the Angel of the Laodiceans: Laodicea situated at the river Lycus was once a great city and famous, abounding both in citizens & riches, and also in all other things, as we showed in the first chapter, verse 11. It was built by Antiochus, the son of Stratonice, and for his wife Laodice, on her behalf, called this city Laodicea, as it were, the Princess and ruler of the people, to whom she should administer justice and make laws. From whence we call her Glorious, great both by name, and also in their own opinion, which boasts that she is rich, and wants nothing, verse 17. It is from Philadelphia more toward the east than the south, being distant from it according to Ptolemy not above a tenth of a degree. She is the third city since there was mention made of Jezebel, the reproach of whom Sardis took away from the churches. She has this property to her, that she has none, to whom she can be opposed, as in the former churches. To Ephesus was opposed Thyatira, to Smyrna Sardis, to Pergamum Philadelphia, Laodicea the seven have no fellow. The Antitype is the third reformed church, which before I note or show, the unjust suspicion and offence of some men is to be put away by inter‑treaty. No disease or corruption of mind has moved me to seek out an odious application. No man’s either riches or honours, God is witness, grieveth me. I am content with my little. Neither have I counted anything to be more foolish, than to please one’s self by displeasing others. But how dishonest and filthy a thing it is, to sit as the fly upon the sores of the brethren? My soul has always abhorred such dealings. But when I considered that these seven cities were set forth for a type of all churches among the Gentiles, and then also perceived the course it itself of the time, and the marvelous concurrence of all things, I did not unfaithfully hide the truth with silence, lest I should make myself guilty of others’ blood. Far be it, that I should disdain willfully that church which through the mercy of God has brought me forth, nourished and sustained me, which I desire in my daily prayers and labour, to be most blessed. But seeing the sore cannot be cured, unless it be touched, neither truly touched without grief, I thought I must not refuse to cast myself against what troubles so ever, rather than to betray the salvation of her, of which every one of us ought to have greater regard and care than of his own. Truly he that gathers the tears of his children in his bottle knows that I have not viewed round about this Laodicea with dry eyes. I could not but mourn from the bottom of my heart when I beheld in her Christ loathing us, and very greatly provoked against us. Therefore let no man blame me for that, which is not so much my will, as the duty of a faithful interpreter compels me to bring forth. And I hope that the lovers of the truth will not despise and refuse such equal and reasonable request: with which hope supported, but especially with his aid, who is the leader of my way and life, I will gird and make myself ready unto the thing itself. The Antitype I say is the third reformed church, that is, ours of England. For all the purer churches are comprehended in this trifoliate difference: for either they persist and continue in those steps which Luther has traced out, such as are the churches of Germany, especially of Saxony, and those next bordering Switzerland and Denmark; or they abhor that error of consubstantiation, as all the rest with one consent: which yet does not agree in all things, but follow a differing manner of governing and administering, the French and their companions one, our English another, a certain propre and peculiar one. Whereupon there are three distinct severally, unto which the three types Sardis, Philadelphia, Laodicea, after that Jezebel was overthrown, that is the yoke of the Roman tyranny shaken of, does answer. And to the last Laodicea, the English do agree, whose last original took her beginning at the year 1547, when Edward the King of most famous memory, came to the rule and government of the commonwealth, but then at length she was confirmed and established, when eleven years after our most peaceable Queen Elizabeth began the kingdom. Most mighty King Henry, his father, had expelled the Pope, but retained the Popish superstition. And before he began to stir any whit, even against the Pope, the churches of Germany and Helvetia were founded. The Scottish church is later in beginning than ours: yet by right it is numbered with them, with which it agrees in ordinances: into whose times she is cast, which is to be esteemed rather from the agreement of things, then alone from the difference of time. Therefore our English church alone constitutes the Antitype answering to Laodicea; as she which began last of those, in which there appears no difference of any moment.

¶ These things say that Amen: Amen is used as a proper name and is unchangeable, as before “He that is, He that was, and He that comes.” This threefold property pertains to it, that it may teach how Christ would present Himself in governing this Church. The first is taken from the first chapter, verse 18. Although “Amen” there lacks the article, and neither is it read by the common interpreter at all, yet notwithstanding this place gives conjecture that it ought to be read. The second is taken not from the same chapter, but from the common Epistle, verse 5. Neither is the third found in explicit words, but in verse 8 where He is called “the beginning and the end,” from which this seems to proceed, the beginning of creation. The first two properties pertain to the double truth, one of promise, the other of teaching: in respect that He is called “that Amen,” according to the Apostle, “In Him are all the promises of God, yea and amen,” 2 Corinthians 1:20. In respect of this, He is a faithful and true witness.

As such, Christ takes this name upon Him now because He should show Himself very clearly and be famous for performing His promises. But what are they? All blessings of heaven, earth, cattle, children, peace, warfare, good health, and the like, to those who obey the voice of the Lord; but all contrary things to those who refuse, Deuteronomy 28. Which, how they were performed to the Laodiceans, is not plainly apparent to us, as we are destitute in this point of view of history.

As touching our England, nothing can be more clear than the excellent goodness of God in this thing. For the space of these forty-two years and more, what abundance of all good things has been poured forth upon our island! He has given us a most peaceable Queen, excelling so in all praise, as no age has seen the like. Together with her He has given peace. What good thing has not issued from thence? From hence the laws are in force, judgments are exercised, every one enjoys his own, injuries are restrained, wantonness is repressed, the nobility is honored, the common people go about their work with all diligence, arts do flourish, handicrafts are used, cities are built excellently, riches increased, infinite youth grow up, the fields abound with corn, the pastures with cattle, the mountains with sheep. What need I use many words? Hence is a port and place of refuge opened to the banished for Christ’s sake, affords aid to those oppressed by tyrants, neither have we almost any other labor than that we may help those who need, and all this even while our ears do ring with the noise and tumult of the nations round about us, no less than the waves of the sea. England never had so long quietness of days, at which our felicity strangers are astonished, our enemies are grieved, we ourselves almost know it not. But praise be to Thee, most true Amen, who has given us this ease and rest. In bestowing largely upon us so many good things, Thou hast shown truly to the world that Thy Gospel is a guest not going away scot-free, which doth so abundantly bless those that receive and entertain it. Keep and continue these good things unto us, yea Thou wilt keep them, who art Amen, if we shall keep and defend Thy truth.

¶ That faithful witness is true: The second attribute is truth in teaching. These things pertain to the prophetic office of Christ, as has been said in the first verse of the first chapter, where he is called faithful because of the diligent work with which he carries out his office with great faithfulness, to whom the Father has entrusted a matter of great importance; this is true for the soundness and sincerity of speech, without any, even the slightest, trace of falsehood.

In this kind of truth He should manifest Himself in a wonderful manner in this Church.
But regarding the city of Laodicea, we have no more to say than before.
In the Antitype, those former riches of His grace are, if it may be said, surpassed and exceeded.
And to what end were all the good things if we could not have the wholesome doctrine of truth?
But ever since the first years of our most peaceful Queen, He has continually raised up diligent and learned pastors and teachers who have preached the word purely and sincerely.
Even today, many, by His infinite mercy, bestow all their labor on imparting to His people the whole will of God, pure and uncorrupted by any leaven of falsehood.
Although not without cause indeed, one may marvel how, in such disorderly custom and license to do all they will (except defamation of dignities), the doctrine has continued so long, whole and sound.

But He who is a faithful and true witness sanctifies the pastors with truth beyond all hope: in whose lips He dwells even now; although by many obscure tokens He threatens that He will go away soon, unless He is met soon.

¶ The beginning of the creature of God: the last property which is of power. For whether we interpret the Greek word for beginning or for dominion, it comes to the same end, seeing it is necessary that all things be subject to His government, who in the beginning made them. In this respect, Christ has shown Himself wonderful also among us. What has not the Pope of Rome endeavored and undertaken, that he might trouble our peace, partly by execrations, excommunications, and bulls, sounding an alarm to open rebellion, partly attempting privately, Jesuits being sent by stealth, and other secret murderers who should kill the sacred Princess with sword, poison, torments, devilish arts, or any other way. We know that not long ago the Prince of Orange was set upon with the desire to kill him by a popish cutthroat, and was wounded. Late is the memory of Henry, King of France, whose murder Jacobus Clemens, a monk, attempted and accomplished. And Henry the Fourth, who now enjoys the sovereignty, escaped hardly the bloody hands of John Castell the Jesuit, being stricken through the jawbone with a knife, and two of his teeth dashed out. But our Queen, assailed by many at many times, with sundry treasons, has been kept whole and sound from the least harm. From whence was this, I pray? Was opportunity wanting to these wicked men? The only Prince of the creature, to whose beck all things obey, has laughed to scorn and deluded the counsels of the wicked, repressed the endeavors of the ungodly, and made frustrate their subtle devisings, and restrained them lest they should touch His anointed, nor hurt the nurse of His Prophets. His power is no less famous in bridling the Spaniard, with whom we have been at war now for so many years. What is there that He does not think to effect by His riches, who alone procures trouble almost to all Europe and other parts of the world? The invincible navy of the year 1588 swallowed up in hope our whole country, our lives, and goods. But, Good God, how was it disappointed without any labor of ours, through all the seas cast asunder, scattered here and there, and broken in pieces? It came out one way against us, and fled seven ways before our face. This is Thy praise alone, O most mighty Governor, whom the winds, the waves, the hearts and hands of men will, whether they will or not, obey. O ye Kings, why do ye not regard? Why do you not learn, ye that judge the earth? Will ye fight yet still against the Prince of the creatures to your own destruction? If ye shall go on to be so made, we in the meantime will betake us under His wings, by whose defense alone we stand safe against all your assaults. Such is then the threefold property whereby Christ shows Himself to be seen in this our Laodicea, to wit: constancy in promising, sincerity in teaching, then an invincible power in defending.

15 I know your works, that you are neither cold nor hot. In declaring the greatness of their sin, He makes no mention of any good thing, contrary to that of the other churches, none of which was in such a desperate state, not even Pergamus nor Sardis, as to be void of all praise. But this evil, as though it could not endure the fellowship of any good thing, hears nothing but reprimand, without confirmation of any honesty. Not that there were not many singular men, whose faithfulness and diligence the Spirit might approve (for it cannot be but that where Christ is a faithful and true witness, there some should take singular pains), but because He respects the common form and outward face of the Church, namely, of what quality it is, not so much for its own sake, as for the administration of the Angels, which was such that he who considered the matter but with indifferent eyes would judge it worthy of being void and empty of all virtue. It is a horrible evil which refuses all fellowship with goodness. And although by this silence we may be able to conjecture how grievous the disease is, nevertheless afterward it is described more plainly of what quality it is, and first, for more clarity, by a denial of contraries: “I know,” says He, “that you are neither cold nor hot, but something compact and joined together of both.” Whereupon this evil consists of a temperature and mixture of certain contraries. Now He called him cold, who with a quiet mind can endure that the duties of godliness should be neglected and despised, little or nothing at all regarding what manner of worship either he himself or others hold. He called him hot, who boils with a strong affection and desire through vehement heat and fervency, as scalding water seething in the pot with a certain restless motion, for so the Greek word zestos signifies, of which sort are those who can by no means suffer superstitions and ungodly religions, but do try all lawful means, that there may be an amendment. For hot is not here sinful, as a rash zeal, as it comes to pass in habits, in which both extremes swerve from the right; but it is of praise, as Apollos being fervent in spirit, Acts 18:25. And Paul exhorts that they be fervent in spirit, Rom. 12:11. If by excess he should degenerate from the truth, lukewarmness, holding the middle, there was some consideration of honesty. But fervency or zeal is an affection, following the love of holiness, with a great and earnest affection of mind; whose defect, whether that more removed from coldness, or this nearer to lukewarmness, is blamed. And lukewarmness, placed in the midst of these extremes, whereby a man, staying himself from committing grievous sins, embraces godliness so far as may be enough to maintain the reputation of an honest, prudent, and civil man. The college then of the Laodicean pastors was, as it were, a senate of prudent and moderate men in the matter of religion, even as at this day the lukewarm have the common report in every place. Yet it is not plainly mentioned from what mixture of things this lukewarmness arose. Before these times of John, Paul bids the Colossians say to Archippus, who then was the pastor of the Laodicean Church, that he would look to fulfill in the Lord the ministry which he has received, Col. 4:17. From which it appears that pastoral faithfulness began then to shake and lean, which afterward fell most shamefully when the Spirit sent these epistles to the angels. In our England, the matter is clearer, where there is such a form of church established, as is neither cold nor hot, but set in the middle and made of both. It is not cold, in as much as it professes the healthy, pure, and entire doctrine of salvation, whereby we have bid farewell and forsaken the Romish Antichrist, and have risen from that cold death wherein we lay before. Hot indeed she is not, whose outward government for the most part is still Romish: in the degrees of their clergy, in elections, ordinations, and whole administration of the censures. This mixing of the pure doctrine and Romish regimen together makes this lukewarmness, whereby we stand in the middle between cold and hot, between the Romish and Reformed churches, of both of which we are compact, as Martin Bucer, of godly memory, complains in a certain epistle sent to a most beloved friend of his at Cambridge, written January 12, 1553. He, in the times of King Edward the VI, was used among others who should determine the reforming of our church. But in what things both his own and Peter Martyr’s authority prevailed, he himself manifests in that epistle even now spoken of: for so he writes, “Whereas you put me in mind of the purity of the rites and ceremonies, know that no stranger is asked concerning those things; yet of ourselves, when we may, we fail not to do our duty by writings and in presence, and chiefly that the people may be provided with true pastors, also of the most purity, both of doctrine and ceremonies.” And in another place: “There be some who by most human wisdom and vanishing cogitations would join together God and Belial, by the leaven of Antichrist.” These are things he did write, which we today find by experience too true.

¶ I would that you were cold or hot. I would to God that you were either wholly Roman, or at length admitted a full reformation. He shows the horrible greatness of the evil by comparison, wherein he prefers a wicked and no religion before this mingled lukewarmness. But does not lukewarmness come nearer to good? From whence then has it more fault? Certainly sin is more sinful where grace is more plentiful. The fall of the angels in heaven, left to themselves, had no way to obtain pardon. The sin of our first parents was more wicked being committed in paradise; most foul was the idolatry of the twenty-five men committed between the gallery and the altar itself, Ezekiel 8:18. God will be sanctified in those who approach unto him, and suffers more easily His grace not to be known than to be despised. The servant that knows his master’s will and does it not shall be beaten with many stripes. Wherefore, if Baal be God, follow him; why halt ye between both? As though it were hard to judge whether it were better. God abhors to come into this trial. There is more sound judgment in him who, not knowing the truth, continues in his superstition than in him who, being somewhat enlightened, is tossed this way and that way, uncertain still what to follow. Therefore a mean here is worst of all: which, under a show of prudent moderation and tranquility, is honored by the world, which God esteems less than His next extremes on both sides. Is it then better to fall away to Rome? Far be it from us. For in this place Christ prefers the blind Papists before those angels who, bewitched with ambition and covetousness, refuse holy reformation. He says not that the condition of the whole Church is worse, to which the true food of salvation is ministered, of which no power is granted in the Roman Church.

16 Therefore, because you are lukewarm, etc.
The anger also of the punishment discovers the horror of the sin, which seems to be confirmed by another;
For the Greek word which Theod. Beza translates, therefore the common Interpreter has it, but it is a single swearing and confirmation by other in this place, as though he should say, So, or thus let this or that be done to me, as it is certain that I will vomit you out of my mouth,
After which the word ‘So’ is used by the Latinists, as in that ode of Horace. So the mighty God of Cyprus, etc., as it has been observed by Henry Steven. And with the Hebrew ‘Amen’ is the same with sic, as in Isaiah. So he bore our sorrows, that is, certainly, chapter 53:4, and Ecclesiastes chapter 8:10. And so I saw the wicked buried, that is, truly, certainly, as some would. And such silence is often used in execrations; Therefore I swore in my wrath, if they shall enter into my rest, Hebrews 3:11.

¶ It shall come to pass that I will vomit you: as it happens with meats, which either hot or cold are retained in the stomach because of their exceeding quality, which causes sensation and excites the stomach to embrace them; but that which is lukewarm, because of its near and familiar heat, is neither felt upon entering, nor being entered is it for that reason digested, but remaining idle, and eventually causing trouble by its lingering there, is thrust out of doors with vomiting as an unprofitable guest. But we must beware that similitudes are not twisted beyond what they intend, as though naughty and wicked men should remain constantly in Christ as cold meats remain in the stomach. For such were never in Christ; neither does he indicate what he approves simply, but what he prefers. Furthermore, the matters are referred to his external administration, whereby he bears longer with the notably negligent, or rather all strangers altogether, than with the lukewarm, as the experience of all times proves, and at this day we see in the Roman Church, which although she has utterly forsaken the truth, has flourished a long time, while in the meantime God rebukes immediately the true, and does not delay chastisement to any long time if he sees them slacken their earnest affection and lean more toward lukewarmness. But what is it to be vomited out of his mouth? Will Christ, in whose mouth and lips the very truth rests and abides, take away his truth from this Angel, delivering him into absurd opinions, so that he should believe lies again? The itching desire of many men at this day to give again to the people monstrous and rejected opinions makes this interpretation probable. We know what has been taught within these few years in the Schools, is preached usually in the assemblies, is disputed at the public Comices, and was published in print last summer. But this should be the punishment as well of the people as of the Angels, to whom it seems to be proper. Therefore I have no certainty regarding this matter. Surely the event will declare it shortly. In the meantime, let us know that this shall be a fearful punishment: for first, Christ will take great pleasure in rejecting from himself this Angel. For what can be more pleasant to a man who has a disposition and will to vomit than to be immediately relieved of the cause of his grief? Even as Moses threatens the apostate Jews, that Jehovah will rejoice in destroying and rooting them out, as he once rejoiced to do them good, Deuteronomy 28:63. Secondly, because he will cast out this Angel with great dishonor. For an unclean place is sought for vomiting; however, Antonius in the assembly of the people of Rome, governing the public business, filled his own bosom and the tribunal with gobbets of meat. Thirdly, that the Angel shall never recover his former dignity. For far be it from the Prince and Author of all cleanness to ever return to his vomit. But this punishment was not to be inflicted on the whole Laodicean Church, but on the Angel alone, that is, on all lukewarm pastors, partly because of what we have just spoken, partly because the Church is usually mentioned expressly when treated of. As to the Ephesian Angel, “I will remove your candlestick out of its place,” Revelation 2:5. It shall therefore be peculiar to the ecclesiastical men without the destruction of the whole Church. Neither is it to be doubted but the same eventually happened to the Laodicean Angel, which here is denounced, which thing is also certainly to be expected in his Antitype, unless she shall prevent it by repentance. For it shall come to pass that that faithful witness shall overthrow this whole hierarchy, and not always suffer men seeking only honors and riches, not those things which are Christ, to enjoy even this false felicity. Certainly a great and reproachful judgment abides those lukewarm ones, of whom, though they be troubled with no fear, as having put to flight all the noise thereof, yet though all shall hold their peace, he will not deceive, who has threatened that he will punish. It is also to be feared that the Church may feel some adversity through contagion and consenting to. Such as are the Angels, such does she become for the most part; and none is so ignorant of the matters who does not plainly see that the whole body is sick of the same disease. But have mercy upon us, O thou beginning of the workmanship of God; deal not with us according to our sins, thou knowest our making, that we are dust and ashes. How should not the earth grow cold? Raise up in us the burning heat of thy love; dissolve, I pray thee, our ice; neither suffer us to please ourselves in our imparted godliness, but kindle us with thy heavenly fire unto full heat and fervency, that we may both avoid thy loathsomeness of us, and may always enjoy that pleasantness which thou givest to those whom thou lovest: Amen.

¶ For you say, I am rich: thus was the nature of the sin. The cause is double: a false persuasion of their own worthiness, and ignorance of their misery. That grew from their wealth, which was earthly and not spiritual riches, for against these he opposes the riches which he bids the Angel to buy of him in the next verse.

Neither could he have been lukewarm if he had expected spiritual riches from anyone other than Christ alone; rather, he was thoroughly cold, and altogether a stranger to grace, having become void and separated from Christ (Galatians 5:4).

But he seems to have abounded in earthly riches, because of the wealth of the city which we spoke of (Revelation 1:11). For which cause, perhaps, Archippus was more negligent of his ministry, whereupon Paul would have admonished him (Colossians 4:17), although small fruit seems to have followed that, seeing that even unto these times of this Revelation, there was such great matter of boasting, and that also not newly bred, but gathered from old times.

The abundance therefore of things for this life begat this lukewarmness. And it is no new thing that prosperity steals away our minds and draws men away from God. This warning is often in the law, that they should take heed of themselves lest, being fulfilled and filled with good things, they should forget Jehovah. And the boasting is threefold: the first of the present wealth; the second of long continuation; the third of perfection and absolute sufficiency for every use.

For so the words require that “I am rich” should refer to the present riches; “I have been rich” to those past; “I want nothing” to a certain fullness. From which further must needs spring a certain persuasion of a permanent state, and also constant felicity for the time to come. And it is to be observed that he brings in this Angel boasting in his own words, otherwise than was done hitherto; yet this not in vain, seeing nothing is uttered rashly of the Holy Spirit.

But as to the Angel of Laodicea, a clearer application offers itself: in our England, the congruency is so manifest that nothing could have been expressed more vividly. For what other cause can we attribute our lukewarmness, the Popish government mingled with the pure doctrine, than the love of riches and honors? Men will not allow this hope to be taken from them, but they would rather have half‑godlike together with the enjoyment of their riches than a full and perfect reformation with the loss of them.

Yet lest they should seem to prefer anything before the truth with dishonor, they somewhat proudly praise our present happiness in published books and in assemblies, as we may see from the writings of many men which have come forth in these last years. Not without cause therefore does the Spirit make this Angel vaunt himself, but in the same setting before our eyes our notable glorying.

And we have said that the first bragging was of the present riches. How does our Angel triumph in this respect, and lift up the head above all other reformed churches? In other places there are poor and base pastors, almost of a vulgar state and condition, nor of any greater authority than their godliness and learning can procure to them, but our bishops are peers of the realm, superior in honor to many great states, also in riches, company of men and maidservants, in magnificence of houses, and all other pomp of the world, equal to any even the greatest earls.

How rich is the rest of the clergy? The deans, archdeacons, prebendaries, chaplains, heaping and gathering together many benefices, as they call them, do match squires at least in early revenues. Does not this amplify and greatly increase the glory of the church, that her ministers shine in garments of silk and velvet, walk in the streets with the retinue of noble men, and so drive far off the contempt of the ministry? Where can one see, after the Pope is expelled, a church rejoicing in such rich things and prosperity? Nowhere indeed; neither do I envy nor grudge it; only our rejoicing is not good. And would God that our riches served to promote God’s glory rather than hinder it; but they have brought in this miserable lukewarmness, while that we may retain them, we make no reckoning of true godliness.

The second boasting is of long continuation, for this plenty is not new, but has been confirmed now by the space of forty‑two years, with how great prosperity of all things.

Who may be bold enough to reprove the condition of this church as maimed and imperfect, which the experience of long time has approved to be most happy? Not I indeed, unless prosperity were an argument rather of God’s patience than of man’s justice.

In the third place he boasts that he wants nothing: “What do you tell me,” says he, “of other reformed churches? I see no cause why other reformed churches should not imitate ours rather than us them, seeing we are inferior to them in nothing.”

The answer to the admonition made to the parliament, p. 226: “Yes, why do you call me back to the first church? As though we were bound by the first beginnings and principles as with fetters, and it were not lawful for us to alter those things which at their first origin were not so profitable as at this day they seem hurtful,” this is in a certain apology of the government of the church, p. 81, a bold, if not ungodly, assertion to affirm that anything ordained of the apostles should be no less noxious to our churches than profitable for them, for which they were appointed.

But I remit this to the heat of contention. In the meantime, let such a man know that the apostles’ church was most perfect, and was not to be made perfect by the inventions of those who came after, but that all others are to be tried and examined by its standard. That saying of the first council of Nicaea is to be celebrated, which is: “Let the old customs hold,” and that also of Tertullian against Praxeas: “Behold, whatsoever is first, that is true; and whatsoever is later, that is false.” And it is not to be doubted that Paul taught Timothy most fully how he should behave himself in the house of God (1 Timothy 3:15). Is all that instruction abrogated for age? Should time teach better and more certain things, to which the apostles should give place?

Surely the Church, as Adam in the first beginning was purest, the farther she proceeds, the more filth she gathers, unless God extraordinarily makes the light shine out of darkness, as lately in this last age. That first Church was the Garden of Eden, as we have shown in Revelation 2:7. The Church of the following ages, compared with that, was a wide and barren wilderness. Perfection is not to be measured by the multitude of professors, or by the amplitude of riches, but by the integrity and purity of God in his institution and the abundance of heavenly gifts. Let it then be enough to praise men’s inventions; let us tread under foot the sacred truth in comparison with them.

¶ And knowest not that thou art wretched? The other cause of the evil is the ignorance of their misery. For prosperity blinds the mind of the world, so that it cannot see indeed in what state it is. Therefore in many words he declares this misery, because in so deep drowsiness, a light upbraiding would not cause any feeling. He makes a fivefold degree of it, of which the first two are as certain common accidents; the last three show the very kind of the disease. For the remedy is threefold, of gold, of garments, and of eye salve in the verse following, and teaches that the disease consists chiefly in these three things. The accidents are referred either to his own sense or to the compassion of others: in respect of that, the Angel is wretched; in respect of this, miserable. A man is wretched who is consumed with some great sorrow, whether it arises from a public calamity or from some private and domestic grief. And there is none placed in any dignity whatsoever who can keep himself from this anguish, whereupon kings in tragedies lament that they so often are wretched. Such heaviness of mind did lie once upon the Angel of Laodicea, as is at this day in our England. How, wilt thou say, where no public calamity presses? The Spirit speaks of private sorrow, as is evident from the glorying of this Angel, for which there can be no place in common mourning and sorrow. But this interior grief does torment miserably the English Angel. For how great griefs does he feel who desires exceedingly riches and honors, and cannot get them? Or at least, who cannot securely enjoy those things being gotten, whom many godly and learned men inveigh against with grievous words, and not only this, but also prove manifestly from the truth of God that such dignities are unmeet for the ministers of Christ, and that they cannot stand together with the faithfulness of pastors and bishops? How must it need be that these disturbers should be very grievous, especially seeing this opinion is now favored by the multitude, and the nobility has perceived plainly long ago the truth of it?

If one could open the breast of this Angel, doubtless he might see his heart almost consumed with this grief, however outwardly all things are joyful and the commonwealth flourishes with happy tranquility. And I doubt not but that the Angel will confess that I have touched his most inward sense in this matter. This Angel is miserable to others, not to the wicked Papists, to whom the former grief is not sufficient, but to the godly brethren, both at home and in other nations, who being free of all partiality acknowledge the condition of the bishops and other clergy, who give themselves wholly to ambition and labor for honors, to be miserable and unhappy, however greatly it may please ourselves. For what is more worthy of pity than to see brethren snared by the vain glory of the world, altogether desiring and enforcing themselves to get earthly dignities, and making shipwreck of the heavenly crown? If they had always lain in the snares of the Devil, the thing were not so much to be lamented; but after they have escaped from his snares by the wholesome knowledge of the gospel, they are entangled again in the same by this way: what godly man cannot both be grieved at their change and also bewail the common misery of us all, who by a thousand means are drawn into the same destruction? Such therefore are the accidents, grievous indeed of themselves, yet but as a flea biting in comparison with the disease itself, which now let us touch as gently as we can, with the mind only to heal and not to exasperate it. The first matter to be purged is poverty. And knowest not, says he, that thou art poor? Of what sort of poor? Not the poor in spirit of whom Christ speaks, Matthew 5:3— for this is a blessed poverty—but a wretched poverty. Also, the Angel boasts that he is and has been rich, and that he wants nothing, so that he is far from that holy humility. This poverty therefore is the timorous beggar’s, which both quakes at the sight of a richer man, nor either speaks or does anything but to the pleasure of a mightier man, and also sustains the wretched life by begging money and relief. For the Greek word ptakos, “poor,” has the name both from fearfulness, and also is noted with the same name of him that, lying at the gate of the rich man, desired to be filled with the crumbs which fell from his table, Luke 16:20. Which of these agrees with our Angel? Is not all this dishonest covetousness far removed from the great riches ministered to ours? I would to God it were indeed, but here, as always, I am compelled to admire the infinite wisdom of God, who has opened our secret imposture with a word so fit for the thing, as nothing could be spoken or thought more fit. For first, how servile a fear possesses the Angel, from which may easily appear that he speaks almost nothing which he thinks may displease anyone. The bishops fear the Peers; the parish pastors, the bishops, whom they perceive to be ready to scourge them, if any provoked at home will crave their aid, especially if he can object that their mind is out of love with some ceremonies. So reprehensions are silent, naughtiness reigns, the hand of God is heavy upon us, and whither the matter will grow at last, prudent men fear not without just cause. But chiefly, the beggary of asking is notable. For run over with your eyes and minds the whole clergy. Will you that we begin at the weakest? Those that they call curates, both in very truth and also in the judgment of all men, are beggars, in whom we may see that which was threatened to the family of Eli: men bowing themselves for a piece of silver and a morsel of bread, and requiring to be joined to one of the priests so that they may eat a piece of bread, 1 Samuel 2:36. In the rest, who through their greater abundance walk more under-propped, what running up and down? What bountiful giving and bribes? What importunate and earnest entreating? How great flattering enticements of humble service and soothing of all duties, that they may procure ecclesiastical offices to themselves? Very many fly to the King’s Court, or to the house of a most noble man, the Lord Keeper of the Great Seal. For these places are like the beautiful gate of the Temple of Solomon: in this men enter in great multitudes, and there is great hope of carrying away the penny, Acts 3:2. Others follow the States and Peers, to whom they become either domestic chaplains, or that I may say, vassals: for what cause, I pray? That as soon as any benefice, as they call it, shall happen to be void, they may enjoy the same by the gift of their lords. And this is thought to be an honest way to get an ecclesiastical charge. But is not this flattery mere beggary? In obtaining a divine office, is favor any less dishonest than money? If we weigh the matter rightly, it is of the same fault and blame, to enter either by bribe or by favor. The other rabble is diligent about the common sort of patrons in the country, in whose porches they sit, flatter, and speak fair to their wives, flatter their children, win their servants by gifts, and in every place behave themselves like wretched beggars. Some more craftily, even as those who sit on a way having two paths and in public ways offer piled rods and sticks to those who travel by, so that they may get some money, so they either by bountiful giving of present money, or by agreement to give a certain yearly rent, make a way for themselves.

But you will say, this is the corruption not of our laws, but of the men. Certainly, as long as this way of obtaining ecclesiastical charges holds, which hitherto has prevailed, no remedy can be brought for this beggary. Have we not known this sufficiently by experience? In the late assembly of all degrees of the realm, a sore and heavy ordinance was made against it; has anything been effected thereby? Nothing at all, only that the thing is done more warily and subtly. We avail nothing with our laws, where the laws of Christ are not kept. But that we may proceed, when the thing is begged by the patron, how much less business remains to the unlearned route to obtain the institution of the bishop? Here not only a humble request must be made to the chief lord, but to the examiners, grooms of the chamber, clerks, butlers, yea to the lesser Jack, not because ignorance shall keep him from entrance, but because he is wont to bring the most gain to the servants, who has need of more favor. There is no tower made so strong which an ass laden with gold does not vanquish, nor almost any so unlearned or foolish who takes the repulse. But what engines and crafty means are used, let them look to it.

There is the same consideration of prebendaries, archdeacons, and deacons. Are the bishops themselves devoid of this avarice? What does it mean that they often attend at court and with the peers of the realm? Why do they not wait until they are summoned? Why are they not pulled away from their studies against their will? Yes, if anyone should appeal to their consciences, are those large estates and farms in their bishoprics let out for hire at their own discretion to farmers who desire them, or are they given bribes to the attendants of their dignity? But are they only beggars when seeking the office? Some indeed have come to such beggary that if their seat is to be changed, they do not pay their first fruits, except they have shamefully gathered some alms from poor rectors under the name of benevolence. You are therefore a beggar, O English angel. And therefore it is ordinary and usual that the best are passed over, and others less worthy are held in higher estimation. For as we bestow some alms upon the blind, lame, and those full of sores, we ignore those who appear physically well and in fine clothing; so men with a blind mind, deformed and maimed in doctrine and understanding, gather together much alms, while those with more learning and far better judgment suffer hunger and perish by famine, which comes to pass either because they cannot cry out as loudly, or because they are more ashamed to beg, or because men have less pity for them.

But it is not my purpose to plead their cause; your beggarliness, O Angel, is something I must reproach, which you will or will not acknowledge if you weigh it with yourself in earnest.
You do indeed abound in riches, but nothing is more filthy than the way you acquire them.
After a beggar has filled his purse with alms, does he cast away his patched cloak and flaunt himself in silk, pretending to be rich and wealthy? What else is there to boast about other than the bragging of riches that you have gathered most dishonestly by begging?

And yet I do not speak these things for that purpose, as though the stipend of the godly pastors, who holily both enter into and execute their office, should be mere alms. For the labourer is worthy of his wages; neither can this distribution be said to be freely bestowed, any more than it is to someone who lives on his public office. God, who made the earth, has so given it to the children of men that He reserves a portion for Himself, which He has bestowed on those who earnestly bend themselves to holy things. Therefore the patrons do not give of their own when they appoint the yearly rents to the pastors of the churches for their pains, but deliver them to those to whom they are due, and of which they have been the keepers only. We speak not, I say, of such special persons, but generally of the state of the clergy, the manner of which is so ordained that the Angel manifestly grows rich by alms, and indeed is no other thing than a lord‑beggar.

There is added to beggary blindness, whereby the evil becomes far more grievous: for what is more pitiful than a blind beggar, whom necessity constrains to seek his living abroad, and whose lack of sight prevents him from seeking? But this is a blindness of mind, whereby a man, being deprived of a witty and prudent mind, cannot provide for himself touching things profitable and honest before God and men. The Angel then, being void of this wisdom, sins even so in administering his office as he sinned by beggary in the manner of getting. And this is the worst kind of blindness, which for the most part neither acknowledges his own darkness nor can suffer admonition patiently; yea, he uses the staff whereby he ought to have tried the way, against him that shows him the danger.

Yet you are to be admonished, O miserable Angel, however froward and angry you shall be: it may come to pass that at length you may see and be wise; if not, at least I may be without danger of setting a stumbling block before the blind, if I have seen the pit and not shown it to him. And that I may deal with you more favourably, I will make yourself judge whether you be better sighted than I accuse you; although this be unreasonable in one’s own cause, wherein you must needs be twice blind. Call therefore to remembrance with me your last constitutions, which are wont to be wisest, handled in the Convocation at London and published in the year 1597.

What medicine do you make for the Church being sick? First you decreed that fit men be admitted unto ecclesiastical holy orders and benefices, as they call them. The title indeed recreated many, and very many judged thee now at length to use thine eyes. This kind of men has made the Church sad a great while. There was hope of remedy when thou shouldst see and acknowledge the disease: for of evil manners arise good laws. But how wisely hast thou met with this evil and satisfied men’s expectation, weigh well with thyself, after give sentence. You know that it was ordained in a statute of the realm that none should be admitted unto holy orders except he be four‑and‑twenty years old at least, and have brought before the diocesan the testimony of such men as the bishop knows to be of sound religion, both of his honest life and also of his professing the doctrine of our Church; yea, have been able to render a reason of his faith in the Latin tongue; or at the least has been endowed with some special gift of preaching.

Although this was long ago enacted, the Church has been greatly troubled with a new rabble of most unworthy men. With what cautions then hast thou helped the imbecility of the law? For wise and quick‑sighted men are wont, when they have perceived the weakness of the law, to help with more sharp laws for that point whereby they see the impudency of men to break through. You indeed have established many things, but I pray you, what serves for the worthiness of ministers, that no man be received to holy orders unless at the same time he shall exhibit the presentation of himself to some benefice then void? Or who shall not bring a certificate from some church wherein he may serve the cure of souls—that is, where he may play the curate under some one in reading of prayers; or who has not been appointed in some college; or at least who is not to be admitted by the same bishop unto some benefice or to a cure? To what idiot or any the worst man may not these things pertain?

But you proceed and add other things as vain as these: moreover, if he shall be, say you, of another diocese, unless he shall bring dimissory letters, be full four‑and‑twenty years old, and has taken some degree in the university (which last is required only in men of another diocese), finally that holy orders be not given except on the Lord’s day or holy days. Excellent ordinances indeed, for which the reformed churches may be ashamed. What do these things profit at all, that a fit man be admitted? What that after should be ordained ministers either more learned or more honest? Wilt thou, on the Holy Spirit crying by Paul, “Who is fit for these things?”, obtrude a man with a presentation, with a certificate, with dimissory letters, or who has been licensed on the Lord’s days?

But I will not debate the matter harder; only I appeal to your conscience: what, I pray, have you provided in this matter, who has covered the wall ready to fall with such foolish plastering? What touching plurality of benefices? You decreed that it is to be restrained. And well indeed: for it is a heinous thing that one should be a shepherd of sheep which he feeds not, or at least should receive any fruit from them who take no profit from him. It would be meet therefore that here you should bring forth whatsoever skill you have to cure this evil, which not only the divine oracles but also common sense condemns of sacrilege. What remedy then do you apply? Namely: let no man enjoy this faculty unless he be at least a Master of Arts and a public and fit preacher of God’s word. A notable physician indeed.

What have Masters of Arts deserved so ill at your hands that you would have those first burdened with so great a sin? You confess that plurality is an evil thing and to be corrected, yet you permit this mischief to them: indeed it is a notable privilege of their degree whereby they first are licensed to be evil. But whether you think that the destruction by these means would slay more secretly? There are so many, thanks be to God, as if all, hindered by no other religion, should use the liberty of your constitution, more parishes, I believe, should want pastors resident with them than at this day they want. So you do stay and repress prudently the evil by augmenting it. But perchance it is enough for you to deceive men only with a title and pretence of repressing plurality.

Moreover there is an ordinance made touching hospitality in the benefices cared for. And this is the calamity of our Church, that the ministers do not feed the poor with beef. That of binding the regulars to make sermons in their own proper persons would seem to belong to a sharper sight, unless perchance it should call them away from other places where their labour is more necessary; I let pass the matrimonial ordinances. That is worthy remembrance touching excess about excommunication to be reformed. For you see it to be defiled shamefully with many pollutions: I would to God you would see and regard as well those things which belong to the holy and lawful reforming of it.

But why do you first deny that herein anything can be innovated or altered without a great mutation to the whole ecclesiastical jurisdiction and of very many laws of this realm; yet afterward you would reduce the same to its ancient honour and dignity? Would you make a reformation without an alteration? You will have nothing to be changed, that the laws may not be violated; yet you pretend to recall the former comeliness. It pities me that you can not see your own blindness.

But by this provision you have openly shown what reform we must expect, such indeed by which no amendment may be made. Therefore the title might have been enough for this thing; yet that you might seem to do that which you do not at all, you use a certain form of ordinances. For let us see how they answer and agree to the promise. First you ordain that in grievous crimes the sentence be pronounced either by the archbishop, bishop, dean, archdeacon, or prebendary in his own person. What is this ancient use of pronouncing the sentence by those whose names, except only the bishop, had not been heard indeed in the Church as long as the true honor and dignity of excommunication remained? Why is there no place left for the pastor of every congregation to whom once it belonged to pronounce the sentence? Peradventure it makes no difference to him what is done to his sheep, or it may be that he is not fit nor endowed with judgment and wisdom enough. In very deed this feature might perchance have prevailed somewhat in time past; but now it ought not, seeing you have set us free enough from it in the first book of the Decrees.

For it is not to be doubted but that he who has been furnished with a presentation, a certificate, and the other things with which you have instructed him in the same place should be fit enough and more than fit for every part of his office. Or if I must deal with you in earnest, what would allow the pastor, using the counsel of others and making diligent inquiry, to not pronounce the sentence as well as either the bishop, the prebendary, or anyone else? But you will say, we will not have this matter handled by common advice, but will rely on the judgment of one alone. Is this the meaning of your reformation, and yet dare you make mention of the honor and dignity of the ancient use?

Christ commanded to tell this to the church: will anyone sustain this church’s position?
One indeed pronounced the sentence for the sake of order, but the matter was judged not by his sentence only, but by the advice of the whole assembly and council.
Paul would not have excommunicated the incestuous man unless the brethren were gathered together and consented, as we read in the First Epistle to the Corinthians, chapter five, verse four.
And so the church continued for some ages afterward, as is clear from Origen, Tertullian, Cyprian, and others.
I would marvel that you promise so boldly concerning the former and ancient dignity, yet I know that blind men do not fear the faces of men.
But what if this amending of yours, which you pretend, does open a way to impunity for grievous crimes?

The commissary, as long as it pertained to him, twice at least every year compelled the churchwardens by virtue of an oath that they should present wicked men; now, while he should do that, there is perhaps no cause when the priest associated with him cannot denounce the sentence against such a man. And in deed it is not to be hoped that the churchwardens willingly will flee to the bishops, archdeacons, or prebendaries whom they do not know where they may find, or who perchance are far off from them, and a journey cannot be made without charges, when being present, and that at other men’s costs they can scarcely be driven by oath to betray the guilty. You ought to have minded these things, and not used a remedy worse than the disease itself. Secondly you speak of excommunication for contumacy, which has no new thing from your former decrees. But the repeating of the old manner is with you a reformation, lest perchance any box should want a superscription although there be nothing in it. I pass by the change of penance, the foul things of the officials, the excess of apparitors (of taking away whom you ought to have intended rather than of moderating them) and registers. You yourself how may you speak how well you have used your eyes who, passing by many great evils, either are wholly occupied about trifles; or if perchance you have touched any weighty matters, you make them either worse by curing, or indeed nothing better. Certainly by many reasons your blindness is proved. But Christ open your eyes: I will not so much deal with you by words as for you by prayers. For I have not purposed the handling, but only the judging of these things. The third part of the disease is nakedness: garments are used that we may provide for shamefulness. Out of which when one is put, his ignominy is set openly in the sight of men, according to that of the prophet, “Behold, I am against thee, saith the Lord of hosts, and will uncover thy skirts, unfolding them upon thy face, that I may show thy nakedness to the nations, and to the kingdoms thy nakedness,” Nahum 3:5. Therefore this nakedness is a reproach, dishonour and contempt of which this Angel is sick. For it cannot be that our clergy should not be contemned by men who manifestly and clearly do see how beggarly ecclesiastical stipends are sought and desired, how filthily and negligently the holy offices are administered, how all care of the flock is naught set by, and the study of God’s glory is cast away. When I say men see these things, can it be that they should not despise the Angel seeking only his own things, not those which are Christ’s. And the Angel himself at certain times sees the same thing in some sort, as can testify the oft complaints of their public sermons, although he knows not the cause, or he would not know it, fearing more, as it were, the remedy than the disease. But it appears plainly how greatly he is despised from that which happened a few years since. A certain man set forth books who called himself a Marmer of Prelates, in which he dealt boldly with the Angel. How acceptable to the people were those merry conceits in words? How plausible almost to all men? How gladly and greedily and with how great pleasure were they received everywhere? No man is so ignorant and unskillful in things that, mindful of the time, he may say thus to himself, “For Jehovah has poured contempt upon the princes: those that honour him he honours, and the despisers of him shall be made light: he has made our priests to be abject to all the people, because they have broken his covenant.” These things, I say, a man considering with himself had not swerved from the truth. For if there had been any estimation of the Angel men would rather have mourned than laughed and delivered those writings to the fire before they would have worn them with so often handling and looking on them. I would not tell you these things unless the Spirit did affirm plainly that you do not know your own nakedness. That false glory wherein you flourish does not earnestly make you mind or regard what men speak and think of you. But learn from here, if you be wise, how servants going before in great number and having chains, and a great troupe of serving men following after, are of no force to drive away contempt and to deliver from the despising of the common people; or if you cannot perceive these things so well in yourself, behold the Papists and the Pope their prince: how doth he now stink for his desert with the greatest part of men, contemned, naught set by, vile and hated of all the godly; whose feet notwithstanding some princes being bewitched yet do kiss, and then whom no mortal man has been in time past of more imperial majesty. Remember our former prelates whose riches were greater than yours, their authority greater, their power more to be feared; yet because the common sort of people did see them to be mere gluttons, how did they deride them? The pride of our Wolsey was mocked openly. For the honours of this world are fig leaves, or as it were torn and ragged clothes which cover not the nakedness but make more deformed through the loops. Mind these things, and be not proud of your golden feathers, but rather where you are naked cover your shame, lest through vain boasting of the part adorned you lie despised with the common people for your other deformity. And thus at length I have opened this rotten sore; if my pains and travail shall be acceptable, and if being cleansed it does fare well, how great thanks shall I give to our God? But if the evil only shall be stirred up and provoked, and the handling shall disquiet those that are sick, I will comfort myself with the conscience of duty and the usual wages of the physician.

18 I counsel thee to buy gold from me: hitherto the cause, now the remedy is taught; both from whence it is to be fetched and by what means, and also what the matter of the medicine itself is. It is to be fetched from Christ alone; He alone has borne all our infirmities and alone yet can heal our griefs. The way to fetch is by buying: not because He requires a price; for He sells wine and milk without money or the changing of things, Isaiah 55:1–2. But because He will have a desire to be brought, even as in getting of things with great cost: in which together also He shows the dignity of the remedy, which otherwise is not dear at any price. The medicine is threefold after the manner of the disease which we have shown to be threefold: gold, white garments, and eye salve; gold is set against poverty; white garments cover nakedness; and eye salve does help against blindness.

We have said that wretchedness and misery were accidents which forthwith vanish when their fountains are taken away. Of what sort every one of them is may easily be understood by their contraries. Gold is opposed to the riches and poverty of the Angel, that is, to the hegemony of benefices and ecclesiastical offices. For the former riches are not true, and do not let but that the Angel may be the most base and vile beggar. But the gold of Christ drives far off this beggary. It is therefore the most holy manner appointed by Christ himself of calling, choosing, ordaining and appointing ecclesiastical men, each to his office; whereby pastors do not seek the office but are sought for; are not promoted for a piece of money but for goodness and virtue, not for favor but learning, not at the will and pleasure of any man but by the election and consent of his flock. Christ will have this gold to be bought from Him because He himself has described plainly this whole way and has not left it free to men to deal in this matter at their pleasure. As long as the thing shall be in the power of one patron and bishop there will never be wanting bribe‑givers and such as will suffer themselves to be corrupted with rewards. But if Christ’s rule be kept, this begging poverty would flee away never to return again. For this gold is tried in the fire, proved oftentimes and wholly refined. We see its excellency in the primitive church and also among our neighbors today. It does not fear any touchstone, does not fear any fire, does not burst asunder by any knocking of the hammer, but it has abided invincible in time past and yet does abide, with the great glory of those that are made rich thereby. White apparel is opposed to the former honors and nakedness, that is, contempt. These garments also Christ will have to be bought from Him, being most precious and most praiseworthy. For what contempt can come to those whom their worthiness has chosen, their learning ordained, their holiness put in authority? Whom many have earnestly desired for their tried godliness do admire for their diligence in teaching, do fear because of the most free truth, and revere as examples of all virtue and honesty. “Be an example,” says Paul, “to the faithful in speech, in conversation, in love, in spirit, in faith, in chastity; let no man despise thy youth,” 1 Timothy 4:12. Behold the way to deliver from contempt. These garments are full of majesty, with which youth being covered is not despised. And so once the prophets went adorned whose hairy garment had more estimation with all men than the silk and vain painting of others. Those wicked men and scorners of the prophets who were together with Jehu, when the prophet, having entered in, did lead him out from the company unwittingly, did show what good opinion of the prophet they had fixed in their minds. “What,” say they, “would that made man have with thee?” Yea rather, why do you make men ask what that made man would have? But their tongue spoke according to their wicked custom: their desire to know did show abundantly what authority and credit they gave to him secretly; whereupon when the message was known assuredly they created him king whom the made man had anointed for king. The Baptist with his leather girdle and garment of camel’s hair was safe from the injury of the priests because of the honor with which the common people honored him. The strength of the divine institution is great in which God himself gives authority either by the voluntary obedience of men or by some punishment inflicted from God. There is no need of the show of earthly riches and honors which at first are wont to dazzle the eyes of the unskillful, but at length when the vanity of it is perceived it is no less despised than frogs fallen from the air. Therefore garments are to be bought from Christ by which alone our nakedness is covered, appearing otherwise very deformed whatever clothes thou put on it. Eye salve of old was all kind of medicine, made in that manner that it might be kept while need should require. At length the name remained chiefly in those which are prepared for the diseases of the eyes because the physicians have used an abundance of it. Here it is applied against blindness, namely the wisdom of the flesh and ignorance of spiritual things. We read that a certain sensible thing was made of the spittle of Christ and of earth, John 9:6, as it were by the knowledge of Christ by the word that proceeds out of his mouth and also the knowledge of ourselves, who in the beginning of the earth savored nothing but the earth. Both these are to be joined together and to be kneaded into one lump; they profit nothing asunder.

For our misery being known particularly brings forth desperation; and Christ being received without the feeling of our own unworthiness is unprofitable and unfruitful. And yet we are not a table to mix and compound these things together, but it must be obtained from him who came into the world to judgment, that those who do not see should see, and those who see should be made blind, John 9:39. First, therefore, we must remove our own wisdom, which as long as it reigns and does possess us so wholly that it leaves no place for true and heavenly. For, O Angel, would you have devised a reformation taken wholly out of your own mind unless you had been full of the opinion of your own wisdom? Overlook your decrees: where is the Spirit called to counsel? By what authority of God’s word is the amending of things confirmed? After what example of the pure church are our matters corrected and amended? There is a deep silence about all these things; nowhere are heard Paul or any other witnesses of the holy truth upon whose credit the things established might rest and stay themselves. I believe you shall scarce find a synod even in the most corrupt times in which divine authority is more dumb and speechless. This opinion is to be laid away, O Angel; you must acknowledge that you are earth, and that you have no eye salve in you until you are mollified with heavenly spit and subdued into a liniment. Depend therefore on the mouth of Christ from which flows that which is profitable to doctrine, to confutation, to correction, to instruction which is in righteousness, so that a man of God may be perfect in every good work, 2 Timothy 3:16–17. From hence is compounded that eye salve which will take away the scales of the eyes and endow you with that sharpness of sight that you may see plainly how you ought to behave yourself in the house of God. Neither must you give ear to them who not only unskillfully but also ungodly cry out that the rules of these things are not to be fetched from this shop. Christ would not set himself forth to be a seller of eye salve unless he had it abundantly enough to help our need, and it were not lawful to buy it from any other. So then the medicine is threefold: gold against poverty, which earthly riches do not ease; white raiment against nakedness, which the honors of the world do not hide; eye salve against blindness, which the wisdom of the flesh does not take away. From which now at length it may be understood that those riches of which, in the former verse, the Angel boasted are not the righteousness of faith alone, as the counterfeit Ambrose speaks unwisely. For those riches rested not on Christ alone. Whereupon he warns that he would buy gold from him, which he should do in vain if before the Angel did abound in the same. But the righteousness of faith has all its treasures placed in Christ alone, of which he is made partaker whoever believes truly and renounces all other righteousness, John 6:48; Romans 3:7. Therefore, O Ribera, draw water from a pumice stone rather than overthrow the righteousness of faith from this place. But such trifles of yours fall upon themselves so that I need not spend time confuting them.

19 As many as I love, &c. An exhortation to use the remedy: and first from the chastising of those whom he loves. A reason indeed of very great moment. Whoever is either among sons or among the reprobates: if he receives no son whom he rebukes and does not chastise, what shall be done with the multitude of the rest? A horrible destruction remains for those whom he will never spare so little, who do not suffer his own children to escape uncorrected. Therefore a chastisement is at hand unless you repent before time, and that very grievous and full of trouble, as the very words themselves do show: which are wont to be used for comfort in a bitter affliction where the mind is so stricken as if it were forsaken by God. Therefore he says they are sons whom he beats with cruel punishments, lest through the grievousness of the punishment they should despair of his fatherly goodness. Therefore it is not time now to strive and to contend with mutual hatred and reproaches, but the ears are to be lifted up to the alarm of Christ, and we must either think forthwith of the remedy or some great and lamentable calamity is to be expected shortly. And it is to be observed that he does rebuke and chasten; that is, convince and punish. These two things are to be joined together. Punishment is unprofitable where words are silent; stripes are fierce. From whence chastisement is well called discipline, wherein the offender feels pain and learns together. But what shall then be the fruit of so long and spiteful contention when the convinced and chastised son shall be compelled, whether he, or not, to sing a contrary song? Were it not better to give now ear to learn than to expect that sorrowful change of our judgment? Although Christ has indeed convinced already, seeing now by the space of many years that many notable men do labour in this thing so that the brethren may understand the truth. What remains now but that at length he fetches out his rods and chastises those whom he has rebuked for so long a time without fruit?

¶ Be hot, therefore; strain therefore your zeal to the utmost. The translation persists in the former metaphor, but the Spirit speaks now properly, teaching that the former heat was nothing else than zeal. Forsake, saith he, your lukewarmness; purge out all the Roman leaven that you may not hang no longer in the midst between the reformed and the anti-Christian church: cast away for his sake honours and riches who for your sake were most despised and most poor. Let faithful pastors be appointed for the several congregations; let them that have charge and rule be compelled unto diligence; let the changers and corrupters of the doctrine be repressed; let the censures be restored to the pastors over their flock. And dispute not with Christ how profitably the polity used of the enemy may be joined with the Gospel. He that reproves in his people the manners of the East and would not have his to be shorn after the similitude of the Gentiles will not easily suffer this society with Antichrist which our carnal wisdom minds. This is the force of this zeal which unless we shall receive forthwith we shall undergo some sharp chastisement.

¶ And repent: repent of the injuries which you have done to the brethren in casting some into prison, in turning others out of their goods, in depriving many of the power to preach the word, in reproaching and traducing all with the odious name of Anabaptists. You know that they have no fellowship with them in any of their errors. Those who reproach your superstitions teach most purely and holy concerning the magistrate: whom they honour no less faithfully and reverently than any other whatsoever. If I should say that he were esteemed more holy and religiously by them than by all others, I would not lie. For those who cleave to God with the firmest minds are such as observe his decrees most closely and in all true obedience yield themselves to him whom they acknowledge to be ordained of God among men in his fear. That was a notable calumny whereby both you have deceived the prince and also procured hatred to your brethren. But you saw that this weapon was most ready at hand and to them hurtful above all others. Repent and wash away your former offences with tears; forget your riches, the more you love, the more pain you shall feel. It is forsaken with much ado where it cleaves so near the heart. But Christ is determined, unless you repent in time, to spew you out of his mouth.

20 Behold I stand at the door: a second reason persuading to use the remedy taken from the readiness of Christ to dwell with them who shall receive him which belongs to every one of the members. That former respected properly the angel; but why does he say that he stands at the door and knocks? Why does he not open the door and go straight in, especially seeing he has the key of David with which he opens and no man shuts? These things are spoken most elegantly and most significantly in respect of the Laodicean church and ours in which Christ stands at the doors, an entry in some sort stopped up against him. The Philadelphia church in which once flourished God’s ordinance and in whose antitype it is forced at this day all the relics of Antichrist being thrust forth has the door unlocked and opened; and especially because of the true use of excommunication restored whereby the gates of heaven are both shut and opened, and also the doors of every one’s conscience are opened so that Christ may pass in without any tarrying. For where good heed is taken to every one’s manners and according to the present occasion men are admonished, reproved, cut off, received again, and the other things are performed faithfully and diligently with the regard had of every one’s salvation, all doors and bars of the heart are cast down and removed, and in very truth the gates then lift up their heads that the King of Glory may enter in. But when England is lukewarm because of the contagion of the Roman government (as once Laodicea for some such like mixture) and has no administration of the censures granted unto lawful pastors as Christ has appointed: as often as the word is preached Christ stands knocking as it were at the doors shut, to whom no other way is open into men’s hearts than by the word; whose power we read to have been great once when in one sermon three thousand were converted, Acts 2:41. Neither is it at this day of itself less mighty: yet there is a diverse reason of a church to be gathered and one gathered. God shows himself extraordinarily bountiful in inviting his people which after he has gathered together he will have them to grow by the way appointed. As touching the fruit of the gospel therefore the people receive no less loss of so excellent an ordinance than the angel acknowledges himself maimed and lame being spoiled of his lawful power. This key is wanting to our church and therefore it is no marvel if Christ be hindered that he cannot enter in readily seeing the doors are shut. But are we then destitute of every good thing? In no wise; for we enjoy still a double good thing wholesome to the elect: the first of which is the going in of Christ unto those that do open to him. The second is their most sweet setting down with Christ. That is the most sweet solace of receiving Christ which the saints perceive as often as at the word preached they feel their hearts to be opened by faith by the work of the Spirit. For then he enters in and suppers with us, imparting himself most benignly and sweetly, even as he bade Zacchaeus desiring to see him and climbing up on a wild fig tree to come down and to make ready for him entertainment at his house, Luke 19:5. And he suppers not going away scot‑free who does give them that thus embrace him that they be made the sons of God, John 1:12. He again entertains us that we may sup together with him as often as with pure minds we come to the sacrament of the supper wherein he feeds us with his own flesh and blood most sumptuous delicious dainties above all that can be spoken or thought.

In which sense it is spoken in Luke 13:29, “Then they shall come from the east and from the west and from the north and from the south and shall sit down in the kingdom of God,” that is, men shall assemble together to the gospel from all quarters, shall embrace the doctrine of the kingdom and shall be partakers of Christ truly whose pledges they shall take, bread and wine, sitting down at his table in celebrating his sacred supper. For he speaks of the calling of the Gentiles whose faith and assenting to the whole truth he signifies by one sacramental action. These guests now Christ would call when in the meantime the Jews of whom he speaks in the parable did abhor and despise the way of salvation as we see it has come to pass now for the space of many ages. Whereunto pertains that which in the same place the Jews excluded do allege requiring an entry for themselves because of their former familiarity in eating and drinking in his sight, verse 26, as though they should say, “O Lord, we communicating at your table have feasted merrily with you in eating of your sacrifices; wilt thou lock the door now against us?” For in this respect the meat of the sacrifices was the same thing to the Jews that the bread and wine is to us. Neither are these things notwithstanding so to be taken as though the elect were limited within the bounds of this life; but because the supper which is made on earth is a pledge of the eternal feast in the heavens. These things therefore prove that a double and great good thing abides in the English church, that is to say the preaching of the word and the lawful administration of the sacraments. In both which Christ bestows himself upon his people, keeping a mutual feast with them; he first being received by us by hearing, secondly entertaining us again with the supper of his body. O we therefore most impure as often as we fly from and forsake hearing of the word, for we refuse Christ to be our guest: O wicked despisers that we are as often as we withdraw ourselves from receiving the sacrament with our brethren, for we despise Christ bidding us to supper. But these things are added for the singular comfort of the godly. For who would not quake and think of flying very quickly from this church when they should hear that the condition of the ministers is hated by Christ who, if not repenting, will vomit out of his mouth shortly unless by the words of Christ himself they were assured of their communicating with him? Praise be to you therefore, most meek Lamb, who finding the door shut does not depart quickly being moved with anger and fury and deprive us of all means of salvation but leaves yet an abundance of yourself to all that do open to you knocking by the word and despise not your sweetest invitation by the sacraments.

Therefore wicked and blasphemous is their error who fall away so from this church as if Christ were banished wholly from here and that there could be no hope of salvation for them that tarry there. Let them mind here Christ feasting with his people. Will they be ashamed to sit down there where they see Christ not ashamed? Are they holier and purer than he? But why do they not convince themselves by their own experience? They cannot deny but that they believed in Christ before they made a separation from us: where did this faith come from? Came it not from our preaching in our church? Can any then preach except he be sent? Romans 10:13 etc. Why then do they so perversely refuse for some blemish in the outward calling that word whose divine force they feel in their hearts? Although the fruit itself do no more free from blame our corruptions than a true child adultery. And therefore neither may we either take pleasure in them nor they forsake and fall away from us for some blemishes. Wherefore return to the unity of the church which hath begotten and nourished you. If you fly from this Christ who suppers with his elect in our assemblies and welcomes them again, you shall find him nowhere. In the meantime let us also mind how great evil we call for upon ourselves who by holding hard our superstitions do throw our brethren into so great danger. Certainly if that has any weight which the truth himself once confirmed, it would be better for such men that a millstone being hanged about their necks they were drowned in the bottom of the sea, Matthew 18:6. I wish health of mind to both. But moreover this place is to be delivered from the fraud of the Papists who will have it to be in the power of men to open to Christ knocking. “Whether,” says Bellarmine, “does he not know that they cannot open? Should he not be a fool who would knock at the door of his neighbour if he knew certainly that none were within who could open?” in his first book of Grace and Free Will, chap. 11. I answer: he should not without cause be a fool if his only end of knocking were that he might enter in; but Christ knocks at the door of the reprobates whom he knows neither to be willing nor able to open not that he may enter in but partly that he may upbraid them with their impotency gotten by their own fault, partly that he may increase their condemnation. For so speaks the evangelist expressly, “Therefore they could not believe,” John 12:34. Why then uses he words to them who have not ability to believe? Christ himself shows: “If I had not come,” says he, “and spoken unto them, they should not have had sin; but now they have no cloak for their sin,” John 15:22. Therefore he spoke unto them that for the contempt and hatred of his only begotten son their condemnation might be the greater. Such are the powers of the natural man as is the love of the truth in the Papists who seeing it refuse it wickedly.

21 To him who overcomes I will give a seat: word for word in the Greek is “He who overcomes I will give him,” by the nominative case absolute, as was observed before, Chapter 2:26. This third reason is taken from the reward of being a companion and partaker of his throne: not because the glory of every one of the children shall be equal to the honor of the man Christ, but because the glory and majesty of the head shall redound to every one of the members. Therefore the thrones are not peculiar to the twelve apostles of which see Matthew 19:28 but common to all the elect. Although in a certain peculiar manner they are attributed in the same place to the apostles, as it may be we will show in another place. And we have said often that the rewards are fitted unto the times and to contain a prophecy which is here also to be respected. Christ therefore mentions the throne which he obtained after his sacrifice finished on the cross showing that the like things are to be endured also of his; afterward they shall be partakers of his throne. Therefore by this making mention of it he lessens the affliction and so the consolation of it he sets himself for an example as though he should bid us look upon him and not to be overcome by any troubles when we see that he ascended into his throne of supreme dignity by this way. And we know how much this contending for reformation has cost many and excellent men whose sufferings shall not be forgotten although they be not recited of me. Only let them comfort their faintness of heart with the expectation of his throne. What though they be trodden under foot while they shall see others to flourish with the dignity of peers of the realm? Christ has prepared for them a throne with himself. Let no man regard an earthly chair: as hitherto they have confirmed abundantly that they are far off from such desire, whatsoever ambitious men prate otherwise who do conjecture of others by themselves.

22 Let him who has an ear hear: now therefore whoever has felt Christ to be your guest and has tasted again the dainties of his table, lift up your ears and attend to what the Spirit says to the churches. Let man go and rest not in him but regard the convenience of all things from the beginning to the end. And complain not of newness and strangeness as though you would appoint Christ to whom and when he should reveal his secrets. We know that some things have been sealed up until the appointed time. But if it is necessary that you confess it to be a divine truth, let us all endeavor earnestly, princes, peers, angels, people, so that we may turn away the evil that hangs over our heads. What a horrible thing it is to be vomited out of Christ’s mouth with loathing and abhorrence? The land once cast out the Canaanites and they were destroyed utterly. Shall their punishment be lighter for those whom Christ himself will spew out instead of the land? Therefore let us use the remedy seriously. We need zeal to attain a full reformation: we hang yet between heaven and hell: the contagious vapor of the Roman marshes molests and annoys us; our silver until now is foul with dross; our wine is mixed with water; Christ will no longer tolerate such angels that are in the middle. What if this admonition is the last token and sign to you of being wary? Let us therefore listen and not sharpen our teeth against the stone that is hurled: but let us quake in fear of the hand that threw it. You, O Christ, who once took Lot by the hand to pull him out of the city, open our hearts that are slow and extend the time that we may obey your warnings and exhortations.

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2025-08-07
在云服务器端口25受限环境下部署Mailcow邮件服务器

在云服务器端口25受限环境下部署Mailcow邮件服务器

背景与挑战

在现代云计算环境中,主流云服务提供商(如GCP、AWS)为了防止垃圾邮件传播,普遍禁用了虚拟机实例的端口25出站流量。这给自建邮件服务器带来了巨大挑战。本文记录了在这种受限环境下,通过日本ConoHa.jp服务器作为SMTP中继,成功部署Mailcow邮件服务器的完整过程。

系统架构设计

graph TB
    subgraph "外部网络"
        Client[用户客户端
IMAP/SMTP] ExtMail[外部邮件服务
Gmail/Outlook] Internet[互联网] end subgraph "ConoHa 中继服务器 (10.8.0.34)" ConoHA[Ubuntu Server
Postfix + iptables] VPN1[OpenVPN Client] end subgraph "Mailcow 服务器 (10.8.0.33)" Mailcow[Mailcow Docker
Postfix + Dovecot] VPN2[OpenVPN Client] end subgraph "VPN 隧道网络 (10.8.0.0/24)" VPNTunnel[加密隧道] end %% 连接关系 Client -->|IMAP/SMTP 连接| ConoHA ConoHA <-->|VPN 隧道| VPNTunnel VPNTunnel <-->|VPN 隧道| VPN2 VPN1 -.-> VPNTunnel VPN2 -.-> Mailcow ConoHA -->|端口转发| Internet Internet <-->|SMTP| ExtMail %% 数据流标注 Client -.->|1\. 用户连接
端口: 993,143,587,465| ConoHA ConoHA -.->|2\. 入站邮件转发
端口: 25| Mailcow Mailcow -.->|3\. 出站邮件中继
relayhost: 10.8.0.34:25| ConoHA ConoHA -.->|4\. 外网发送
端口: 25| ExtMail style Client fill:#e1f5fe style ExtMail fill:#e8f5e8 style ConoHA fill:#fff3e0 style Mailcow fill:#f3e5f5 style VPNTunnel fill:#e0f2f1

数据流向说明:

  1. 入站邮件: 外网 → ConoHa(iptables DNAT) → VPN → Mailcow
  2. 出站邮件: Mailcow → VPN → ConoHa(Postfix relay) → 外网
  3. 用户连接: 客户端 → ConoHa(端口转发) → VPN → Mailcow

核心组件

  • 主服务器 (10.8.0.33): Mailcow Docker化邮件服务器,运行在macOS
  • 中继服务器 (10.8.0.34): ConoHa.jp Ubuntu服务器,负责端口25流量转发
  • VPN网络: OpenVPN连接两台服务器,提供安全的内网通信

部署步骤

1. ConoHa中继服务器配置

1.1 安装OpenVPN 3客户端

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# 添加OpenVPN官方源
sudo mkdir -p /etc/apt/keyrings && curl -fsSL https://packages.openvpn.net/packages-repo.gpg | sudo tee /etc/apt/keyrings/openvpn.asc

DISTRO=$(lsb_release -c | awk '{print $2}')
echo "deb [signed-by=/etc/apt/keyrings/openvpn.asc] https://packages.openvpn.net/openvpn3/debian $DISTRO main" | sudo tee /etc/apt/sources.list.d/openvpn-packages.list

sudo apt update && sudo apt install openvpn3

1.2 配置VPN连接

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# 导入VPN配置文件
openvpn3 config-import --config free-smtp-server.ovpn --name dtype --persistent
openvpn3 config-acl --show --lock-down true --grant root --config dtype

# 设置开机自启
sudo systemctl enable --now openvpn3-session@dtype.service

1.3 配置网络转发

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# 启用IP转发
echo 'net.ipv4.ip_forward=1' | sudo tee -a /etc/sysctl.conf
sudo sysctl -p

# 配置入站邮件服务端口转发
sudo iptables -t nat -A PREROUTING -p tcp --dport 993 -j DNAT --to-destination 10.8.0.33:993 # IMAPS
sudo iptables -t nat -A PREROUTING -p tcp --dport 143 -j DNAT --to-destination 10.8.0.33:143 # IMAP
sudo iptables -t nat -A PREROUTING -p tcp --dport 587 -j DNAT --to-destination 10.8.0.33:587 # SMTP STARTTLS
sudo iptables -t nat -A PREROUTING -p tcp --dport 465 -j DNAT --to-destination 10.8.0.33:465 # SMTPS

# 配置入站邮件接收转发(排除内网流量避免循环)
sudo iptables -t nat -A PREROUTING ! -s 10.8.0.0/24 -p tcp --dport 25 -j DNAT --to-destination 10.8.0.33:25

# 配置转发规则
sudo iptables -A FORWARD -p tcp -d 10.8.0.33 -m multiport --dports 993,143,587,465,25 -j ACCEPT

# 配置出站NAT
sudo iptables -t nat -A POSTROUTING -o tun0 -j MASQUERADE

1.4 安装和配置Postfix中继服务

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# 安装Postfix
sudo apt update && sudo apt install postfix

# 配置为邮件中继服务器
sudo postconf -e "mynetworks = 127.0.0.0/8 10.8.0.33/32"
sudo postconf -e "inet_interfaces = all"
sudo postconf -e "relayhost = "
sudo postconf -e "mydestination = localhost"

# 重启服务
sudo systemctl restart postfix

# 配置防火墙
sudo ufw allow from 10.8.0.33 to any port 25

2. Mailcow服务器配置

2.1 OpenVPN客户端配置

.ovpn配置文件中添加:

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route 10.8.0.0 255.255.255.0
route-nopull

2.2 出站邮件中继配置

方案一:使用内网Postfix中继(推荐)

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# 配置Mailcow使用ConoHa服务器作为中继
docker-compose exec postfix-mailcow postconf -e "relayhost = [10.8.0.34]:25"
docker-compose restart postfix-mailcow

方案二:使用Gmail SMTP中继(备选)

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# 配置Gmail作为SMTP中继
docker-compose exec postfix-mailcow postconf -e 'relayhost = [smtp.gmail.com]:587'
docker-compose exec postfix-mailcow postconf -e 'smtp_use_tls = yes'
docker-compose exec postfix-mailcow postconf -e 'smtp_sasl_auth_enable = yes'
docker-compose exec postfix-mailcow postconf -e 'smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd'
docker-compose exec postfix-mailcow postconf -e 'smtp_tls_security_level = encrypt'

# 创建Gmail认证文件
echo "[smtp.gmail.com]:587 your-email@gmail.com:your-app-password" | docker-compose exec -T postfix-mailcow tee /etc/postfix/sasl_passwd
docker-compose exec postfix-mailcow postmap /etc/postfix/sasl_passwd
docker-compose exec postfix-mailcow chmod 600 /etc/postfix/sasl_passwd
docker-compose exec postfix-mailcow chmod 600 /etc/postfix/sasl_passwd.db
docker-compose restart postfix-mailcow

2.3 Linux环境下的iptables方案(可选)

如果Mailcow部署在Linux系统上,可以使用iptables在宿主机级别进行流量重定向:

10.8.0.33 (Mailcow服务器) 的设置:

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# 将出站端口25流量重定向到中继服务器
sudo iptables -t nat -A OUTPUT -p tcp --dport 25 -j DNAT --to-destination 10.8.0.34:25

# 对重定向的流量进行源地址转换
sudo iptables -t nat -A POSTROUTING -d 10.8.0.34 -p tcp --dport 25 -j MASQUERADE

10.8.0.34 (中继服务器) 的设置:

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# 允许来自Mailcow服务器的转发流量
sudo iptables -A FORWARD -s 10.8.0.33 -p tcp --dport 25 -j ACCEPT

# 对来自Mailcow的流量进行源地址转换后转发到外网
sudo iptables -t nat -A POSTROUTING -s 10.8.0.33 -p tcp --dport 25 -j MASQUERADE

这种方案的优势是在网络层直接处理,无需修改应用配置,但需要Linux系统支持。

故障排除经验

问题1:防火墙阻止连接

现象: Connection refused错误

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(connect to 10.8.0.34[10.8.0.34]:25: Connection refused)

解决方案:

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# 检查服务监听状态
sudo ss -tlnp | grep :25

# 配置UFW防火墙
sudo ufw allow from 10.8.0.33 to any port 25

问题2:避免路由循环

现象: 邮件在两个服务器间循环
解决方案: 在iptables PREROUTING规则中排除内网源地址

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sudo iptables -t nat -A PREROUTING ! -s 10.8.0.0/24 -p tcp --dport 25 -j DNAT --to-destination 10.8.0.33:25

最终配置验证

测试入站邮件

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# 从外部发送邮件到 your-email@your-domain.com
# 检查Mailcow日志
docker-compose logs -f postfix-mailcow

测试出站邮件

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# 检查邮件队列
docker-compose exec postfix-mailcow postqueue -p

# 强制发送队列中的邮件
docker-compose exec postfix-mailcow postqueue -f

验证中继工作状态

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# 查看成功的中继日志
docker-compose logs postfix-mailcow | grep "relay=10.8.0.34"
# 应该看到类似输出:
# status=sent (250 2.0.0 Ok: queued as XXXXX)

性能与安全考量

  1. 网络延迟: VPN隧道会增加约20-50ms延迟,但对邮件服务影响较小
  2. 单点故障: ConoHa服务器是关键节点,建议配置监控和备份方案
  3. 安全性: 所有邮件流量通过加密VPN传输,相比直连更安全
  4. 成本优化: ConoHa服务器选择最低配置即可满足中继需求

总结

通过VPN+中继服务器的架构,成功解决了云服务商端口25限制的问题。该方案具有以下优势:

  • 灵活性: 可以随时更换云服务商而不影响邮件服务
  • 可扩展性: 中继服务器可以同时为多个Mailcow实例提供服务
  • 成本效益: 相比企业级邮件服务,成本显著降低
  • 完全控制: 保持对邮件数据和配置的完全控制权

这套解决方案为在受限云环境中部署自托管邮件服务器提供了可行的技术路径。

Read More

2025-06-14
IoT技术学习指南

IoT Technology Study Guide

I. Quiz (10 Short Answer Questions)

1. What is the primary role of IoT Gateways in an IoT system, particularly concerning data flow and processing location?
IoT Gateways gather data from IoT devices, performing preliminary processing and filtering. They are crucial for mediating communication between IoT devices and the IoT server/cloud, often undertaking edge computing to reduce data transmission and latency.

2. Explain the core concept of “data-driven systems” (CPS: Cyber Physical System) in the context of IoT and manufacturing.
Data-driven systems, particularly Cyber-Physical Systems (CPS), integrate physical and cyber spaces by collecting data from the physical world (via sensors and actuators) and analyzing it in the cyber world. This analyzed information is then fed back to the physical world to create new value or optimize operations, such as in “Industrie 4.0” which leverages digital twins for production simulation.

3. What is the purpose of “Data Augmentation” in the context of IoT data analysis?
Data Augmentation is used to increase the quantity of training data for machine learning, especially deep learning, when sufficient data is not readily available. It involves transforming existing data (e.g., resizing, rotating images, adding noise) to create new, diverse samples, thereby improving the robustness and accuracy of analysis models.

4. Describe the key difference between batch processing and streaming processing in IoT data handling.
Batch processing involves collecting and storing large volumes of data over a period before processing it in a single run, suitable for non-real-time analysis. Streaming processing, on the other hand, processes data as it arrives, providing near real-time insights and enabling immediate responses, crucial for applications requiring low latency.

5. What is the main benefit of using Edge Computing in an IoT system compared to solely relying on Cloud Computing for data processing?
Edge computing processes data closer to the source of its generation, reducing latency and network bandwidth consumption. This is particularly beneficial for real-time applications like autonomous driving or robot control, where immediate decision-making based on local data is critical.

6. Explain the concept of “protocol conversion” within IoT Gateways and why it is necessary.
Protocol conversion allows different IoT devices and networks, which may use various communication protocols, to communicate with each other and with the IoT server/cloud. The IoT Gateway acts as a mediator, translating between these disparate protocols to ensure seamless data exchange across the entire IoT system.

7. What is the primary function of MEMS (Micro Electro Mechanical Systems) in IoT devices?
MEMS are miniature integrated devices that combine mechanical and electrical components, often used as sensors or actuators in IoT devices. They are crucial for miniaturization and integration, enabling the development of compact, low-power IoT devices such as pressure sensors or accelerometers found in smartphones.

8. Describe the two main approaches to machine learning mentioned in the text: supervised learning and unsupervised learning.
Supervised learning involves training a model with labeled data (input data paired with correct output/target data) to learn a mapping function, used for tasks like classification or regression. Unsupervised learning, conversely, works with unlabeled data to find hidden patterns or structures, such as clustering or anomaly detection.

9. What are the key advantages of using a “mesh” network topology for IoT area networks?
A mesh network offers high reliability and fault tolerance because data can travel along multiple paths between nodes. If one path fails, an alternative route can be used. This redundancy also allows for wider coverage and more robust communication, though it can increase network complexity and power consumption.

10. In the context of IoT security, what is “Zero Trust” and why is it increasingly important?
Zero Trust is a security model that assumes no user or device, whether inside or outside the network, should be trusted by default. Instead, every access attempt is verified, authenticated, and authorized before granting access to resources. This approach is increasingly vital in IoT due to the large number and diversity of connected devices and the potential for new attack vectors.

II. Quiz Answer Key

1. IoT Gateways’ Role: IoT Gateways collect and perform initial processing (filtering, timing adjustment) on data from IoT devices. They serve as a bridge between IoT devices and the IoT server/cloud, enabling edge computing by handling data close to its source, which is critical for minimizing latency and network load.

2. Data-Driven Systems (CPS): CPS integrates the physical and cyber realms. Data from physical sensors is analyzed in the cyber space, and the derived insights are fed back to control physical actuators. This creates a continuous loop, allowing for optimization and value creation, such as enhancing manufacturing efficiency in “Industrie 4.0” through virtual representations called digital twins.

3. Data Augmentation: This technique addresses data scarcity by artificially expanding datasets. It modifies existing data (e.g., image transformations like rotation or scaling, or adding noise to sensor data) to generate new, diverse samples. This helps train more robust machine learning models, particularly deep learning models, by preventing overfitting and improving generalization.

4. Batch vs. Streaming Processing: Batch processing handles data accumulated over a period, making it suitable for non-real-time analytical tasks where immediate results aren’t critical. Streaming processing, conversely, processes data continuously as it arrives, providing real-time insights and enabling immediate reactions, which is essential for time-sensitive IoT applications.

5. Edge Computing Benefit: Edge computing reduces reliance on centralized cloud processing by performing computations closer to the data source. This significantly lowers network latency, decreases bandwidth usage, and enhances real-time response capabilities, making it ideal for applications that demand instant decisions or operate in environments with limited connectivity.

6. Protocol Conversion in IoT Gateways: IoT Gateways perform protocol conversion to enable interoperability between devices and networks that use different communication standards (e.g., Bluetooth, ZigBee, Wi-Fi, cellular). This translation function ensures that data from diverse IoT devices can be understood and processed by the central IoT server or cloud, facilitating a cohesive system.

7. MEMS Function: MEMS (Micro Electro Mechanical Systems) are fundamental to IoT devices due to their ability to integrate mechanical and electrical functions at a micro-scale. They commonly serve as miniaturized sensors (e.g., pressure, acceleration, gyroscope) and actuators, contributing to the compact size, low power consumption, and multi-functional capabilities of modern IoT gadgets.

8. Supervised vs. Unsupervised Learning: Supervised learning trains models on labeled datasets, meaning each input has a corresponding correct output, enabling tasks like classification and regression by learning the mapping. Unsupervised learning, however, analyzes unlabeled data to discover inherent patterns, structures, or groupings within the data itself, often used for clustering or anomaly detection.

9. Mesh Network Advantages: A mesh network topology in IoT offers enhanced reliability and robustness because each device can connect to multiple other devices, creating redundant paths for data transmission. This decentralized structure improves fault tolerance, extends network coverage, and can handle increased data traffic by distributing the load.

10. Zero Trust in IoT Security: Zero Trust is a security model where no entity (user, device, application) is inherently trusted, regardless of its location relative to the network perimeter. All access requests are rigorously authenticated and authorized, minimizing the risk of unauthorized access and lateral movement by attackers, which is crucial given the distributed and diverse nature of IoT deployments.

III. Essay Format Questions (No Answers Provided)

  1. Discuss the evolution of IoT from its early concepts to its current state, highlighting the key technological advancements (e.g., processing power, communication technologies, AI integration) that have enabled its widespread adoption and the creation of new value.

  2. Compare and contrast the roles and advantages of Cloud Computing and Edge Computing in IoT system architecture. Provide specific examples of IoT applications where one approach might be more beneficial than the other, or where a hybrid approach is optimal.

  3. Analyze the importance of data collection, processing, and analysis techniques in realizing the full potential of IoT. Elaborate on how different data processing methods (e.g., batch, streaming, CEP) and data analysis techniques (e.g., statistical analysis, machine learning, deep learning) contribute to extracting valuable insights and enabling data-driven actions.

  4. Examine the various wireless communication technologies used in IoT (e.g., Bluetooth, Wi-SUN, LAN, 5G), outlining their characteristics, typical applications, and the trade-offs involved in selecting one over another for specific IoT deployments. Consider factors such as range, power consumption, data rate, and network topology.

  5. Information security is a critical concern in IoT system development and operation. Discuss the main security threats and vulnerabilities prevalent in IoT, and describe various countermeasures and technologies (e.g., authentication, encryption, firewalls, malware protection, Zero Trust) that can be implemented to mitigate these risks and ensure the safety and reliability of IoT systems.

IV. Glossary of Key Terms

Actuator (アクチュエータ): A device that converts an electrical signal into a physical action, such as motion, light, or heat. In IoT, actuators are used to control physical devices based on data received from sensors or commands from the system.

Agile Development (アジャイル型開発): A software development methodology characterized by iterative development cycles, rapid prototyping, and flexible adaptation to changing requirements, emphasizing collaboration and continuous feedback.

Ambient (アンビエント): A Web service for IoT data visualization and storage, offering simple user registration and free usage, with support for Python libraries.

Analog-to-Digital (A/D) Conversion (A/D変換): The process of converting analog electrical signals (like those from many sensors) into digital data that can be processed by computers.

Apache Hadoop (Apache Hadoop): An open-source software framework for distributed storage and processing of very large data sets on computer clusters. It is often used for batch processing of big data.

Arduino (アルドゥイーノ): An open-source electronics platform based on easy-to-use hardware and software, popular for building interactive objects and prototypes, especially in IoT.

Authentication (認証): The process of verifying the identity of a user, device, or system attempting to access resources in an IoT environment.

AutoEncoder (オートエンコーダ): A type of neural network used for unsupervised learning, specifically for data compression or dimensionality reduction. It learns to reconstruct its input, often used for feature extraction or anomaly detection.

Batch Processing (バッチ処理): A method of processing data where a large volume of data is collected and processed together in a single operation, typically at scheduled intervals, rather than continuously.

Bayesian Network (ベイジアンネットワーク): A probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph, used for inference and decision-making under uncertainty.

BCP (Business Continuity Plan) (BCP): A plan designed to ensure that business operations can continue during and after a major disruption or disaster, including strategies for data backup, system recovery, and alternative work arrangements.

Big Data (ビッグデータ): Extremely large datasets that may be analyzed computationally to reveal patterns, trends, and associations, especially relating to human behavior and interactions.

Bluetooth (ブルートゥース): A short-range wireless technology standard used for exchanging data between fixed and mobile devices over short distances, commonly found in IoT for personal area networks.

Broker (ブローカー): In messaging systems like MQTT, a central server that receives messages from publishers and distributes them to appropriate subscribers based on topics.

Caffe (カフェ): A deep learning framework developed by Berkeley Vision and Learning Center, known for its speed and efficiency in image recognition tasks.

Calibration (キャリブレーション): The process of adjusting a sensor or device to ensure its measurements are accurate and consistent with a known standard.

CC License (Creative Commons license) (CCライセンス): A public copyright license that allows creators to communicate which rights they reserve and which rights they waive for the benefit of recipients or other creators.

CCD (Charge-Coupled Device) (CCD): A semiconductor device that converts light into an electrical charge, commonly used as an image sensor in digital cameras and other imaging applications.

CEP (Complex Event Processing) (CEP): A technology that processes data from multiple sources in real time to identify patterns or relationships, enabling immediate action based on complex events.

Classification (分類): A machine learning task of categorizing data into predefined classes based on learned patterns from training data.

Cloud Computing (クラウドコンピューティング): A model for delivering on-demand computing services—including servers, storage, databases, networking, software, analytics, and intelligence—over the Internet (“the cloud”).

CMOS (Complementary Metal-Oxide-Semiconductor) (CMOS): A type of semiconductor technology used in integrated circuits, including image sensors, known for its low power consumption.

CoAP (Constrained Application Protocol) (CoAP): A specialized web transfer protocol for use with constrained nodes and constrained networks in the IoT, designed for efficiency and low overhead.

Cold Data (コールドデータ): Data that is infrequently accessed or used, often stored in cost-effective, long-term storage solutions.

Convolutional Neural Network (CNN) (畳み込みニューラルネットワーク): A type of deep learning neural network primarily used for analyzing visual imagery, highly effective for image recognition and processing tasks.

CPS (Cyber Physical System) (サイバーフィジカルシステム): See “Data-driven systems.”

CSV (Comma-Separated Values) (CSV): A simple file format used to store tabular data, where each line of the file is a data record and each record consists of one or more fields, separated by commas.

Data Augmentation (データ水増し): See “Augmentation.”

Data Cleansing (データクレンジング): The process of identifying and correcting or removing incorrect, incomplete, or irrelevant data from a dataset.

Data Preprocessing (データ前処理): The steps taken to transform raw data into a clean, organized, and suitable format for analysis, often involving cleansing, transformation, and normalization.

Data Transformation/Integration (データ変換・統合): The process of converting data from one format or structure into another, and combining data from different sources into a unified view.

Deep Learning (深層学習): A subset of machine learning that uses multi-layered neural networks (deep neural networks) to learn complex patterns from large amounts of data, often achieving high accuracy in tasks like image and speech recognition.

Digital Signature (デジタル署名): A cryptographic technique used to verify the authenticity and integrity of digital messages or documents, ensuring that the sender is who they claim to be and that the message has not been altered.

Digital Transformation (DX) (デジタルトランスフォーメーション): The process of adopting digital technology to transform business processes, culture, and customer experiences to meet changing business and market requirements.

Disclosure Requirement (説明可能性): In AI and machine learning, the ability to explain how a model arrived at a particular prediction or decision, crucial for trust and accountability, especially in sensitive applications.

Distributed File System (HDFS) (分散ファイルシステム): A distributed, scalable, and portable file system designed to store very large files across multiple machines, part of the Hadoop ecosystem.

DMZ (Demilitarized Zone) (閉域網): A physical or logical subnetwork that contains and exposes an organization’s external-facing services to an untrusted, larger network, usually the internet.

DNA Sensor (DNAセンサ): A biosensor that detects specific DNA sequences, often used in medical diagnostics, environmental monitoring, and food safety.

DDoS Attack (Distributed Denial of Service Attack) (DDoS攻撃): A malicious attempt to disrupt the normal traffic of a targeted server, service, or network by overwhelming it with a flood of Internet traffic from multiple compromised computer systems.

Drone (ドローン): An unmanned aerial vehicle (UAV) that can be controlled remotely or fly autonomously, used in IoT for various applications like surveillance, delivery, and data collection.

Dust Networks (Dust Networks): A company specializing in low-power wireless mesh networking technology for industrial IoT applications.

DX (Digital Transformation) (DX): See “Digital Transformation.”

Edge AI (エッジAI): Artificial intelligence processing performed directly on the edge devices themselves (e.g., sensors, cameras, IoT gateways) rather than in a centralized cloud, enabling real-time decision-making and reduced latency.

Edge Computing (エッジコンピューティング): A distributed computing paradigm that brings computation and data storage closer to the sources of data, improving response times and saving bandwidth.

Edgecross Consortium (Edgecross コンソーシアム): A Japanese consortium focused on promoting edge computing and the integration of IT and OT (Operational Technology) in manufacturing.

Electrocardiogram (ECG) (心電計): A test that measures the electrical activity of the heartbeat, used in wearable bio-sensors to monitor cardiac health.

EnOcean (エンオーシャン): A wireless standard focused on ultra-low power consumption, often utilizing energy harvesting, making it suitable for batteryless IoT devices.

Energy Harvesting (エネルギーハーベスティング): The process of capturing and storing small amounts of energy from ambient sources (e.g., solar, thermal, vibration, radio waves) to power low-power electronic devices, like IoT sensors.

EPFC (Edge Platform Consortium) (EPFC): A consortium focused on edge platform development for connecting cyber and physical spaces.

Ethernet (イーサネット): A family of wired computer networking technologies commonly used in local area networks (LANs).

FPGA (Field Programmable Gate Array) (FPGA): An integrated circuit designed to be configured by a customer or a designer after manufacturing, allowing for flexible hardware acceleration and custom logic for specific computing tasks, including AI at the edge.

FTP (File Transfer Protocol) (FTP): A standard network protocol used for the transfer of computer files between a client and server on a computer network.

GAN (Generative Adversarial Networks) (敵対的生成ネットワーク): A class of machine learning frameworks composed of two neural networks, one generating data and the other discriminating between real and fake data, used for generative AI like image creation.

Gateways (ゲートウェイ): Devices that connect different networks and protocols, serving as an intermediary between IoT devices and the cloud, performing functions like data aggregation, protocol conversion, and local processing.

Generative AI (生成AI): A type of artificial intelligence that can create new content, such as text, images, audio, and video, by learning from existing data.

GPIO (General Purpose Input/Output) (GPIO): A generic pin on an integrated circuit whose behavior (input or output) can be controlled by the user at runtime.

GNSS (Global Navigation Satellite System) (GNSS): A general term for satellite navigation systems that provide autonomous geo-spatial positioning, including GPS.

Grad-CAM (Grad-CAM): A technique used in deep learning to visualize the parts of an image that are most relevant to a convolutional neural network’s decision, providing interpretability for image recognition models.

Graph DB (グラフ型DB): A NoSQL database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. Ideal for relationships (e.g., social networks).

HBase (HBase): An open-source, non-relational, distributed database modeled after Google’s Bigtable, part of the Hadoop ecosystem, suitable for large datasets.

HDFS (Hadoop Distributed File System) (HDFS): See “Distributed File System.”

HEMS (Home Energy Management System) (HEMS): A system that monitors and manages energy consumption in households, optimizing energy usage of various appliances.

Histogram (ヒストグラム): A graphical representation of the distribution of numerical data, often used in statistical analysis.

Hot Data (ホットデータ): Data that is frequently accessed or actively used, typically stored on high-performance storage for quick retrieval.

HTTP (Hypertext Transfer Protocol) (HTTP): The foundation of data communication for the World Wide Web, used for communication between web servers and clients.

Hybrid Cloud (ハイブリッドクラウド): A cloud computing environment that uses a mix of on-premises, private cloud and public cloud services with orchestration between the platforms.

IaaS (Infrastructure as a Service) (IaaS): A cloud computing service model where providers offer virtualized computing resources over the internet, such as virtual machines, storage, and networks.

I2C (Inter-Integrated Circuit) (I2C): A two-wire serial communication bus interface developed by Philips Semiconductors, used to connect low-speed devices such as microcontrollers, EEPROMs, A/D converters, and I/O interfaces.

IC (Integrated Circuit) Card (ICチップ認証): A smart card that authenticates identity using an integrated circuit chip, often used for secure transactions or access control.

IEEE802.11 (IEEE802.11): A set of media access control (MAC) and physical layer (PHY) specifications for implementing wireless local area network (WLAN) computer communication in the 2.4, 5, and 60 GHz frequency bands.

IEEE802.15.4 (IEEE802.15.4): A standard that specifies the physical layer and media access control for low-rate wireless personal area networks (LR-WPANs), often used as the basis for ZigBee and Wi-SUN.

IFTTT (イフトット): “If This Then That,” a web-based service that allows users to create chains of simple conditional statements, called “applets,” to automate various online tasks and connect different services and devices, including IoT.

Image Sensor (画像センサ): A device that converts an optical image into an electronic signal, such as CCD or CMOS sensors, used in IoT for visual monitoring and image recognition.

Industrie 4.0 (インダストリー4.0): The fourth industrial revolution, characterized by the digitalization of manufacturing and integration of cyber-physical systems, IoT, and AI to create smart factories.

Intrusion Detection System (IDS) (侵入検知システム): A security technology that monitors network traffic or system activities for malicious activity or policy violations and generates alerts.

IoT Area Network (IoTエリアネットワーク): A network specifically designed for IoT devices within a limited geographical area, typically using short-range wireless communication technologies.

IoT Devices (IoTデバイス): Physical objects that are embedded with sensors, software, and other technologies for the purpose of connecting and exchanging data with other devices and systems over the internet.

IoT Gateway (IoTゲートウェイ): See “Gateways.”

IoT Platform (IoTプラットフォーム): A cloud-based or on-premises service that provides tools and functionalities for managing IoT devices, collecting and processing data, and enabling applications.

IoT Server (IoTサーバ): A central component in an IoT system, typically residing in the cloud, responsible for receiving, storing, analyzing, and managing data from IoT devices, and issuing control commands.

IPA (Information-Technology Promotion Agency, Japan) (IPA): A Japanese government-affiliated organization that promotes IT and cybersecurity, including IoT security guidelines.

ISMS (Information Security Management System) (情報セキュリティマネジメントシステム): A systematic approach to managing sensitive company information so that it remains secure, including policies, processes, and technologies.

ISM Band (ISMバンド): Industrial, Scientific, and Medical radio bands, which are reserved internationally for the use of radio frequency (RF) energy for industrial, scientific, and medical purposes other than telecommunications. Many IoT devices operate in these unlicensed bands.

ISDN (Integrated Services Digital Network) (ISDN): A set of communication standards for simultaneous digital transmission of voice, video, data, and other network services over the traditional circuits of the public switched telephone network.

JSON (JavaScript Object Notation) (JSON): A lightweight data-interchange format, commonly used for transmitting data between a server and web application, and increasingly in IoT due to its simplicity.

Julia (ジュリア): A high-level, high-performance, dynamic programming language for technical computing, suitable for data science and machine learning.

Keras (ケラス): An open-source neural network library written in Python, designed to enable fast experimentation with deep neural networks.

Key-Value Type (キーバリュー型): A simple NoSQL database model that stores data as a collection of key-value pairs, where a key serves as a unique identifier for its corresponding value.

LIME (Local Interpretable Model-agnostic Explanations) (LIME): A technique for explaining the predictions of any machine learning model by approximating it locally with an interpretable model.

Linear Regression (線形回帰): A statistical method that models the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

LLM (Large Language Model) (LLM): A type of artificial intelligence model trained on vast amounts of text data, capable of understanding and generating human-like language, often used in generative AI applications.

Local 5G (ローカル5G): Private 5G networks deployed by businesses or local governments for their specific needs, offering high reliability, low latency, and enhanced security compared to public networks.

Long Polling (ロングポーリング方式): A communication technique where the client holds a connection open to the server until new data is available or a timeout occurs, reducing polling frequency and improving real-time updates compared to traditional polling.

LoRaWAN (LoRaWAN): A Low Power Wide Area Network (LPWAN) specification intended for wireless battery operated Things in a regional, national or global network, designed for low-power, long-range communication.

LPWA (Low Power Wide Area) (LPWA): A class of wireless communication technologies designed for low-power, long-range communication, typically for IoT devices that transmit small amounts of data infrequently.

LTE (Long Term Evolution) (LTE): A standard for wireless broadband communication for mobile devices and data terminals, based on GSM/EDGE and UMTS/HSPA network technologies, and often extended to IoT (e.g., LTE-M).

LTE-M (LTE-M): A type of LPWA technology based on LTE, designed for IoT devices that require higher bandwidth than other LPWA technologies, while still maintaining low power consumption.

LwM2M (Lightweight M2M) (LwM2M): A device management protocol for IoT devices, optimized for constrained devices and networks, offering functionalities for device management and data reporting.

Machine Learning (機械学習): A field of artificial intelligence that uses statistical techniques to enable computer systems to “learn” from data, without being explicitly programmed, performing tasks like prediction, classification, and pattern recognition.

Mahout (Mahout): An Apache open-source project that provides implementations of scalable machine learning algorithms, often used in conjunction with Hadoop.

MEC (Multi-access Edge Computing) (マルチアクセス・エッジ・コンピューティング): A network architecture concept that enables cloud computing capabilities and an IT service environment at the edge of the network, closer to mobile subscribers and IoT devices.

Mediation Filter (メディアンフィルタ): A non-linear digital filtering technique, often used to remove noise from images or signals while preserving edges.

MEMS (Micro Electro Mechanical Systems) (MEMS): See “MEMS.”

Mesh Network (メッシュ型): A network topology where each node (device) connects directly to multiple other nodes, creating redundant pathways for data and improving reliability and coverage.

Min-Max Normalization (min-max正規化): A data normalization technique that rescales a feature to a fixed range, typically 0 to 1, by subtracting the minimum value and dividing by the range (max - min).

MISO (MISO): A communication mode where there are multiple inputs and a single output, referring to antenna configurations.

Mixup (Mixup): A data augmentation technique for deep learning that involves creating new training samples by linearly interpolating existing pairs of samples and their labels.

MQTT (MQ Telemetry Transport) (MQTT): A lightweight messaging protocol for small sensors and mobile devices, optimized for high-latency or unreliable networks, widely used in IoT.

MRAM (磁気抵抗メモリ): A non-volatile random-access memory technology that stores data using magnetic states, offering high speed and endurance.

MPU (Microprocessor Unit) (MPU): The central processing unit of a computer system, responsible for executing instructions and processing data. In IoT, refers to the main processing unit on a device or gateway.

MSE (Mean Squared Error) (平均二乗誤差): A common metric used to measure the average of the squares of the errors or deviations, often used to evaluate the accuracy of regression models.

NB-IoT (Narrow Band-IoT) (NB-IoT): A low-power wide-area (LPWA) technology standard published by 3GPP, designed for IoT devices that require very low power consumption and can operate on narrow frequency bands.

Network-Slicing (ネットワーク・スライシング): A network architecture concept in 5G that allows multiple virtual networks to run on top of a shared physical infrastructure, each optimized for specific services or applications (e.g., high-speed, low-latency, massive IoT).

Neural Network (ニューラルネットワーク): A computational model inspired by the structure and function of biological neural networks, used in machine learning for tasks like pattern recognition and prediction.

NoSQL (NoSQL): A class of non-relational databases that provide a mechanism for storage and retrieval of data that is modeled in means other than the tabular relations used in relational databases. Often used for big data and real-time web applications.

Numpy (NumPy): A fundamental package for scientific computing with Python, providing support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays.

OneM2M (oneM2M): A global standardization initiative for machine-to-machine (M2M) communications and the Internet of Things (IoT), specifying common service layer architecture.

Open Innovation (オープンイノベーション): A paradigm where organizations utilize external ideas and internal ideas to advance their technology or services, often involving collaboration with external partners, open-source projects, and crowd-sourcing.

OpenStack (OpenStack): A suite of open-source software tools for building and managing cloud computing platforms, offering IaaS (Infrastructure as a Service) capabilities for private and public clouds.

OpenCV (OpenCV): An open-source computer vision and machine learning software library, widely used for image processing and computer vision applications, including in IoT for visual data analysis.

OSGi (Open Services Gateway initiative) (OSGI): A set of specifications that define a modular service platform, enabling dynamic component management (installation, updates, removal) without requiring system restarts.

PaaS (Platform as a Service) (PaaS): A cloud computing service model that provides a platform allowing customers to develop, run, and manage applications without the complexity of building and maintaining the infrastructure typically associated with developing and launching an app.

PBL (Problem-Based Learning) (PBL): A student-centered pedagogy in which students learn about a subject through the experience of solving an open-ended problem.

PH Sensor (PHセンサ): A sensor used to measure the pH (acidity or alkalinity) of a solution, important in various applications including environmental monitoring and chemical processes.

Photodiode (フォトダイオード): A semiconductor device that converts light into an electrical current, used in light sensors.

Phototransistor (フォトトランジスタ): A semiconductor device that combines a photodiode and a transistor, offering higher sensitivity to light than a photodiode.

Physical Security (物理セキュリティ): Measures designed to protect physical assets and premises from unauthorized access, damage, or theft, including physical barriers, surveillance, and access controls.

PicoChip (ピコチップ): A type of integrated circuit designed for high-performance, low-power processing, often used in edge computing and signal processing.

Piezoelectric Sensor (圧電センサ): A sensor that uses the piezoelectric effect to measure changes in pressure, acceleration, temperature, or force by converting them into an electrical charge.

PLC (Power Line Communication) (PLC): A technology that uses electrical power lines to transmit data, enabling network communication over existing electrical wiring, often used in smart homes and industrial settings.

PoC (Proof of Concept) (PoC): A realization of a certain method or idea to demonstrate its feasibility, or a demonstration in principle, used to verify that a concept or theory has practical potential.

Polling Method (ポーリング方式): A data collection method where the IoT server or service platform periodically requests data from the IoT device.

Private Cloud (プライベートクラウド): A cloud computing environment dedicated to a single organization, offering enhanced control and security, either on-premises or hosted by a third-party provider.

Protocol Conversion (プロトコル変換): See “Explain the concept of ‘protocol conversion’.”

Prototyping (プロトタイピング): The process of creating a preliminary version (prototype) of a system or product to test concepts, gather feedback, and iterate on the design before full-scale development.

Publish-Subscribe (Pub/Sub) Model (パブリッシュ・サブスクライブ方式): A messaging pattern where senders (publishers) do not programmatically send messages directly to specific receivers (subscribers), but instead categorize published messages into classes without knowledge of which subscribers, if any, there may be. Subscribers express interest in one or more classes and receive messages accordingly.

PWM (Pulse Width Modulation) (PWM): A technique for controlling analog circuits using digital outputs, widely used to control the speed of DC motors or the brightness of LEDs.

PyTorch (PyTorch): An open-source machine learning framework developed by Facebook’s AI Research lab, known for its flexibility and ease of use in deep learning research and development.

Python (パイソン): A popular high-level, general-purpose programming language, widely used in data science, machine learning, and IoT development due to its extensive libraries and readability.

Q-learning (Q学習): A reinforcement learning algorithm that helps an agent learn to make decisions in an environment by evaluating the quality of actions in specific states, aiming to maximize cumulative rewards.

Raspberry Pi (ラズベリーパイ): A series of small single-board computers developed by the Raspberry Pi Foundation, widely used in IoT projects, education, and embedded systems due to their versatility and affordability.

RDB (Relational Database) (リレーショナルデータベース): A type of database that stores and provides access to data points that are related to one another. Data is organized into tables with rows and columns.

Reinforcement Learning (強化学習): A type of machine learning where an agent learns to make decisions by taking actions in an environment to maximize a cumulative reward, often used for robotic control and autonomous systems.

Relational Database (リレーショナルデータベース): See “RDB.”

Remote Control (遠隔制御): The ability to control an IoT device or system from a distant location, often via a network connection.

Replicated Data Type (レプリカ型DB): A database where data is duplicated across multiple servers or locations to improve availability, fault tolerance, and performance.

Resilience (耐障害性): The ability of a system to recover from failures and maintain functionality, even in the face of disruptions or attacks.

RFID (Radio Frequency Identification) (RFID): A technology that uses electromagnetic fields to automatically identify and track tags attached to objects.

RNN (Recurrent Neural Network) (再帰型ニューラルネットワーク): A type of neural network that processes sequential data by maintaining an internal memory, suitable for tasks like natural language processing and time-series analysis.

Robot (ロボット): An automated machine designed to perform specific tasks, often controlled by an IoT system, ranging from industrial robots to service robots in homes.

RMSE (Root Mean Squared Error) (二乗平均平方根誤差): A frequently used measure of the differences between values predicted by a model or estimator and the values observed.

ROC Curve (ROC曲線): A graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied, commonly used to evaluate machine learning models.

RS232C (RS232C): A standard for serial communication transmission of data.

RS485 (RS485): A standard for serial communication that enables data transmission over longer distances and in noisy environments.

SaaS (Software as a Service) (SaaS): A cloud computing service model where software applications are hosted by a vendor and made available to customers over the Internet.

Sampling Frequency (サンプリング周波数): The number of samples per unit time taken from a continuous signal to make a discrete signal, influencing the accuracy of data representation.

SD-WAN (Software-Defined Wide Area Network) (SD-WAN): A virtual WAN architecture that allows enterprises to leverage any combination of transport services, including MPLS, LTE, and broadband internet services, to securely connect users to applications.

Secure Boot (セキュアブート): A security mechanism that ensures only trusted software (signed by an approved authority) can be loaded during the boot process of a device, preventing malicious software from taking control.

Security Policy (セキュリティポリシー): A set of rules and guidelines that define how an organization protects its information assets, outlining acceptable use, access controls, and incident response procedures.

Self-Certification (自己適合宣言): A process where a product vendor declares that their product meets certain technical standards or security requirements, without external verification.

Semiconductor Sensor (半導体センサ): A sensor that uses the properties of semiconductor materials to detect physical quantities (e.g., light, temperature, pressure) and convert them into electrical signals.

Sensor (センサ): A device that detects and responds to some type of input from the physical environment (e.g., light, heat, motion, pressure) and converts it into a signal that can be read by other electronic devices.

Serial Communication (シリアル通信): A method of data transmission where data is sent one bit at a time over a single channel, often used for communication between microcontrollers and other peripherals.

SI Units (国際単位系) (SI単位): The international system of units of measurement, including meters for length, kilograms for mass, and seconds for time.

Sigfox (シグフォックス): A low-power wide-area network (LPWAN) connectivity solution designed for IoT devices requiring minimal bandwidth and long battery life.

Smart Factory (スマート工場): A highly digitized and connected manufacturing facility that uses IoT, AI, and automation to optimize production processes, improve efficiency, and enable real-time decision-making.

Smart Meter (スマートメータ): An electronic device that records consumption of electric energy or water and communicates that information to the supplier for monitoring and billing.

Smartphone Gateway (スマートフォンゲートウェイ): A smartphone acting as an IoT gateway, leveraging its connectivity and processing power to collect data from nearby IoT devices and relay it to the cloud.

Solana (ソラナ): A high-performance blockchain platform. (This appears to be an outlier term and not directly related to IoT technology in the provided text, but it is in the glossary).

Solvent Extraction (溶媒抽出): A method used to separate compounds based on their differential solubility in two immiscible liquids. (This also appears to be an outlier term).

SoS (System of Systems) (SoS): A collection of independent, operational systems that are integrated to deliver a new capability or performance that is not possible by individual systems alone.

Spatial Intelligence System (空間知能化システム): A system that enables objects and robots to perceive their physical surroundings and adjust their behavior accordingly, often used for home automation and elder care.

SPI (Serial Peripheral Interface) (SPI): A synchronous serial communication interface specification used for short-distance communication, primarily in embedded systems.

Standardization (標準化): The process of developing and implementing technical standards, which are agreed-upon protocols, procedures, or specifications, to ensure interoperability, quality, and consistency in products and services.

Star Network (スター型): A network topology in which each node (device) is individually connected to a central hub, making it easy to add or remove devices but creating a single point of failure.

Statistical Analysis (統計解析): The process of collecting, analyzing, interpreting, presenting, and organizing data to identify patterns, relationships, and trends.

Stepping Motor (ステッピングモータ): A brushless DC electric motor that divides a full rotation into a number of equal steps, allowing precise control of position.

Streaming Processing (ストリーミング処理): See “Batch Processing.”

Strain Sensor (ひずみセンサ): A sensor that measures the deformation or strain of an object, often used in load cells and pressure sensors.

Stuxnet (スタックスネット): A malicious computer worm, infamous for its attack on Iran’s nuclear program, highlighting the vulnerabilities of industrial control systems to cyberattacks.

Supervised Learning (教師あり学習): See “Machine Learning.”

SVM (Support Vector Machine) (SVM): A supervised machine learning model that uses classification algorithms for two-group classification problems, widely used for pattern recognition.

TCPIP (TCP/IP): Transmission Control Protocol/Internet Protocol, the foundational set of communication protocols for the Internet, widely used for data transfer in computer networks.

Telework (テレワーク): Working remotely, typically from home, using information and communication technologies.

Temperature Sensor (温度センサ): A device that measures temperature, converting thermal energy into an electrical signal, commonly used in various IoT applications.

TensorFlow (テンソルフロー): An open-source machine learning framework developed by Google, widely used for deep learning and neural network development.

Thin Client (シンクライアント): A lightweight computer that relies heavily on a server to perform most of its processing.

Time Series Data (時系列データ): Data points indexed in time order, crucial for analyzing trends, forecasting, and detecting anomalies over time.

TLS (Transport Layer Security) (TLS): A cryptographic protocol designed to provide communication security over a computer network, widely used for secure web browsing (HTTPS).

Topic (トピック): In a publish-subscribe messaging model like MQTT, a string that acts as a subject or category to which messages are published and from which subscribers receive messages.

TransferJet (トランスファージェット): A close-proximity wireless transfer technology for high-speed data exchange between devices over very short distances.

Transistor (トランジスタ): A semiconductor device used to amplify or switch electronic signals and electrical power.

Tree Network (ツリー型): A network topology that combines aspects of bus and star topologies, with multiple star networks connected via a central bus.

Two-Way Communication (双方向通信方式): A communication method where both parties can send and receive information simultaneously, enabling interactive control and feedback.

Ultrasonic Sensor (超音波センサ): A sensor that emits ultrasonic waves and measures the time it takes for them to reflect back, used for distance measurement, object detection, and flow measurement.

UART (Universal Asynchronous Receiver/Transmitter) (UART): A hardware device that translates data between parallel and serial forms, commonly used for serial communication between microcontrollers and other devices.

Unsupervised Learning (教師なし学習): See “Machine Learning.”

UWB (Ultra-Wideband) (UWB): A radio technology for short-range, high-bandwidth communications, enabling high-precision localization and data transfer.

V2X (Vehicle-to-Everything) (V2X): A communication system that allows vehicles to exchange information with their surroundings, including other vehicles (V2V), infrastructure (V2I), pedestrians (V2P), and the network (V2N).

VAE (Variational AutoEncoder) (変分オートエンコーダ): A generative model that learns a probabilistic mapping from input data to a latent space, used for generating new data samples.

WAN (Wide Area Network) (広域通信網): A telecommunications network that extends over a large geographic area, such as a country or continent, often connecting multiple local area networks (LANs).

Waterfall Model (ウォーターフォール型開発): A traditional, linear software development methodology where each phase of the development lifecycle (e.g., requirements, design, implementation, testing) must be completed before the next phase can begin.

Wearable Biosensor (ウェアラブル生体センサ): Sensors integrated into wearable devices that monitor physiological parameters (e.g., heart rate, body temperature, acceleration) for health and fitness tracking.

Web Services (Webサービス): Software systems designed to support interoperable machine-to-machine interaction over a network.

WebSocket (WebSocket): A computer communications protocol that provides full-duplex communication channels over a single TCP connection, enabling real-time interactive communication between a client and a server.

Wi-Fi (Wi-Fi): A wireless networking technology that allows devices to connect to a local area network (LAN) and the internet using radio waves.

Wi-SUN (Wi-SUN): A wireless communication standard for IoT that uses the IEEE 802.15.4g standard, optimized for wide-area communication with low power consumption, often used for smart meters and home energy management systems.

WIMAX (Worldwide Interoperability for Microwave Access) (WiMAX): A family of wireless broadband communication standards based on the IEEE 802.16 standard, offering long-range wireless data over various modes.

XML (Extensible Markup Language) (XML): A markup language that defines a set of rules for encoding documents in a format that is both human-readable and machine-readable, often used for data interchange.

X-ray (X線): A form of electromagnetic radiation, used in various imaging techniques. (This also appears to be an outlier term).

Z-Wave (Z-Wave): A wireless communication protocol primarily used for home automation, providing a mesh network for smart home devices.

Zero Trust (ゼロトラスト): See “Zero Trust.”

ZigBee (ZigBee): A low-cost, low-power, wireless mesh network standard based on IEEE 802.15.4, often used for home automation, smart lighting, and industrial applications.

IoT技术学习指南

I. 测验(10道简答题)

1. IoT网关在IoT系统中的主要作用是什么,特别是在数据流和处理位置方面?
IoT网关从IoT设备收集数据,执行初步处理和过滤。它们是IoT设备与IoT服务器/云之间通信的重要媒介,通常承担边缘计算任务,以减少数据传输量和延迟。

2. 解释IoT和制造业背景下”数据驱动系统”(CPS:网络物理系统)的核心概念。
数据驱动系统,特别是网络物理系统(CPS),通过传感器和执行器从物理世界收集数据,在网络世界中分析这些数据,将物理和网络空间集成在一起。然后将分析后的信息反馈到物理世界,创造新价值或优化操作,例如在”工业4.0”中利用数字孪生进行生产模拟。

3. 在IoT数据分析背景下,”数据增强”的目的是什么?
数据增强用于在机器学习(尤其是深度学习)中增加训练数据的数量,特别是在没有足够数据时。它涉及转换现有数据(例如调整图像大小、旋转、添加噪声)来创建新的、多样化的样本,从而提高分析模型的稳健性和准确性。

4. 描述IoT数据处理中批处理和流处理的主要区别。
批处理涉及在一段时间内收集和存储大量数据,然后一次性处理,适用于非实时分析。而流处理则在数据到达时进行处理,提供近实时的洞察并能够立即响应,对于需要低延迟的应用至关重要。

5. 与仅依靠云计算进行数据处理相比,在IoT系统中使用边缘计算的主要优势是什么?
边缘计算在更靠近数据生成源的地方处理数据,减少延迟和网络带宽消耗。这对于自动驾驶或机器人控制等实时应用特别有益,因为这些应用需要基于本地数据立即做出决策。

6. 解释IoT网关中”协议转换”的概念及其必要性。
协议转换允许使用各种通信协议的不同IoT设备和网络之间相互通信,并与IoT服务器/云通信。IoT网关充当中介,在这些不同协议之间进行转换,确保整个IoT系统中数据交换的无缝性。

7. MEMS(微机电系统)在IoT设备中的主要功能是什么?
MEMS是结合机械和电气组件的微型集成设备,通常在IoT设备中用作传感器或执行器。它们对于小型化和集成至关重要,使得能够开发紧凑、低功耗的IoT设备,如智能手机中的压力传感器或加速度计。

8. 描述文本中提到的机器学习的两种主要方法:监督学习和无监督学习。
监督学习涉及使用标记数据(输入数据与正确输出/目标数据配对)训练模型来学习映射函数,用于分类或回归等任务。相反,无监督学习使用未标记数据查找隐藏模式或结构,如聚类或异常检测。

9. 在IoT区域网络中使用”网状”网络拓扑的主要优势是什么?
网状网络提供高可靠性和容错性,因为数据可以在节点之间通过多条路径传输。如果一条路径失败,可以使用替代路由。这种冗余性还允许更广的覆盖范围和更强大的通信,尽管可能增加网络复杂性和功耗。

10. 在IoT安全的背景下,什么是”零信任”,为什么它越来越重要?
零信任是一种安全模型,假设网络内外的任何用户或设备默认都不应被信任。相反,每次访问尝试都要经过验证、认证和授权才能访问资源。由于IoT中连接设备的数量和多样性以及潜在的新攻击向量,这种方法在IoT中越来越重要。

II. 测验答案要点

1. IoT网关的作用: IoT网关收集并对来自IoT设备的数据进行初始处理(过滤、时序调整)。它们作为IoT设备和IoT服务器/云之间的桥梁,通过在接近数据源的地方处理数据来实现边缘计算,这对于最小化延迟和网络负载至关重要。

2. 数据驱动系统(CPS): CPS集成了物理和网络领域。来自物理传感器的数据在网络空间中进行分析,得出的洞察反馈到控制物理执行器。这创建了一个连续循环,允许优化和价值创造,例如通过称为数字孪生的虚拟表示在”工业4.0”中提高制造效率。

3. 数据增强: 这种技术通过人工扩展数据集来解决数据稀缺问题。它修改现有数据(例如图像变换如旋转或缩放,或向传感器数据添加噪声)以生成新的、多样化的样本。这有助于训练更稳健的机器学习模型,特别是深度学习模型,通过防止过拟合和改善泛化来实现。

4. 批处理与流处理: 批处理处理一段时间内积累的数据,适用于非实时分析任务,不需要立即结果。相反,流处理在数据到达时连续处理数据,提供实时洞察并实现立即反应,这对于时间敏感的IoT应用至关重要。

5. 边缘计算优势: 边缘计算通过在更接近数据源的地方执行计算来减少对集中式云处理的依赖。这显著降低了网络延迟,减少了带宽使用,并增强了实时响应能力,使其成为需要即时决策或在连接有限环境中操作的应用的理想选择。

6. IoT网关中的协议转换: IoT网关执行协议转换,以实现使用不同通信标准(例如蓝牙、ZigBee、Wi-Fi、蜂窝)的设备和网络之间的互操作性。这种转换功能确保来自各种IoT设备的数据可以被中央IoT服务器或云理解和处理,促进系统的凝聚性。

7. MEMS功能: MEMS(微机电系统)由于能够在微尺度上集成机械和电气功能,对IoT设备至关重要。它们通常用作小型化传感器(例如压力、加速度、陀螺仪)和执行器,有助于现代IoT设备的紧凑尺寸、低功耗和多功能能力。

8. 监督学习与无监督学习: 监督学习在标记数据集上训练模型,意味着每个输入都有相应的正确输出,通过学习映射来实现分类和回归等任务。然而,无监督学习分析未标记数据以发现数据本身内在的模式、结构或分组,通常用于聚类或异常检测。

9. 网状网络优势: IoT中的网状网络拓扑提供增强的可靠性和稳健性,因为每个设备可以连接到多个其他设备,为数据传输创建冗余路径。这种分散式结构改善了容错性,扩展了网络覆盖范围,并可以通过分布负载来处理增加的数据流量。

10. IoT安全中的零信任: 零信任是一种安全模型,其中没有实体(用户、设备、应用程序)本质上是可信的,无论其相对于网络边界的位置如何。所有访问请求都经过严格的身份验证和授权,最小化未经授权访问和攻击者横向移动的风险,这对于IoT部署的分布式和多样化特性至关重要。

III. 论述题格式问题(未提供答案)

  1. 讨论IoT从早期概念到当前状态的演变,突出关键技术进步(例如处理能力、通信技术、AI集成),这些进步使其广泛采用和创造新价值成为可能。

  2. 比较和对比云计算和边缘计算在IoT系统架构中的作用和优势。提供具体的IoT应用示例,其中一种方法可能比另一种更有益,或者混合方法是最优的。

  3. 分析数据收集、处理和分析技术在实现IoT全部潜力中的重要性。详细说明不同的数据处理方法(例如批处理、流处理、CEP)和数据分析技术(例如统计分析、机器学习、深度学习)如何有助于提取有价值的洞察并实现数据驱动的行动。

  4. 检查IoT中使用的各种无线通信技术(例如蓝牙、Wi-SUN、LAN、5G),概述它们的特性、典型应用,以及在特定IoT部署中选择一种技术而非另一种技术所涉及的权衡。考虑范围、功耗、数据速率和网络拓扑等因素。

  5. 信息安全是IoT系统开发和运营中的关键关注点。讨论IoT中普遍存在的主要安全威胁和漏洞,并描述可以实施的各种对策和技术(例如身份验证、加密、防火墙、恶意软件保护、零信任)来缓解这些风险,确保IoT系统的安全性和可靠性。

IV. 关键术语词汇表

执行器(アクチュエータ): 将电信号转换为物理动作的设备,如运动、光或热。在IoT中,执行器用于根据从传感器接收的数据或系统命令控制物理设备。

敏捷开发(アジャイル型開発): 以迭代开发周期、快速原型制作和灵活适应变化需求为特征的软件开发方法,强调协作和持续反馈。

Ambient(アンビエント): 用于IoT数据可视化和存储的Web服务,提供简单的用户注册和免费使用,支持Python库。

模拟-数字(A/D)转换(A/D変換): 将模拟电信号(如许多传感器的信号)转换为计算机可处理数字数据的过程。

Apache Hadoop(Apache Hadoop): 用于在计算机集群上分布式存储和处理超大数据集的开源软件框架。通常用于大数据的批处理。

Arduino(アルドゥイーノ): 基于易用硬件和软件的开源电子平台,在构建交互对象和原型(尤其是IoT)方面很受欢迎。

身份验证(認証): 验证试图访问IoT环境中资源的用户、设备或系统身份的过程。

自动编码器(オートエンコーダ): 用于无监督学习的神经网络类型,专门用于数据压缩或降维。它学习重构其输入,通常用于特征提取或异常检测。

批处理(バッチ処理): 一种数据处理方法,其中大量数据被收集并在单个操作中一起处理,通常在预定间隔进行,而不是连续进行。

贝叶斯网络(ベイジアンネットワーク): 通过有向无环图表示一组变量及其条件依赖关系的概率图形模型,用于在不确定性下进行推理和决策制定。

BCP(业务连续性计划)(BCP): 旨在确保业务运营在重大中断或灾难期间和之后能够继续的计划,包括数据备份、系统恢复和替代工作安排的策略。

大数据(ビッグデータ): 可以通过计算分析以揭示模式、趋势和关联的极大数据集,特别是与人类行为和交互相关的。

蓝牙(ブルートゥース): 用于在短距离内在固定和移动设备之间交换数据的短程无线技术标准,常见于IoT个人区域网络。

代理(ブローカー): 在MQTT等消息系统中,接收来自发布者的消息并根据主题将其分发给适当订阅者的中央服务器。

Caffe(カフェ): 由伯克利视觉和学习中心开发的深度学习框架,以其在图像识别任务中的速度和效率而闻名。

校准(キャリブレーション): 调整传感器或设备以确保其测量准确并与已知标准一致的过程。

CC许可证(创意共享许可证)(CCライセンス): 允许创作者传达他们保留哪些权利以及为受益人或其他创作者放弃哪些权利的公共版权许可证。

CCD(电荷耦合器件)(CCD): 将光转换为电荷的半导体器件,常用作数码相机和其他成像应用中的图像传感器。

CEP(复杂事件处理)(CEP): 实时处理来自多个源的数据以识别模式或关系的技术,基于复杂事件能够立即采取行动。

分类(分類): 基于从训练数据中学习的模式将数据分类到预定义类别的机器学习任务。

云计算(クラウドコンピューティング): 通过互联网(”云”)提供按需计算服务的模型,包括服务器、存储、数据库、网络、软件、分析和智能。

CMOS(互补金属氧化物半导体)(CMOS): 用于集成电路(包括图像传感器)的半导体技术类型,以低功耗著称。

CoAP(受约束应用协议)(CoAP): 专为IoT中受约束节点和受约束网络使用而设计的专业网络传输协议,设计用于效率和低开销。

冷数据(コールドデータ): 不经常访问或使用的数据,通常存储在成本效益高的长期存储解决方案中。

卷积神经网络(CNN)(畳み込みニューラルネットワーク): 主要用于分析视觉图像的深度学习神经网络类型,在图像识别和处理任务中高度有效。

CPS(网络物理系统)(サイバーフィジカルシステム): 见”数据驱动系统”。

CSV(逗号分隔值)(CSV): 用于存储表格数据的简单文件格式,文件的每一行都是数据记录,每个记录由一个或多个字段组成,用逗号分隔。

数据增强(データ水増し): 见”增强”。

数据清洗(データクレンジング): 识别和纠正或删除数据集中不正确、不完整或不相关数据的过程。

数据预处理(データ前処理): 将原始数据转换为清洁、有组织且适合分析的格式所采取的步骤,通常涉及清洗、转换和标准化。

数据转换/集成(データ変換・統合): 将数据从一种格式或结构转换为另一种格式或结构,并将来自不同源的数据合并为统一视图的过程。

深度学习(深層学習): 机器学习的一个子集,使用多层神经网络(深度神经网络)从大量数据中学习复杂模式,通常在图像和语音识别等任务中实现高准确性。

数字签名(デジタル署名): 用于验证数字消息或文档真实性和完整性的加密技术,确保发送者是他们声称的身份,消息未被更改。

数字化转型(DX)(デジタルトランスフォーメーション): 采用数字技术来转变业务流程、文化和客户体验以满足不断变化的业务和市场需求的过程。

解释性要求(説明可能性): 在AI和机器学习中,能够解释模型如何得出特定预测或决策的能力,对于信任和问责制至关重要,特别是在敏感应用中。

分布式文件系统(HDFS)(分散ファイルシステム): 设计用于在多台机器上存储非常大文件的分布式、可扩展和便携式文件系统,是Hadoop生态系统的一部分。

DMZ(非军事化区域)(閉域網): 包含并暴露组织面向外部服务给不可信、更大网络(通常是互联网)的物理或逻辑子网络。

DNA传感器(DNAセンサ): 检测特定DNA序列的生物传感器,通常用于医学诊断、环境监测和食品安全。

DDoS攻击(分布式拒绝服务攻击)(DDoS攻撃): 通过来自多个受损计算机系统的互联网流量洪水压倒目标服务器、服务或网络的正常流量的恶意企图。

无人机(ドローン): 可远程控制或自主飞行的无人驾驶飞行器(UAV),在IoT中用于监控、交付和数据收集等各种应用。

Dust Networks(Dust Networks): 专业从事工业IoT应用的低功耗无线网状网络技术的公司。

DX(数字化转型)(DX): 见”数字化转型”。

边缘AI(エッジAI): 直接在边缘设备本身(例如传感器、摄像头、IoT网关)而不是集中式云中执行的人工智能处理,实现实时决策制定和减少延迟。

边缘计算(エッジコンピューティング): 将计算和数据存储更接近数据源的分布式计算范式,改善响应时间并节省带宽。

Edgecross联盟(Edgecross コンソーシアム): 专注于促进边缘计算和制造业中IT与OT(运营技术)集成的日本联盟。

心电图(ECG)(心電計): 测量心跳电活动的测试,用于可穿戴生物传感器中监测心脏健康。

EnOcean(エンオーシャン): 专注于超低功耗的无线标准,通常利用能量收集,使其适用于无电池IoT设备。

能量收集(エネルギーハーベスティング): 从环境源(例如太阳能、热能、振动、无线电波)捕获和存储少量能量以为低功耗电子设备(如IoT传感器)供电的过程。

EPFC(边缘平台联盟)(EPFC): 专注于连接网络和物理空间的边缘平台开发的联盟。

以太网(イーサネット): 局域网(LAN)中常用的有线计算机网络技术系列。

FPGA(现场可编程门阵列)(FPGA): 设计为在制造后由客户或设计师配置的集成电路,允许灵活的硬件加速和特定计算任务的自定义逻辑,包括边缘AI。

FTP(文件传输协议)(FTP): 用于在计算机网络上的客户端和服务器之间传输计算机文件的标准网络协议。

GAN(生成对抗网络)(敵対的生成ネットワーク): 由两个神经网络组成的机器学习框架类别,一个生成数据,另一个区分真实和虚假数据,用于生成AI如图像创建。

网关(ゲートウェイ): 连接不同网络和协议的设备,作为IoT设备和云之间的中介,执行数据聚合、协议转换和本地处理等功能。

生成AI(生成AI): 一种人工智能类型,可以通过从现有数据学习来创建新内容,如文本、图像、音频和视频。

GPIO(通用输入/输出)(GPIO): 集成电路上的通用引脚,其行为(输入或输出)可以在运行时由用户控制。

GNSS(全球导航卫星系统)(GNSS): 提供自主地理空间定位的卫星导航系统的通用术语,包括GPS。

Grad-CAM(Grad-CAM): 深度学习中用于可视化图像中与卷积神经网络决策最相关部分的技术,为图像识别模型提供可解释性。

图数据库(グラフ型DB): 使用图结构进行语义查询的NoSQL数据库,使用节点、边和属性来表示和存储数据。适用于关系(例如社交网络)。

HBase(HBase): 基于Google的Bigtable建模的开源、非关系型分布式数据库,是Hadoop生态系统的一部分,适用于大数据集。

HDFS(Hadoop分布式文件系统)(HDFS): 见”分布式文件系统”。

HEMS(家庭能源管理系统)(HEMS): 监控和管理家庭能源消耗的系统,优化各种设备的能源使用。

直方图(ヒストグラム): 数值数据分布的图形表示,通常用于统计分析。

热数据(ホットデータ): 经常访问或积极使用的数据,通常存储在高性能存储中以便快速检索。

HTTP(超文本传输协议)(HTTP): 万维网数据通信的基础,用于Web服务器和客户端之间的通信。

混合云(ハイブリッドクラウド): 使用本地、私有云和公有云服务混合的云计算环境,在平台之间进行编排。

IaaS(基础设施即服务)(IaaS): 云计算服务模型,提供商通过互联网提供虚拟化计算资源,如虚拟机、存储和网络。

I2C(集成电路间)(I2C): 由飞利浦半导体开发的双线串行通信总线接口,用于连接低速设备,如微控制器、EEPROM、A/D转换器和I/O接口。

IC(集成电路)卡(ICチップ認証): 使用集成电路芯片进行身份验证的智能卡,通常用于安全交易或访问控制。

IEEE802.11(IEEE802.11): 一套媒体访问控制(MAC)和物理层(PHY)规范,用于在2.4、5和60 GHz频段实现无线局域网(WLAN)计算机通信。

IEEE802.15.4(IEEE802.15.4): 指定低速率无线个人区域网络(LR-WPAN)的物理层和媒体访问控制的标准,通常用作ZigBee和Wi-SUN的基础。

IFTTT(イフトット): “If This Then That”,基于Web的服务,允许用户创建称为”小程序”的简单条件语句链,以自动化各种在线任务并连接不同的服务和设备,包括IoT。

图像传感器(画像センサ): 将光学图像转换为电子信号的设备,如CCD或CMOS传感器,在IoT中用于视觉监控和图像识别。

工业4.0(インダストリー4.0): 第四次工业革命,以制造业数字化和网络物理系统、IoT和AI的集成为特征,创建智能工厂。

入侵检测系统(IDS)(侵入検知システム): 监控网络流量或系统活动以检测恶意活动或政策违规并生成警报的安全技术。

IoT区域网络(IoTエリアネットワーク): 专为有限地理区域内的IoT设备设计的网络,通常使用短程无线通信技术。

IoT设备(IoTデバイス): 嵌入传感器、软件和其他技术的物理对象,目的是通过互联网与其他设备和系统连接和交换数据。

IoT网关(IoTゲートウェイ): 见”网关”。

IoT平台(IoTプラットフォーム): 基于云或本地的服务,提供管理IoT设备、收集和处理数据以及启用应用程序的工具和功能。

IoT服务器(IoTサーバ): IoT系统中的中央组件,通常位于云中,负责接收、存储、分析和管理来自IoT设备的数据,并发出控制命令。

IPA(日本信息技术推进机构)(IPA): 推进IT和网络安全(包括IoT安全指南)的日本政府附属组织。

ISMS(信息安全管理系统)(情報セキュリティマネジメントシステム): 管理敏感公司信息以保持其安全的系统方法,包括政策、流程和技术。

ISM频段(ISMバンド): 工业、科学和医疗无线电频段,国际上保留用于除电信以外的工业、科学和医疗目的的射频(RF)能量使用。许多IoT设备在这些未授权频段中运行。

ISDN(综合业务数字网)(ISDN): 通过公共交换电话网络的传统电路同时数字传输语音、视频、数据和其他网络服务的通信标准集。

JSON(JavaScript对象表示法)(JSON): 轻量级数据交换格式,常用于服务器和Web应用程序之间传输数据,由于其简洁性在IoT中越来越多地使用。

Julia(ジュリア): 用于技术计算的高级、高性能、动态编程语言,适用于数据科学和机器学习。

Keras(ケラス): 用Python编写的开源神经网络库,旨在实现深度神经网络的快速实验。

键值类型(キーバリュー型): 简单的NoSQL数据库模型,将数据存储为键值对的集合,其中键作为其对应值的唯一标识符。

LIME(本地可解释模型无关解释)(LIME): 通过本地使用可解释模型近似任何机器学习模型的预测来解释的技术。

线性回归(線形回帰): 通过将线性方程拟合到观察数据来建模因变量与一个或多个自变量之间关系的统计方法。

LLM(大语言模型)(LLM): 在大量文本数据上训练的人工智能模型类型,能够理解和生成类似人类的语言,通常用于生成AI应用。

本地5G(ローカル5G): 企业或地方政府为其特定需求部署的私有5G网络,与公共网络相比提供高可靠性、低延迟和增强安全性。

长轮询(ロングポーリング方式): 客户端保持与服务器的连接打开直到新数据可用或发生超时的通信技术,与传统轮询相比减少轮询频率并改善实时更新。

LoRaWAN(LoRaWAN): 低功耗广域网(LPWAN)规范,用于区域、国家或全球网络中的无线电池操作物联网设备,设计用于低功耗、远程通信。

LPWA(低功耗广域)(LPWA): 专为低功耗、远程通信设计的无线通信技术类别,通常用于不频繁传输少量数据的IoT设备。

LTE(长期演进)(LTE): 基于GSM/EDGE和UMTS/HSPA网络技术的移动设备和数据终端无线宽带通信标准,通常扩展到IoT(例如LTE-M)。

LTE-M(LTE-M): 基于LTE的LPWA技术类型,专为需要比其他LPWA技术更高带宽的IoT设备设计,同时仍保持低功耗。

LwM2M(轻量级M2M)(LwM2M): IoT设备的设备管理协议,针对受约束的设备和网络进行优化,提供设备管理和数据报告功能。

机器学习(機械学習): 人工智能领域,使用统计技术使计算机系统能够从数据中”学习”,而无需明确编程,执行预测、分类和模式识别等任务。

Mahout(Mahout): Apache开源项目,提供可扩展机器学习算法的实现,通常与Hadoop结合使用。

MEC(多接入边缘计算)(マルチアクセス・エッジ・コンピューティング): 在网络边缘(更接近移动用户和IoT设备)启用云计算能力和IT服务环境的网络架构概念。

中值滤波器(メディアンフィルタ): 非线性数字滤波技术,通常用于从图像或信号中去除噪声,同时保持边缘。

MEMS(微机电系统)(MEMS): 见”MEMS”。

网状网络(メッシュ型): 每个节点(设备)直接连接到多个其他节点的网络拓扑,为数据创建冗余路径并提高可靠性和覆盖范围。

最小-最大标准化(min-max正規化): 数据标准化技术,通过减去最小值并除以范围(最大值-最小值)将特征重新缩放到固定范围(通常为0到1)。

MISO(MISO): 具有多个输入和单个输出的通信模式,指天线配置。

Mixup(Mixup): 深度学习的数据增强技术,涉及通过线性插值现有样本对及其标签来创建新的训练样本。

MQTT(MQ遥测传输)(MQTT): 为小型传感器和移动设备优化的轻量级消息协议,针对高延迟或不可靠网络进行优化,在IoT中广泛使用。

MRAM(磁阻存储器)(磁気抵抗メモリ): 使用磁状态存储数据的非易失性随机存取存储器技术,提供高速度和耐久性。

MPU(微处理器单元)(MPU): 计算机系统的中央处理单元,负责执行指令和处理数据。在IoT中,指设备或网关上的主处理单元。

MSE(均方误差)(平均二乗誤差): 用于测量误差或偏差平方平均值的常用指标,通常用于评估回归模型的准确性。

NB-IoT(窄带物联网)(NB-IoT): 3GPP发布的低功耗广域(LPWA)技术标准,专为需要极低功耗并可在窄频段运行的IoT设备设计。

网络切片(ネットワーク・スライシング): 5G中的网络架构概念,允许多个虚拟网络在共享物理基础设施上运行,每个都针对特定服务或应用(例如高速、低延迟、大规模IoT)进行优化。

神经网络(ニューラルネットワーク): 受生物神经网络结构和功能启发的计算模型,用于机器学习中的模式识别和预测等任务。

NoSQL(NoSQL): 非关系数据库类别,提供存储和检索数据的机制,这些数据的建模方式不同于关系数据库中使用的表格关系。通常用于大数据和实时Web应用。

Numpy(NumPy): Python科学计算的基础包,为大型多维数组和矩阵提供支持,以及大量高级数学函数来操作这些数组。

OneM2M(oneM2M): 机器对机器(M2M)通信和物联网(IoT)的全球标准化倡议,指定通用服务层架构。

开放创新(オープンイノベーション): 组织利用外部思想和内部思想来推进其技术或服务的范式,通常涉及与外部合作伙伴、开源项目和众包的协作。

OpenStack(OpenStack): 用于构建和管理云计算平台的开源软件工具套件,为私有云和公有云提供IaaS(基础设施即服务)功能。

OpenCV(OpenCV): 开源计算机视觉和机器学习软件库,广泛用于图像处理和计算机视觉应用,包括IoT中的视觉数据分析。

OSGi(开放服务网关倡议)(OSGI): 定义模块化服务平台的规范集,支持动态组件管理(安装、更新、删除),无需系统重启。

PaaS(平台即服务)(PaaS): 云计算服务模型,提供平台允许客户开发、运行和管理应用程序,而无需构建和维护通常与开发和启动应用程序相关的基础设施的复杂性。

PBL(基于问题的学习)(PBL): 以学生为中心的教学法,学生通过解决开放性问题的经验来学习某个主题。

PH传感器(PHセンサ): 用于测量溶液pH(酸性或碱性)的传感器,在各种应用中很重要,包括环境监测和化学过程。

光电二极管(フォトダイオード): 将光转换为电流的半导体器件,用于光传感器。

光电晶体管(フォトトランジスタ): 结合光电二极管和晶体管的半导体器件,比光电二极管对光具有更高的灵敏度。

物理安全(物理セキュリティ): 旨在保护物理资产和场所免受未经授权访问、损坏或盗窃的措施,包括物理屏障、监控和访问控制。

PicoChip(ピコチップ): 专为高性能、低功耗处理设计的集成电路类型,通常用于边缘计算和信号处理。

压电传感器(圧電センサ): 使用压电效应通过将压力、加速度、温度或力的变化转换为电荷来测量的传感器。

PLC(电力线通信)(PLC): 使用电力线传输数据的技术,在现有电气线路上实现网络通信,通常用于智能家居和工业环境。

PoC(概念验证)(PoC): 实现某种方法或想法以证明其可行性,或原理演示,用于验证概念或理论是否具有实际潜力。

轮询方法(ポーリング方式): IoT服务器或服务平台定期从IoT设备请求数据的数据收集方法。

私有云(プライベートクラウド): 专用于单个组织的云计算环境,提供增强的控制和安全性,无论是本地还是由第三方提供商托管。

协议转换(プロトコル変換): 见”解释’协议转换’的概念”。

原型制作(プロトタイピング): 创建系统或产品的初步版本(原型)以测试概念、收集反馈并在全面开发之前迭代设计的过程。

发布-订阅(Pub/Sub)模型(パブリッシュ・サブスクライブ方式): 消息模式,发送者(发布者)不直接向特定接收者(订阅者)发送消息,而是将发布的消息分类为类别,而不知道是否有订阅者。订阅者表达对一个或多个类别的兴趣并相应地接收消息。

PWM(脉宽调制)(PWM): 使用数字输出控制模拟电路的技术,广泛用于控制直流电机速度或LED亮度。

PyTorch(PyTorch): Facebook AI研究实验室开发的开源机器学习框架,以其在深度学习研究和开发中的灵活性和易用性而闻名。

Python(パイソン): 流行的高级、通用编程语言,由于其广泛的库和可读性,在数据科学、机器学习和IoT开发中广泛使用。

Q学习(Q学習): 强化学习算法,通过评估特定状态下动作的质量来帮助代理学习在环境中做出决策,旨在最大化累积奖励。

树莓派(ラズベリーパイ): 树莓派基金会开发的一系列小型单板计算机,由于其多功能性和可负担性,在IoT项目、教育和嵌入式系统中广泛使用。

RDB(关系数据库)(リレーショナルデータベース): 存储并提供对彼此相关的数据点的访问的数据库类型。数据组织成具有行和列的表。

强化学习(強化学習): 一种机器学习类型,代理通过在环境中采取行动来学习做出决策,以最大化累积奖励,通常用于机器人控制和自主系统。

关系数据库(リレーショナルデータベース): 见”RDB”。

远程控制(遠隔制御): 从远程位置控制IoT设备或系统的能力,通常通过网络连接。

复制数据类型(レプリカ型DB): 数据在多个服务器或位置复制以提高可用性、容错性和性能的数据库。

弹性(耐障害性): 系统从故障中恢复并保持功能的能力,即使面临中断或攻击。

RFID(射频识别)(RFID): 使用电磁场自动识别和跟踪附着在物体上的标签的技术。

RNN(循环神经网络)(再帰型ニューラルネットワーク): 通过维护内部记忆处理顺序数据的神经网络类型,适用于自然语言处理和时间序列分析等任务。

机器人(ロボット): 设计用于执行特定任务的自动化机器,通常由IoT系统控制,从工业机器人到家庭服务机器人。

RMSE(均方根误差)(二乗平均平方根誤差): 经常用于测量模型或估计器预测值与观察值之间差异的度量。

ROC曲线(ROC曲線): 图形图表,说明二进制分类器系统在其辨别阈值变化时的诊断能力,常用于评估机器学习模型。

RS232C(RS232C): 串行通信数据传输标准。

RS485(RS485): 串行通信标准,能够在更长距离和嘈杂环境中进行数据传输。

SaaS(软件即服务)(SaaS): 云计算服务模型,软件应用程序由供应商托管并通过互联网提供给客户。

采样频率(サンプリング周波数): 从连续信号中获取每单位时间样本数以制作离散信号,影响数据表示的准确性。

SD-WAN(软件定义广域网)(SD-WAN): 虚拟WAN架构,允许企业利用任何传输服务组合,包括MPLS、LTE和宽带互联网服务,安全地连接用户到应用程序。

安全启动(セキュアブート): 安全机制,确保在设备启动过程中只能加载受信任的软件(由批准的授权机构签名),防止恶意软件控制。

安全策略(セキュリティポリシー): 定义组织如何保护其信息资产的规则和指导方针集,概述可接受的使用、访问控制和事件响应程序。

自我认证(自己適合宣言): 产品供应商声明其产品符合某些技术标准或安全要求的过程,无需外部验证。

半导体传感器(半導体センサ): 使用半导体材料特性检测物理量(例如光、温度、压力)并将其转换为电信号的传感器。

传感器(センサ): 检测并响应来自物理环境的某种输入(例如光、热、运动、压力)并将其转换为其他电子设备可读信号的设备。

串行通信(シリアル通信): 数据传输方法,数据在单个通道上一次发送一位,通常用于微控制器和其他外围设备之间的通信。

SI单位(国际单位制)(SI単位): 国际测量单位系统,包括长度米、质量千克和时间秒。

Sigfox(シグフォックス): 为需要最小带宽和长电池寿命的IoT设备设计的低功耗广域网(LPWAN)连接解决方案。

智能工厂(スマート工場): 高度数字化和连接的制造设施,使用IoT、AI和自动化来优化生产过程、提高效率并实现实时决策。

智能电表(スマートメータ): 记录电能或水消耗并将该信息传达给供应商进行监控和计费的电子设备。

智能手机网关(スマートフォンゲートウェイ): 充当IoT网关的智能手机,利用其连接和处理能力从附近的IoT设备收集数据并将其中继到云。

Solana(ソラナ): 高性能区块链平台。(这似乎是一个异常术语,与提供文本中的IoT技术没有直接关系,但在词汇表中)。

溶剂萃取(溶媒抽出): 基于两种不混溶液体中的差异溶解度分离化合物的方法。(这也似乎是一个异常术语)。

SoS(系统之系统)(SoS): 独立、可操作系统的集合,集成以提供单个系统无法实现的新能力或性能。

空间智能系统(空間知能化システム): 使物体和机器人能够感知其物理环境并相应调整其行为的系统,通常用于家庭自动化和老年护理。

SPI(串行外围接口)(SPI): 用于短距离通信的同步串行通信接口规范,主要用于嵌入式系统。

标准化(標準化): 开发和实施技术标准的过程,这些是商定的协议、程序或规范,以确保产品和服务的互操作性、质量和一致性。

星型网络(スター型): 每个节点(设备)单独连接到中央集线器的网络拓扑,便于添加或删除设备,但创建单点故障。

统计分析(統計解析): 收集、分析、解释、呈现和组织数据以识别模式、关系和趋势的过程。

步进电机(ステッピングモータ): 无刷直流电机,将完整旋转分为若干相等步骤,允许精确位置控制。

流处理(ストリーミング処理): 见”批处理”。

应变传感器(ひずみセンサ): 测量物体变形或应变的传感器,通常用于称重传感器和压力传感器。

Stuxnet(スタックスネット): 恶意计算机蠕虫,因其对伊朗核计划的攻击而臭名昭著,突出了工业控制系统对网络攻击的脆弱性。

监督学习(教師あり学習): 见”机器学习”。

SVM(支持向量机)(SVM): 使用分类算法进行两组分类问题的监督机器学习模型,广泛用于模式识别。

TCP/IP(TCP/IP): 传输控制协议/互联网协议,互联网的基础通信协议集,广泛用于计算机网络中的数据传输。

远程办公(テレワーク): 远程工作,通常在家中,使用信息和通信技术。

温度传感器(温度センサ): 测量温度的设备,将热能转换为电信号,常用于各种IoT应用。

TensorFlow(テンソルフロー): Google开发的开源机器学习框架,广泛用于深度学习和神经网络开发。

瘦客户端(シンクライアント): 严重依赖服务器执行大部分处理的轻量级计算机。

时间序列数据(時系列データ): 按时间顺序索引的数据点,对于分析趋势、预测和检测随时间变化的异常至关重要。

TLS(传输层安全)(TLS): 旨在为计算机网络提供通信安全的加密协议,广泛用于安全Web浏览(HTTPS)。

主题(トピック): 在MQTT等发布-订阅消息模型中,作为主题或类别的字符串,消息发布到该主题,订阅者从中接收消息。

TransferJet(トランスファージェット): 近距离无线传输技术,用于在非常短距离内设备之间进行高速数据交换。

晶体管(トランジスタ): 用于放大或切换电子信号和电力的半导体器件。

树型网络(ツリー型): 结合总线和星型拓扑方面的网络拓扑,多个星型网络通过中央总线连接。

双向通信(双方向通信方式): 双方可以同时发送和接收信息的通信方法,实现交互控制和反馈。

超声波传感器(超音波センサ): 发射超声波并测量其反射回来所需时间的传感器,用于距离测量、物体检测和流量测量。

UART(通用异步接收器/发送器)(UART): 在并行和串行形式之间转换数据的硬件设备,常用于微控制器和其他设备之间的串行通信。

无监督学习(教師なし学習): 见”机器学习”。

UWB(超宽带)(UWB): 用于短程、高带宽通信的无线电技术,实现高精度定位和数据传输。

V2X(车联万物)(V2X): 允许车辆与其环境交换信息的通信系统,包括其他车辆(V2V)、基础设施(V2I)、行人(V2P)和网络(V2N)。

VAE(变分自编码器)(変分オートエンコーダ): 学习从输入数据到潜在空间的概率映射的生成模型,用于生成新数据样本。

WAN(广域网)(広域通信網): 延伸到大地理区域(如国家或大陆)的电信网络,通常连接多个局域网(LAN)。

瀑布模型(ウォーターフォール型開発): 传统的、线性软件开发方法,开发生命周期的每个阶段(例如需求、设计、实施、测试)必须在下一阶段开始之前完成。

可穿戴生物传感器(ウェアラブル生体センサ): 集成到可穿戴设备中的传感器,监测生理参数(例如心率、体温、加速度)用于健康和健身跟踪。

Web服务(Webサービス): 设计用于支持网络上可互操作的机器对机器交互的软件系统。

WebSocket(WebSocket): 在单个TCP连接上提供全双工通信通道的计算机通信协议,实现客户端和服务器之间的实时交互通信。

Wi-Fi(Wi-Fi): 允许设备使用无线电波连接到局域网(LAN)和互联网的无线网络技术。

Wi-SUN(Wi-SUN): 使用IEEE 802.15.4g标准的IoT无线通信标准,针对低功耗的广域通信进行优化,通常用于智能电表和家庭能源管理系统。

WiMAX(全球微波接入互操作性)(WiMAX): 基于IEEE 802.16标准的无线宽带通信标准系列,在各种模式下提供远程无线数据。

XML(可扩展标记语言)(XML): 定义一套规则的标记语言,用于以人类可读和机器可读的格式编码文档,通常用于数据交换。

X射线(X線): 电磁辐射的一种形式,用于各种成像技术。(这也似乎是一个异常术语)。

Z-Wave(Z-Wave): 主要用于家庭自动化的无线通信协议,为智能家居设备提供网状网络。

零信任(ゼロトラスト): 见”零信任”。

ZigBee(ZigBee): 基于IEEE 802.15.4的低成本、低功耗无线网状网络标准,通常用于家庭自动化、智能照明和工业应用。

IoT技術ぎじゅつ学習がくしゅうガイドがいど

I. クイズくいず(10といたんこたえ問題もんだい

1. IoTシステムしすてむにおけるIoTゲートウェイの主なおもな役割やくわりなにですか?特にとくにデータでーたフローふろー処理しょり場所ばしょ関してかんして
IoTゲートウェイはIoTデバイスでばいすからデータでーた収集しゅうしゅうし、予備よびてき処理しょりとフィルタリングを実行じっこうします。これらはIoTデバイスでばいすとIoTサーバーさーばー/クラウドかん通信つうしん媒介ばいかいする重要なじゅうような役割やくわり担いにないデータでーた送信そうしんりょう遅延ちえん削減さくげんするためにエッジコンピューティングを行うおこなうことが多いおおいです。

2. IoTと製造せいぞうぎょう文脈ぶんみゃくで「データでーた駆動くどうシステムしすてむ」(CPS:サイバーフィジカルシステムしすてむ)の核心かくしん概念がいねん説明せつめいしてください。
データでーた駆動くどうシステムしすてむ特にとくにサイバーフィジカルシステムしすてむ(CPS)は、センサーせんさーとアクチュエーターを通じてつうじて物理ぶつり世界せかいからデータでーた収集しゅうしゅうし、サイバー世界せかいでそれを分析ぶんせきすることで、物理ぶつり空間くうかんとサイバー空間くうかん統合とうごうします。この分析ぶんせきされた情報じょうほう物理ぶつり世界せかいにフィードバックばっくされ、新しいあたらしい価値かち創造そうぞうしたり操作そうさ最適さいてきしたりします。例えばたとえば、「インダストリー4.0」では生産せいさんシミュレーションしみゅれーしょんデジタルでじたるツインを活用かつようします。

3. IoTデータでーた分析ぶんせき文脈ぶんみゃくで「データでーた水増しみずまし」の目的もくてきなにですか?
データでーた水増しみずましは、十分なじゅうぶんなデータでーた容易によういに利用りようできない場合ばあい機械きかい学習がくしゅう特にとくに深層しんそう学習がくしゅうトレーニングとれーにんぐデータでーたりょう増やすふやすために使用しようされます。既存きそんデータでーた変換へんかんれい画像がぞうのリサイズ、回転かいてんノイズのいず追加ついか)して新しいあたらしい多様なたようなサンプルさんぷる作成さくせいし、分析ぶんせきモデルもでるの堅牢せい精度せいど向上こうじょうさせます。

4. IoTデータでーた処理しょりにおけるバッチ処理しょりとストリーミング処理しょり主なおもな違いちがい説明せつめいしてください。
バッチ処理しょり一定いってい期間きかんにわたって大量のたいりょうのデータでーた収集しゅうしゅう保存ほぞんし、一度にいちどに処理しょりする方法ほうほうで、リアルりあるタイムたいむ分析ぶんせき適しててきしています。一方いっぽう、ストリーミング処理しょりデータでーた到着とうちゃく処理しょりし、じゅんリアルりあるタイムたいむ洞察どうさつ提供ていきょうし、即座そくざ応答おうとう可能にかのうにするため、てい遅延ちえん要求ようきゅうされるアプリケーションあぷりけーしょんには重要ですじゅうようです

5. データでーた処理しょりをクラウドコンピューティングだけに依存いぞんする場合ばあい比較ひかくして、IoTシステムしすてむでエッジコンピューティングを使用しようする主なおもな利点りてんなにですか?
エッジコンピューティングは、データでーた生成せいせいみなもとにより近いちかい場所ばしょデータでーた処理しょりし、遅延ちえんネットワークねっとわーく帯域たいいきはば消費しょうひ削減さくげんします。これは自動じどう運転うんてんロボットろぼっと制御せいぎょなどのリアルりあるタイムたいむアプリケーションあぷりけーしょん特にとくに有益でゆうえきでローカルろーかるデータでーた基づくもとづく即座そくざ意思いし決定けってい重要ですじゅうようです

6. IoTゲートウェイないの「プロトコル変換へんかん」の概念がいねんとその必要ひつようせい説明せつめいしてください。
プロトコル変換へんかんにより、様々なさまざまな通信つうしんプロトコルを使用しようする異なることなるIoTデバイスでばいすネットワークねっとわーく相互そうご通信つうしんし、IoTサーバーさーばー/クラウドと通信つうしんできるようになります。IoTゲートウェイは仲介ちゅうかいしゃとして機能きのうし、これらの異なることなるプロトコルかん変換へんかん行いおこない、IoTシステムしすてむ全体ぜんたいでのシームレスなデータでーた交換こうかん確保かくほします。

7. IoTデバイスでばいすにおけるMEMS(マイクロエレクトロメカニカルシステムしすてむ)の主なおもな機能きのうなにですか?
MEMSは機械きかいてきおよび電気でんきてきコンポーネントを組み合わせたくみあわせた小型こがた統合とうごうデバイスでばいすで、IoTデバイスでばいすセンサーせんさーやアクチュエーターとして使用しようされることが多いおおいです。小型こがた統合とうごう重要でじゅうようで、スマートフォンの圧力あつりょくセンサーせんさー加速かそくけいなどのコンパクトこんぱくとてい消費しょうひ電力でんりょくのIoTデバイスでばいす開発かいはつ可能にかのうにします。

8. テキストてきすと言及げんきゅうされている機械きかい学習がくしゅうの2つの主要なしゅようなアプローチあぷろーち説明せつめいしてください:教師きょうしあり学習がくしゅう教師きょうしなし学習がくしゅう
教師きょうしあり学習がくしゅうは、ラベルらべる付きつきデータでーた正しいただしい出力しゅつりょく/ターゲットたーげっとデータでーたたいになった入力にゅうりょくデータでーた)を使用しようしてマッピング関数かんすう学習がくしゅうするモデルもでるトレーニングとれーにんぐし、分類ぶんるい回帰かいきなどのタスクに使用しようされます。対照たいしょう的にてきに教師きょうしなし学習がくしゅうは、ラベルらべるなしデータでーた使用しようして隠れたかくれたパターンぱたーん構造こうぞう見つけみつけ、クラスタリングや異常いじょう検知などに使用しようされます。

9. IoTエリアえりあネットワークねっとわーくで「メッシュ」ネットワークねっとわーくトポロジーを使用しようする主なおもな利点りてんなにですか?
メッシュネットワークねっとわーくは、ノードかんデータでーた複数ふくすう経路けいろ通ってかよって移動いどうできるため、高いたかい信頼しんらいせいたい障害しょうがいせい提供ていきょうします。1つの経路けいろ失敗しっぱいした場合ばあい代替だいたいルートるーと使用しようできます。この冗長性じょうちょうせいにより、より広いひろいカバレッジとより堅牢な通信つうしん可能にかのうになりますが、ネットワークねっとわーく複雑ふくざつせい消費しょうひ電力でんりょく増加ぞうかする可能かのうせいがあります。

10. IoTセキュリティせきゅりてぃ文脈ぶんみゃくで「ゼロぜろトラスト」とはなにであり、なぜ重要じゅうようせい増してましているのですか?
ゼロぜろトラストは、ネットワークねっとわーく内外ないがい問わとわず、どのユーザーゆーざーデバイスでばいすデフォルトでふぉると信頼しんらいされるべきではないという前提ぜんてい立つたつセキュリティせきゅりてぃモデルもでるです。代わりかわりに、すべてのアクセスあくせす試行しこうがリソースへのアクセスあくせす許可きょかされるまえ検証けんしょう認証にんしょう承認しょうにんされます。このアプローチあぷろーちは、接続せつぞくされるデバイスでばいすかず多様たようせい、および新しいあたらしい攻撃こうげきベクターの可能かのうせいにより、IoTにおいて重要じゅうようせい増してましています。

II. クイズくいず解答かいとう要点ようてん

1. IoTゲートウェイの役割やくわり IoTゲートウェイはIoTデバイスでばいすからのデータでーた収集しゅうしゅうし、初期しょき処理しょり(フィルタリング、タイミングたいみんぐ調整ちょうせい)を行いおこないます。IoTデバイスでばいすとIoTサーバーさーばー/クラウドかん橋渡しはしわたしとして機能きのうし、データでーたソースそーす近いちかい場所ばしょデータでーた処理しょりすることでエッジコンピューティングを可能にかのうにし、遅延ちえんネットワークねっとわーく負荷ふか最小さいしょう重要ですじゅうようです

2. データでーた駆動くどうシステムしすてむ(CPS): CPSは物理ぶつりとサイバー領域りょういき統合とうごうします。物理ぶつりセンサーせんさーからのデータでーたがサイバー空間くうかん分析ぶんせきされ、られた洞察どうさつ物理ぶつりアクチュエーターを制御せいぎょするためにフィードバックばっくされます。これにより継続けいぞく的なてきなループが作成さくせいされ、最適さいてき価値かち創造そうぞう可能にかのうになります。例えばたとえば「インダストリー4.0」では、デジタルでじたるツインと呼ばよばれる仮想かそう表現ひょうげん通じてつうじて製造せいぞう効率こうりつ向上こうじょうさせます。

3. データでーた水増しみずまし この技術ぎじゅつは、データでーたセットせっと人工じんこう的にてきに拡張かくちょうすることでデータでーた不足にふそくに対処たいしょします。既存きそんデータでーた修正しゅうせいれい回転かいてん拡大かくだい縮小しゅくしょうなどの画像がぞう変換へんかんセンサーせんさーデータでーたへのノイズのいず追加ついか)して新しいあたらしい多様なたようなサンプルさんぷる生成せいせいします。これにより、学習がくしゅう防ぎふせぎ一般いっぱん改善かいぜんすることで、より堅牢な機械きかい学習がくしゅうモデルもでる特にとくに深層しんそう学習がくしゅうモデルもでるトレーニングとれーにんぐ役立ちやくだちます。

4. バッチ処理しょり vs ストリーミング処理しょり バッチ処理しょり一定いってい期間きかん蓄積ちくせきされたデータでーた扱いあつかい即座そくざ結果けっか重要でじゅうようでないリアルりあるタイムたいむ分析ぶんせきタスクに適しててきしています。対照たいしょう的にてきに、ストリーミング処理しょりデータでーた到着とうちゃく連続れんぞく的にてきに処理しょりし、リアルりあるタイムたいむ洞察どうさつ提供ていきょうし、即座そくざ反応はんのう可能にかのうにするため、時間じかん敏感なびんかんなIoTアプリケーションあぷりけーしょん不可欠ですふかけつです

5. エッジコンピューティングの利点りてん エッジコンピューティングは、データでーたソースそーすにより近いちかい場所ばしょ計算けいさん実行じっこうすることで、中央ちゅうおう集権しゅうけん的なてきなクラウド処理しょりへの依存いぞん減らしへらします。これによりネットワークねっとわーく遅延ちえん大幅におおはばに減少げんしょうし、帯域たいいきはば使用しようりょう削減さくげんされ、リアルりあるタイムたいむ応答おうとう能力のうりょく向上こうじょうするため、即座そくざ判断はんだん必要なひつようなアプリケーションあぷりけーしょん接続せつぞく限定げんていされた環境かんきょう動作どうさするアプリケーションあぷりけーしょん理想りそう的ですてきです

6. IoTゲートウェイでのプロトコル変換へんかん IoTゲートウェイは、異なることなる通信つうしん標準ひょうじゅんれい:Bluetooth、ZigBee、Wi-Fi、セルラー)を使用しようするデバイスでばいすネットワークねっとわーくかん相互そうご運用うんようせい可能にかのうにするプロトコル変換へんかん実行じっこうします。この変換へんかん機能きのうにより、多様なたようなIoTデバイスでばいすからのデータでーた中央ちゅうおうIoTサーバーさーばーやクラウドによって理解りかい処理しょりされ、一貫いっかんしたシステムしすてむ促進そくしんされます。

7. MEMS機能きのう MEMS(マイクロエレクトロメカニカルシステムしすてむ)は、マイクロスケールすけーる機械きかいてきおよび電気でんきてき機能きのう統合とうごうする能力のうりょくにより、IoTデバイスでばいすにとって基本きほん的ですてきです。これらは一般いっぱん的にてきに小型こがたされたセンサーせんさーれい圧力あつりょく加速かそく、ジャイロスコープ)やアクチュエーターとして機能きのうし、現代げんだいのIoTガジェットのコンパクトこんぱくとサイズさいずてい消費しょうひ電力でんりょく機能きのう能力のうりょく貢献こうけんします。

8. 教師きょうしあり学習がくしゅう vs 教師きょうしなし学習がくしゅう 教師きょうしあり学習がくしゅうは、かく入力にゅうりょく対応たいおうする正しいただしい出力しゅつりょく持つもつラベルらべる付きつきデータセットでモデルもでるトレーニングとれーにんぐし、マッピングを学習がくしゅうすることで分類ぶんるい回帰かいきなどのタスクを可能にかのうにします。しかし、教師きょうしなし学習がくしゅうは、ラベルらべるなしデータでーた分析ぶんせきしてデータでーた自体じたい内在ないざいするパターンぱたーん構造こうぞうグループぐるーぷ発見はっけんし、しばしばクラスタリングや異常いじょう検知に使用しようされます。

9. メッシュネットワークねっとわーく利点りてん IoTにおけるメッシュネットワークトポロジーは、かくデバイスでばいす複数ふくすうほかデバイスでばいす接続せつぞくでき、データでーた伝送でんそうのための冗長じょうちょう経路けいろ作成さくせいするため、強化きょうかされた信頼しんらいせい堅牢けんろうせい提供ていきょうします。この分散ぶんさん構造こうぞうたい障害しょうがいせい改善かいぜんし、ネットワークねっとわーくカバレッジを拡張かくちょうし、負荷ふか分散ぶんさんすることで増加ぞうかしたデーでータトラフィックを処理しょりできます。

10. IoTセキュリティせきゅりてぃにおけるゼロトラスト: ゼロぜろトラストは、ネットワークねっとわーく境界きょうかい対するたいする位置いち関係かんけいなく、どのエンティティ(ユーザーゆーざーデバイスでばいすアプリケーションあぷりけーしょん)も本質ほんしつ的にてきに信頼しんらいされないセキュリティせきゅりてぃモデルもでるです。すべてのアクセスあくせす要求ようきゅう厳密にげんみつに認証にんしょう承認しょうにんされ、不正ふせいアクセスあくせす攻撃こうげきしゃ水平すいへい移動いどうリスクりすく最小さいしょうします。これはIoTデプロイメントの分散ぶんさん的でてきで多様なたような性質せいしつにとって重要ですじゅうようです

III. エッセイえっせい形式けいしき問題もんだい解答かいとうなし)

  1. IoTの初期しょき概念がいねんから現在げんざい状態じょうたいへの進化しんかについて議論ぎろんし、広範囲なこうはんいな採用さいよう新しいあたらしい価値かち創造そうぞう可能にかのうにした主要なしゅような技術ぎじゅつてき進歩しんぽれい処理しょり能力のうりょく通信つうしん技術ぎじゅつ、AI統合とうごう)を強調きょうちょうしてください。

  2. IoTシステムしすてむアーキテクチャにおけるクラウドコンピューティングとエッジコンピューティングの役割やくわり利点りてん比較ひかく対照たいしょうしてください。一方いっぽうアプローチあぷろーち他方たほうより有益であったりゆうえきであったり、ハイブリッドアプローチあぷろーち最適であるさいてきである特定とくていのIoTアプリケーションあぷりけーしょんれい提供ていきょうしてください。

  3. IoTの完全なかんぜんな可能かのうせい実現じつげんするうえでのデータでーた収集しゅうしゅう処理しょり分析ぶんせき技術ぎじゅつ重要じゅうようせい分析ぶんせきしてください。異なることなるデータでーた処理しょり方法ほうほうれい:バッチ、ストリーミング、CEP)とデータでーた分析ぶんせき技術ぎじゅつれい統計とうけい分析ぶんせき機械きかい学習がくしゅう深層しんそう学習がくしゅう)が、価値かちある洞察どうさつ抽出ちゅうしゅつデータでーた駆動くどうかたアクションあくしょん実現じつげんにどのように貢献こうけんするかを詳述しょうじゅつしてください。

  4. IoTで使用しようされる様々なさまざまな無線むせん通信つうしん技術ぎじゅつれい:Bluetooth、Wi-SUN、LAN、5G)を検討けんとうし、その特性とくせい典型てんけい的なてきなアプリケーションあぷりけーしょん特定とくていのIoTデプロイメントでいちつをより選択せんたくするさいのトレードオフを概説してください。範囲はんい消費しょうひ電力でんりょくデータでーたレートれーとネットワークねっとわーくトポロジーじーなどの要因よういん考慮こうりょしてください。

  5. 情報じょうほうセキュリティせきゅりてぃはIoTシステムしすてむ開発かいはつ運用うんようにおける重要なじゅうような関心かんしんことです。IoTで普遍ふへん的なてきな主要なしゅようなセキュリティせきゅりてぃ脅威きょうい脆弱ぜいじゃくせいについて議論ぎろんし、これらのリスクりすく軽減けいげんし、IoTシステムしすてむ安全あんぜんせい信頼しんらいせい確保かくほするために実装じっそうできる様々なさまざまな対策たいさく技術ぎじゅつれい認証にんしょう暗号あんごう、ファイアウォール、マルウェア保護ほごゼロぜろトラスト)を説明せつめいしてください。

IV. 主要しゅよう用語ようご用語ようごしゅう

アクチュエータ(アクチュエータ): 電気でんき信号しんごう運動うんどうひかりねつなどの物理ぶつりてき動作どうさ変換へんかんするデバイスでばいす。IoTでは、センサーせんさーから受信じゅしんしたデータでーたシステムしすてむからのコマンドこまんど基づいてもとづいて物理ぶつりデバイスでばいす制御せいぎょするために使用しようされます。

アジャイル開発かいはつ(アジャイルけい開発かいはつ): 反復はんぷくてき開発かいはつサイクルさいくる迅速なじんそくなプロトタイピング、変化へんかする要件ようけんへの柔軟なじゅうなんな適応てきおう特徴とくちょうとするソフトウェアそふとうぇあ開発かいはつ方法ほうほうろんで、協調きょうちょう継続けいぞくてきフィードバックばっく重視じゅうしします。

Ambient(アンビエント): IoTデータでーたの可視保存ほぞんのためのWebサービスさーびすで、簡単なかんたんなユーザーゆーざー登録とうろく無料むりょう使用しよう提供ていきょうし、Pythonライブラリらいぶらりサポートさぽーとします。

アナログあなろぐ-デジタルでじたる(A/D)変換へんかん(A/D変換へんかん): アナログあなろぐ電気でんき信号しんごう多くおおくセンサーせんさーからの信号しんごうなど)をコンピューターこんぴゅーたー処理しょりできるデジタルでじたるデータでーた変換へんかんするプロセスぷろせす

Apache Hadoop(Apache Hadoop): コンピュータークラスターうえでの非常にひじょうに大きなおおきなデータでーたセットせっと分散ぶんさんストレージと処理しょりのためのオープンおーぷんソースそーすソフトウェアそふとうぇあフレームワーク。ビッグびっぐデータでーたのバッチ処理しょりによく使用しようされます。

Arduino(アルドゥイーノ): 使いつかいやすいハードウェアはーどうぇあソフトウェアそふとうぇあ基づくもとづくオープンソースエレクトロニクスプラットフォームで、特にとくにIoTにおけるインタラクティブオブジェクトおぶじぇくととプロトタイプの構築こうちく人気にんきがあります。

認証にんしょう認証にんしょう): IoT環境かんきょうでリソースへのアクセスあくせす試みるこころみるユーザーゆーざーデバイスでばいす、またはシステムしすてむ身元みもと検証けんしょうするプロセスぷろせす

オートエンコーダ(オートエンコーダ): 教師きょうしなし学習がくしゅう使用しようされる神経しんけいネットワークねっとわーく一種いっしゅで、特にとくにデータでーた圧縮あっしゅく次元じげん削減さくげん使用しようされます。入力にゅうりょくさい構成こうせいすることを学習がくしゅうし、しばしば特徴とくちょう抽出ちゅうしゅつ異常いじょう検知に使用しようされます。

バッチ処理しょり(バッチ処理しょり): 大量のたいりょうのデータでーた収集しゅうしゅうし、通常つうじょう予定よていされた間隔かんかく連続れんぞく的でてきではなく、単一のたんいつの操作そうさでまとめて処理しょりするデータでーた処理しょり方法ほうほう

ベイジアンネットワークねっとわーく(ベイジアンネットワークねっとわーく): 有向非環グラフぐらふ介してかいして変数へんすうセットせっととその条件じょうけん付きつき依存いぞん関係かんけい表現ひょうげんする確率かくりつてきグラフィカルぐらふぃかるモデルもでるで、不確実ふかくじつせいでの推論すいろん意思いし決定けってい使用しようされます。

BCP(事業じぎょう継続けいぞく計画けいかく)(BCP): 大きなおおきな混乱こんらん災害さいがいあいだあと事業じぎょう運営うんえい継続けいぞくできることを確保かくほするように設計せっけいされた計画けいかくで、データでーたバックアップばっくあっぷシステムしすてむ復旧ふっきゅう代替だいたい作業さぎょう手配てはい戦略せんりゃく含みふくみます。

ビッグびっぐデータでーたビッグびっぐデータでーた): 計算けいさん的にてきに分析ぶんせきしてパターンぱたーんトレンドとれんど関連かんれんせい特にとくに人間にんげん行動こうどう相互そうご作用さよう関するかんするものを明らかにあきらかにできる極めてきわめて大きなおおきなデータでーたセットせっと

Bluetooth(ブルートゥース): たん距離きょり固定こていおよびモバイルもばいるデバイスでばいすかんデータでーた交換こうかんするためのたん距離きょり無線むせん技術ぎじゅつ標準ひょうじゅんで、IoTのパーソナルエリアえりあネットワークねっとわーくでよくられます。

ブローカーぶろーかーブローカーぶろーかー): MQTTなどのメッセージングシステムしすてむで、パブリッシャーからメッセージめっせーじ受信じゅしんし、トピックに基づいてもとづいて適切なてきせつなサブスクライバーに配信はいしんする中央ちゅうおうサーバーさーばー

Caffe(カフェかふぇ): Berkeley Vision and Learning Centerによって開発かいはつされた深層しんそう学習がくしゅうフレームワークで、画像がぞう認識にんしきタスクでの速度そくど効率こうりつ知らしられています。

キャリブレーション(キャリブレーション): センサーせんさーデバイスでばいす測定そくてい既知のきちの標準ひょうじゅん正確でせいかくで一貫いっかんせいがあることを確保かくほするために調整ちょうせいするプロセスぷろせす

CCライセンスらいせんす(Creative Commonsライセンスらいせんす)(CCライセンスらいせんす): 作成さくせいしゃ受益じゅえきしゃ作成さくせいしゃのためにどの権利けんり保留ほりゅうし、どの権利けんり放棄ほうきするかを伝えるつたえることを可能にかのうにする公的こうてき著作ちょさくけんライセンスらいせんす

CCD(電荷でんか結合けつごうデバイスでばいす)(CCD): ひかり電荷でんか変換へんかんする半導体はんどうたいデバイスでばいすで、デジタルでじたるカメラかめらその他そのた画像がぞう応用おうよう画像がぞうセンサーせんさーとして一般いっぱん的にてきに使用しようされます。

CEP(複合ふくごうイベントいべんと処理しょり)(CEP): 複雑なふくざつなイベントいべんと基づいてもとづいて即座にそくざにアクションあくしょん取るとることを可能にかのうにする、パターンぱたーん関係かんけい特定とくていするために複数ふくすうソースそーすからのデータでーたリアルりあるタイムたいむ処理しょりする技術ぎじゅつ

分類ぶんるい分類ぶんるい): トレーニングとれーにんぐデータでーたから学習がくしゅうしたパターンぱたーん基づいてもとづいてデータでーた事前じぜん定義ていぎされたクラスくらす分類ぶんるいする機械きかい学習がくしゅうタスク。

クラウドコンピューティング(クラウドコンピューティング): サーバーさーばー、ストレージ、データベースでーたべーす、ネットワーキング、ソフトウェアそふとうぇあ分析ぶんせき、インテリジェンスを含むふくむオンデマンドコンピューティングサービスさーびすインターネットいんたーねっと(「クラウド」)経由けいゆ提供ていきょうするモデルもでる

CMOS(相補かた金属きんぞく酸化さんかまく半導体はんどうたい)(CMOS): 画像がぞうセンサーせんさー含むふくむ集積しゅうせき回路かいろ使用しようされる半導体はんどうたい技術ぎじゅつ一種いっしゅで、てい消費しょうひ電力でんりょく知らしられています。

CoAP(制約せいやくアプリケーションあぷりけーしょんプロトコル)(CoAP): IoTの制約せいやくノードと制約せいやくネットワークねっとわーくでの使用しように特化したWeb転送てんそうプロトコルで、効率こうりつせいていオーバーおーばーヘッドへっどのために設計せっけいされています。

コールドデータでーた(コールドデータでーた): 頻繁にひんぱんにアクセスあくせすまたは使用しようされないデータでーたで、しばしばコストこすと効率こうりつ良いよい長期ちょうきストレージソリューションそりゅーしょん保存ほぞんされます。

畳みたたみ込みこみニューラルネットワークねっとわーく(CNN)(畳みたたみ込みこみニューラルネットワークねっとわーく): 主におもに視覚しかく画像がぞう分析ぶんせき使用しようされる深層しんそう学習がくしゅうニューラルネットワークねっとわーく一種いっしゅで、画像がぞう認識にんしき処理しょりタスクで高いたかい効果こうかがあります。

CPS(サイバーフィジカルシステムしすてむ)(サイバーフィジカルシステムしすてむ):データでーた駆動くどうシステムしすてむ」を参照さんしょう

CSV(カンマ区切りくぎり)(CSV): ひょう形式けいしきデータでーた保存ほぞんするための簡単なかんたんなファイルふぁいる形式けいしきで、ファイルふぁいるかくぎょうデータでーたレコードれこーどで、かくレコードれこーどがカンマで区切らくぎられた1つ以上いじょうフィールドふぃーるど構成こうせいされます。

データでーた水増しみずましデータでーた水増しみずまし):水増しみずまし」を参照さんしょう

データでーたクレンジング(データでーたクレンジング): データでーたセットせっとから不正確ふせいかく完全かんぜん、または無関係なむかんけいなデータでーた特定とくていし、修正しゅうせいまたは削除さくじょするプロセスぷろせす

データでーたまえ処理しょりデータでーたまえ処理しょり): なまデータでーた分析ぶんせき適したてきしたクリーンでくりーんで整理せいりされた形式けいしき変換へんかんするために取らとられるステップすてっぷで、しばしばクレンジング、変換へんかん正規せいき含みふくみます。

データでーた変換へんかん統合とうごうデータでーた変換へんかん統合とうごう): データでーたいちつの形式けいしき構造こうぞうから別のべつのものに変換へんかんし、異なることなるソースそーすからのデータでーた統一とういつされたビューに結合けつごうするプロセスぷろせす

深層しんそう学習がくしゅう深層しんそう学習がくしゅう): 多層たそうニューラルネットワークねっとわーく深層しんそうニューラルネットワークねっとわーく)を使用しようして大量のたいりょうのデータでーたから複雑なふくざつなパターンぱたーん学習がくしゅうする機械きかい学習がくしゅうのサブセットで、しばしば画像がぞう音声おんせい認識にんしきのようなタスクで高いたかい精度せいど達成たっせいします。

デジタルでじたる署名しょめいデジタルでじたる署名しょめい): デジタルでじたるメッセージめっせーじ文書ぶんしょの真正せい完全かんぜんせい確認かくにんするために使用しようされる暗号あんごう技術ぎじゅつで、送信そうしんしゃ主張しゅちょうする身元みもとであり、メッセージめっせーじ変更へんこうされていないことを確保かくほします。

デジタルでじたるトランスフォーメーション(DX)(デジタルでじたるトランスフォーメーション): 変化へんかするビジネスびじねす市場しじょう要件ようけん満たすみたすために、ビジネスびじねすプロセスぷろせす文化ぶんか顧客こきゃく体験たいけん変革へんかくするデジタルでじたる技術ぎじゅつ採用さいようするプロセスぷろせす

説明せつめい可能かのうせい説明せつめい可能かのうせい): AIと機械きかい学習がくしゅうにおいて、モデルもでるがどのように特定とくてい予測よそく決定けってい到達とうたつしたかを説明せつめいする能力のうりょくで、特にとくに敏感なびんかんなアプリケーションあぷりけーしょんでの信頼しんらい説明せつめい責任せきにんにとって重要ですじゅうようです

分散ぶんさんファイルふぁいるシステムしすてむ(HDFS)(分散ぶんさんファイルふぁいるシステムしすてむ): 複数ふくすうマシンましんにわたって非常にひじょうに大きなおおきなファイルふぁいる保存ほぞんするように設計せっけいされた分散ぶんさん、スケーラブル、ポータブルぽーたぶるファイルふぁいるシステムしすてむで、Hadoopエコえこシステムしすてむ一部いちぶです。

DMZ(武装ぶそう地帯ちたい)(閉域網): 通常つうじょうインターネットいんたーねっとである信頼しんらいできない大きなおおきなネットワークねっとわーく組織そしき外部がいぶ向けむけサービスさーびす含みふくみ公開こうかいする物理ぶつりてきまたは論理ろんりてきサブさぶネットワークねっとわーく

DNAセンサーせんさー(DNAセンサーせんさー): 特定とくていのDNA配列はいれつ検出けんしゅつするバイオセンサーせんさーで、しばしば医学いがく診断しんだん環境かんきょう監視かんし食品しょくひん安全であんぜんで使用しようされます。

DDoS攻撃こうげき分散ぶんさんサービスさーびす拒否きょひ攻撃こうげき)(DDoS攻撃こうげき): 複数ふくすう侵害しんがいされたコンピューターこんぴゅーたーシステムしすてむからのインターネットいんたーねっとトラフィックの洪水こうずい標的ひょうてきサーバーさーばーサービスさーびす、またはネットワークねっとわーく正常なせいじょうなトラフィックを圧倒あっとうする悪意あくいある試みこころみ

ドローン(ドローン): 遠隔えんかく制御せいぎょまたは自律じりつ飛行ひこう可能なかのうな無人むじん航空こうくう(UAV)で、IoTで監視かんし配送はいそうデータでーた収集しゅうしゅうなどの様々なさまざまなアプリケーションあぷりけーしょん使用しようされます。

Dust Networks(Dust Networks): 産業さんぎょうIoTアプリケーションあぷりけーしょん向けむけてい電力でんりょく無線むせんメッシュネットワーキング技術ぎじゅつ専門せんもんとする企業きぎょう

DX(デジタルでじたるトランスフォーメーション)(DX):デジタルでじたるトランスとらんすフォーメーション」を参照さんしょう

エッジAI(エッジAI): 中央ちゅうおう集権しゅうけん的なてきなクラウドではなく、エッジデバイスでばいす自体じたいれいセンサーせんさーカメラかめら、IoTゲートウェイ)で直接ちょくせつ実行じっこうされる人工じんこう知能ちのう処理しょりで、リアルりあるタイムたいむ意思いし決定けってい遅延ちえん削減さくげん可能にかのうにします。

エッジコンピューティング(エッジコンピューティング): 計算けいさんデータでーたストレージをデータでーたソースそーすにより近づけるちかづける分散ぶんさんコンピューティングパラダイムぱらだいむで、応答おうとう時間じかん改善かいぜんし、帯域たいいきはば節約せつやくします。

Edgecrossコンソーシアム(Edgecrossコンソーシアム): 製造せいぞうぎょうにおけるエッジコンピューティングとITとOT(運用うんよう技術ぎじゅつ)の統合とうごう促進そくしん焦点しょうてん当てたあてた日本にほんのコンソーシアム。

心電計(ECG)(心電計): 心拍しんぱく電気でんき活動かつどう測定そくていするテストてすとで、心臓しんぞう健康けんこう監視かんしするためにウェアラブルバイオセンサーで使用しようされます。

EnOcean(エンオーシャン): ちょうてい消費しょうひ電力でんりょく焦点しょうてん当てたあてた無線むせん標準ひょうじゅんで、しばしばエネルギーえねるぎーハーベスティングを利用りようし、バッテリーばってりーレスれすIoTデバイスでばいす適しててきしています。

エネルギーえねるぎーハーベスティング(エネルギーえねるぎーハーベスティング): 環境かんきょうげんれい太陽たいようねつ振動しんどう電波でんぱ)から少量のしょうりょうのエネルギーえねるぎー捕獲ほかく保存ほぞんして、IoTセンサーせんさーのようなてい電力でんりょく電子でんしデバイスでばいす電力でんりょく供給きょうきゅうするプロセスぷろせす

EPFC(エッジプラットフォームコンソーシアム)(EPFC): サイバーと物理ぶつり空間くうかん接続せつぞくするエッジプラットフォーム開発かいはつ焦点しょうてん当てたあてたコンソーシアム。

イーサネットねっと(イーサネット): ローカルろーかるエリアえりあネットワークねっとわーく(LAN)で一般いっぱん的にてきに使用しようされる有線ゆうせんコンピューターこんぴゅーたーネットワーキング技術ぎじゅつファミリーふぁみりー

FPGA(フィールドふぃーるどプログラマブルゲートげーとアレイ)(FPGA): 製造せいぞう顧客こきゃくまたは設計せっけいしゃ設定せっていできるように設計せっけいされた集積しゅうせき回路かいろで、エッジでのAIを含むふくむ特定とくていのコンピューティングタスクのための柔軟なじゅうなんなハードウェアはーどうぇあアクセラレーションとカスタムロジックを可能にかのうにします。

FTP(ファイルふぁいる転送てんそうプロトコル)(FTP): コンピューターこんぴゅーたーネットワークねっとわーくじょうクライアントくらいあんとサーバーさーばーかんコンピューターこんぴゅーたーファイルふぁいる転送てんそうするために使用しようされる標準ひょうじゅんネットワークねっとわーくプロトコル。

GAN(敵対てきたいてき生成せいせいネットワークねっとわーく)(敵対てきたいてき生成せいせいネットワークねっとわーく): いちつがデータでーた生成せいせいし、もういちつがじっデータでーたデータでーた区別くべつする2つのニューラルネットワークねっとわーく構成こうせいされる機械きかい学習がくしゅうフレームワークのクラスくらすで、画像がぞう作成さくせいのような生成せいせいAIに使用しようされます。

ゲートウェイ(ゲートウェイ): 異なることなるネットワークねっとわーくとプロトコルを接続せつぞくするデバイスでばいすで、IoTデバイスでばいすとクラウドかん仲介ちゅうかいとして機能きのうし、データでーた集約しゅうやく、プロトコル変換へんかんローカルろーかる処理しょりなどの機能きのう実行じっこうします。

生成せいせいAI(生成せいせいAI): 既存きそんデータでーたから学習がくしゅうすることで、テキストてきすと画像がぞう音声おんせい動画どうがなどの新しいあたらしいコンテンツこんてんつ作成さくせいできる人工じんこう知能ちのう一種いっしゅ

GPIO(汎用はんよういれ出力しゅつりょく)(GPIO): 集積しゅうせき回路かいろじょう汎用はんようピンぴんで、その動作どうさ入力にゅうりょくまたは出力しゅつりょく)を実行じっこうユーザーゆーざー制御せいぎょできます。

GNSS(ぜんたま衛星えいせい測位システムしすてむ)(GNSS): GPSを含むふくむ自律じりつ的なてきな地理ちり空間くうかん測位を提供ていきょうする衛星えいせいナビゲーションシステムしすてむ総称そうしょう

Grad-CAM(Grad-CAM): 深層しんそう学習がくしゅうで、畳みたたみ込みこみニューラルネットワークねっとわーく決定けってい最ももっとも関連かんれんする画像がぞう部分ぶぶん視覚しかくするために使用しようされる技術ぎじゅつで、画像がぞう認識にんしきモデルもでる解釈かいしゃく可能かのうせい提供ていきょうします。

グラフぐらふかたDB(グラフぐらふけいDB): ノード、エッジ、プロパティを使用しようしてデータでーた表現ひょうげん保存ほぞんするためにグラフぐらふ構造こうぞう使用しようしたセマンティッククエリようのNoSQLデータベースでーたべーす関係かんけいれいソーシャルそーしゃるネットワークねっとわーく)に理想りそう的ですてきです

HBase(HBase): GoogleのBigtableをモデルもでるにしたオープンおーぷんソースそーす関係かんけいかた分散ぶんさんデータベースでーたべーすで、Hadoopエコえこシステムしすてむ一部いちぶであり、だい規模きぼデータでーたセットせっと適しててきしています。

HDFS(Hadoop分散ぶんさんファイルふぁいるシステムしすてむ)(HDFS):分散ぶんさんファイルふぁいるシステムしすてむ」を参照さんしょう

HEMS(ホームほーむエネルギーえねるぎー管理かんりシステムしすてむ)(HEMS): 家庭かていエネルギーえねるぎー消費しょうひ監視かんし管理かんりし、様々なさまざまな機器ききエネルギーえねるぎー使用しよう最適さいてきするシステムしすてむ

ヒストグラム(ヒストグラム): 数値すうちデータでーた分布ぶんぷグラフィカルぐらふぃかる表現ひょうげんで、しばしば統計とうけい分析ぶんせき使用しようされます。

ホットほっとデータでーたホットほっとデータでーた): 頻繁にひんぱんにアクセスあくせすされるまたは積極せっきょく的にてきに使用しようされるデータでーたで、通常つうじょう迅速なじんそくな検索けんさくのためにこう性能せいのうストレージに保存ほぞんされます。

HTTP(ハイパーテキストてきすと転送てんそうプロトコル)(HTTP): World Wide Webのデータでーた通信つうしん基盤きばんで、Webサーバーさーばークライアントくらいあんとかん通信つうしん使用しようされます。

ハイブリッドクラウド(ハイブリッドクラウド): オンプレミス、プライベートぷらいべーとクラウド、パブリックぱぶりっくクラウドサービスさーびす組み合わせくみあわせ使用しようし、プラットフォームかんでオーケストレーションを行うおこなうクラウドコンピューティング環境かんきょう

IaaS(サービスさーびすとしてのインフラストラクチャ)(IaaS): プロバイダーぷろばいだーインターネットいんたーねっと経由けいゆ仮想かそうマシンましん、ストレージ、ネットワークねっとわーくなどの仮想かそうコンピューティングリソースを提供ていきょうするクラウドコンピューティングサービスさーびすモデルもでる

I2C(集積しゅうせき回路かいろかん)(I2C): Philips Semiconductorsによって開発かいはつされた2せんしきシリアル通信つうしんバスばすインターフェースで、マイクロコントローラー、EEPROM、A/Dコンバーター、I/Oインターフェースなどの低速ていそくデバイスでばいす接続せつぞくするために使用しようされます。

ICチップちっぷ認証にんしょう(ICチップちっぷ認証にんしょう): 集積しゅうせき回路かいろチップちっぷ使用しようして身元みもと認証にんしょうするスマートすまーとカードかーどで、しばしば安全なあんぜんな取引とりひきアクセスあくせす制御せいぎょ使用しようされます。

IEEE802.11(IEEE802.11): 2.4、5、60 GHz周波しゅうはすうたいでの無線むせんローカルろーかるエリアえりあネットワークねっとわーく(WLAN)コンピューターこんぴゅーたー通信つうしん実装じっそうするためのメディアめでぃあアクセスあくせす制御せいぎょ(MAC)と物理ぶつりそう(PHY)仕様しようセットせっと

IEEE802.15.4(IEEE802.15.4): ていレートれーと無線むせんパーソナルエリアえりあネットワークねっとわーく(LR-WPAN)の物理ぶつりそうメディアめでぃあアクセスあくせす制御せいぎょ指定していする標準ひょうじゅんで、しばしばZigBeeとWi-SUNの基盤きばんとして使用しようされます。

IFTTT(イフトット): “If This Then That”、ユーザーゆーざーが「アプレット」と呼ばよばれる単純なたんじゅんな条件じょうけんぶんチェーンちぇーん作成さくせいして、IoTを含むふくむ様々なさまざまなオンラインおんらいんタスクを自動じどうし、異なることなるサービスさーびすデバイスでばいす接続せつぞくできるWebベースべーすサービスさーびす

画像がぞうセンサーせんさー画像がぞうセンサーせんさー): 光学こうがく画像がぞう電子でんし信号しんごう変換へんかんするデバイスでばいすで、CCDやCMOSセンサーせんさーなど、IoTで視覚しかく監視かんし画像がぞう認識にんしき使用しようされます。

インダストリー4.0(インダストリー4.0): だい4産業さんぎょう革命かくめいで、製造せいぞうぎょうデジタルでじたるとサイバーフィジカルシステムしすてむ、IoT、AIの統合とうごう特徴とくちょうとし、スマートすまーとファクトリーを創造そうぞうします。

侵入しんにゅう検知システムしすてむ(IDS)(侵入しんにゅう検知システムしすてむ): 悪意あくいある活動かつどうポリシーぽりしー違反いはんについてネットワークねっとわーくトラフィックやシステムしすてむ活動かつどう監視かんしし、アラートを生成せいせいするセキュリティせきゅりてぃ技術ぎじゅつ

IoTエリアえりあネットワークねっとわーく(IoTエリアえりあネットワークねっとわーく): 限定げんていされた地理ちりてきエリアえりあないのIoTデバイスでばいす専用せんよう設計せっけいされたネットワークねっとわーくで、通常つうじょうたん距離きょり無線むせん通信つうしん技術ぎじゅつ使用しようします。

IoTデバイスでばいす(IoTデバイスでばいす): インターネットいんたーねっと経由けいゆデバイスでばいすシステムしすてむ接続せつぞくデータでーた交換こうかんする目的もくてきで、センサーせんさーソフトウェアそふとうぇあその他そのた技術ぎじゅつ埋めうめ込まこまれた物理ぶつりオブジェクトおぶじぇくと

IoTゲートウェイ(IoTゲートウェイ): 「ゲートウェイ」を参照さんしょう

IoTプラットフォーム(IoTプラットフォーム): IoTデバイスでばいす管理かんりデータでーた収集しゅうしゅう処理しょりアプリケーションあぷりけーしょん有効ゆうこうのためのツールつーる機能きのう提供ていきょうするクラウドベースまたはオンプレミスのサービスさーびす

IoTサーバーさーばー(IoTサーバーさーばー): 通常つうじょうはクラウドに存在そんざいするIoTシステムしすてむ中央ちゅうおうコンポーネントで、IoTデバイスでばいすからのデータでーた受信じゅしん保存ほぞん分析ぶんせき管理かんり、および制御せいぎょコマンドこまんど発行はっこう担当たんとうします。

IPA(独立どくりつ行政ぎょうせい法人ほうじん情報じょうほう処理しょり推進すいしん機構きこう)(IPA): IoTセキュリティせきゅりてぃガイドラインがいどらいん含むふくむITとサイバーセキュリティせきゅりてぃ推進すいしんする日本にほん政府せいふ関連かんれん組織そしき

ISMS(情報じょうほうセキュリティせきゅりてぃマネジメントまねじめんとシステムしすてむ)(情報じょうほうセキュリティせきゅりてぃマネジメントまねじめんとシステムしすてむ): ポリシーぽりしープロセスぷろせす技術ぎじゅつ含むふくむ敏感なびんかんな企業きぎょう情報じょうほう安全にあんぜんに保つたもつための体系たいけいてきアプローチあぷろーち

ISMバンドばんど(ISMバンドばんど): 電気でんき通信つうしん以外いがい工業こうぎょう科学かがく医療いりょう目的もくてきでの無線むせん周波しゅうはすう(RF)エネルギーえねるぎー使用しようのために国際こくさい的にてきに予約よやくされた工業こうぎょう科学かがく医療いりょう無線むせんバンドばんど多くおおくのIoTデバイスでばいすがこれらの免許めんきょ不要ふようバンドばんど動作どうさします。

ISDN(総合そうごうデジタルでじたる通信つうしんもう)(ISDN): 公衆こうしゅう交換こうかん電話でんわもう従来じゅうらい回路かいろ通じてつうじて音声おんせいビデオびでおデータでーたその他そのたネットワークねっとわーくサービスさーびす同時どうじデジタルでじたる伝送でんそうのための通信つうしん標準ひょうじゅんセットせっと

JSON(JavaScript Object Notation)(JSON): サーバーさーばーとWebアプリケーションあぷりけーしょんかんでのデータでーた送信そうしんによく使用しようされる軽量けいりょうデータでーた交換こうかんフォーマットふぉーまっとで、その簡潔かんけつせいによりIoTでますます使用しようされています。

Julia(ジュリア): 技術ぎじゅつ計算けいさんのためのこうレベルれべるこう性能せいのう動的どうてきプログラミングぷろぐらみんぐ言語げんごで、データでーたサイエンスさいえんす機械きかい学習がくしゅう適しててきしています。

Keras(ケラス): Pythonで書かかかれたオープンおーぷんソースそーすニューラルネットワークねっとわーくライブラリらいぶらりで、深層しんそうニューラルネットワークねっとわーくでの高速こうそく実験じっけん可能にかのうにするように設計せっけいされています。

キーきーバリューかたキーきーバリューけい): データでーたキーきーあたいペアぺあコレクションこれくしょんとして保存ほぞんするシンプルなしんぷるなNoSQLデータベースでーたべーすモデルもでるで、キーきー対応たいおうするあたい一意いちい識別しきべつとして機能きのうします。

LIME(Local Interpretable Model-agnostic Explanations)(LIME): 解釈かいしゃく可能なかのうなモデルもでるローカルにろーかるに近似きんじすることで、任意のにんいの機械きかい学習がくしゅうモデルもでる予測よそく説明せつめいする技術ぎじゅつ

線形せんけい回帰かいき線形せんけい回帰かいき): 観測かんそくデータでーた線形せんけい方程式ほうていしき当てはめるあてはめることで、従属じゅうぞく変数へんすうと1つ以上いじょう独立どくりつ変数へんすうかん関係かんけいモデルもでるする統計とうけい手法しゅほう

LLM(だい規模きぼ言語げんごモデルもでる)(LLM): 膨大なぼうだいなりょうテキストてきすとデータでーた訓練くんれんされた人工じんこう知能ちのうモデルもでる一種いっしゅで、人間にんげんのような言語げんご理解りかい生成せいせいする能力のうりょくがあり、しばしば生成せいせいAIアプリケーションあぷりけーしょん使用しようされます。

ローカルろーかる5G(ローカルろーかる5G): 企業きぎょう地方ちほう自治じちたい特定とくていニーズにーず合わせてあわせて展開てんかいするプライベートぷらいべーと5Gネットワークねっとわーくで、公共こうきょうネットワークねっとわーく比較ひかくして高いたかい信頼しんらいせいてい遅延ちえん強化きょうかされたセキュリティせきゅりてぃ提供ていきょうします。

ロングろんぐポーリング方式ほうしきロングろんぐポーリング方式ほうしき): クライアントくらいあんと新しいあたらしいデータでーた利用りよう可能にかのうになるかタイムたいむアウトあうと発生はっせいするまでサーバーさーばーへの接続せつぞく開いたひらいたままにする通信つうしん技術ぎじゅつで、従来じゅうらいのポーリングと比較ひかくしてポーリング頻度ひんど減らしへらしリアルりあるタイムたいむ更新こうしん改善かいぜんします。

LoRaWAN(LoRaWAN): 地域ちいきくに、またはグローバルぐろーばるネットワークねっとわーくでのワイヤレスわいやれすバッテリーばってりー動作どうさThingsを対象たいしょうとしたてい電力でんりょく広域こういきネットワークねっとわーく(LPWAN)仕様しようで、てい電力でんりょくちょう距離きょり通信つうしんよう設計せっけいされています。

LPWA(てい電力でんりょく広域こういき)(LPWA): てい電力でんりょくちょう距離きょり通信つうしんよう設計せっけいされた無線むせん通信つうしん技術ぎじゅつクラスくらすで、通常つうじょう少量のしょうりょうのデータでーた頻繁でひんぱんでなく送信そうしんするIoTデバイスでばいすようです。

LTE(Long Term Evolution)(LTE): GSM/EDGEとUMTS/HSPAネットワークねっとわーく技術ぎじゅつ基づくもとづくモバイルもばいるデバイスでばいすデータでーた端末たんまつ無線むせんブロードバンド通信つうしん標準ひょうじゅんで、しばしばIoT(れい:LTE-M)に拡張かくちょうされます。

LTE-M(LTE-M): LTEベースべーすのLPWA技術ぎじゅつ一種いっしゅで、のLPWA技術ぎじゅつよりも高いたかい帯域たいいきはば必要ひつようとするIoTデバイスでばいすよう設計せっけいされ、同時にどうじにてい消費しょうひ電力でんりょく維持いじします。

LwM2M(Lightweight M2M)(LwM2M): IoTデバイスでばいすようデバイスでばいす管理かんりプロトコルで、制約せいやくされたデバイスでばいすネットワークねっとわーくよう最適さいてきされ、デバイスでばいす管理かんりデータでーたレポートれぽーと機能きのう提供ていきょうします。

機械きかい学習がくしゅう機械きかい学習がくしゅう): 明示めいじ的にてきにプログラムぷろぐらむされることなく、統計とうけい技術ぎじゅつ使用しようしてコンピューターこんぴゅーたーシステムしすてむデータでーたから「学習がくしゅう」できるようにする人工じんこう知能ちのう分野ぶんやで、予測よそく分類ぶんるいパターンぱたーん認識にんしきなどのタスクを実行じっこうします。

Mahout(Mahout): スケーラブルな機械きかい学習がくしゅうアルゴリズムあるごりずむ実装じっそう提供ていきょうするApacheオープンおーぷんソースそーすプロジェクトぷろじぇくとで、しばしばHadoopと組み合わせてくみあわせて使用しようされます。

MEC(マルチまるちアクセスあくせす・エッジ・コンピューティング)(マルチまるちアクセスあくせす・エッジ・コンピューティング): モバイルもばいる加入かにゅうしゃとIoTデバイスでばいすにより近いちかいネットワークねっとわーくのエッジでクラウドコンピューティング機能きのうとITサービスさーびす環境かんきょう可能にかのうにするネットワークねっとわーくアーキテクチャ概念がいねん

メディアンフィルタふぃるた(メディアンフィルタふぃるた): エッジを保持ほじしながら画像がぞう信号しんごうからノイズのいず除去じょきょするためにしばしば使用しようされる線形せんけいデジタルでじたるフィルタリング技術ぎじゅつ

MEMS(マイクロエレクトロメカニカルシステムしすてむ)(MEMS): 「MEMS」を参照さんしょう

メッシュかた(メッシュけい): かくノード(デバイスでばいす)が複数ふくすうほかのノードに直接ちょくせつ接続せつぞくするネットワークねっとわーくトポロジーで、データでーた冗長じょうちょうパスぱす作成さくせいし、信頼しんらいせいとカバレッジを向上こうじょうさせます。

min-max正規せいき(min-max正規せいき): 最小さいしょうあたい引いてひいて範囲はんい最大さいだい-最小さいしょう)で割るわることにより、特徴とくちょう固定こてい範囲はんい通常つうじょう0から1)にさいスケールすけーるするデータでーた正規せいき技術ぎじゅつ

MISO(MISO): 複数ふくすう入力にゅうりょく単一のたんいつの出力しゅつりょく持つもつ通信つうしんモードもーどで、アンテナあんてな構成こうせい指しさします。

Mixup(Mixup): 既存きそんサンプルさんぷるペアぺあとそのラベルらべるを線形補間することで新しいあたらしい訓練くんれんサンプルさんぷる作成さくせいする深層しんそう学習がくしゅうデータでーた拡張かくちょう技術ぎじゅつ

MQTT(MQテレメトリ転送てんそう)(MQTT): 小型こがたセンサーせんさーモバイルもばいるデバイスでばいすよう軽量けいりょうメッセージングプロトコルで、こう遅延ちえんまたは信頼しんらいせい低いひくいネットワークねっとわーくよう最適さいてきされ、IoTで広くひろく使用しようされています。

MRAM(磁気じき抵抗ていこうメモリめもり)(磁気じき抵抗ていこうメモリめもり): 磁気じき状態じょうたい使用しようしてデータでーた保存ほぞんする揮発きはつせいランダムアクセスあくせすメモリめもり技術ぎじゅつで、高速こうそく耐久たいきゅうせい提供ていきょうします。

MPU(マイクロプロセッサユニットゆにっと)(MPU): 命令めいれい実行じっこうデータでーた処理しょり担当たんとうするコンピューターこんぴゅーたーシステムしすてむ中央ちゅうおう処理しょり装置そうち。IoTでは、デバイスでばいすやゲートウェイじょうしゅ処理しょりユニットゆにっと指しさします。

MSE(平均へいきんじょう誤差ごさ)(平均へいきんじょう誤差ごさ): エラーえらーまたは偏差へんさじょう平均へいきん測定そくていするために使用しようされる一般いっぱん的なてきな指標しひょうで、しばしば回帰かいきモデルもでる精度せいど評価ひょうかするために使用しようされます。

NB-IoT(ナローバンドIoT)(NB-IoT): 3GPPによって公開こうかいされたてい電力でんりょく広域こういき(LPWA)技術ぎじゅつ標準ひょうじゅんで、非常にひじょうに低いひくい消費しょうひ電力でんりょく必要ひつようとし、狭いせまい周波しゅうはすうたい動作どうさできるIoTデバイスでばいすよう設計せっけいされています。

ネットワークねっとわーく・スライシング(ネットワークねっとわーく・スライシング): 5Gのネットワークねっとわーくアーキテクチャ概念がいねんで、共有きょうゆう物理ぶつりインフラストラクチャじょう複数ふくすう仮想かそうネットワークねっとわーく実行じっこうでき、それぞれが特定とくていサービスさーびすアプリケーションあぷりけーしょんれい高速こうそくてい遅延ちえんだい規模きぼIoT)よう最適さいてきされます。

ニューラルネットワークねっとわーく(ニューラルネットワークねっとわーく): 生物せいぶつがくてきニューラルネットワークねっとわーく構造こうぞう機能きのうにインスパイアされた計算けいさんモデルもでるで、パターンぱたーん認識にんしき予測よそくなどのタスクの機械きかい学習がくしゅう使用しようされます。

NoSQL(NoSQL): 関係かんけいデータベースでーたべーす使用しようされるひょう形式けいしき関係かんけい以外いがい手段しゅだんモデルもでるされたデータでーた保存ほぞん検索けんさくメカニズムめかにずむ提供ていきょうする関係かんけいデータベースでーたべーすクラスくらすビッグびっぐデータでーたリアルりあるタイムたいむWebアプリケーションあぷりけーしょんでしばしば使用しようされます。

Numpy(NumPy): Pythonでの科学かがく計算けいさんのための基本きほんパッケージぱっけーじで、大きなおおきな次元じげん配列はいれつ行列ぎょうれつサポートさぽーとと、これらの配列はいれつ操作そうさする大量のたいりょうのこうレベルれべる数学すうがく関数かんすう提供ていきょうします。

OneM2M(oneM2M): マシンましんかん(M2M)通信つうしんモノものインターネットいんたーねっと(IoT)のグローバルぐろーばる標準ひょうじゅんイニシアチブいにしあちぶで、共通きょうつうサービスさーびすそうアーキテクチャを指定していします。

オープンおーぷんイノベーション(オープンおーぷんイノベーション): 組織そしき外部がいぶアイデアあいであ内部ないぶアイデアあいであ活用かつようして技術ぎじゅつサービスさーびす進歩しんぽさせるパラダイムぱらだいむで、しばしば外部がいぶパートナーぱーとなーオープンおーぷんソースそーすプロジェクトぷろじぇくと、クラウドソーシングとの協力きょうりょく含みふくみます。

OpenStack(OpenStack): プライベートぷらいべーとクラウドとパブリックぱぶりっくクラウドにIaaS(サービスさーびすとしてのインフラストラクチャ)機能きのう提供ていきょうする、クラウドコンピューティングプラットフォームを構築こうちく管理かんりするためのオープンおーぷんソースそーすソフトウェアそふとうぇあツールつーるスイート。

OpenCV(OpenCV): IoTでの視覚しかくデータでーた分析ぶんせき含むふくむ画像がぞう処理しょりコンピューターこんぴゅーたービジョンびじょんアプリケーションあぷりけーしょん広くひろく使用しようされるオープンソースコンピューターこんぴゅーたービジョンびじょん機械きかい学習がくしゅうソフトウェアそふとうぇあライブラリらいぶらり

OSGi(オープンおーぷんサービスさーびすゲートウェイイニシアチブいにしあちぶ)(OSGI): システムしすてむさい起動きどう必要ひつようとせずに動的どうてきコンポーネント管理かんりインストールいんすとーる更新こうしん削除さくじょ)を可能にかのうにするモジュラーサービスさーびすプラットフォームを定義ていぎする仕様しようセットせっと

PaaS(サービスさーびすとしてのプラットフォーム)(PaaS): 顧客こきゃくアプリケーションあぷりけーしょん開発かいはつ起動きどう通常つうじょう関連かんれんするインフラストラクチャの構築こうちく維持いじ複雑ふくざつさなしに、アプリケーションあぷりけーしょん開発かいはつ実行じっこう管理かんりできるプラットフォームを提供ていきょうするクラウドコンピューティングサービスさーびすモデルもでる

PBL(問題もんだいベースべーす学習がくしゅう)(PBL): 学生がくせいオープンおーぷんエンドえんど問題もんだい解決かいけつする経験けいけん通じてつうじて主題しゅだいについて学ぶまなぶ学生がくせい中心ちゅうしん教育きょういくほう

PHセンサーせんさー(PHセンサーせんさー): 溶液ようえきのpH(酸性さんせいまたはアルカリあるかりせい)を測定そくていするセンサーせんさーで、環境かんきょう監視かんし化学かがくプロセスぷろせす含むふくむ様々なさまざまなアプリケーションあぷりけーしょん重要ですじゅうようです

フォトダイオード(フォトダイオード): ひかり電流でんりゅう変換へんかんする半導体はんどうたいデバイスでばいすで、ひかりセンサーせんさー使用しようされます。

フォトトランジスタ(フォトトランジスタ): フォトダイオードとトランジスタを組み合わせたくみあわせた半導体はんどうたいデバイスでばいすで、フォトダイオードよりもひかり対するたいする感度かんど高いたかいです。

物理ぶつりセキュリティせきゅりてぃ物理ぶつりセキュリティせきゅりてぃ): 物理ぶつりバリアばりあ監視かんしアクセスあくせす制御せいぎょ含むふくむ承認しょうにんアクセスあくせす損傷そんしょう盗難とうなんから物理ぶつり資産しさん施設しせつ保護ほごするように設計せっけいされた対策たいさく

ピコチップ(ピコチップ): こう性能せいのうてい電力でんりょく処理しょりよう設計せっけいされた集積しゅうせき回路かいろ一種いっしゅで、しばしばエッジコンピューティングと信号しんごう処理しょり使用しようされます。

圧電センサーせんさー(圧電センサーせんさー): 圧電効果こうか使用しようして、圧力あつりょく加速かそく温度おんどちから変化へんか電荷でんか変換へんかんすることで測定そくていするセンサーせんさー

PLC(電力でんりょくせん通信つうしん)(PLC): 電力でんりょくせん使用しようしてデータでーた送信そうしんする技術ぎじゅつで、既存きそん電気でんき配線はいせんでのネットワークねっとわーく通信つうしん可能にかのうにし、しばしばスマートすまーとホームほーむ工業こうぎょう環境かんきょう使用しようされます。

PoC(概念がいねん実証じっしょう)(PoC): その実現じつげん可能かのうせい実証じっしょうするための特定とくてい方法ほうほうアイデアあいであ実現じつげん、または原理げんり実証じっしょうで、概念がいねん理論りろん実用じつよう的なてきな可能かのうせい持つもつことを検証けんしょうするために使用しようされます。

ポーリング方式ほうしき(ポーリング方式ほうしき): IoTサーバーさーばーまたはサービスさーびすプラットフォームがIoTデバイスでばいすから定期ていき的にてきにデータでーた要求ようきゅうするデータでーた収集しゅうしゅう方法ほうほう

プライベートぷらいべーとクラウド(プライベートぷらいべーとクラウド): 単一たんいつ組織そしき専用せんようのクラウドコンピューティング環境かんきょうで、オンプレミスまたは第三者だいさんしゃプロバイダーぷろばいだーによってホストほすとされるかに関わらかかわらず、強化きょうかされた制御せいぎょセキュリティせきゅりてぃ提供ていきょうします。

プロトコル変換へんかん(プロトコル変換へんかん): 「’プロトコル変換へんかん‘の概念がいねん説明せつめいする」を参照さんしょう

プロトタイピング(プロトタイピング): 本格ほんかく的なてきな開発かいはつまえ概念がいねんテストてすとし、フィードバックばっく収集しゅうしゅうし、設計せっけい反復はんぷくするために、システムしすてむ製品せいひん予備よびはん(プロトタイプたいぷ)を作成さくせいするプロセスぷろせす

パブリッシュ・サブさぶスクライブ方式ほうしき(パブリッシュ・サブさぶスクライブ方式ほうしき): 送信そうしんしゃ(パブリッシャー)が特定とくてい受信じゅしんしゃ(サブスクライバー)に直接ちょくせつメッセージめっせーじ送信そうしんせず、代わりかわり公開こうかいされたメッセージめっせーじクラスくらす分類ぶんるいし、サブスクライバーがいるかどうかを知らしらないメッセージングパターンぱたーん。サブスクライバーは1つ以上いじょうクラスくらす興味きょうみ表明ひょうめいし、それに応じておうじてメッセージめっせーじ受信じゅしんします。

PWM(パルスはば変調へんちょう)(PWM): デジタルでじたる出力しゅつりょく使用しようしてアナログあなろぐ回路かいろ制御せいぎょする技術ぎじゅつで、DCモーターもーたー速度そくどやLEDの明るあかるさを制御せいぎょするために広くひろく使用しようされます。

PyTorch(PyTorch): FacebookのAI研究けんきゅうしょによって開発かいはつされたオープンソース機械きかい学習がくしゅうフレームワークで、深層しんそう学習がくしゅう研究けんきゅう開発かいはつでの柔軟じゅうなんせい使いつかいやすさで知らしられています。

Python(パイソン): 人気にんきこうレベルれべる汎用はんようプログラミングぷろぐらみんぐ言語げんごで、その豊富なほうふなライブラリらいぶらり読みよみやすさのため、データでーたサイエンスさいえんす機械きかい学習がくしゅう、IoT開発かいはつ広くひろく使用しようされています。

Q学習がくしゅう(Q学習がくしゅう): 環境かんきょうでの行動こうどう通じてつうじて意思いし決定けってい学習がくしゅうするエージェントを支援しえんする強化きょうか学習がくしゅうアルゴリズムあるごりずむで、特定とくてい状態じょうたいでの行動こうどう品質ひんしつ評価ひょうかし、累積るいせき報酬ほうしゅう最大さいだい目指しめざします。

ラズベリーパイぱい(ラズベリーパイぱい): ラズベリーパイぱい財団ざいだんによって開発かいはつされた小型こがたシングルしんぐるボードぼーどコンピューターこんぴゅーたーシリーズしりーずで、その多様たようせい手頃なてごろな価格かかくのため、IoTプロジェクトぷろじぇくと教育きょういく組みくみ込みこみシステムしすてむ広くひろく使用しようされています。

RDB(リレーショナルデータベースでーたべーす)(リレーショナルデータベースでーたべーす): 互いにたがいに関連かんれんするデータでーたポイントぽいんと保存ほぞんし、アクセスあくせす提供ていきょうするデータベースでーたべーす一種いっしゅデータでーたぎょうれつ持つもつテーブルてーぶる整理せいりされます。

強化きょうか学習がくしゅう強化きょうか学習がくしゅう): エージェントが環境かんきょう行動こうどう取るとることで累積るいせき報酬ほうしゅう最大さいだいするために意思いし決定けってい学習がくしゅうする機械きかい学習がくしゅう一種いっしゅで、しばしばロボットろぼっと制御せいぎょ自律じりつシステムしすてむ使用しようされます。

リレーショナルデータベースでーたべーす(リレーショナルデータベースでーたべーす): 「RDB」を参照さんしょう

遠隔えんかく制御せいぎょ遠隔えんかく制御せいぎょ): 通常つうじょうネットワークねっとわーく接続せつぞく介してかいして遠隔えんかくからIoTデバイスでばいすシステムしすてむ制御せいぎょする能力のうりょく

レプリカかたDB(レプリカかたDB): 可用せいたい障害しょうがいせいパフォーマンスぱふぉーまんす向上こうじょうさせるために、複数ふくすうサーバーさーばー場所ばしょデータでーた複製ふくせいされるデータベースでーたべーす

たい障害しょうがいせいたい障害しょうがいせい): 中断ちゅうだん攻撃こうげき直面ちょくめんしても、障害しょうがいから回復かいふく機能きのう維持いじするシステムしすてむ能力のうりょく

RFID(無線むせん周波しゅうはすう識別しきべつ)(RFID): 電磁でんじじょう使用しようしてオブジェクトおぶじぇくと取り付けとりつけられたタグたぐ自動じどう的にてきに識別しきべつ追跡ついせきする技術ぎじゅつ

RNN(再帰型ニューラルネットワークねっとわーく)(再帰型ニューラルネットワークねっとわーく): 内部ないぶメモリめもり維持いじすることで順次じゅんじデータでーた処理しょりするニューラルネットワークの一種いっしゅで、自然しぜん言語げんご処理しょり時系列じけいれつ分析ぶんせきなどのタスクに適しててきしています。

ロボットろぼっとロボットろぼっと): 特定とくていのタスクを実行じっこうするように設計せっけいされた自動じどうマシンましんで、しばしばIoTシステムしすてむによって制御せいぎょされ、産業さんぎょうロボットろぼっとから家庭かていサービスさーびすロボットろぼっとまで様々ですさまざまです

RMSE(じょう平均へいきん平方へいほう誤差ごさ)(じょう平均へいきん平方へいほう誤差ごさ): モデルもでる推定すいていうつわによって予測よそくされたあたい観測かんそくされたあたいあいだ差異さい測定そくていするために頻繁にひんぱんに使用しようされる指標しひょう

ROC曲線きょくせん(ROC曲線きょくせん): 識別しきべつ閾値が変化へんかするにつれてしん分類ぶんるいシステムしすてむ診断しんだん能力のうりょく示すしめすグラフィカルぐらふぃかるプロットで、機械きかい学習がくしゅうモデルもでる評価ひょうかによく使用しようされます。

RS232C(RS232C): データでーたのシリアル通信つうしん送信そうしん標準ひょうじゅん

RS485(RS485): より長いながい距離きょり騒音そうおん環境かんきょうでのデータでーた送信そうしん可能にかのうにするシリアル通信つうしん標準ひょうじゅん

SaaS(サービスさーびすとしてのソフトウェアそふとうぇあ)(SaaS): ソフトウェアそふとうぇあアプリケーションあぷりけーしょんがベンダーによってホストほすとされ、インターネットいんたーねっと経由けいゆ顧客こきゃく提供ていきょうされるクラウドコンピューティングサービスさーびすモデルもでる

サンプリング周波しゅうはすう(サンプリング周波しゅうはすう): 離散りさん信号しんごう作成さくせいするために連続れんぞく信号しんごうから取得しゅとくされる単位たんい時間じかんあたりのサンプルさんぷるすうで、データでーた表現ひょうげん精度せいど影響えいきょうします。

SD-WAN(ソフトウェアそふとうぇあ定義ていぎ広域こういきネットワークねっとわーく)(SD-WAN): 企業きぎょうがMPLS、LTE、ブロードバンドインターネットいんたーねっとサービスさーびす含むふくむ任意のにんいの組み合わせくみあわせ転送てんそうサービスさーびす活用かつようして、ユーザーゆーざーアプリケーションあぷりけーしょん安全にあんぜんに接続せつぞくできる仮想かそうWAN アーキテクチャ。

セキュアブート(セキュアブート): デバイスでばいすのブートプロセスぷろせすちゅうに、承認しょうにんされた権限けんげんによって署名しょめいされた信頼しんらいできるソフトウェアそふとうぇあのみがロードろーどされることを確保かくほし、悪意あくいあるソフトウェアそふとうぇあ制御せいぎょ取るとることを防ぐふせぐセキュリティせきゅりてぃメカニズムめかにずむ

セキュリティせきゅりてぃポリシーぽりしーセキュリティせきゅりてぃポリシーぽりしー): 組織そしきがその情報じょうほう資産しさんをどのように保護ほごするかを定義ていぎするルールるーるガイドラインがいどらいんセットせっとで、許可きょかされる使用しようアクセスあくせす制御せいぎょ、インシデント対応たいおう手順てじゅんを概説します。

自己じこ適合てきごう宣言せんげん自己じこ適合てきごう宣言せんげん): 製品せいひんベンダーが、外部がいぶ検証けんしょうなしに、自社じしゃ製品せいひん特定とくてい技術ぎじゅつ標準ひょうじゅんセキュリティせきゅりてぃ要件ようけん満たすみたすことを宣言せんげんするプロセスぷろせす

半導体はんどうたいセンサーせんさー半導体はんどうたいセンサーせんさー): 半導体はんどうたい材料ざいりょう特性とくせい使用しようして物理ぶつりりょうれいひかり温度おんど圧力あつりょく)を検出けんしゅつし、電気でんき信号しんごう変換へんかんするセンサーせんさー

センサーせんさーセンサーせんさー): 物理ぶつり環境かんきょうからの何らかなんらか入力にゅうりょくれいひかりねつ動きうごき圧力あつりょく)を検出けんしゅつし、それに応答おうとうして電子でんしデバイスでばいす読みよみ取れるとれる信号しんごう変換へんかんするデバイスでばいす

シリアル通信つうしん(シリアル通信つうしん): 単一たんいつチャネルちゃねる一度にいちどに1ビットびっとずつデータでーた送信そうしんするデータでーた送信そうしん方法ほうほうで、しばしばマイクロコントローラーと周辺しゅうへん機器ききかん通信つうしん使用しようされます。

SI単位たんい国際こくさい単位たんいけい)(SI単位たんい): ながさのメートルめーとる質量しつりょうキロきろグラムぐらむ時間じかんびょう含むふくむ国際こくさい測定そくてい単位たんいシステムしすてむ

シグフォックス(シグフォックス): 最小さいしょうげん帯域たいいきはば長いながいバッテリーばってりー寿命じゅみょう必要ひつようとするIoTデバイスでばいすよう設計せっけいされたてい電力でんりょく広域こういきネットワークねっとわーく(LPWAN)接続せつぞくソリューションそりゅーしょん

スマートすまーと工場こうじょうスマートすまーと工場こうじょう): IoT、AI、自動じどう使用しようして生産せいさんプロセスぷろせす最適さいてきし、効率こうりつ向上こうじょうさせ、リアルりあるタイムたいむ意思いし決定けってい可能にかのうにする高度にこうどにデジタルでじたるされ接続せつぞくされた製造せいぞう施設しせつ

スマートすまーとメータめーたスマートすまーとメータめーた): 電気でんきエネルギーえねるぎーみず消費しょうひ記録きろくし、監視かんし請求せいきゅうのためにその情報じょうほう供給きょうきゅう業者ぎょうしゃ伝達でんたつする電子でんしデバイスでばいす

スマートフォンゲートウェイ(スマートフォンゲートウェイ): IoTゲートウェイとして機能きのうするスマートフォンで、その接続せつぞくせい処理しょり能力のうりょく活用かつようして近くちかくのIoTデバイスでばいすからデータでーた収集しゅうしゅうし、クラウドにリレーりれーします。

ソラナ(ソラナ): こう性能せいのうブロックぶろっくチェーンちぇーんプラットフォーム。(これは提供ていきょうされたテキストてきすとないのIoT技術ぎじゅつ直接ちょくせつ関係かんけいしない例外れいがい的なてきな用語ようごのようですが、用語ようごしゅうにあります)。

溶媒抽出ちゅうしゅつ(溶媒抽出ちゅうしゅつ): 2つの混和こんわせい液体えきたいでの異なることなる溶解ようかい基づいてもとづいて化合かごうぶつ分離ぶんりするために使用しようされる方法ほうほう。(これも例外れいがい的なてきな用語ようごのようです)。

SoS(システムしすてむ・オブ・システムズ)(SoS): 個々ここシステムしすてむでは不可能なふかのうな新しいあたらしい能力のうりょく性能せいのう提供ていきょうするために統合とうごうされた独立どくりつした運用うんようシステムしすてむコレクションこれくしょん

空間くうかん知能ちのうシステムしすてむ空間くうかん知能ちのうシステムしすてむ): オブジェクトおぶじぇくとロボットろぼっと物理ぶつりてき環境かんきょう知覚ちかくし、それに応じておうじて行動こうどう調整ちょうせいできるようにするシステムしすてむで、しばしば家庭かてい自動じどう高齢こうれいしゃケアけあ使用しようされます。

SPI(シリアル周辺しゅうへんインターフェース)(SPI): たん距離きょり通信つうしん主におもに組みくみ込みこみシステムしすてむ使用しようされる同期どうきシリアル通信つうしんインターフェース仕様しよう

標準ひょうじゅん標準ひょうじゅん): 製品せいひんサービスさーびす相互そうご運用うんようせい品質ひんしつ一貫いっかんせい確保かくほするための合意ごういされたプロトコル、手順てじゅん仕様しようである技術ぎじゅつ標準ひょうじゅん開発かいはつ実装じっそうするプロセスぷろせす

スターすたーかたスターすたーけい): かくノード(デバイスでばいす)が中央ちゅうおうハブはぶ個別こべつ接続せつぞくされるネットワークねっとわーくトポロジーで、デバイスでばいす追加ついか削除さくじょ簡単ですかんたんですが、単一たんいつ障害しょうがいてん作成さくせいします。

統計とうけい解析かいせき統計とうけい解析かいせき): パターンぱたーん関係かんけいトレンドとれんど特定とくていするためにデータでーた収集しゅうしゅう分析ぶんせき解釈かいしゃく提示ていじ整理せいりするプロセスぷろせす

ステッピングモータ(ステッピングモータ): フルふる回転かいてん多数たすう等しいひとしいステップすてっぷ分割ぶんかつするブラシレスDC電気でんきモーターもーたーで、精密なせいみつな位置いち制御せいぎょ可能にかのうにします。

ストリーミング処理しょり(ストリーミング処理しょり): 「バッチ処理しょり」を参照さんしょう

ひずみセンサーせんさー(ひずみセンサーせんさー): オブジェクトおぶじぇくと変形へんけいやひずみを測定そくていするセンサーせんさーで、しばしばロードろーどセルせる圧力あつりょくセンサーせんさー使用しようされます。

スタックスネット(スタックスネットねっと): イランいらんかくプログラムぷろぐらむへの攻撃こうげき悪名高いあくめいたかい悪意あくいあるコンピューターこんぴゅーたーワームで、工業こうぎょう制御せいぎょシステムしすてむのサイバー攻撃こうげき対するたいする脆弱ぜいじゃくせい浮き彫りうきぼりにしました。

教師きょうしあり学習がくしゅう教師きょうしあり学習がくしゅう):機械きかい学習がくしゅう」を参照さんしょう

SVM(サポートベクターマシン)(SVM): 2グループぐるーぷ分類ぶんるい問題もんだい分類ぶんるいアルゴリズムあるごりずむ使用しようする教師きょうしあり機械きかい学習がくしゅうモデルもでるで、パターンぱたーん認識にんしき広くひろく使用しようされます。

TCP/IP(TCP/IP): インターネットいんたーねっと基盤きばん通信つうしんプロトコルセットせっとである伝送でんそう制御せいぎょプロトコル/インターネットいんたーねっとプロトコルで、コンピューターこんぴゅーたーネットワークねっとわーくでのデータでーた転送てんそう広くひろく使用しようされます。

テレワーク(テレワーク): 通常つうじょう自宅じたくから、情報じょうほう通信つうしん技術ぎじゅつ使用しようしてリモートで作業さぎょうすること。

温度おんどセンサーせんさー温度おんどセンサーせんさー): 温度おんど測定そくていし、ねつエネルギーえねるぎー電気でんき信号しんごう変換へんかんするデバイスでばいすで、様々なさまざまなIoTアプリケーションあぷりけーしょんでよく使用しようされます。

テンソルフローふろー(テンソルフロー): Googleによって開発かいはつされたオープンソース機械きかい学習がくしゅうフレームワークで、深層しんそう学習がくしゅうとニューラルネットワークねっとわーく開発かいはつ広くひろく使用しようされます。

シンクライアント(シンクライアント): 処理しょり大部分だいぶぶんサーバーさーばー大きくおおきく依存いぞんする軽量けいりょうコンピューターこんぴゅーたー

時系列じけいれつデータでーた時系列じけいれつデータでーた): 時間じかん順にじゅんにインデックス付けつけされたデータでーたポイントぽいんとで、時間じかんにわたるトレンドとれんど分析ぶんせき予測よそく異常いじょう検知にとって重要ですじゅうようです

TLS(トランスポートそうセキュリティせきゅりてぃ)(TLS): コンピューターこんぴゅーたーネットワークねっとわーくでの通信つうしんセキュリティせきゅりてぃ提供ていきょうするように設計せっけいされた暗号あんごうプロトコルで、安全なあんぜんなWebブラウジング(HTTPS)に広くひろく使用しようされます。

トピック(トピック): MQTTなどのパブリッシュ・サブさぶスクライブメッセージングモデルもでるで、メッセージめっせーじ公開こうかいされ、サブさぶスクすくライバーがメッセージめっせーじ受信じゅしんする主題しゅだいカテゴリかてごりとして機能きのうする文字もじれつ

トランスファージェット(トランスファージェット): 非常にひじょうに短いみじかい距離きょりでのデバイスでばいすかん高速こうそくデータでーた交換こうかんのための近接きんせつ無線むせん転送てんそう技術ぎじゅつ

トランジスタ(トランジスタ): 電子でんし信号しんごう電力でんりょく増幅ぞうふくまたは切り替えるきりかえるために使用しようされる半導体はんどうたいデバイスでばいす

ツリーつりーかた(ツリーかた): バスばすスターすたーかたトポロジーじー側面そくめん組み合わせたくみあわせたネットワークねっとわーくトポロジーで、複数ふくすうのスターネットワークが中央ちゅうおうバスばす介してかいして接続せつぞくされます。

双方向そうほうこう通信つうしん方式ほうしき双方向そうほうこう通信つうしん方式ほうしき): りょう当事とうじしゃ同時にどうじに情報じょうほう送受信そうじゅしんできる通信つうしん方法ほうほうで、対話たいわけい制御せいぎょとフィードバックばっく可能にかのうにします。

ちょう音波おんぱセンサーせんさーちょう音波おんぱセンサーせんさー): ちょう音波おんぱ発しはっし、それらが反射はんしゃして戻ってもどってくるのにかかる時間じかん測定そくていするセンサーせんさーで、距離きょり測定そくていオブジェクトおぶじぇくと検出けんしゅつ流量りゅうりょう測定そくてい使用しようされます。

UART(汎用はんよう同期どうき受信じゅしん/送信そうしん)(UART): 並列へいれつ直列ちょくれつ形式けいしきかんデータでーた変換へんかんするハードウェアはーどうぇあデバイスでばいすで、マイクロコントローラーとデバイスでばいすかん直列ちょくれつ通信つうしんによく使用しようされます。

教師きょうしなし学習がくしゅう教師きょうしなし学習がくしゅう):機械きかい学習がくしゅう」を参照さんしょう

UWB(ちょうひろ帯域たいいき)(UWB): たん距離きょりこう帯域たいいきはば通信つうしんのための無線むせん技術ぎじゅつで、こう精度せいど位置いち特定とくていデータでーた転送てんそう可能にかのうにします。

V2X(Vehicle-to-Everything)(V2X): 車両しゃりょうがその環境かんきょう情報じょうほう交換こうかんすることを可能にかのうにする通信つうしんシステムしすてむで、車両しゃりょう(V2V)、インフラストラクチャ(V2I)、歩行ほこうしゃ(V2P)、ネットワークねっとわーく(V2N)を含みふくみます。

VAE(変分オートエンコーダ)(変分オートエンコーダ): 入力にゅうりょくデータでーたから潜在せんざい空間くうかんへの確率かくりつてきマッピングを学習がくしゅうする生成せいせいモデルもでるで、新しいあたらしいデータでーたサンプルさんぷる生成せいせい使用しようされます。

WAN(広域こういきネットワークねっとわーく)(広域こういき通信つうしんもう): くに大陸たいりくなどの大きなおおきな地理ちりてき領域りょういき拡張かくちょうする電気でんき通信つうしんネットワークねっとわーくで、しばしば複数ふくすうローカルろーかるエリアえりあネットワークねっとわーく(LAN)を接続せつぞくします。

ウォーターフォールけい開発かいはつ(ウォーターフォールけい開発かいはつ): 開発かいはつライフらいふサイクルさいくるかく段階だんかいれい要件ようけん設計せっけい実装じっそうテストてすと)が次のつぎの段階だんかい始まるはじまるまえ完了かんりょうしなければならない従来じゅうらい線形せんけいソフトウェアそふとうぇあ開発かいはつ方法ほうほうろん

ウェアラブル生体せいたいセンサーせんさー(ウェアラブル生体せいたいセンサーせんさー): 健康けんこうとフィットネス追跡ついせきのために生理せいりがくてきパラメーター(れい心拍しんぱくすう体温たいおん加速かそく)を監視かんしするウェアラブルデバイスに統合とうごうされたセンサーせんさー

Webサービスさーびす(Webサービスさーびす): ネットワークねっとわーくじょうでの相互そうご運用うんよう可能なかのうなマシンましんかん相互そうご作用さようサポートさぽーとするように設計せっけいされたソフトウェアそふとうぇあシステムしすてむ

WebSocket(WebSocket): 単一のたんいつのTCP接続せつぞくぜん二重通信つうしんチャネルちゃねる提供ていきょうするコンピューターこんぴゅーたー通信つうしんプロトコルで、クライアントくらいあんとサーバーさーばーかんリアルりあるタイムたいむ対話たいわ通信つうしん可能にかのうにします。

Wi-Fi(Wi-Fi): デバイスでばいす無線むせん電波でんぱ使用しようしてローカルろーかるエリアえりあネットワークねっとわーく(LAN)とインターネットいんたーねっと接続せつぞくすることを可能にかのうにする無線むせんネットワーキング技術ぎじゅつ

Wi-SUN(Wi-SUN): IEEE 802.15.4g標準ひょうじゅん使用しようするIoTの無線むせん通信つうしん標準ひょうじゅんで、てい電力でんりょく消費しょうひでの広域こういき通信つうしんよう最適さいてきされ、しばしばスマートメーターと家庭かていエネルギーえねるぎー管理かんりシステムしすてむ使用しようされます。

WiMAX(Worldwide Interoperability for Microwave Access)(WiMAX): IEEE 802.16標準ひょうじゅん基づくもとづく無線むせんブロードバンド通信つうしん標準ひょうじゅんファミリーふぁみりーで、様々なさまざまなモードもーどちょう距離きょり無線むせんデータでーた提供ていきょうします。

XML(拡張かくちょう可能かのうマークアップ言語げんご)(XML): 人間にんげん読めてよめて機械きかい読めるよめる形式けいしき文書ぶんしょエンコードえんこーどするためのルールるーるセットせっと定義ていぎするマークアップ言語げんごで、しばしばデータでーた交換こうかん使用しようされます。

X線えっくすせんX線えっくすせん): 様々なさまざまな画像がぞう技術ぎじゅつ使用しようされる電磁でんじ放射ほうしゃいち形態けいたい。(これも例外れいがい的なてきな用語ようごのようです)。

Z-Wave(Z-Wave): 主におもに家庭かてい自動じどう使用しようされる無線むせん通信つうしんプロトコルで、スマートすまーとホームほーむデバイスでばいすようのメッシュネットワークねっとわーく提供ていきょうします。

ゼロぜろトラスト(ゼロトラスト):ゼロぜろトラスト」を参照さんしょう

ZigBee(ZigBee): IEEE 802.15.4に基づくもとづくていコストこすとてい電力でんりょく無線むせんメッシュネットワークねっとわーく標準ひょうじゅんで、しばしば家庭かてい自動じどうスマートすまーと照明しょうめい工業こうぎょうアプリケーションあぷりけーしょん使用しようされます。

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2024-07-31
量子力学

第一公设:状态空间

公设 1:与任何物理系统相关的是一个称为系统状态空间的复向量空间。如果系统是孤立的,那么系统完全由其状态向量描述,该状态向量是系统状态空间中的一个单位向量。

这段话可能看起来内容很复杂,但你已经知道了大部分内容。特别是,我们已经广泛地探讨过量子比特,并且我们已经在实际操作中看到了这个公设。

对于量子比特,量子系统状态空间是一个二维复向量空间。量子系统状态向量 $\left|\psi\right\rangle$ 的所有概率振幅(特定分量的系数)都可以是复数,我们用 $\alpha$ 和 $\beta$ 来表示它们,因此状态向量是 $\alpha \left| 0 \right\rangle + \beta \left| 1 \right\rangle$。这里的约束条件是『概率振幅的长度的平方和为 $1$』,即 $\left| \alpha \right|^2 + \left| \beta \right|^2 = 1$。

这被称为归一化约束:『量子系统状态向量的所有概率振幅的长度的平方之和必须等于 $1$』。

之所以这么称呼是因为如果你将 $\left| 0 \right\rangle$ 和 $\left| 1 \right\rangle$ 视为正交规范向量,那么归一化约束是这种要求:『状态向量的长度 $\|\left|\psi\right\rangle\|$ 等于 $1$』。因此,状态向量是该状态空间中的单位向量或规范化向量,这就是为什么称之为「归一化约束」。

『状态向量是单位向量』的条件表达了这种思想:『基于计算基的测量的结果的概率加起来为 $1$』。

第二公设:幺正动力学

量子力学的第一公设告诉我们如何描述状态。那么状态如何变化,即量子系统的动力学呢?这就是第二公设的内容。在之前的文章中,我们看到量子门是通过作用于量子系统状态空间的幺正矩阵来描述的。第二公设告诉我们,对于任何孤立的量子系统来说,情况也是类似的:

公设2:孤立量子系统的演化由作用于系统状态空间的幺正矩阵描述。即,时间 $t_1$ 时系统的状态 $|\psi\rangle$ 与时间 $t_2$ 时的状态 $|\psi'\rangle$ 通过幺正矩阵 $U$ 相关联:$|\psi'\rangle = U |\psi\rangle$。该矩阵 $U$ 可以依赖于时间 $t_1$ 和 $t_2$,但不依赖于状态 $|\psi\rangle$ 和 $|\psi'\rangle$。

我们的量子门展示了这个公设的实际应用。例如,Pauli $X$ 门,也称为量子 NOT 门,就是一个例子。它在量子回路和矩阵表示中如下所示,以及其对状态的显式作用:

$$ X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} $$$$ X (\alpha |0\rangle + \beta |1\rangle) = \beta |0\rangle + \alpha |1\rangle $$

Hadamard 门 $H$ 也是如此:

$$ H = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} $$$$ H(\alpha|0\rangle + \beta|1\rangle) = \frac{\alpha + \beta}{\sqrt{2}}|0\rangle + \frac{\alpha - \beta}{\sqrt{2}}|1\rangle $$

依此类推,通过受控 NOT 门,Toffoli 门,以及我们之前遇到的所有其他量子门。

为什么在第二公设中出现的是幺正矩阵?如果你试着在纸上写下几个矩阵,很快就会发现大多数矩阵都不是幺正的,甚至远非如此。为什么我们不能在第二公设中使用一般的矩阵?一个部分解释是,幺正矩阵是唯一保持长度不变的矩阵。如果我们希望量子态保持归一化,那么幺正矩阵是唯一能做到这一点的矩阵,因为任何其他矩阵都会导致范数的变化。而这种归一化又与测量结果的概率和为一的要求有关。在这种意义上,量子力学的公设形成了一个紧密相连的网络,一个公设中的幺正性要求反映了另一个地方的要求,例如状态向量的归一化或概率和为一。

如何确定描述特定物理情境所需的幺正变换?正如你从我们对第一公设的讨论中所猜到的,第二公设对此问题保持沉默。需要逐案解决。像量子电动力学(QED)和标准模型这样的理论提供了额外的规则,指定了它们所描述系统的精确(幺正)动力学。就像之前一样:量子力学是一个框架,而不是一个完整的物理理论。但告诉我们用幺正变换来描述动力学已经是一个非常具有约束性的声明了。而且,和以前一样,量子回路模型是一个有用的例子来源,使用它是建立直觉的好方法。

更广泛地说:尽管量子力学在1920年代达到了最终形式,但物理学家们花了二十世纪的大部分时间来弄清楚需要什么样的幺正动力学、状态空间和量子态来描述这个或那个系统。你不能只解决这个问题一次:光学物理学家需要为光解决它,原子物理学家需要为原子解决它,粒子物理学家一直在为标准模型所描述的全部粒子的“众神”谱系解决它。尽管如此,尽管关于这两个公设的应用还有很多要学习,但它们已经为我们提供了一个非常具有约束力的框架,用于思考世界是什么以及它如何变化。

你可能注意到,就像第一公设一样,第二公设也有一个关于使用幺正矩阵描述孤立系统动力学的警告。当然,在自然界中,大多数物理系统并不是孤立的,甚至不接近孤立。例如,假设你正在尝试建造一台量子计算机,使用原子来存储量子比特的状态。例如,我们可以用电子的两个不同轨道壳层对应 $|0\rangle$ 和 $|1\rangle$ 状态。再假设你通过短暂照射激光光束在原子上来实现量子门,使电子在壳层之间移动。

这样的原子并不是孤立的:它与激光强烈相互作用。但事实证明,即使在激光照射下,原子的动力学仍然可以用幺正变换来很好地描述。这并不是显而易见的;它需要详细的研究。但是结果是,虽然第二公设只直接适用于孤立系统,但令人惊讶的是,通常情况下可以用幺正动力学来描述非孤立系统的动力学。实际上,当我们上面说量子门是第二公设的例子时,这并不完全正确。通常,量子门涉及非孤立系统。但通过精心设计,它们仍然实现了幺正操作。

我们以最常在量子回路上下文中使用的形式提出了第二公设,即通过离散门操作引起量子态的离散变化。现在我们将简要展示另一种形式,其中量子态的演化在连续时间内平滑变化,变化由微分方程描述。我们不会经常使用这种形式,所以你不需要深入理解所有细节——这里只是让你了解一下大意。控制量子态随时间变化率的方程如下:

$$ i \frac{d |\psi\rangle}{dt} = H |\psi\rangle. $$

这个方程被称为薛定谔方程。矩阵 $ H $ 是一个(固定的)厄米矩阵,称为系统的哈密顿量。(这与哈达玛门不同,这只是一个不幸的符号巧合)。你可以认为哈密顿量 $ H $ 告诉量子态如何变化。薛定谔方程因此提供了量子态动力学的连续时间描述,而第二公设则侧重于离散时间描述。

通过求解薛定谔方程,我们可以将系统在时间 $ t_2 $ 的状态与时间 $ t_1 $ 的状态联系起来。解为:

$$ |\psi_{t_2}\rangle = e^{-iH(t_2 - t_1)} |\psi_{t_1}\rangle. $$

当然,尽管写出矩阵指数很容易,但在实际计算中往往需要相当多的工作!

传统的量子力学处理方法花费大量时间讨论用于描述不同物理系统的哈密顿量,并(通常相当繁琐地)计算矩阵指数的值。这些是重要且有价值的技术问题,但对理解量子力学的基本原理并不是必需的。尽管如此,值得注意的是,上述解与第二公设是一致的:特别是,可以证明 $ e^{-iH(t_2 - t_1)} $ 是一个幺正矩阵。实际上,如果你在想“薛定谔方程中的因子 $ i $ 是从哪里来的”或“为什么哈密顿量 $ H $ 需要是厄米矩阵”,答案都是为了得到幺正演化。因此,一切都很好地结合在一起。事实上,还有一个非正式的论证,可以让你反过来从第二公设出发(加上一些额外的假设)推导出薛定谔方程。我们这里不深入讨论细节,但值得注意的是,这是可能的。

从这段讨论中值得记住的是一些基本概念:哈密顿量的术语,薛定谔方程的作用(定性上),以及薛定谔方程与第二公设的广泛联系。我们不会要求你记住薛定谔方程的细节——这些确实需要更深入的解析和一些详细的例子。另一方面,了解薛定谔方程的作用是有价值的:它描述了孤立物理系统的量子态随时间变化的速率。下面的问题有点超出本文的主要范围。但它们被包括在这里,这样如果你在以后的阅读中遇到诸如“哈密顿量”之类的术语,你会有一个基本的理解基础。

第三公设:测量

第三公设是量子力学公设中最奇特的。为了解释其内容,有必要回顾一下《非常好奇的量子计算》中的一段内容:

假设有一位(假设的!)量子物理学家名叫爱丽丝,她在实验室里准备了一个量子态为 $\alpha |0\rangle + \beta |1\rangle$ 的量子比特。然后她将她的量子比特交给另一位量子物理学家鲍勃,但并没有告诉他 $\alpha$ 和 $\beta$ 的值。鲍勃有没有办法弄清楚 $\alpha$ 和 $\beta$ 呢?也就是说,他是否能通过某种实验来弄清这个量子态的身份?

令人惊讶的答案是:不行!事实上,如果 $\alpha$ 和 $\beta$ 是未知的,就没有办法弄清它们。换句话说,任何系统的量子态——无论是量子比特还是其他系统——都不能直接观察到。

[我们] 之所以说这是令人惊讶的,是因为它与我们平时日常思维方式中对世界运作方式的理解非常不同。如果你的车有问题,机械师可以使用诊断工具来了解发动机的内部状态。诊断工具越好,他们能了解的就越多。当然,发动机的某些部分可能不太方便接触——也许他们不得不拆开某个部分,或者使用显微镜,但如果机械师告诉你物理定律禁止他们弄清发动机的内部状态,你可能会感到怀疑。

在早期的文章中,我们描述了计算基中的测量。这个过程控制了你如何从量子计算机中获取信息。回忆一下最简单的版本,即仅测量一个量子比特在计算基中的情况。在这个过程中,如果你测量一个量子态为 $\alpha |0\rangle + \beta |1\rangle$ 的量子比特,那么你将以 $|\alpha|^2$ 的概率得到结果 $0$,以 $|\beta|^2$ 的概率得到结果 $1$。在这两种情况下,后验状态分别是 $|0\rangle$ 和 $|1\rangle$。

第三公设概括了这种测量的思想:

公设3: 量子测量由一组测量算符 $\{M_m\}$ 描述。(在初等线性代数中,术语“算符”通常与“矩阵”基本上可以互换使用。在无限维空间中,这两个术语的含义略有不同,但在我们有限维的上下文中可以互换使用。测量算符这个术语比测量矩阵更常见,所以我们采用这个术语。)每个 $M_m$ 是作用于被测系统状态空间的矩阵。索引 $m$ 取值对应于实验中可能出现的测量结果。如果量子系统的状态在测量前是 $|\psi\rangle$,那么结果 $m$ 出现的概率由下式给出:

$$ p(m) = \| M_m | \psi \rangle \|^2 = \langle \psi | M_m^\dagger M_m | \psi \rangle, $$

而系统在测量后的状态,通常称为后验状态,为

$$ \frac{M_m |\psi\rangle}{\| M_m | \psi \rangle \|} = \frac{M_m |\psi\rangle}{\sqrt{\langle \psi | M_m^\dagger M_m | \psi \rangle}}. $$

(值得注意的是:(a) 分母只是概率 $p(m)$ 的平方根;(b) 这是一个适当归一化的量子态。)测量算符满足完备性关系(我们所陈述的公设是一些量子力学教科书中所给出的表述的推广,基于通常称为投影测量的概念。这两个表述是等价的,与其他公设结合使用时。我们选择当前的表述是因为它在数学上更简单和更强大,而不是基于投影测量的表述。我们认为这种表述应该从量子力学教科书中删除。),

$$ \sum_m M_m^\dagger M_m = I. $$

在这个公设中有很多内容。但它主要表达了我们已经看到的想法,尽管之前是隐藏的。我们会在稍后给出一个具体的例子,但首先要解释完备性关系的含义。它只是表达了概率和为1的想法。通过在完备性关系前乘以 $\langle \psi|$ 并在后乘以 $|\psi\rangle$,我们可以看到这给出了

$$ \sum_m p(m) = \sum_m \langle \psi | M_m^\dagger M_m | \psi \rangle = \langle \psi | I | \psi \rangle = \langle \psi | \psi \rangle = 1, $$

其中我们假设 $|\psi\rangle$ 是一个量子态,因此被归一化后的长度为1。

为了理解第三公设的意义,最好通过具体案例来说明,比如在计算基中测量单个量子比特。在这种情况下,测量算符是 $M_0 = |0\rangle\langle 0|$ 和 $M_1 = |1\rangle\langle 1|$。如果我们用显式的振幅写出量子态 $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$,应用第三公设最简单。根据第三公设,结果 $0$ 的概率为:

$$ p(0) = \langle \psi | M_0^\dagger M_0 | \psi \rangle = \langle \psi | 0 \rangle \langle 0 | 0 \rangle \langle 0 | \psi \rangle. $$

当然,$|0\rangle$ 是归一化的,所以 $\langle 0 | 0 \rangle = 1$,这变成了:

$$ p(0) = \langle \psi | 0 \rangle \langle 0 | \psi \rangle = |\langle 0 | \psi \rangle|^2. $$

但 $\langle 0 | \psi \rangle = \alpha$,因此这告诉我们测量结果 $0$ 的概率是 $p(0) = |\alpha|^2$,正如我们所预期的。完全相同的计算,只是将 $0$ 替换为 $1$,显示了 $p(1) = |\beta|^2$,也如我们所预期的。

后验状态呢?让我们考虑测量结果 $m = 0$ 的情况。在这种情况下,第三公设告诉我们后验状态为

$$ \frac{| 0 \rangle \langle 0 | \psi\rangle}{\sqrt{p(0)}}. $$

我们已经看到 $p(0) = |\alpha|^2$。当然,$\langle 0 | \psi \rangle = \alpha$。因此,后验状态为:

$$ \frac{\alpha}{|\alpha|} |0\rangle. $$

这是一个看起来很奇怪的状态!前面的因子 $\alpha / |\alpha|$ 看起来很复杂,但它只是一个全局相位因子。在《非常好奇的量子计算》中,我们观察到这样的全局相位因子永远不会影响测量概率,因此通常认为只在全局相位因子上有所不同的量子态是相同的。因此,上述状态可以被认为等同于量子态 $|0\rangle$,正如我们预期的那样。在类似的方式下,我们可以显示,如果测量结果是 $1$,则后验状态是 $|1\rangle$(同样,我们忽略全局相位因子)。

《非常好奇的量子计算》中,我们对忽略全局相位因子的论证是含糊的。事实上,这些公设可以用来使论证无懈可击。假设我们有两个量子态,它们通过一个全局相位因子相关联,$|\psi'\rangle = e^{i\theta} |\psi\rangle$。那么这两个状态的测量概率总是相同的:

$$ p'(m) = \langle \psi' | M_m^\dagger M_m | \psi' \rangle = \langle \psi | M_m^\dagger M_m | \psi \rangle = p(m). $$

虽然我们不会明确展示,但全局相位因子也会在幺正动力学和后验状态计算中保持不变。因此,这样的相位因子对任何可观测量都没有影响。实际上,有时人们会用不同的表述重新陈述这些公设,完全消除这样的全局相位因子。我们没有这样做的原因是这会显著复杂化表述。使用我们已经提出的非正式论证既更简单也更符合常规。

顺便提一句,你可能会想,如果在第三公设中,后验状态中的分母 $\sqrt{\langle \psi | M_m^\dagger M_m | \psi \rangle}$ 为零会发生什么?那样不会使后验状态未定义吗?幸运的是,这只能在测量结果的概率为零时发生。这也意味着测量结果永远不会发生,所以我们不需要担心。

我们进行了大量工作只是为了分析一个量子测量!好消息是我们很少需要进行这样的工作。相反,你会建立一个常见测量算符模式的库。实际上,在量子计算中,你主要会对计算基中的测量感兴趣。而且还有一些其他常见的测量,我们将在本文后面讨论。在实践中,你很少需要进行如上所述的计算。

让我们介绍一种新类型的测量,这是我们在之前的文章中没有见过的。这是一种单量子比特测量,但不是在计算基中进行的测量。回忆一下等幅叠加态:

$$ |+⟩ = \frac{|0⟩ + |1⟩}{\sqrt{2}}; \quad |−⟩ = \frac{|0⟩ - |1⟩}{\sqrt{2}}。$$

现在我们定义的测量是所谓的“在 $ |+⟩, |−⟩ $ 基中进行的测量”。特别地,我们定义测量算符 $ M_+ = |+⟩⟨+| $ 和 $ M_− = |−⟩⟨−| $。我们不会详细推导计算过程,但如果你愿意,可以检查完备关系 $ M_+^\dagger M_+ + M_-^\dagger M_- = I $。进行这个检查只是一个小小的矩阵计算。我们要重点理解的是测量概率和后验状态。

从被测量的状态展开为 $ |ψ⟩ = α |0⟩ + β |1⟩ $ 开始是很有诱惑力的——事实上,这是一个好主意!如果你这样做了,你可以推导出测量概率和后验状态。但有一个技巧可以简化这个过程。值得停下来想一下,看你能不能想出这个技巧是什么。有什么想法吗?

这个技巧是:观察到我们同样可以将 $ |ψ⟩ $ 展开为 $ |+⟩ $ 和 $ |−⟩ $ 态,即 $ |ψ⟩ = γ |+⟩ + δ |−⟩ $。我们当然可以这样做,因为 $ |+⟩ $ 和 $ |−⟩ $ 是二维向量空间中线性无关(实际上是正交归一)的态。你现在能猜出测量概率和后验状态是什么吗,通过与在计算基中测量的类比?

我们稍后会详细计算,但值得先陈述结果:$ + $ 结果的概率是 $ |γ|^2 $,后验状态是 $ |+⟩ $;而 $ − $ 结果的概率是 $ |δ|^2 $,后验状态是 $ |−⟩ $。这很像计算基中的测量,计算过程也很像之前计算基中测量的过程。特别地,对于 $ + $ 测量,我们有:

$$ p(+) = ⟨ψ| M_+^\dagger M_+ |ψ⟩ = (γ^* ⟨+| + δ^* ⟨−|) |+⟩⟨+|+⟩⟨+| (γ |+⟩ + δ |−⟩)。$$

当然,$ ⟨+|+⟩ = 1 $。如果你忘了,快速计算表明 $ ⟨+|−⟩ = 0 $,即 $ |+⟩ $ 和 $ |−⟩ $ 状态是正交的。因此,上述表达式变成:

$$ p(+) = (γ^* ⟨+| + δ^* ⟨−|) |+⟩⟨+| (γ |+⟩ + δ |−⟩) = \left|γ\right|^2。$$

类似但更简单的计算表明 $ M_+ |ψ⟩ = γ |+⟩ $,因此对应的后验状态是 $ \frac{γ}{|γ|} |+⟩ $,这在一个全局相位因子上是 $ |+⟩ $ 状态。类似的计算表明,$ − $ 结果的概率是 $ |δ|^2 $,后验状态是 $ |−⟩ $(同样,忽略全局相位)。实际上,我们只说后验状态分别是 $ |+⟩ $ 和 $ |−⟩ $。

如果我们坚持 $ |ψ⟩ = α |0⟩ + β |1⟩ $ 会发生什么?计算会稍微复杂一些,但当然我们最终会得到相同的结果,尽管是用 $ α $ 和 $ β $ 表示,而不是 $ γ $ 和 $ δ $。


可观察量

更一般地说,如果我们有一组测量算符 $\{M_m\}$,那么平均结果是 $$ \sum_m p(m)m = \sum_m \langle \psi | M_m^\dagger M_m | \psi \rangle m, $$ 其中左边的项只是平均值的定义,而右边的项来自第三公设。但我们可以将求和放到内部,我们看到平均值只是 $ \langle \psi | M | \psi \rangle $,其中 $$ M := \sum_m m M_m^\dagger M_m. $$

$M$ 被称为对应于测量 $\{M_m\}$ 的可观察量。这个可观察量是一个单一的、固定的算符,仅依赖于测量结果 $m$ 和测量算符 $M_m$。然而,如果你知道可观察量,那么计算平均测量结果通常很容易:它只是 $ \langle \psi | M | \psi \rangle $。事实上,这非常方便,以至于它经常以缩写形式表示为 $ \langle M \rangle := \langle \psi | M | \psi \rangle $。因此,人们经常使用 $\langle M \rangle$ 作为量子力学中平均值的符号。

更一般地说,我们可以颠倒这个过程,使用某个可观察量来定义量子测量。具体来说,假设 $M$ 是一个作用在量子系统状态空间上的厄米矩阵。那么,线性代数中的一个称为谱定理的结果保证了 $M$ 可以分解为: $$ M = \sum_{\lambda} \lambda |\lambda\rangle\langle\lambda|, $$ 其中求和是对 $M$ 的所有特征值 $\lambda$ 和相应的(规范化的)特征向量 $|\lambda\rangle_{\text{norm}} = \frac{|\lambda\rangle}{\| | \lambda \rangle \|} = \frac{|\lambda\rangle}{\sqrt{\langle \lambda | \lambda \rangle}}$ 进行的。我们可以定义一个量子测量,其测量算符为 $M_{\lambda} = |\lambda\rangle\langle\lambda|$。容易验证完备性关系是真实的,因此这是一个有效的量子测量。此外,你可以验证 $M$ 是对应于这些测量算符的可观察量。

我们需要验证 $M_{\lambda} = |\lambda\rangle\langle\lambda|$ 的完备性关系,即 $$ \sum_{\lambda} M_{\lambda}^\dagger M_{\lambda} = I. $$

这可以通过以下方法来证明:

  • 选择一个任意的量子态 $ |\psi\rangle $,计算 $ \sum_{\lambda} |\lambda\rangle\langle\lambda| $ 作用在 $ |\psi\rangle $ 上的结果:

$$ \left( \sum_{\lambda} |\lambda\rangle\langle\lambda| \right) |\psi\rangle. $$

  • 展开这个表达式:

$$ \left( \sum_{\lambda} |\lambda\rangle\langle\lambda| \right) |\psi\rangle = \sum_{\lambda} |\lambda\rangle\langle\lambda|\psi\rangle. $$

  • 由于 $ \langle\lambda|\psi\rangle $ 是 $ |\psi\rangle $ 在 $ |\lambda\rangle $ 基底上的投影系数,这里我们可以得到:

$$ \sum_{\lambda} |\lambda\rangle\langle\lambda|\psi\rangle = |\psi\rangle. $$

  • 这表明,无论 $ |\psi\rangle $ 是什么,应用 $ \sum_{\lambda} |\lambda\rangle\langle\lambda| $ 后得到的结果仍然是 $ |\psi\rangle $。因此:

$$ \sum_{\lambda} M_{\lambda}^\dagger M_{\lambda} = \sum_{\lambda} |\lambda\rangle\langle\lambda| = I. $$

如果量子系统的状态在测量前是 $|\psi\rangle$,那么结果 $\lambda$ 出现的概率由下式给出:

$$ p(\lambda) = \langle \psi | M_{\lambda}^\dagger M_{\lambda} | \psi \rangle = \langle \psi | (|\lambda\rangle\langle\lambda|)^\dagger (|\lambda\rangle\langle\lambda|) | \psi \rangle = \langle \psi | \lambda \rangle \langle\lambda|\lambda\rangle \langle \lambda | \psi \rangle = (\langle \lambda | \psi \rangle)^\dagger \langle \lambda | \psi \rangle = |\langle \lambda | \psi \rangle|^2, $$

而系统在测量后的状态,通常称为后验状态,为

$$ \frac{M_{\lambda} |\psi\rangle}{\sqrt{\langle \psi | M_{\lambda}^\dagger M_{\lambda} | \psi \rangle}} = \frac{(|\lambda\rangle\langle\lambda|) |\psi\rangle}{|\langle \lambda | \psi \rangle|} = \frac{|\lambda\rangle \langle\lambda|\psi\rangle}{|\langle \lambda | \psi \rangle|} = \frac{\langle\lambda|\psi\rangle}{|\langle \lambda | \psi \rangle|} |\lambda\rangle. $$

第三公设还有另一种看法,似乎它几乎是第二公设的推广。假设我们进行一个只有单一测量结果的测量。这听起来很奇怪——如果测量设备总是显示相同的答案,你会认为它坏了——但至少在逻辑上是有意义的。根据第三公设,这样的测量将由一个单一的测量算符描述,我们可以称之为 $M$(不需要标签,因为结果总是相同的)。

在这种情况下,完备性关系变为 $M^\dagger M = I$。这只是 $M$ 是幺正的条件。当然,结果的概率是 $\langle \psi | M^\dagger M | \psi \rangle = \langle \psi | I | \psi \rangle = 1$,所以这个结果会以概率 $1$ 发生,即每次都会发生。考虑到只有一个可能的结果,这正是我们所期望的!因此,第二公设似乎是第三公设的特例,其中只有一个结果。

我们说“似乎”。事情并没有那么简单。毕竟,第三公设讨论的是一个系统正在被测量,可能是通过与某些测量设备的相互作用,而第二公设讨论的是孤立物理系统的动力学。所以这两个公设讨论的是完全不同的物理情况。要说第二公设是第三公设的特例,仅仅数学上对得上是不够的:你还需要一个统一且概念上合理的物理图景。不过,你可以想象尝试重新表述这些公设,使第二和第三公设成为单一公设的统一方面。试图找到概念上的统一使其成立是很有趣的。我们在这里不做,但你可能会喜欢思考如何做到这一点。


为什么存在两种动力学?

量子力学的一个奇特之处在于它有两种不同的描述状态变化的方式:幺正动力学和与测量相关的动力学。这引发了一系列引人注目的难题。假设我们有一个正在被测量的量子系统——我们称之为 Q。测量装置本身也是一个量子系统。因此,似乎应该可以找到一个包含 Q 和测量装置且孤立的更大的量子系统。根据第二公设,该更大的系统正在进行幺正演化。

这意味着量子力学现在提供了两种看似不同的描述被测量系统演化的方式:要么通过测量算符和概率,如第三公设所述;要么在更大的系统的幺正演化下,以完全确定的方式进行。

对于同一情形有两种不同的描述方式引出了许多问题:我们能保证这两种描述总是相互一致的吗?是否可以从一种描述推导出另一种描述?概率是如何从看似确定的更大系统的描述中产生的?特别是,当组合系统的量子态以纯确定的方式演化时,被测量系统的量子态为何以随机的方式变化?我们不应该能从组合系统状态的确定性演化中推导出测量概率吗?简而言之:我们如何调和这两种观点?

这些都是很好的问题。这些问题及其他相关问题通常被称为量子力学中的测量问题。许多物理学家提出了测量问题的解决方案。不幸的是,整个物理学界尚未达成完全一致的解决方案。我们听到过许多变体:“这个问题已经被玻尔解决了;被冯·诺伊曼解决了;被埃弗雷特解决了;被玻姆解决了;等等”。然而,对于已经发表的数十或数百种解决方案,也有标准的反驳意见。实际上,一个有趣的(非常大的)项目想法是收集完整的论证树,包含所有最强的论据和反驳意见,以及争论的关键点。



将经典物理量替换为算符是量子化过程的核心步骤。这种替换反映了量子力学的基本原理,即物理量不再是确定的数值,而是通过算符作用于波函数或量子态上来描述。这一过程允许我们使用量子力学的数学框架来描述和预测物理系统的行为,从而揭示经典力学所不能解释的现象。

厄米共轭 (Hermitian Conjugate)

定义: 一个算子 $ A $ 的厄米共轭 $ A^\dagger $ 是通过取其复共轭转置得到的,即 $ (A^\dagger)_{ij} = \overline{A_{ji}} $。

详细解释: 厄米共轭是定义自伴性和幺正性的基础。它的计算涉及两个步骤:首先取矩阵的转置,然后对每个元素取复共轭。

自伴性 (Self-adjointness)

定义: 一个算子 $ A $ 如果满足 $ A = A^\dagger $,则称其为自伴算子。这里 $ A^\dagger $ 是 $ A $ 的厄米共轭。

详细解释: 在量子力学中,自伴算子对应于可观察量。自伴性保证了算子的特征值都是实数,且其特征向量构成完备正交系。

幺正性 (Unitarity)

定义: 一个算子 $ U $ 如果满足 $ U^\dagger U = UU^\dagger = I $,则称其为幺正算子。这里 $ I $ 是单位算子, $ U^\dagger $ 是 $ U $ 的厄米共轭。

详细解释: 幺正算子在量子力学中描述保守系统中的时间演化算子,因为它保持内积,即保持概率守恒。

应用:

  • 自伴性:在量子力学中,自伴算子对应物理上的可观测量,如位置、动量和哈密顿算子。
  • 幺正性:幺正算子用于描述量子系统的时间演化(例如量子态的时间演化算子)。

Pauli-Fierz 哈密顿算符的自伴性

Pauli-Fierz 哈密顿算符的自伴性是量子力学和量子场论中的一个关键数学性质,尤其在非相对论量子电动力学 (NRQED) 的背景下。Pauli-Fierz 哈密顿算符描述了带电粒子(如电子)与电磁场在非相对论情况下的相互作用。

Pauli-Fierz 哈密顿算符是什么?

Pauli-Fierz 哈密顿算符的形式如下:

$$ H_{\text{NRQED}} = \sum_{j=1}^N \frac{1}{2m} \left( \mathbf{p}_j - e \mathbf{A}(\mathbf{q}_j) \right)^2 + V_c(\mathbf{q}) + H_f $$

这里:

  • $ \mathbf{p}_j $ 是粒子的动量。
  • $ \mathbf{q}_j $ 是粒子的位置。
  • $ e $ 是粒子的电荷。
  • $ \mathbf{A}(\mathbf{q}_j) $ 是在位置 $ \mathbf{q}_j $ 处的电磁场矢势。
  • $ V_c(\mathbf{q}) $ 表示带电粒子之间的库仑相互作用。
  • $ H_f $ 是自由电磁场(光子)的哈密顿算符。

自伴性

在量子力学中,一个算符(如哈密顿算符)必须是自伴的,以确保其本征值(对应于可测量的量如能量)是实数,并且它能够产生幺正的时间演化(确保概率随时间的守恒)。

对于 Pauli-Fierz 哈密顿算符,证明自伴性涉及几个步骤:

  1. 定义域:需要定义一个合适的算符作用域,使得哈密顿算符在该域上是良定义并且有下界。
  2. 对称性:证明哈密顿算符在该定义域上是对称的。一个对称算符 $ H $ 满足 $ \langle \psi, H \phi \rangle = \langle H \psi, \phi \rangle $ 对于定义域内所有的 $\psi$ 和 $\phi$ 成立。
  3. 自伴扩展:为了使算符是自伴的,它必须与其伴随算符 $ H^* $ 具有相同的定义域,并满足 $ H = H^* $。这通常是一个复杂的任务,通常需要证明哈密顿算符有一个唯一的自伴扩展。

在量子电动力学中的重要性

Pauli-Fierz 哈密顿算符的自伴性确保了几个关键性质:

  • 实数本征值:系统的能谱是实数,这是物理测量所必需的。
  • 幺正演化:时间演化算符 $ e^{-iHt} $ 是幺正的,确保了概率的守恒。
  • 稳定性:系统是稳定的,即能量有下界。

数学技术

证明自伴性通常使用来自泛函分析和算符理论的高级数学技术,如:

  • Kato-Rellich 定理:用于证明自伴算符的某些扰动仍然是自伴的。
  • 形式方法:涉及与算符相关的二次型技术。
  • 谱理论:分析算符的谱以确保其是实数且行为良好。

文献中的引用

Pauli-Fierz 哈密顿算符的自伴性已经在各种背景下被广泛研究和证明。主要参考文献包括:

  • H. Spohn 和 R. D. Lang,他们研究了量子电动力学和 Pauli-Fierz 哈密顿算符的数学基础。
  • M. Reed 和 B. Simon 在他们的“现代数学物理方法”系列中详细讨论了这一主题。

理解 Pauli-Fierz 哈密顿算符的自伴性对于确保 NRQED 模型的数学一致性和物理可靠性至关重要。


如何用非相对论性量子电动力学推导出非相对论性量子运动学(Non-relativistic Quantum Kinematics)?

要从非相对论性量子电动力学(NRQED)推导出非相对论性量子力学(NRQM),需要理解这两者之间的关系和概念。NRQED 是一个包含更多相互作用和复杂性的理论,而 NRQM 是一个简化的子集,专注于粒子的波函数和基本量子行为。以下是一个简化的过程,展示如何从 NRQED 推导出 NRQM 。

概念简介

非相对论性量子电动力学(NRQED)

NRQED 描述低能量情况下电子与电磁场的相互作用。它包含电子的非相对论性运动以及电子与光子的相互作用。NRQED 通常使用量子场论的方法,包括拉格朗日量、路径积分和费曼图。

非相对论性量子力学(NRQM)

NRQM 描述单个或多个粒子的波函数演化,不涉及电磁场的量子效应。其核心方程是薛定谔方程。

推导过程

  1. NRQED 的基本拉格朗日量 NRQED 的拉格朗日量描述了电子(费米子)和电磁场(光子)的相互作用。它通常包括自由电子部分、自由电磁场部分以及它们之间的相互作用项。 $$ \mathcal{L}_{NRQED} = \mathcal{L}_{\text{electron}} + \mathcal{L}_{\text{photon}} + \mathcal{L}_{\text{interaction}} $$

    • 自由电子部分: $$ \mathcal{L}_{\text{electron}} = \psi^\dagger \left( i \hbar \frac{\partial}{\partial t} + \frac{\hbar^2}{2m} \nabla^2 \right) \psi $$
    • 自由电磁场部分: $$ \mathcal{L}_{\text{photon}} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} $$
    • 相互作用部分(最简单的情况下): $$ \mathcal{L}_{\text{interaction}} = -e \psi^\dagger \psi A_0 + \frac{e}{m} \psi^\dagger \mathbf{p} \cdot \mathbf{A} \psi $$
  2. 忽略电磁场的贡献 要从 NRQED 得到 NRQM,我们可以假设在某些情况下,电磁场的贡献可以忽略。这意味着光子的自由部分和相互作用部分不再起主要作用,只关注电子的运动。

  3. 简化拉格朗日量 在忽略电磁场后,NRQED 的拉格朗日量简化为仅包含电子的部分: $$ \mathcal{L}_{\text{electron}} = \psi^\dagger \left( i \hbar \frac{\partial}{\partial t} + \frac{\hbar^2}{2m} \nabla^2 \right) \psi $$

    这与非相对论性量子力学中的拉格朗日量形式一致。

  4. 从拉格朗日量到哈密顿量 使用标准的量子场论方法,将拉格朗日量转换为哈密顿量: $$ \mathcal{H}_{\text{electron}} = \psi^\dagger \left( -\frac{\hbar^2}{2m} \nabla^2 \right) \psi $$

    这是电子的自由哈密顿量,在无相互作用的情况下,描述了电子的运动。

  5. 得到薛定谔方程 通过量子化电子场并引入波函数$\psi$,可以得到薛定谔方程: $$ i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \psi $$

    这是非相对论性量子力学的核心方程,描述了单个粒子的波函数随时间的演化。

总结

通过简化非相对论性量子电动力学(NRQED)中的拉格朗日量,并忽略电磁场的贡献,我们可以得到仅包含电子部分的拉格朗日量或哈密顿量。这实际上就是非相对论性量子力学(NRQM)的核心内容。最终,通过量子化电子场并引入波函数,我们得到了薛定谔方程,从而在理论上从 NRQED 推导出了 NRQM。这展示了 NRQM 是 NRQED 的一种简化形式,适用于不考虑电磁相互作用的情况。

最小作用量原理和拉格朗日量之间的关系在于拉格朗日量是描述物理系统动态行为的函数,而最小作用量原理使用拉格朗日量来确定系统的真实路径或演化。

最小作用量原理

最小作用量原理(Principle of Least Action)是物理学中的一个基本原理,它断言在一个物理系统中,实际发生的运动或过程是使得作用量(Action)达到最小值(或极值)的运动或过程。

拉格朗日量

拉格朗日量(Lagrangian)是一个函数,它在经典力学中通常表示为:

$$ L = T - V $$

其中 $ T $ 是系统的动能,$ V $ 是系统的势能。在一般形式下,拉格朗日量是系统广义坐标 $ q $ 和广义速度 $ \dot{q} $ 的函数,即:

$$ L = L(q, \dot{q}, t) $$

作用量

作用量(Action)是拉格朗日量关于时间的积分,定义为:

$$ S = \int_{t_1}^{t_2} L(q, \dot{q}, t) \, dt $$

其中 $ t_1 $ 和 $ t_2 $ 是时间的起始和结束点。

最小作用量原理与拉格朗日量的关系

根据最小作用量原理,一个系统的真实路径是使作用量 $ S $ 最小的路径。这意味着要找到使作用量 $ S $ 取极值的路径。数学上,这可以通过变分法来实现,即通过求解以下欧拉-拉格朗日方程:

$$ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}} \right) - \frac{\partial L}{\partial q} = 0 $$

欧拉-拉格朗日方程

欧拉-拉格朗日方程是从最小作用量原理导出的,其推导过程如下:

  1. 取一个路径 $ q(t) $ 并在其上加上一个微小变化 $ \delta q(t) $。
  2. 计算作用量的变化 $ \delta S $。
  3. 要使 $ \delta S = 0 $,这对应于路径 $ q(t) $ 使作用量 $ S $ 取极值。

令 $ \delta S = 0 $,并进行积分和变分处理,可以得到欧拉-拉格朗日方程。

物理意义

  • 拉格朗日量:提供了系统的动力学描述,通过动能和势能的差描述系统的行为。
  • 作用量:是系统在一个时间段内的总量度,通过拉格朗日量的积分得到。
  • 最小作用量原理:通过使作用量极小化,确定了系统的实际运动路径或过程。
  • 欧拉-拉格朗日方程:通过解决这个方程,可以找到系统的运动方程,从而描述系统的动态行为。

总结

最小作用量原理通过作用量的极值化来确定物理系统的真实路径,而作用量本身是通过拉格朗日量的时间积分定义的。拉格朗日量包含了系统的动能和势能信息,是描述系统动力学的核心函数。通过求解欧拉-拉格朗日方程,可以得到系统的运动方程,这在经典力学、场论和量子力学等多个物理学分支中都有广泛应用。

费曼路径积分(Feynman Path Integral)

费曼路径积分是由理查德・费曼提出的一种量子力学表述方法,它将粒子从一个点到另一个点的概率振幅的计算视为对所有可能路径的概率振幅进行求和。具体来说,粒子从空间点 $ q_1 $ 在时间 $ t_1 $ 移动到空间点 $ q_2 $ 在时间 $ t_2 $ 的概率振幅 $ K(q_2, t_2; q_1, t_1) $ 可以表示为所有可能路径的总和,每条路径 $ q(t) $ 都有一个对应的相位因子 $ e^{iS[q]/\hbar} $,其中 $ S[q] $ 是路径的作用量。

路径积分公式如下:

$$ K(q_2, t_2; q_1, t_1) = \int \mathcal{D}[q(t)] \, e^{iS[q]/\hbar} $$

这里 $ \int \mathcal{D}[q(t)] $ 表示对所有可能路径的积分。

作用量(Action)

作用量 $ S $ 是一个量度,它是路径上的拉格朗日量 $ L $ 关于时间的积分:

$$ S[q] = \int_{t_1}^{t_2} L(q, \dot{q}, t) \, dt $$

其中 $ L $ 是拉格朗日量,它通常表示为动能 $ T $ 和势能 $ V $ 的差:

$$ L = T - V $$

路径积分和作用量的关系

  1. 路径的权重:在路径积分公式中,每条路径的贡献由一个相位因子 $ e^{iS[q]/\hbar} $ 来决定。这个相位因子中的 $ S[q] $ 是路径的作用量。因此,作用量直接影响到每条路径在路径积分中的权重。

  2. 经典路径和作用量极值:当 $\hbar \rightarrow 0$ 时,路径积分中的相位因子变化迅速,只有那些作用量 $ S $ 取极值的路径对积分有主要贡献。这些路径满足经典力学中的欧拉-拉格朗日方程,描述了经典路径。

  3. 量子态的演化:路径积分方法将量子态的演化描述为对所有可能路径的求和,这些路径的振幅由作用量决定。因此,作用量在量子态的时间演化中起着核心作用。

具体例子

例如,对于自由粒子,拉格朗日量 $ L $ 仅由动能组成:

$$ L = \frac{1}{2}m\dot{q}^2 $$

作用量 $ S $ 则为:

$$ S[q] = \int_{t_1}^{t_2} \frac{1}{2}m\dot{q}^2 \, dt $$

在路径积分中,计算所有可能路径的振幅 $ e^{iS[q]/\hbar} $,并对这些路径进行积分,即可得到粒子从 $ q_1 $ 到 $ q_2 $ 的传播振幅。

总结

费曼路径积分和作用量的关系非常密切。路径积分方法通过对所有可能路径进行求和来描述量子系统的演化,而这些路径的量子振幅由路径的作用量 $ S[q] $ 确定。作用量的极值路径对应于经典路径,在经典极限下路径积分主要由这些路径贡献。因此,作用量在费曼路径积分中起到了核心的作用,通过影响每条路径的权重来决定系统的量子行为。


费曼图的修正・费曼图的阶数・费曼未来求和(Feynman Sum Over Futures)・费曼路径概率振幅模为相同路径的个数

「作用量」与「概率力」所做的功是什么关系?


概率波的塌缩・量子态的突变・费曼图的衍生・初态相同的费曼图之间的终态突变

如果采用「波粒二象性」这种物理图像,那么就会有「波的塌缩」这种物理图像,并会有「电子吸收光子时,波是怎么塌缩的?」这种物理问题。

我们用原子发射器发射一个原子,等待光屏上某个位置出现一个亮点,然后再发射一个,以此类推。一开始实验的现象符合我们的常识。每一个原子从原子发生器射出后,就像子弹一样穿过缝隙、撞击光屏的某一点而激发一个亮点。但是从原子发生器到第二块光屏,原子的运动真的跟子弹一样吗?如果说实验一开始看不出量子力学有什么奇特之处,当撞击到光屏上的原子越来越多时,相应被激发的光点逐渐积累,光屏上又出现了明暗相间的干涉图形。原子是一个一个单独通过缝隙的,所以排除了原子与原子之间发生碰撞或者干扰的可能性,这说明原子发生器并没有像造浪机一样射出原子波。同时我们也无法回答一个已经提到过的问题,只打开一侧的缝隙时,光屏上的那道条带却在我们打开第二条缝隙的时候消失了,尽管额外的一条缝隙在我们看来只是增加了原子撞击后方光屏的途径而已,但是原子在原本位置上的撞击还是消失了。看起来就像是从一侧缝隙穿过的原子似乎知道另一侧的缝隙有没有打开,并据此改变了自己的运动轨迹!

——《神秘的量子生命》

只有两种可能:

  1. 电子们是神。
  2. 电子们被神所引导。

主恢复说:

  1. 众子们是神。
  2. 众子们被神所引导。

我们可以一个一个地释放电子出来,而不是一次释放一群电子出来。

从两门出来的是两个不同电子的经历不一样。如果电子是通过相互交换信息知道门的开闭情况,那么实验过程中应该会有一些迹象或者端倪,可以表明出电子们的所知有限。否则,电子可能一开始就知道全宇宙的情况。

实际上,电子可能没有必要知道全宇宙的情况。因为,神知道全宇宙的情况并且可以给每个电子相应的引导。

借助探测器,我们就能够对穿过缝隙的原子进行检测。比如,在左侧的缝隙安装一个探测器,每当有原子通过左侧缝隙撞向后方光屏的时候,它就能给出一个信号(比如“哔哔”的声音)。同样的道理,我们也可以在右侧的缝隙再安装一个探测器。接下来,如果有原子通过左侧或者右侧的缝隙,那我们就能听到来自相应一侧的探测器信号;而如果原子真的能够以某种方式在通过双缝时摈弃它如同子弹一般的粒子性,同时穿过两个缝隙,那么两侧的探测器应当会同时响起。

如今我们知道,当只发射一个原子并在后方光屏上激发一个光点的时候,左边或者右边的探测器就会给出信号,但是从来不会出现两个探测器同时被激发的情况。这似乎足以证明,虽然原子束发生了干涉现象,但是每个原子的确是从左右缝隙中的一条,而不是同时从两条中穿过。但是先不要急于下结论,随着原子的发射和光屏上光点的积累,我们发现光屏上出现的图形不再是干涉图像。后方光屏上显示的仅仅是两道明亮的条带,原子的运动方向就如我们在使用子弹的实验中看到的那样,被严格“限制”在两条缝隙之后。

——《神秘的量子生命》

如果电子遇到了光子,那么电子就会改变自己的计划。

我们可以在门后设置一位盲人守门员扔出苹果喂他的小狗。如果苹果被进门的小孩子接住并吃掉了,那么另一侧的小狗因为没有吃到苹果就会汪汪叫。

如果我们在门后设置一位盲人守门员伸手摸小孩子或者扔苹果喂小孩子,小孩子们的行为就又会变化,以至于改变自己的计划。

波的表现形式在任何时刻都囊括了整个环境的信息。这个波并不能被直接识别,但是它会产生经验性结果,因为它会按照某种方式影响粒子的运动,并且能附加在常规的力效应之上。

——《牛津通识读本精选集・量子理论》

玻姆的导航波理论

如果光子遇到电子,那么神就会改变对电子的引导。

我把光子遇到电子、类比为、守门员的手掌摸到小孩子或者守门员的苹果落到小孩子。

也许探测器就是问题所在,是探测器干扰了原子穿过缝隙时奇异而又脆弱的运动方式。我们可以通过移除一个探测器的方式来验证,比如移走右侧的探测器。即便少了一台探测器,我们依旧可以获得和两台探测器时一样的信息:在发射原子后,如果探测器发出信号并且光屏上出现亮点,那么原子就是经过了左侧的缝隙;而如果发射的原子仅仅在光屏上激发了亮点却没有触发探测器,那么原子就是通过右侧的缝隙到达光屏的。这样我们依然可以知道原子经过了哪一侧的缝隙,但是我们仅仅“干扰”了其中一侧的原子。如果探测器的确是造成原子运动改变的原因,那么我们将看到触发探测器的原子表现为粒子性,而没有触发探测器的原子(也就是穿过右侧缝隙的原子)表现为波动性。要是果真如此,我们也许能在光屏上看到子弹样图形(从左侧缝隙穿过的原子)和干涉样图形(从右侧缝隙穿过的原子)的混合图像。

但是这样的图像并没有出现。即便撤走了一边的探测器,我们还是看不到原先的干涉图形,光屏上只能看到每条缝隙后面的子弹样图形。看起来仅仅一个用于检测原子的探测器存在,就足以打乱两条缝隙内原子的波动性运动,哪怕这个探测器与另一条缝隙间还有一定的距离!

当然,也可能是左侧的探测器对原子的运动产生了物理阻挡,就像湍急溪流中的一块大石头改变了水流一样,因此我们尝试关闭探测器。探测器依旧在原位,如果它阻挡了原子的运动,那它还会有阻挡的影响。然而,当探测器还在原来的位置,只是关闭了之后,干涉条纹居然重新在光屏上出现了!所有的原子又再次表现出波的性质。为什么左边的探测器在工作的时候原子表现为粒子性,而一旦关闭,原子就表现为波动性呢?为什么通过右侧缝隙的原子会知道左侧的探测器到底是打开的还是关闭的呢?

——《神秘的量子生命》

概率波会塌缩成测量出的概率波。

在费曼图中,路径概率振幅的长度等于相同路径的个数。

神是怎么引导电子们的?

  • 对于想吃苹果的小孩子们,神预定了对他们的引导。
  • 对于不想吃苹果的小孩子们,神预定了对他们的引导。
    • 有些小孩子不想吃苹果也不想从守门员的旁边经过。他们要走的路是宽的。
    • 有些小孩子不想吃苹果却想冒险从守门员的苹果树旁边经过。他们要走的路是窄的。

概率振幅的定义

在量子力学中,概率振幅(probability amplitude)是用来描述一个量子态向另一个量子态转变的可能性的一个复数。通过概率振幅,可以计算出相应的概率。

波函数和概率振幅

波函数 $\psi$ 是描述量子系统状态的核心工具。波函数本身是一个概率振幅的例子。对于一个粒子在位置 $\mathbf{r}$ 处的波函数 $\psi(\mathbf{r})$,它的模平方 $ |\psi(\mathbf{r})|^2 $ 表示在位置 $\mathbf{r}$ 处找到粒子的概率密度。

关系式

若 $\psi(\mathbf{r})$ 是波函数,则: $$ P(\mathbf{r}) = |\psi(\mathbf{r})|^2 $$ 其中 $P(\mathbf{r})$ 是粒子在位置 $\mathbf{r}$ 处的概率密度。

量子态转变和概率振幅

假设量子系统从初态 $|\psi_i\rangle$ 演化到末态 $|\psi_f\rangle$,则概率振幅通常表示为 $\langle \psi_f | \psi_i \rangle$。这个内积是一个复数,其模平方给出量子态从 $|\psi_i\rangle$ 转变到 $|\psi_f\rangle$ 的概率。

$$ P_{i \to f} = |\langle \psi_f | \psi_i \rangle|^2 $$

叠加原理

概率振幅遵循叠加原理,这意味着多个路径或态的概率振幅可以叠加。假设一个系统可以通过两条不同路径从初态 $|\psi_i\rangle$ 到末态 $|\psi_f\rangle$,对应的概率振幅分别为 $\langle \psi_f | \psi_i \rangle_1$ 和 $\langle \psi_f | \psi_i \rangle_2$,则总的概率振幅是这些单个振幅的和:

$$ \langle \psi_f | \psi_i \rangle = \langle \psi_f | \psi_i \rangle_1 + \langle \psi_f | \psi_i \rangle_2 $$

干涉现象

由于概率振幅是复数,当多个振幅相加时,它们的相位关系会导致干涉现象。正干涉(相长干涉)或负干涉(相消干涉)取决于振幅的相对相位,这会影响最终的概率。

例子

  1. 双缝实验

    • 在双缝实验中,电子通过两条路径到达屏幕上的某一点。每条路径对应一个概率振幅,两个路径的概率振幅相加后取模平方得到最终在该点的概率。不同路径的振幅相位差导致屏幕上出现干涉条纹。
  2. 量子态叠加

    • 若有两个态 $|\psi_1\rangle$ 和 $|\psi_2\rangle$,则它们的叠加态 $|\psi\rangle = a|\psi_1\rangle + b|\psi_2\rangle$ 中,$a$ 和 $b$ 是复数系数(概率振幅)。叠加态的模平方 $|a|^2 + |b|^2$ 给出态的概率。

总结

概率振幅是量子力学中一个基本概念,描述了量子态之间转变的可能性。它是一个复数,其模平方给出概率。通过概率振幅的叠加和相位关系,可以解释和预测量子系统的各种干涉和叠加现象。

振幅叠加(Quantum Superposition)

振幅叠加描述的是量子态在不同可能状态上的相干叠加。一个量子系统可以处于多个态的线性叠加,这种叠加态具有相干性和量子干涉效应。

数学描述

如果一个量子系统可以处于状态 $|\psi_1\rangle$ 和 $|\psi_2\rangle$,那么它的叠加态可以表示为: $$ |\psi\rangle = \alpha |\psi_1\rangle + \beta |\psi_2\rangle $$ 其中 $\alpha$ 和 $\beta$ 是复数系数,满足归一化条件: $$ |\alpha|^2 + |\beta|^2 = 1 $$

这种叠加态的密度矩阵表示为: $$ \rho = |\psi\rangle \langle \psi| = (\alpha |\psi_1\rangle + \beta |\psi_2\rangle)(\alpha^* \langle \psi_1| + \beta^* \langle \psi_2|) $$ $$ \rho = |\alpha|^2 |\psi_1\rangle \langle \psi_1| + \alpha \beta^* |\psi_1\rangle \langle \psi_2| + \alpha^* \beta |\psi_2\rangle \langle \psi_1| + |\beta|^2 |\psi_2\rangle \langle \psi_2| $$

用矩阵表示为: $$ \rho = \begin{pmatrix} |\alpha|^2 & \alpha \beta^* \\ \alpha^* \beta & |\beta|^2 \end{pmatrix} $$ 这个矩阵的迹(trace)为1: $$ \text{Tr}(\rho) = 1 $$

物理意义

  • 相干性:叠加态中,不同量子态之间的相位关系保留,导致量子干涉现象。
  • 量子干涉:相干性使得不同路径或状态的叠加可以相互干涉,产生干涉条纹等量子现象。

概率混合(Classical Probability Mixture)

概率混合描述的是系统在不同纯态上的经典概率分布。每个纯态出现的概率是确定的,但系统整体上处于哪种状态是不确定的。

数学描述

如果一个系统有两个可能的纯态 $|\psi_1\rangle$ 和 $|\psi_2\rangle$,其概率分别是 $p_1$ 和 $p_2$,那么混合态的密度矩阵为: $$ \rho = p_1 |\psi_1\rangle \langle \psi_1| + p_2 |\psi_2\rangle \langle \psi_2| $$ 其中 $p_1 + p_2 = 1$。

用矩阵表示为: $$ \rho = \begin{pmatrix} p_1 & 0 \\ 0 & p_2 \end{pmatrix} $$ 同样,这个矩阵的迹(trace)为1: $$ \text{Tr}(\rho) = 1 $$

物理意义

  • 无相干性:混合态中,不同纯态之间没有相位关系,不存在量子干涉现象。
  • 经典概率分布:混合态反映的是系统在不同纯态上的经典概率分布,类似于经典统计力学中的概率分布。

纯态与混合态的区别

  • 纯态(叠加态):系统的状态由一个确定的波函数 $|\psi\rangle$ 描述,密度矩阵 $\rho = |\psi\rangle \langle \psi|$ 是一个投影算符,满足 $\rho^2 = \rho$、$\text{Tr}(\rho^2) = \text{Tr}(\rho) = 1$。
  • 混合态(经典概率分布):系统的状态是若干纯态的概率混合,密度矩阵是这些纯态的加权和,满足 $\rho^2 \neq \rho$(除非是特殊情况)、$\text{Tr}(\rho^2) < \text{Tr}(\rho) = 1$。

数学表示

纯度 $ P $ 可以通过下式计算: $$ P = \text{Tr}(\rho^2) $$

其中,$\rho$ 是系统的密度矩阵。

物理意义

纯度反映了量子系统在实验观测中所表现出的确定性和相干性。纯度越接近1,系统越接近于一个确定的量子态;纯度越接近0,系统越是一个混合态,显示出更多的不确定性和经典的特征。

量子相干性

量子相干性是量子力学中的一个基本概念,它指的是量子系统中不同量子态之间存在的相位关系。这些相位关系使得量子态可以干涉,从而展示出量子特有的行为。

系统与环境之间的相干性是指量子系统和其环境在量子叠加态下共同表现的量子相干性。这种相干性意味着系统和环境之间存在着量子纠缠,并且这种纠缠影响着它们的整体行为。理解系统与环境之间的相干性对于量子去相干理论和量子测量问题非常重要。

系统与环境之间的相干性

当我们讨论系统与环境之间的相干性时,我们通常指的是量子系统和其外部环境之间的量子纠缠。这个纠缠可以用以下几个方面来解释:

  1. 量子纠缠

    • 当量子系统与环境发生相互作用时,它们的量子态可以纠缠在一起。纠缠态是一种特殊的量子态,其中系统和环境的状态不能独立描述,而是必须作为一个整体来描述。
    • 在纠缠态中,系统的状态和环境的状态紧密关联,一个的状态会影响另一个的状态。
  2. 量子叠加

    • 在没有相互作用的情况下,系统可以处于多个量子态的叠加态。这种叠加态具有相干性,因为不同态之间存在相位关系。
    • 当系统与环境相互作用时,这种叠加态会扩展到包含环境的状态。
  3. 相干性丧失

    • 相干性丧失(去相干)是指量子系统在与环境相互作用过程中失去量子相干性的现象。去相干的结果是,量子系统的叠加态变成了经典的概率混合态。
    • 去相干过程中,系统的量子态与环境的量子态纠缠在一起。环境态的变化使得系统不同态之间的相位关系被清除,导致系统的状态相干性消失。

系统与环境相干性的例子

  1. 双缝干涉实验

    • 在经典的双缝干涉实验中,电子可以通过两条路径到达屏幕,产生干涉图样。这是因为电子处于两条路径的叠加态,并且保持相干性。
    • 如果电子与环境(例如空气分子)相互作用,这种相互作用会导致电子的路径信息泄露到环境中,从而破坏电子的相干性,最终导致干涉图样消失。
  2. Schrödinger's Cat

    • Schrödinger's Cat 思想实验展示了宏观量子叠加态的概念。在这个实验中,猫的生死状态与一个微观量子态(如放射性原子)的状态纠缠在一起。
    • 实际上,猫与其周围环境(空气分子、光子等)之间的相互作用会迅速导致去相干,使得我们只能观察到猫处于死或活的经典状态,而不是叠加态。

去相干的机制

量子去相干是理解为什么我们在宏观世界中看不到量子叠加态的关键。以下是去相干的主要机制:

  1. 环境相互作用

    • 当一个量子系统与大量环境粒子相互作用时,这些相互作用会导致系统态与环境态纠缠。
    • 由于环境具有大量自由度,系统与环境的纠缠会使得系统态的相干性被环境的随机扰动所洗出,导致系统态向经典概率分布演化。
  2. 相位随机化

    • 去相干过程中,系统的不同量子态之间的相位关系被环境的自由度随机化。
    • 这种随机化相当于系统态的相干性在环境态的影响下被统计平均化了,使得我们在宏观尺度上只能观察到经典行为。

去相干过程可以看作是系统从振幅叠加态转变为概率混合态的过程。当系统与环境相互作用时,系统的相干性被环境清除,最终系统状态表现为经典概率分布。这解释了为什么在宏观世界中我们观察不到量子叠加态,而是经典概率现象。



量子退相干是量子力学中的一个重要现象,描述了量子系统由于与环境的相互作用而丧失相干性的过程。多种理论模型被提出和研究以解释和描述量子退相干的机制。以下是一些主要的量子退相干模型:

1. 环境诱导退相干模型(Environment-Induced Decoherence)

描述:

  • 这种模型研究了量子系统与其周围环境的相互作用如何导致系统的相干性丧失。
  • 主要观点是,系统和环境之间的纠缠会导致系统的密度矩阵从纯态变为混合态,从而丧失相干性。

关键点:

  • Hamiltonian:包含系统、环境和它们之间的相互作用项。
  • 主方程:常用Lindblad方程或量子主方程来描述系统的演化。

参考模型:

  • Caldeira-Leggett 模型:一个著名的环境诱导退相干模型,主要研究量子系统(如一个粒子)与大量环境振动模式(例如,热浴)的相互作用。

2. 相干态表示模型(Coherent State Representation)

描述:

  • 使用相干态来描述环境中的振动模式,并研究这些模式如何与系统相互作用。
  • 相干态表示环境的经典极限,在这种表示下,退相干效应显现得更清晰。

关键点:

  • Wigner函数:用于描述系统的量子态,可以看作是经典相空间中的概率分布。
  • Feynman-Vernon路径积分方法:用于处理系统与环境之间的相互作用。

3. 自旋浴模型(Spin-Boson Model)

描述:

  • 这种模型研究一个两能级系统(自旋1/2粒子)与一个由无穷多谐振子(热浴)组成的环境之间的相互作用。
  • 该模型可以推广到多自旋系统,与多模环境相互作用。

关键点:

  • Hamiltonian:包含自旋与环境谐振子的相互作用项。
  • 解决方法:通过积分出环境自由度,得到自旋系统的有效动力学行为。

4. 动力学退相干模型(Dynamical Decoherence Model)

描述:

  • 研究系统与环境之间动态相互作用导致的退相干。
  • 通过具体的动力学过程,如碰撞和相互作用,研究退相干时间和机制。

关键点:

  • 散射理论:用于描述粒子与环境中的其他粒子之间的碰撞过程。
  • Lindblad主方程:用来描述系统的非单位时间演化。

5. 噪声模型(Noise Models)

描述:

  • 研究系统在噪声背景下的演化,噪声可以是经典的(如随机电场)或量子的(如零点能量波动)。
  • 通过引入噪声源来模拟环境的影响,并研究其对系统相干性的影响。

关键点:

  • 随机Hamiltonian:包含系统与噪声源的相互作用项。
  • 随机过程:用来描述噪声的时间演化,如白噪声和色噪声。

6. 路径积分方法(Path Integral Methods)

描述:

  • 使用Feynman路径积分方法来研究系统与环境的相互作用。
  • 可以处理复杂的相互作用形式,特别是非微扰相互作用。

关键点:

  • 影响函数(Influence Functional):用于描述环境对系统演化的影响。
  • 路径积分:用于求解系统的时间演化算符。

总结

量子退相干的理论模型涵盖了从微观机制到宏观现象的广泛研究领域。这些模型不仅帮助理解量子系统在现实环境中的行为,也为量子计算和量子信息处理提供了重要的理论基础和指导。在实践中,选择合适的模型取决于具体的量子系统和环境的特性。


Göran Lindblad 在 1976 年通过对量子力学中开放系统的非单位时间演化进行严格分析,推导出了 Lindblad 方程。这个方程描述了系统与其环境相互作用时的动力学行为。以下是 Lindblad 方程推导的关键步骤和基本思想:

推导思路

  1. 开放量子系统的动力学

    • 考虑一个量子系统 $ S $ 和一个环境 $ E $,合成系统 $ S + E $ 的状态由一个联合密度矩阵 $\rho_{SE}$ 描述。
    • 系统 $ S $ 的状态可以通过对环境自由度 $ E $ 进行部分迹操作得到,即 $\rho_S = \text{Tr}_E (\rho_{SE})$。
  2. 完全正变换(Completely Positive Map)

    • Lindblad 方程假设量子系统的演化是完全正的(completely positive),即密度矩阵在演化过程中不会产生非物理的负概率。
    • 这种演化可以由 Kraus 算符表示,其形式为: $$ \rho(t+\Delta t) = \sum_k M_k \rho(t) M_k^\dagger $$ 其中,Kraus 算符 $M_k$ 满足: $$ \sum_k M_k^\dagger M_k = I $$ 以保证演化过程的概率守恒。
  3. 微分形式

    • Lindblad 方程考虑时间演化的微分形式,即在很短的时间步长 $\Delta t$ 内,系统密度矩阵的变化可以线性化处理。
    • 设 $\rho(t+\Delta t) = \rho(t) + \Delta \rho$,通过展开得到: $$ \Delta \rho = \sum_k M_k \rho(t) M_k^\dagger - \rho(t) $$
  4. 算符表示

    • 将 Kraus 算符 $ M_k $ 表示为: $$ M_k = \delta_{k0} I + \epsilon L_k $$ 其中 $ \epsilon $ 是一个很小的量,$ L_k $ 是跳算符。
  5. Lindblad 形式

    • 将 $ M_k $ 代入微分形式,并展开到一阶,忽略高阶小量,得到: $$ \Delta \rho = -i [H, \rho] \Delta t + \sum_k \left( L_k \rho L_k^\dagger - \frac{1}{2} \{L_k^\dagger L_k, \rho\} \right) \Delta t $$ 其中,$ H $ 是系统的哈密顿量,对应于单位时间内的无耗散演化部分。

完整的 Lindblad 方程

将以上结果推广到连续时间,得到 Lindblad 方程: $$ \frac{d\rho}{dt} = -\frac{i}{\hbar} [H, \rho] + \sum_k \left( L_k \rho L_k^\dagger - \frac{1}{2} \{L_k^\dagger L_k, \rho\} \right) $$

物理意义

  • 哈密顿项 $ H $:描述系统的无耗散演化部分。
  • 跳算符 $ L_k $:描述系统与环境之间的相互作用,每个 $ L_k $ 对应一种特定的耗散机制或相互作用过程。
  • 对易子 $ [H, \rho] $ 和反对易子 $ \{L_k^\dagger L_k, \rho\} $:分别描述了量子系统的单位演化和耗散过程。

总结

Göran Lindblad 的推导利用了完全正变换和微分形式的思想,通过严格的数学推导,得出了开放量子系统在与环境相互作用时的标准演化方程。Lindblad 方程在量子信息、量子计算和量子光学等领域有着广泛的应用,描述了系统在开放条件下的动力学行为。

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2024-05-19
术语表

术语表

激活剂
一种正向调节转录的蛋白质,通常通过在启动子附近结合并与 RNA 聚合酶发生物理相互作用来增加其活性。

激活
参见正向调节。

等分
从较大样品中取出的小体积。

生物砖
符合指定组装标准的 DNA,通常是在 DNA 部分的侧翼添加特定的限制性位点。

细胞密度
给定体积中的细胞数量。

中心法则
分子生物学中关于从遗传密码到身体特征的信息流的统一思想,它指出 DNA 编码指定蛋白质序列的 RNA。

机壳
系统的外壳。该术语在合成生物学领域使用时通常指细胞宿主。

编码序列 (CDS)
请参阅开放阅读框 (ORF)。

密码子
三个连续的核苷酸,编码开放阅读框中的特定氨基酸或终止信号。

胜任的
描述细胞可以从环境中接受 DNA 的状态。

共识序列
在整个基因组或许多基因组中针对特定 DNA 部分发现的最常见的核苷酸模式。

本构
始终处于“打开”状态的功能,与有时“打开”有时“关闭”的功能形成鲜明对比。

文化
在实验室中培养细胞。

下游
相对于另一个 DNA 序列位于 3’ 的 DNA 序列。

紧急行为
由于更改或重新组合复杂系统的组件而产生的意外特征。


一种生物催化剂,通常是蛋白质,通过降低其活化能来加速化学反应。

正向工程
一种构建新系统的方法,首先对系统设计进行高级描述,然后在逻辑上完善该描述以生成构建策略。

基因表达
DNA 序列的读取导致其 RNA 或蛋白质产物的合成。

基因表达单位
包含开放阅读框以及启动转录(例如启动子)和翻译(例如核糖体结合位点)的信息的 DNA 序列。

遗传不稳定性
遗传性状的变异影响其可靠或可预测的功能。

热休克
温度快速升高,通常用于促进微生物转化。

全酶
一种完整的蛋白质复合物,在生化上已准备好执行细胞功能。

诱导性
一种有时“打开”有时“关闭”的功能,以响应细胞环境的变化。大多数情况下,这种变化是由与基因调控序列结合的蛋白质介导的。

抑制
参见负面调节。

逆变器
逻辑门,也称为非门,可将输入信号的状态转换为其相反状态,将“关”变为“开”或将“开”变为“关”。

紫胶操纵子
由 lacZ、lacY、lacA 三个基因组成的单一调控单元,其协调表达使得细胞能够在缺乏葡萄糖和存在乳糖的情况下生存。

滞后期
细胞生长的早期阶段,其特征是细胞密度低且细胞不活跃分裂。

记录阶段
细胞生长阶段,其特征是细胞密度随着时间的推移呈指数增加,因为细胞正在活跃分裂。

逻辑门
用于将给定输入或一组输入状态转换为指定输出状态的数字电路的构建块,例如仅在检测到两个(或更多)输入时才生成输出的与门。

平均无故障时间 (MTF)
预测物体使用寿命的测量方法。

代谢工程
合理操纵细胞的生物化学,以优化所需小分子的生产。

代谢途径
多种基因产物以逐步的方式将起始材料转化为最终产物。

模块化
系统的属性,描述其功能单元可以如何分离和重新组合以生成新系统。

负面监管
减少基因表达单位输出的机制,通常通过阻遏蛋白控制转录。

噪音
生物系统固有的自然变异性,通常被检测为重复之间的测量不一致。

开放阅读框(ORF)
编码蛋白质的 DNA 序列,其中核苷酸三联体(密码子)可被解码为氨基酸序列。

操纵子
开放阅读框的 DNA 簇,其表达由单个启动子控制。

光密度
细胞密度的衡量标准,通常量化为细胞悬浮液散射的 600 nm 光量。

修补
用牙签将细菌菌落散布在新的培养皿上,使其新鲜地长成小而明确的草坪。

质粒
可以在细胞中独立于染色体复制的环状 DNA 序列。实验室中经常使用的 DNA 工程质粒具有共同特征,例如可选择的遗传标记(例如,赋予氨苄青霉素抗性的标记)和可被限制性内切酶识别的 DNA 序列。

聚合酶链式反应 (PCR)
一种实验室技术,可用于复制给定 DNA 序列。

积极监管
一种增加基因表达单位输出的机制,通常通过激活蛋白控制转录。

促销员
结合 RNA 聚合酶以开始转录的 DNA 序列。

可靠性
行为一致。

解除抑制
将负调节状态转变为“开启”状态的机制,其中可以包括去除或抑制负调节剂。

记者
一种易于检测的基因输出,反映了感兴趣的细胞功能。

可抑制的启动子
一段 DNA 序列,既可以结合 RNA 聚合酶以启动转录,也可以结合阻遏蛋白以抑制转录。

阻遏物
一种 DNA 结合蛋白,可减少启动子的转录量。

阻遏蛋白
参见抑制器。

逆向工程
一种构建系统的方法,首先依赖于解构目标系统的现有物理示例。

核糖体结合序列 (RBS)
由 DNA 编码但功能与 mRNA 相同的序列,使细胞的核糖体能够结合 mRNA 模板并启动蛋白质合成。

RNA聚合酶
一种多蛋白酶复合物,可催化 DNA 模板形成 RNA 链。

分光光度计
用于测量未被液体样品吸收或散射的光量的仪器。

固定相
细胞生长的后期阶段,其特征是细胞密度高且细胞分裂不活跃。

基质
与酶结合并发生化学转化的分子。

转录
生成 RNA 分子的过程,其序列与 DNA 上的核苷酸序列互补。

转换
将 DNA 放入细菌细胞中以使细胞具有新特性的过程。

翻译
通过解码 mRNA 链上的密码子生成蛋白质或肽的过程。

真值表
系统行为的直观表示,将系统的每个输入显示为“开”(1) 或“关”(0) 以及与每个输入状态关联的输出。

上游
相对于另一个 DNA 序列位于 5’ 的 DNA 序列。

野生型
具有自然界中其物种最典型特征的生物体。

关于作者

Natalie Kuldell 是麻省理工学院生物工程系的讲师,也是 BioBuilder 教育基金会的创始人兼主席。她是全国各地会议的特邀发言人,从 2013 年的 TEDxBermuda 会议到 NSTA 等教育工作者全国会议和 AAAS 等科学家全国会议。她在合成生物学和教育方面的专业知识以及她的科学背景导致发表了大量文章和书籍。

她于 1987 年以优异成绩毕业于康奈尔大学,获得化学学士学位,并于 1994 年获得哈佛大学细胞与发育生物学博士学位。在哈佛医学院获得博士后奖学金后,她加入了韦尔斯利学院,在那里她担任教授在生物科学系教授和开发课程。 2003 年,她被招募到麻省理工学院,当时他们正在开设生物工程新专业(课程 20)和新系。库德尔博士与屡获殊荣的高中教师合作,将她的麻省理工学院合成生物学教材收集成适合高中和早期大学环境的模块化课程单元。最终的课程以及维持该课程的非营利组织位于 biobuilder.org。

雷切尔·伯恩斯坦为教育和新闻场所撰写有关科学所有领域的文章。她为《科学》、《自然》、《细胞》和《洛杉矶时报》撰写新闻文章,并为在线教育资源 Visionlearning 做出贡献。在她的所有工作中,她的目标是通过娱乐和讲述引人入胜的故事来提供信息和教育。她还曾担任世界上最大的同行评审期刊 PLOS ONE 的编辑。她是一名经过培训的生物物理化学家,于 2005 年在宾夕法尼亚大学获得化学学士学位,并辅修了英语。 2011 年,她在加州大学伯克利分校获得了化学博士学位,研究蛋白质折叠和动力学。她还曾担任《伯克利科学评论》的主编和执行编辑,该杂志分享了加州大学的广阔世界。伯克利研究拥有广泛的受众。

凯伦·英格拉姆是一位利用设计和创意指导来提高科学意识的艺术家。 Ingram 是数字设计领域的资深人士,曾在 Campfire、McCann Erikson 和 UNICEF 等公司工作。她的作品曾发表在《Die Gestalten》、《科学美国人》和《FWA》等出版物上,并被评为“数字先锋”。她为《计算机艺术》杂志和《新骑士》出版物撰写了数字设计教程。

她是布鲁克林科学歌舞表演 The Empiricist League 的联合组织者,也是 SXSW Interactive 的董事会成员,在 SXSW Interactive 中,她提出与科学 + 艺术相关的主题,并主持 SXSW Biohacker Meetup。她是纽约大学 SHERP 创业科学新闻学课程的创意策略讲师。

作为 Genspace(布鲁克林社区生物技术实验室)的成员,Ingram 于 2014 年参加了首届“社区实验室”iGEM 赛道,并将于 2015 年担任设计赛道评委。作为 2015 年合成生物学 LEAP(卓越领导力加速器计划)研究员,Karen被公认为合成生物学领域的新兴领导者。

Kathryn M. Hart 是圣路易斯华盛顿大学生物化学和分子生物物理学系的研究讲师,也是 BioBuilder 教育基金会的硕士教师。她帮助合成生物学工程研究中心 (SynBERC) 为本科生开发了强化实验室技术课程,并为 BioBuilder 教授专业发展和学生研讨会。拥有生物科学背景的她发现,从工程角度教授生物学为引入传统内容以及以设计为导向的问题解决提供了独特的机会。她目前的研究重点是理解和改造蛋白质功能和能量学。她于 2004 年在哈弗福德学院获得生物学学士学位,并于 2013 年在加州大学伯克利分校获得化学博士学位。

尾注

《BioBuilder》封面上的动物是高尔夫球钉水母(Aegina citrea)。高尔夫球钉水母是一种分布广泛的水母,这意味着它在世界各地深海中都能找到,只要那里有浮游生物和小型无脊椎动物供其捕食。

像其他属于Aeginidae科的水母一样,高尔夫球钉水母的特征是其没有灯泡的四条触手,这些触手连接在圆顶形状的伞盖上方。

高尔夫球钉水母所属的目是裸水母目(Narcomedusae),这一目下的水母与大多数水螅虫类物种不同,它们不经过水螅体阶段。相反,这些目下的幼体直接发育成伞状的水母。据了解,裸水母目幼体可以在附着或寄生在其他物种的水母体内完成部分发育。这些寄生的幼体在寄主身上觅食的同时,甚至可以产生新的幼虫。

许多出现在O’Reilly封面上的动物都是濒危物种;它们对世界都很重要。要了解更多关于如何帮助保护这些动物的信息,请访问 animals.oreilly.com

封面图片是基于赫克尔(Haeckel)版画的绘图。封面字体是URW Typewriter和Guardian Sans。正文字体是Adobe Minion Pro;标题字体是Adobe Myriad Condensed;代码字体是Dalton Maag的Ubuntu Mono。

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2024-05-19
实验室试剂和材料

附录 A 实验室试剂和材料

设备

一个储备充足的实验室会有计时器、微量移液器、永久记号笔和冰桶(还有冰!)等东西。 BioBuilder 实验室还假设有一些消耗材料可用。如果从 Ward’s Science 购买试剂盒,则会提供这些耗材,但许多实验室都有以下耗材:

  • 丁腈或乳胶手套
  • 15 ml 和/或 50 ml 锥形螺旋盖管
  • 微量离心管(1.5–2 ml)和架子
  • 无菌试管和试管架
  • 无菌牙签、接种环和/或涂抹棒
  • 10 厘米聚苯乙烯培养皿 - 如果您自己倒盘子

所述每个实验室都需要以下特定实验室设备。

滚轮或摇床   搅拌板和 125 ml 锥形瓶   分光光度计和比色皿/玻璃管*   培养箱 **(30°C 或 37°C)   水浴(42°C)
ETS   x x x
iT x x
CW x x
GB x x

*可以替代浊度标准品。
**也可以在室温下孵育,但需要更长的孵育时间。

试剂制备和储存

除非另有说明,您可以从主要化学品供应商处购买试剂,例如 Sigma-Aldrich 和 VWR。也可以通过 Gold Biotechnology 和 Ward’s Science 等专业供应商以较低的价格购买它们。

固体和液体介质

您还可以通过 Teknova 等供应商购买介质。

Luria Broth (LB) 液体培养基

将 10 g 胰蛋白胨、5 g 酵母提取物和 10 g 氯化钠溶解在水中,制成 1 L LB 培养基。高压灭菌或使用 0.2 μM 过滤器过滤灭菌。

Luria Broth (LB) 琼脂平板

将 10 g 胰蛋白胨、5 g 酵母提取物、10 g NaCl 和 7.5 g 琼脂添加到水中,制成 500 ml LB 琼脂培养基(足够约 25 个平板)。高压灭菌器溶解和灭菌。每个无菌培养皿中倒入约 20 ml LB 琼脂。冷却直至凝固,然后将介质面朝上存放在冰箱中长达几个月。要制作 LB 琼脂 + 氨苄青霉素平板,首先等待培养基冷却到足以触摸 (~55°C),然后添加 500 µl 1000x 氨苄青霉素原液并旋转混合,然后按照上述方法倒入培养皿中。 1个月内使用。

不含色氨酸 (-Trp) 的合成完全 (SC) 琼脂平板

将 3.4 g 不含氨基酸的酵母氮基、1 g 合成完全氨基酸脱落混合物 (-Trp)、10 g 葡萄糖和 10 个琼脂添加到水中,制成 500 ml LB 琼脂培养基。高压灭菌器溶解和灭菌。每个无菌培养皿中倒入约 20 ml SC-Trp 琼脂。冷却直至凝固,然后将介质面朝上存放在冰箱中长达几个月。

酵母提取物蛋白胨葡萄糖 (YPD) 琼脂平板

将 10 g 蛋白胨、5 g 酵母提取物、10 g 葡萄糖和 10 g 琼脂加入水中,制成 500 ml YPD 琼脂培养基。高压灭菌器溶解和灭菌。每个无菌培养皿中倒入约 20 ml YPD 琼脂。冷却直至凝固,然后将介质面朝上存放在冰箱中长达几个月。

库存解决方案

氨比西林(100 毫克/毫升溶液)

将 100 mg 氨苄青霉素溶解在 1 ml 无菌水中制成 1000x 储备液,或使用 0.2 uM 过滤器对溶液进行过滤灭菌。每 1 L LB 或 LB+琼脂中添加 1 ml 储备液,最终工作浓度为 100 ug/ml。冷冻原料可保存长达六个月或在冰箱中保存一周。

香蕉提取物(例如,在 amazon.com 上出售的 Frontier Banana Flavor)

按照 Eau That Smell 实验室协议中的描述制定香蕉气味标准。标准品可在冰箱中保存长达数周。

氯化钙,CaCl_2 (0.1 M 溶液)

将 735 mg CaCl_2 *2H 2 0 溶解于 50 ml 无菌水中或使用 0.2 μM 过滤器过滤灭菌溶液,制成 0.1 M 细菌转化溶液。在室温下储存溶液。

异戊醇

将 700 μl 添加到 1 L LB 培养基中。将 LB+异戊醇在冰箱中保存最多几天。

异丙基 β-D-1-硫代半乳糖苷,IPTG(0.1M 溶液)

将 24 mg IPTG 溶解在 1 ml 无菌水中,制成 100 倍原液,或使用 0.2 μM 过滤器对溶液进行过滤灭菌。每 25 ml LB 中添加 250 μl 储备液,使最终工作浓度为 1 mM。冷冻原料可保存长达 6 个月或在冰箱中保存一周。

邻硝基苯基-β-半乳糖苷,ONPG(0.01% 溶液)

将 40 mg ONPG 溶解在 40 ml 水中,制成 0.01% 的溶液。冷冻保存长达几个月或在冰箱中保存一周。

缓冲区

碳酸氢盐缓冲液(2% 溶液)

将 1 g 碳酸氢钠或 1 g Arm & Hammer 小苏打溶解在 50 ml 水中,制成 2% 的碳酸氢盐溶液。

碳酸盐缓冲液(1M 溶液)

将 5.3 克碳酸钠或 5.3 克纯碱(例如,在 amazon.com 上出售的 Tulip Fashion Art 纯碱)溶解在 50 ml 水中,制成 1M 碳酸盐溶液。

裂解缓冲液(1% SDS 溶液或稀洗洁精)

将 0.5 克 SDS(十二烷基硫酸钠)或 1 滴“喷射”透明液体洗洁精溶解在 50 毫升水中。

### 各种各样的

氯化钡,BaCl_2 (1% 溶液)

将 20 mg BaCl_2 溶解在 2 ml 水中,制成 1% BaCl_2 溶液。每套完整的浊度标准品大约需要 1.75 ml 1 % BaCl_2 。

漂白剂(10% 溶液)

将 10 毫升漂白剂(次氯酸钠)添加到 100 毫升水中,制成 10% 的漂白剂溶液。

电子构建实验所需试剂

请参阅 Mouser Electronics 网站上的 BioBuilder 项目页面

硫酸(1% 溶液)

将 1 ml 浓 H_2 SO_4 添加到 99 ml 水中,制成 1 % H_2 SO_4 溶液。每套完整的浊度标准品大约需要 80 ml 1 % H_2 SO_4 。安全注意事项:使用浓缩 H_2 SO_4 时要格外小心。应在防护罩中小心操作并使用个人防护装备(例如手套、实验室外套和安全眼镜),避免接触皮肤和/或吸入烟雾。

酵母转化试剂盒

MP Biomedicals 出品的 EZ-Yeast™ 转化试剂盒 #112100200

或者

Frozen-EZ 酵母转化 II 试剂盒(Zymo Research 出品)#T2001

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2024-05-16
人脑海马体的经典计算模型


元宇宙中的人工意识

受量子动力学(Quantum Dynamics)支配的元宇宙中的意识属于受绝对真理支配的宇宙中的意识吗?

由量子计算机生成的元宇宙中的意识与由晶体管计算机生成的元宇宙中的意识有什么不同?

量子计算机的意识与晶体管计算机的意识有什么不同?


量子化学经典计算模型

The Classical Computational Model in Quantum Chemistry


在量子化学计算中,精度问题是否会导致混沌现象是一个复杂的问题,需要从多个角度进行分析。首先,我们需要理解什么是混沌现象,然后再探讨量子化学计算的精度问题是否会引发混沌行为。

混沌现象概述

混沌现象通常指在经典力学系统中对初始条件极其敏感的行为,即使是微小的初始条件差异也会导致系统长期行为的巨大差异。这种现象通常发生在非线性动力系统中,具有以下特征:

  • 初始条件敏感性:微小的初始条件变化会导致显著不同的结果。
  • 不可预测性:尽管系统是确定性的,但长期行为难以预测。
  • 分形结构:混沌系统的相空间轨迹通常具有分形结构。

量子化学中的精度问题

量子化学计算中涉及到求解多电子薛定谔方程,用于预测分子结构、反应路径、电子态等。精度问题在量子化学计算中主要体现在以下方面:

  1. 数值近似和截断误差

    • 量子化学计算中使用的近似方法(如Hartree-Fock、DFT、CI、CC等)都会引入近似误差。
    • 基组截断误差:使用有限基组进行计算时,不能完美表示电子波函数。
  2. 数值积分和离散化误差

    • 数值积分中网格的精细程度会影响计算结果的精度。
    • 离散化方法的误差会在计算过程中积累。
  3. 计算机精度

    • 计算中使用的浮点数精度(如双精度浮点数)会导致舍入误差的积累。

量子化学中的混沌现象

量子化学计算中的混沌现象与经典混沌不同,量子系统的本质是线性的,描述其演化的薛定谔方程是线性方程。然而,在一些特定情况下,量子系统中也可以观察到类混沌行为,主要表现在:

  1. 量子混沌

    • 在量子力学中,量子混沌指的是量子系统的能级分布和对应的波函数在某些条件下表现出类似于经典混沌系统的特征。
    • 量子混沌通常研究具有复杂相互作用的系统,如原子核、分子中的多电子系统。
  2. 数值不稳定性

    • 量子化学计算中的数值不稳定性可能导致结果的敏感性,即对初始条件和计算参数的微小变化导致显著不同的结果,但这不完全等同于经典意义上的混沌。

具体示例

考虑使用变分量子特征求解(VQE)方法计算分子基态能量时,精度问题可能引发的复杂行为:

  1. 优化过程中的不稳定性

    • VQE依赖于经典优化算法来最小化期望值。优化算法可能会陷入局部极小值或产生不稳定行为,尤其是在高维参数空间中。
  2. 噪声影响

    • 当前的量子硬件存在噪声,噪声会影响量子态的演化和测量结果,从而导致计算结果的波动。
  3. 离散化误差

    • Trotter-Suzuki分解方法在模拟哈密顿量演化时的时间步长选择会影响结果的精度,步长过大会引入离散化误差。

尽管这些问题会导致计算结果的复杂行为,但它们并不等同于经典混沌。量子系统的行为仍然受线性薛定谔方程的约束,而混沌现象主要在非线性动力系统中表现得更加明显。

总结

量子化学计算中的精度问题会导致结果的敏感性和不稳定性,但严格来说,这些问题并不直接导致经典意义上的混沌现象。量子系统的本质是线性的,量子混沌现象的研究主要集中在量子系统能级和波函数的复杂行为上。通过提高计算方法的精度、优化算法和硬件性能,可以减小这些数值误差和不稳定性,从而提高量子化学计算的可靠性。

NWChem

  • NWChem 是一个开源的计算化学软件包,旨在模拟和预测分子和固体的性质。它支持多种量子化学方法和基组,并具有强大的并行计算功能。NWChem 可以用于计算分子结构、能量、光谱、反应动力学等。
  • NWChem 具有良好的并行化能力,可以有效地处理中等到大规模的量子化学计算。它在大型超级计算机上的性能表现良好,可以处理数百到数千原子的系统,包括分子和固体。

量子运动学经典计算模型

The Classical Computational Model in Quantum Kinematics


再谈退相干

环境中辐射普遍存在,其效应能引起退相干,它们具有的意义超出了与测量问题的部分相关性。不久前的一个重要进展是,人们认识到它们也与我们应该怎样思考所谓混沌系统的量子力学有关。

自然界中存在的固有的不可预测性,并不仅仅来自量子过程。大约40年前,人们认识到即使在牛顿物理学中,也有许多系统对微小的扰动效应极其敏感,进而使它们未来的行为无法被精确预测。这个发现令大多数物理学家非常惊讶。这些混沌系统(对它们的称呼)对细节的敏感,很快达到海森堡不确定性水平或以下。但是,用量子力学观点来处理它们——一个叫作量子混沌学的课题——被证明是有问题的。

困惑的原因如下:混沌系统有一个行为,它的几何特征对应于著名的分形(最熟悉的例子是曼德尔布罗特集,该集是许多迷幻海报的主题)。分形是某种被称作自相似的东西,也就是说,不论在何种尺度上查看,它们看起来本质是相同的(锯齿由锯齿组成,……,一直这样下去)。因此,分形没有天生的特征尺度。然而另一方面,量子系统却有天生的特征尺度,由普朗克常数设定。因此,混沌理论和量子理论并不能顺利地相互适应。

由此产生的失配将导致所谓的“混沌的量子抑制”(量子疤痕):当混沌系统开始在量子水平上依赖细节时,就改变了自己的行为。对物理学家来说,这就导致了另一个问题,该问题最严重的形态源自对土星的第十六颗卫星——土卫七的思考。这个马铃薯形状的岩石块,跟纽约差不多大小,以混沌的方式在翻滚。如果我们将量子抑制概念应用到土卫七上,预期结果将会惊人地有效,尽管它尺寸极大。事实上,基于这个计算,混沌运动最多仅能持续约37年。实际情况是,天文学家观测土卫七的时间比37年短得多,但是没人预期它那怪诞的翻滚行为会很快结束。乍一看,我们面临着一个严重问题。然而,考虑退相干会为我们解决这个问题。退相干存在一个倾向,即驱动事物朝着与经典情形更相似的方向发展,该倾向有一个效应,能反过来抑制混沌的量子抑制。我们还是能够满怀信心地预期,土卫七会继续翻滚很长一段时间。

退相干引起的另一个相当类似的效应是量子芝诺效应。衰变带来的放射性原子核,会被原子核与环境光子相互作用引发的“迷你观察”强制返回到初始状态。持续不断回到起点具有抑制衰变的作用,该现象已经在实验中被观测到。这个效应是根据古希腊哲学家芝诺命名的,他曾思考一支飞行的箭,认为在现在这个时刻观测这支箭,其处于一个特定的固定位置,所以他相信箭不可能真正运动。

这些现象清楚地说明了量子理论和它的经典界限之间的关系是微妙的,涉及不能简单地用“大”和“小”来划分的交错效应。

ーー《量子理论》 [英国]约翰・波尔金霍恩


HF(Hartree-Fock)方法

  • Hartree-Fock 方法是一种单参考的自洽场方法,用于计算原子和分子的基态能量和波函数。HF 方法的理论基础主要是非相对论量子力学和电子的波动性。HF 方法通常用于描述小型分子的电子结构。
  • Hartree-Fock 方法基于单 Slater 行列式理论,假设体系的波函数可以表示为单个 Slater 行列式。它采用了经典的波函数表示方法,并通过解 Hartree-Fock 方程来优化波函数,以最小化体系的总能量。
  • 在严格意义上,HF(Hartree-Fock)方法在某种程度上可以被认为是不含近似的,因为它是基于非相对论量子力学的精确解,但在实际应用中,HF 方法也会涉及到一些近似,例如闭壳层近似和单 Slater 行列式近似等。

密度泛函理论(DFT)

  • DFT 用于研究原子、分子和固体等系统的电子结构和性质。DFT 通过电子密度来描述和计算系统的性质,而不是直接处理复杂的多电子波函数。
  • DFT 的核心是交换-关联能量泛函。这部分能量考虑了电子间的交换和关联效应,是电子总能量的一部分。交换-关联能量泛函的形式决定了计算的精度和适用范围。
  • DFT 通过 Kohn-Sham 方程来描述系统的基态电子结构,将复杂的多电子问题转化为一组单电子问题。这些单电子方程类似于 Schrödinger 方程,但它们包括了一个额外的项,即由交换-关联能量泛函引入的有效势。

要使得密度泛函理论(DFT)完全等价于Hartree-Fock(HF)方法,需要选择一种特定形式的交换-关联能量泛函。Hartree-Fock方法考虑了电子间的交换作用,但忽略了关联效应,因此我们需要构建一种仅包含交换能的泛函,而不包括关联能。

在DFT中,这种交换能泛函被称为Hartree-Fock交换泛函,或简称为Exact Exchange (EXX)。具体来说,EXX泛函是基于Hartree-Fock理论中的交换作用部分构建的。使用这种泛函,DFT中的交换-关联能量泛函仅包含交换能,而没有关联能,从而使得DFT的计算结果等价于HF方法。

具体实现方面,EXX泛函的数学表达式与Hartree-Fock方法中的交换能表达式是一致的。简化后,EXX泛函可以写成:

$$ E_{\text{X}}[\rho] = -\frac{1}{2} \sum_{i,j} \int \int \psi_i^*(\mathbf{r}) \psi_j(\mathbf{r}) \frac{1}{|\mathbf{r} - \mathbf{r}'|} \psi_j^*(\mathbf{r}') \psi_i(\mathbf{r}') \, d\mathbf{r} \, d\mathbf{r}' $$

在这个表达式中,$\psi_i(\mathbf{r})$和$\psi_j(\mathbf{r})$是电子轨道,$\rho(\mathbf{r})$是电子密度,$\mathbf{r}$和$\mathbf{r}'$是位置向量。

总之,要使得DFT完全等价于HF方法,需要使用EXX泛函作为交换-关联能量泛函。这种方式在实践中可以通过自洽场计算实现,使得DFT的结果与HF方法一致,特别是在交换能的计算方面完全相同。


PySCF: Python-based Simulations of Chemistry Framework

  • PySCF 是量子化学和电子结构计算的强大工具,适合研究分子和材料的电子性质。
特性 PySCF NWChem
编程语言 Python C/C++
主要用途 桌面和中小规模量子化学计算,快速原型开发 大规模量子化学计算,高性能计算
计算方法 HF、DFT、MP2、CC、CI 等 HF、DFT、MP2、CC、分子动力学等
模块化和灵活性 高度模块化,易于扩展和定制 功能全面但模块化程度较低
性能 适合中小规模计算,关键部分有 C 扩展 专为高性能计算设计,适合大规模并行计算
硬件兼容性 桌面计算和中小型集群 超级计算机和高性能计算集群
学习曲线 对 Python 用户友好,易于上手 学习曲线较陡,需要更多的时间掌握
集成性 易于与 Python 生态系统和其他工具集成 集成性较低,但可以通过脚本和接口实现
成熟度和稳定性 新兴工具,正在快速发展 成熟稳定,在学术和工业界广泛应用

非相对论性量子电动力学

$Non$-$Relativistic$ $Quantum$ $Electrodynamics$ $=$ $Non$-$Relativistic$ $Quantum$ $Kinematics$ + $Relativistic$ $Quantum$ $Electromagnetic$ $Field$ $Theory$


Consider a Hydrogen atom described by $H = -\Delta_x - \frac{\alpha}{|x|}$. What quantum mechanics teaches about the spectrum of this operator is that it consists of a ground state and excited states

$$ E_n = -\frac{\alpha^2}{4n^2}, \quad n=1,2,3,\ldots $$

and then a continuous spectrum above zero. This means, that the electron in an excited state would stay in such an excited state forever. But experiments tell you that this is simply not true, the lines have a finite width (even at zero temperature) and thus after some time the electron relaxes to a ground state emitting photons. In the Schrödinger equation you know from Quantum Mechanics there are no terms responsible for this effect. The physical reason is coupling of the electron to the quantized electromagnetic field, which is usually not covered by introductory Quantum Mechanics courses. Relaxation of excited atoms to the ground state is one example of a question which cannot be answered within non-relativistic Quantum Mechanics. Non-relativistic QED offers an appropriate framework to study this question. (Relativistic QED is difficult to apply to bound state problems due to its perturbative character - see below).

ーーWojciech Dybalski, Non-relativistic QED, 2 (July 14, 2016).

考虑一个氢原子,其哈密顿量描述为 $H = -\Delta_x - \frac{\alpha}{|x|}$。量子力学教导我们关于这个算符的能谱,它包含一个基态和激发态

$$ E_n = -\frac{\alpha^2}{4n^2}, \quad n=1,2,3,\ldots $$

以及一个在零以上的连续谱。这意味着,处于激发态的电子将永远保持在这种激发态。但是实验表明,这显然是不正确的,光谱线具有有限的宽度(即使在零温度下),因此经过一段时间后,电子会通过发射光子松弛到基态。在你从量子力学中知道的薛定谔方程中,没有能导致这种效应的项。其物理原因是电子与量子化电磁场的耦合,这通常在入门的量子力学课程中没有涉及。激发原子向基态的松弛是一个在非相对论量子力学中无法回答的问题。非相对论量子电动力学(NRQED)提供了一个适当的框架来研究这个问题。(相对论量子电动力学由于其微扰特性,在应用于束缚态问题时较为困难——见下文)。

ーーWojciech Dybalski,《非相对论性量子电动力学》,第2页(2016年7月14日)。


NRQED(Non-Relativistic Quantum Electrodynamics)主要用于描述低能量下电子与电磁场的相互作用。这一理论基于量子场论和非相对论量子力学的基本原则,方程通常是线性的,并且不表现出经典意义上的混沌效应。

以下是对这些问题的具体解释:

方程的线性性质

NRQED 方程主要由以下部分组成:

  1. 非相对论性薛定谔方程: 描述单电子在势场中的运动,其形式为: $$ i \hbar \frac{\partial \psi}{\partial t} = \left( -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r}) \right) \psi $$

  2. 相互作用哈密顿量: NRQED 包含的相互作用部分通过量子场论方法引入,如库仑相互作用、电子和电磁场的相互作用等。这些相互作用通常通过线性算符表示。

例如,电子在电磁场中的相互作用哈密顿量: $$ H_{\text{int}} = \sum_i \left( -e \phi(\mathbf{r}_i) + \frac{e}{m_e} \mathbf{p}_i \cdot \mathbf{A}(\mathbf{r}_i) + \frac{e^2}{2m_e} \mathbf{A}^2(\mathbf{r}_i) \right) $$

这些方程和相互作用哈密顿量都保持线性。

混沌效应

混沌效应通常出现在非线性动力学系统中,这些系统对初始条件非常敏感,导致长期行为变得不可预测。在经典力学中,这种行为通常与非线性方程和复杂的相互作用有关。

然而,在量子力学和量子场论(包括 NRQED)中,方程通常是线性的,这意味着系统的演化是确定性的,只要初始条件和相互作用哈密顿量已知。尽管量子系统可能表现出复杂和非直观的行为,例如量子纠缠和相干性,但这些行为并不等同于经典混沌。

NRQED 中的非线性效应

虽然 NRQED 方程本身是线性的,但在某些近似或特定情况下可能出现有效的非线性效应。例如:

  1. 多体相互作用: 在处理多电子系统时,相互作用可以通过平均场近似或其他方法引入有效的非线性项。然而,这些效应仍然可以用线性方程和叠加原理来处理。

  2. 自能和真空极化: 高阶修正如自能和真空极化可以引入复杂的效应,但这些效应通常通过摄动理论处理,依然保持在线性框架内。

总结

NRQED 中的基本方程是线性的,这确保了量子系统的演化是可预测和可计算的。尽管可能存在复杂的多体相互作用和高阶量子效应,但这些都不导致经典意义上的混沌效应。

NRQED 提供了一种精确的方法来描述低能量下电子与电磁场的相互作用,保持了量子力学的线性和确定性特征。


QuTiP: Quantum Toolbox in Python

  • QuTiP 是用于量子信息和量子计算的理想工具,特别适合模拟量子系统的动力学和开放量子系统的演化。
特性 QuTiP PySCF
主要应用领域 量子信息、量子计算、开放量子系统模拟 量子化学、电子结构计算
主要功能 量子态和量子操作的创建与操纵,开放量子系统的动力学模拟 从头计算量子化学方法(如 HF、DFT、CI、CC)
动力学模拟 支持密度矩阵和态向量的时间演化,Lindblad方程求解 不直接支持,但可以通过电子结构计算间接研究
用户界面 高级函数和类,用户友好 高度模块化,支持自定义和扩展
计算规模 适用于较小规模的量子系统模拟 支持大规模电子结构计算
并行计算 通常用于较小规模系统,较少强调并行计算 支持多线程和分布式计算
可视化工具 丰富的可视化工具,用于绘制量子态、算符和动力学演化的图像 基本的可视化工具,主要集中在电子结构相关的图像
开发和扩展性 高级接口便于快速开发和测试量子信息处理和模拟 模块化设计,便于组合和扩展不同计算模块
常用领域 量子光学、固态物理、原子物理、量子信息科学 材料科学、分子物理、量子化学

人脑海马体非相对论性量子电动力学经典计算模型

The Classical Computational Model of the Human Hippocampus in Non-Relativistic Quantum Electrodynamics


人脑海马体是一个复杂的神经结构,涉及多个关键神经回路,这些回路在记忆形成、存储和检索中起着重要作用。以下是一些主要的关键神经回路:

1. 齿状回-CA3回路(Dentate Gyrus-CA3 Circuit)

  • 结构和功能
    • 齿状回(Dentate Gyrus,DG)是海马体的输入区域,接收来自内嗅皮层的输入信号。
    • 齿状回中的颗粒细胞将信息传递到CA3区的锥体细胞。这一过程通过苔藓纤维路径实现。
  • 作用
    • 齿状回-CA3回路在模式分离(pattern separation)中起重要作用,有助于区分相似但不同的记忆。

2. CA3-CA1回路

  • 结构和功能
    • CA3区的锥体细胞通过Schaffer侧枝路径将信息传递到CA1区的锥体细胞。
  • 作用
    • CA3-CA1回路在模式补全(pattern completion)和记忆回忆中起关键作用。
    • CA3区通过其自联结特性(recurrent connections)可以完成部分记忆片段的补全。

3. CA1-内嗅皮层回路

  • 结构和功能
    • CA1区的锥体细胞将处理后的信息发送回内嗅皮层(Entorhinal Cortex),通过子区间层(subiculum)完成这一传输。
  • 作用
    • 这一回路在记忆信息的输出和整合过程中起重要作用,有助于将海马体的处理结果传递到新皮层进行长时记忆存储。

4. 内嗅皮层-齿状回回路

  • 结构和功能
    • 内嗅皮层的第II层和第III层细胞通过穿通路径(Perforant Pathway)将信息传递到齿状回。
  • 作用
    • 内嗅皮层-齿状回回路在记忆的初步编码和信息过滤中起关键作用。

5. 三突触环路(Trisynaptic Circuit)

  • 结构和功能
    • 三突触环路包括内嗅皮层-齿状回、齿状回-CA3区和CA3区-CA1区的路径。
  • 作用
    • 这是海马体中最著名的回路之一,涉及记忆的初步编码、信息处理和传递。三突触环路是海马体处理信息的主要路径,涉及多个关键的突触连接。

6. 内侧隔区-海马回路(Medial Septum-Hippocampus Circuit)

  • 结构和功能
    • 内侧隔区(Medial Septum)通过纤维束与海马体连接,调节海马体的活动。
  • 作用
    • 该回路在海马体的节律活动(如θ节律)中起关键作用,θ节律与学习和记忆过程密切相关。

7. 海马-杏仁核回路(Hippocampus-Amygdala Circuit)

  • 结构和功能
    • 海马体与杏仁核(Amygdala)之间有直接和间接的神经连接。
  • 作用
    • 该回路在情绪记忆的形成和调控中起重要作用,情绪记忆对于存储和回忆带有情感色彩的记忆非常重要。

8. 海马-前额叶皮层回路(Hippocampus-Prefrontal Cortex Circuit)

  • 结构和功能
    • 海马体与前额叶皮层(Prefrontal Cortex)之间有重要的神经连接,通过直接和间接路径进行通信。
  • 作用
    • 该回路在工作记忆和情景记忆的调控中起关键作用,前额叶皮层整合来自海马体的记忆信息以进行决策和认知控制。

总结

海马体中的这些关键神经回路共同作用,支持复杂的记忆处理和认知功能。了解这些回路的结构和功能对于研究记忆机制、认知过程以及相关的神经疾病(如阿尔茨海默症)具有重要意义。


CA3-CA1回路的非相对论性量子电动力学经典计算模型


人脑海马体中的关键神经细胞类型多样,每种细胞类型在记忆形成、存储和检索等过程中都发挥着重要作用。以下是一些主要的关键神经细胞类型及其功能:

1. 锥体细胞(Pyramidal Cells)

CA1区和CA3区锥体细胞

  • 结构
    • 这些细胞以其三角形的细胞体和丰富的树突分支而得名。
    • CA3区的锥体细胞具有自联结(recurrent connections),而CA1区的锥体细胞则通过Schaffer侧枝路径与CA3区连接。
  • 功能
    • 在信息传递和处理过程中起关键作用。
    • CA3区锥体细胞在模式补全和记忆检索中起重要作用,而CA1区锥体细胞则在信息的整合和输出中起关键作用。

2. 颗粒细胞(Granule Cells)

齿状回(Dentate Gyrus)

  • 结构
    • 小而紧密的细胞,具有丰富的树突和轴突。
  • 功能
    • 颗粒细胞接收来自内嗅皮层的输入信息,并通过苔藓纤维路径将信息传递到CA3区。
    • 在模式分离(pattern separation)中起重要作用,有助于区分相似的记忆。

3. 内侧隔区-投射神经元(Medial Septal Projection Neurons)

  • 结构
    • 这些细胞从内侧隔区向海马体投射。
  • 功能
    • 调控海马体的θ节律(theta rhythm),这种脑电节律与学习和记忆密切相关。

4. 中间神经元(Interneurons)

不同类型的中间神经元在海马体中分布,包括但不限于:

  • 篮状细胞(Basket Cells)

    • 位于CA1和CA3区,通过其轴突包绕锥体细胞的细胞体。
    • 主要释放GABA,起抑制作用,调控锥体细胞的兴奋性。
  • 初级终末细胞(Chandelier Cells)

    • 其轴突形成像烛台一样的结构,包绕锥体细胞的轴突起始段。
    • 也是GABA能细胞,提供强有力的抑制输入。
  • 双极细胞(Bipolar Cells)和双单极细胞(Bitufted Cells)

    • 具有两端各有树突的结构。
    • 这些细胞在局部网络中调节兴奋性和抑制性平衡。

5. 内嗅皮层投射细胞(Entorhinal Cortex Projection Neurons)

  • 结构
    • 这些细胞位于内嗅皮层(Entorhinal Cortex),其轴突通过穿通路径将信息传递到海马体的不同区域。
  • 功能
    • 作为海马体的主要输入源,这些细胞在信息的初步处理和传递中起关键作用。

6. 星形胶质细胞(Astrocytes)

  • 结构
    • 具有星形的细胞体和丰富的树突分支。
  • 功能
    • 在海马体中,星形胶质细胞参与维持细胞外环境的稳态,调节血流,提供代谢支持,并参与突触可塑性和信号传导。

7. 微胶质细胞(Microglia)

  • 结构
    • 小而具有多分支的形态。
  • 功能
    • 作为中枢神经系统的免疫细胞,微胶质细胞在响应损伤和炎症中起关键作用,参与清除细胞碎片和调节神经元功能。

8. 少突胶质细胞(Oligodendrocytes)

  • 结构
    • 具有相对较少的分支,但其分支能够包绕神经轴突,形成髓鞘。
  • 功能
    • 提供髓鞘以加速轴突的信号传导速度。

总结

人脑海马体中包含多种类型的关键神经细胞,包括锥体细胞、颗粒细胞、中间神经元、投射神经元以及各种胶质细胞。这些细胞类型各司其职,共同参与海马体的复杂功能,特别是在记忆和学习过程中发挥关键作用。了解这些细胞类型及其功能对于研究记忆机制、认知功能和相关神经疾病(如阿尔茨海默症)具有重要意义。


在海马CA1区,除了锥体细胞外,TLR9(Toll样受体9)也可能存在于其他类型的神经细胞中。这些神经细胞类型可能包括:

1. 抑制性中间神经元

抑制性中间神经元(interneurons)在调节海马网络的兴奋性和抑制平衡中起关键作用。研究表明,抑制性中间神经元也可能表达TLR9。以下是一些抑制性中间神经元的具体类型:

  • 篮状细胞(Basket cells):这些细胞通过形成篮状突触终末,围绕锥体细胞的细胞体,提供强有力的抑制输入。
  • 腔隙细胞(Chandelier cells):这些细胞在锥体细胞的轴突初段形成突触,对动作电位的启动有重要影响。
  • 双极和双束突细胞(Bipolar and bitufted cells):这些细胞通过其树突和轴突分布在不同的层中,提供层特异性的抑制。

2. 投射神经元

虽然CA1区的主要投射神经元是锥体细胞,但也有其他类型的投射神经元,这些神经元可能表达TLR9并参与远距离信息传递。

3. 其他类型的兴奋性神经元

除了主要的CA1锥体细胞,可能还有其他次要类型的兴奋性神经元,参与局部回路的调控和信息处理。


CA3区锥体细胞的非相对论性量子电动力学经典计算模型


为人脑海马体建立量子化学模型需要收集和使用多种数据,包括但不限于:

  1. 分子结构数据:包括海马体中各种分子的结构信息,如蛋白质、脂质、核酸等。

  2. 分子间相互作用数据:了解分子之间的相互作用,包括氢键、范德华力、离子键等。

  3. 电子结构数据:获得分子中各原子的电子分布情况,包括电子云密度、电子轨道能级等。

  4. 动力学数据:了解分子在海马体中的运动情况,包括振动频率、转动角速度等。

  5. 反应性数据:了解分子在不同条件下的反应性,包括活化能、反应速率等。

  6. 环境因素数据:考虑海马体的生理环境因素对分子结构和性质的影响,如 pH 值、温度、离子浓度等。

  7. 实验数据:通过实验手段获取海马体中分子的实际性质数据,如光谱数据、质谱数据、X射线晶体学数据等。


人脑海马体中有许多与记忆相关的关键蛋白质,其中一些包括:

  1. NR2B:N-甲基-D-天冬氨酸受体亚基2B(N-methyl-D-aspartate receptor subunit 2B),是NMDA型谷氨酸受体的亚基之一,与学习和长期记忆形成有关。

  2. CAMKII:钙/钙调素依赖性蛋白激酶II(Ca2+/calmodulin-dependent protein kinase II),是一种钙调素依赖性酶,参与了突触的可塑性和记忆的形成。

  3. CREB:cAMP反应元件结合蛋白(cAMP response element-binding protein),是一种转录因子,参与调节基因的转录,对长期记忆的形成和保持起重要作用。

  4. PSD-95:附着在神经元突触后膜上的后膜密度蛋白(Postsynaptic density protein 95),是一种突触相关蛋白,调节突触的形成和功能,对学习和记忆具有重要作用。

  5. Arc:活动相关的细胞骨架蛋白(Activity-regulated cytoskeleton-associated protein),是一种突触蛋白,参与突触可塑性和长期记忆的形成。

  6. Synapsin I:突触素I(Synapsin I),是一种突触蛋白,调节突触小泡的释放,参与了记忆的形成和维持。

  7. Bdnf:脑源性神经营养因子(Brain-derived neurotrophic factor),是一种神经营养因子,促进神经元的生存、生长和连接形成,对记忆的形成和维持具有重要作用。

这些蛋白质在海马体中参与了多种分子和细胞水平的过程,包括突触可塑性、长期增强和长期抑制等,对学习和记忆的形成起着关键作用。


在已知的研究中,CA3区锥体细胞中有多种关键分子被发现,它们在突触可塑性、神经传递和细胞健康中发挥重要作用。以下是一些在CA3区锥体细胞中已知的关键分子:

  1. 转录因子Zif268 (Egr1)

    • 作为一个即早基因(IEG),Zif268在神经活动后迅速上调,与突触可塑性和记忆巩固相关。
  2. 脑源性神经营养因子(BDNF)

    • BDNF在突触可塑性和神经元存活中起关键作用。通过其受体TrkB发挥作用,促进突触的形成和维持。
  3. 环磷酸腺苷反应元件结合蛋白(CREB)

    • CREB是一个重要的转录因子,参与长时程增强(LTP)和记忆的转录调控。
  4. NR2B亚基(NMDA受体的一个亚单位)

    • NMDA受体在突触可塑性和LTP中起核心作用。NR2B亚基在CA3神经元中对于高效的突触传递和可塑性至关重要。
  5. 钙结合蛋白(Calbindin)

    • Calbindin调节细胞内钙离子浓度,影响神经元的兴奋性和可塑性。
  6. 突触蛋白 I(Synapsin I)

    • Synapsin I调节突触囊泡,影响神经递质的释放和突触可塑性。
  7. GluA1和GluA2亚基(AMPA受体的亚单位)

    • 这些亚基是AMPA型谷氨酸受体的重要组成部分,参与快速兴奋性突触传递和LTP。
  8. 树突蛋白(Dendrin)

    • Dendrin在树突中表达,与突触形态和功能相关。
  9. 代谢型谷氨酸受体(mGluR2和mGluR3)

    • 这些受体调控突触传递和神经元兴奋性。
  10. 细胞黏附分子N-钙黏蛋白(N-Cadherin)

    • N-Cadherin在突触稳定和可塑性中起关键作用。

电压门控钙离子通道的非相对论性量子电动力学经典计算模型

The Non-Relativistic Quantum Electrodynamics Classical Computational Model of Voltage-gated Calcium Channel


G. Bernroider and J. Summhammer, “Can quantum entanglement between ion transition states effect action potential initiation?,” Cognitive Computation, vol. 4 (2012), pp. 29–37.

摘要 原子决定因素在离子传导蛋白质中的分子模型中的参与,表明需要重新审视基于速率理论模型(例如“门控”粒子)和大块溶解概念的经典概念。在此,我们研究了离子传导分子(电压门控离子通道)内的量子相关机制对传播电压脉冲(动作电位,APs)启动动力学的可能影响。特别是,我们关注动作电位(API)的启动特性。我们将Hodgkin-Huxley方程中的钠电流经典启动参数建模为三个相似但独立的概率机制,这些机制可以变得量子相关。基础物理学是通用的,可以涉及离子转变状态或传导期间“门控状态”下的各种自由度之间的纠缠,例如在不同通道位置的Na⁺离子,或者与蛋白质子区域内原子协调的不同状态(“过滤状态”)。我们发现,包含纠缠钠通道系统状态的霍奇金-赫胥黎方程的半经典版本,可以加速或减缓信号启动时膜电位的上升。原则上,单个钠通道可以将膜驱动到AP阈值,我们建议,观察到的半量子-经典信号描述的效果可能指向Na⁺通道的自我放大,并可能是由于通道原子环境内的量子干涉。如果插入到AP信号的规范生成器中,所建议的量子术语可以进一步增强信号启动的快速性,这是最近在真实皮层神经元中观察到的,并且对于高频输入的编码似乎是不可避免的。

关键词 神经信号,动作电位启动,钠通道,离子转变状态,量子纠缠,量子协同


引言 电可兴奋细胞之间的信号传递通常基于跨细胞质膜的离子的协同转运。自1952年引入以来,Hodgkin-Huxley方程(HH)[1] 在描述导致神经元电压脉冲[2, 3] 和神经元网络行为的离子协同转运方面非常成功。HH模型方程的概念基础是离子通过细胞膜内的通道蛋白质的随机运动,由膜电位差驱动,并由电位依赖的电导率调节。相应的经典电动力学模型的形式化,膜脂双层在其中起到电容器的作用,直接导致HH方程。近年来,然而,原子分辨率的晶体学研究和伴随的混合量子力学和分子动力学研究为生物电现象的研究设定了新框架(例如 [5, 6])。这为理解生物电现象提供了新的视角。


模型:通道内的量子相互作用 特别是分子动力学(MD)模拟研究支持离子-氧配位,表明离子通过通道时“经历”了一系列由四个平面羰基氧原子提供的四个“氧笼”。这些氧原子与其母体骨架氨基酸结构的结合及其典型能量可以预期会强迫它们进入某些量子化的振动状态。这些原子之间的相互作用项可能演变为共同的纠缠量子态。因此,每个氧原子的运动将取决于所有其他氧原子的运动。由于这种运动量子力学上是氧原子至少两个能级的叠加,其振幅相当大[12, 13],这将反过来影响离子通过平面氧原子的概率。然后,离子将通道视为一系列相关的门控:在一个平面通过后,离子可能有更高的机会通过下一个平面,等等。这种情况再次暗示离子电导率和与经典图像的偏离。

所有这些效应可能在实验情况下起作用,并且可能出现额外因素,取决于通道的分子结构在原子尺度上描述的程度。在本文中,我们将重点关注涉及纠缠的第二和第三方面。然而,我们不需要特别选择任何一种所描述的情景,因为这两个方面在从经典概率到量子概率的转变视角中具有相似的效果。我们可以相当广泛地处理这个问题,并考虑将变得量子纠缠的几个独立自由度。这些自由度可以由几个独立离子的运动给出,也可以由相互作用的氧原子提供。在任何情况下,它们也可以由对通过通道的电荷传输相关的其他概率变量提供。另外,由于HH方程背后的传导机制的经典理解,我们也有理由进行相当广泛的处理。在这里,人们假定存在“门”,其确切性质尚未真正指定,但它们控制离子电流的大小。除了它们的整体电压依赖性外,这些“门”被认为以概率方式行为。这个方面,加上门控变量必须在提到的原子分辨率尺度上实例化,自然需要量子理论的描述。在这里,我们量子力学地描述Na⁺通道的“门”,因为Na⁺离子是HH方程中脉冲初始上升的原因。我们预期量子纠缠可能会对观察到的“比预期更快”的动作电位启动(API)机制有所启示。这些在皮层神经元上的实验显示了动作电位的快速启动,无法通过经典的HH方程重现。作者仅通过假设细胞膜的邻近离子导通通道之间的相关性才恢复了观察到的脉冲形状。然而,超出约束膜电场的通道间合作与传统的流体镶嵌模型和HH模型内在的独立“门控”机制相矛盾。在这里,我们建议纠缠可以导致Na⁺通道的自我放大,并可能是由于通道原子环境内的量子干涉。


离子通道型谷氨酸受体的非相对论性量子电动力学经典计算模型

N-甲基-D-天冬氨酸型谷氨酸受体的非相对论性量子电动力学经典计算模型

The Non-Relativistic Quantum Electrodynamics Classical Computational Model of Ionotropic N-Methyl-D-Aspartate Glutamate Receptor


CA1区锥体细胞的非相对论性量子电动力学经典计算模型


Jovasevic, V., Wood, E.M., Cicvaric, A. et al. Formation of memory assemblies through the DNA-sensing TLR9 pathway. Nature 628, 145–153 (2024).

在这篇文章中,涉及的关键分子主要集中在学习和记忆过程中海马神经元的DNA感知和修复机制中。以下是文章中提到的几个关键分子:

  1. TLR9(Toll样受体9)

    • 这是文章中的核心分子,TLR9在海马神经元中通过识别双链DNA(dsDNA)断裂和其他损伤信号,激活下游的炎症反应和DNA修复机制。
  2. γH2AX

    • γH2AX是组蛋白H2AX的磷酸化形式,常用作DNA双链断裂的标志。文章中通过检测γH2AX的聚集来识别神经元中的DNA损伤。
  3. NF-κB(核因子κB)

    • 这是一个转录因子,在TLR9激活后进入细胞核,启动炎症相关基因的表达。
  4. MyD88(髓样分化因子88)

    • MyD88是TLR9信号通路中的一个关键适配蛋白,介导TLR9的下游信号传递,激活NF-κB。
  5. LAMP2(溶酶体相关膜蛋白2)

    • LAMP2是溶酶体的标志蛋白,文章中提到TLR9与LAMP2的共定位增加,表明TLR9在内涵体中的运输和功能变化。
  6. cGAS(环状GMP-AMP合成酶)

    • cGAS是另一个DNA感知器,识别细胞质中的DNA并激活STING通路。虽然文章主要集中在TLR9,但cGAS-STING通路也是DNA感知的重要组成部分。
  7. STING(刺激干扰素基因蛋白)

    • 这是cGAS信号通路的下游效应分子,在DNA感知后激活抗病毒和炎症反应。

这些分子共同作用,形成了神经元对DNA损伤的感知和修复机制,这对于记忆的形成和维持至关重要。研究这些分子及其相互作用有助于理解学习和记忆的分子基础,并可能为神经退行性疾病的治疗提供新策略。


TLR9 的非相对论性量子电动力学经典计算模型

Toll 样受体 9 的非相对论性量子电动力学经典计算模型

Classical Computational Model of Non-Relativistic Quantum Electrodynamics for Toll-like Receptor 9

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2024-05-15
金面包

第10章 金面包

FIGURE

BioBuilder 的 Golden Bread 活动强调设计-构建-测试周期的“构建”阶段。 您将使用一种面包酵母菌株,该酵母菌株已用另一种真菌的基因进行改造,以产生 β-胡萝卜素,这是我们从胡萝卜、红薯和西兰花等食物中自然获得的营养物质。在体内,β-胡萝卜素会转化为维生素 A,这对于视力、免疫系统和其他生物功能至关重要。在一些与营养不良作斗争的发展中国家,维生素 A 缺乏是一个严重的公共卫生问题。研究人员希望,一种旨在产生 β-胡萝卜素的工程化面包酵母菌株(就像您将在本次活动中研究的菌株一样)可以用于面包中,以治疗维生素 A 缺乏症。这种面包由于添加了维生素而呈现金黄色,因此得名“黄金面包”。

对于任何新食品或药物要广泛使用,制造商必须证明他们能够可靠地生产该材料。批次之间的差异不会很大。它必须始终有效。事实上,可靠性对于几乎所有工程工作都至关重要。如果你想一想你最喜欢的工程物体,无论是你的汽车、手机还是冰箱,它的可靠运行可能是它受到喜爱的部分原因。人们讨厌汽车无法启动、电话信号不好以及冰箱变热。我们使这些对象达到相当高的性能标准。事实上,桥梁、ATM 机和投票机等一些工程设备必须始终完美运行。因此,可以公平地说,为了有用,所有工程系统都应该可靠。

FIGURE

在合成生物学领域,可靠性工程师识别生命系统中的不稳定来源,以使系统运行更加可靠。他们有自己的工作要做! BioBuilder 的 Golden Bread 活动强调如何将科学方法与良好的旧工程知识相结合,以评估并改进不可靠的合成细胞。

工程可靠性

如果你家乡的土木工程师已经完成了他们的工作,你就不会觉得开车过桥是一种可怕的经历。您不必在整个过程中屏住呼吸,担心结构会在您的重量下弯曲或坠落到地面。但现在想一想,这种自信从何而来?我们如何知道桥梁是否安全?

答案是桥梁和其他建筑项目的设计都是为了可靠性。设计人员知道桥梁故障可能是致命的、昂贵的,并且会破坏城市的基础设施,因此他们尽一切努力设计和建造一个可靠的系统。在本章中,我们将介绍一些可靠系统设计的具体方法,例如执行例行定期维护以及使用强度高于最低限度所需的材料进行建造。我们还讨论了如何将这些原理扩展到生物系统工程。

定期维修

想象一下,如果您的汽车永远不需要调整该多好。你永远不需要把它带到商店,它的性能总是和下线那天一样完美。您可以节省大量的时间和金钱,而且您永远不会因故障而感到不便。大多数驾驶员可能会很高兴拥有一辆运行 100% 可靠的汽车。

FIGURE

但司机和汽车制造商,即使他们梦想着如此完美的未来,也知道不存在完全可靠的汽车。汽车会因发动机运动部件的摩擦、机油变脏以及轮胎根据季节需要或多或少的空气而遭受物理磨损。工程师们已尽其所能,最大限度地提高工作汽车中每个部件的可靠性,但期望所有部件无限期地完美运行是不合理的。相反,制造商平衡支持汽车正常使用的强大系统和简单的维护计划,以保持汽车尽可能长时间地正常运行。

那么,当工程师知道随着时间的推移,系统必然会腐蚀然后出现故障时,工程师该怎么办呢?在大多数制造领域,工程师将确定系统及其组件的平均无故障时间 (MTF)。这一确定有助于设计人员预测系统何时会崩溃。它还指导设计人员何时以及如何通过系统的定期维护进行干预。工程师在设计过程中纳入 MTF 计算,以便他们可以建议何时维修零件以及如何使用它们以延长使用寿命。

在工程学教授 Henry Petroski 的一本精彩著作《To Engineer is Human》中,他探索了 MTF,寻找一个熟悉的物体,即回形针。您可能从经验中知道,如果您将回形针弯曲足够多次,它最终会断裂,如图 10-1 所示。从物理角度来看,这种断裂的发生是因为弯曲对金属施加了应力,从而增加了材料的物理缺陷,并且随着缺陷的积累,金属断裂。您可以通过计算回形针断裂前可以弯曲的次数来测量回形针的 MTF。 为了获得对您的数字的信心,您需要在几种不同的条件下重复实验几次,以确定平均 MTF。当然,我们大多数人并不担心修理回形针,因为它们很容易更换,但想象一下您有一个非常有价值的回形针。在这种情况下,您将记录它所经历的弯曲次数,以便您知道何时接近 MTF。很难想象回形针可以做什么“维护”,但如果回形针足够有价值,可能会有一些值得尝试的事情。

当将这些想法应用于生物学时,很明显细胞内置了大部分维护程序。生物系统比汽车或回形针等机械结构更具动态性。大多数细胞在生长过程中都处于近乎恒定的更新状态,然后将其遗传指令传递给新细胞。细胞生长和分裂可靠地产生新鲜细胞的供应。细胞也会自我修复,至少在细胞受到的损伤不太严重时是这样。合成生物学基础章节中讨论的生物学的这些方面是合成生物学如此有吸引力的部分原因。合成生物学家拥有可以用来构建的动态材料(细胞!),因此必须充分利用生物学的特征和能力。

FIGURE

图 10-1 回形针的 MTF。如图所示,来回弯曲回形针最终会导致其断裂。断裂前的弯曲次数可用于计算 MTF。

细胞固有的日常维护能力也有一个缺点。每当细胞复制自己的新副本以取代破旧的版本时,细胞分裂过程就会在 DNA 中引入突变,并传递给子细胞。因此,存在代际差异。这种变异会影响细胞的行为,并导致我们在自然界中发现聪明而美丽的系统。这种变异也给合成生物学家带来了重大障碍。影响系统行为的突变可以接管群体,用不再执行设计功能的新细胞完全取代原始细胞(图10-2)。

因此,为了设计一个可靠的生命系统,合成生物学家必须解决随着时间的推移出现的意外遗传变化。正如我们在 BioBuilder 的其他章节中所看到的,更成熟的工程学科和合成生物学之间的相似之处(尽管它们并不完美)可能会有所帮助,接下来我们考虑一些其他的工程可靠性方法。

FIGURE

图 10-2 代际变异。工程细胞(顶部,蓝色)的分裂可以产生精确的副本(第二行,蓝色)或可能无法执行所需功能的突变变体(第二行,绿色)。如果变体更强大,它可以在几轮分裂后接管种群,如底行所示。

冗余

在工程系统中构建冗余是许多领域使用的另一种技术,以确保更可靠的性能。例如,致力于乘客安全的工程师选择在车祸中同时部署安全带和安全气囊。安全带和安全气囊系统独立工作以实现同一目标。它们的独立控制使得两者在碰撞中发生故障的可能性较小。它们的效果也各不相同。根据碰撞的角度,安全带或安全气囊可能在保护车内人员方面发挥更大的作用。拥有两个安全系统可以增加乘客在碰撞中不受伤害的可能性,因此增加的成本是值得的。然而,并非所有资源密集型裁员都是合理的(图 10-3)。相反,考虑一个威胁较小的工程问题:设计手机。消费者通常期望他们的手机只能使用几年。屏幕可能会破裂,软件需要更新,最新手机的物理功能也会得到改进。由于大多数消费者会更换手机,而不是忍受随着时间的推移而出现的许多缺陷,因此手机设计人员没有动力在手机的电气组件中设计太多冗余。电气系统故障(可能是由于手机变湿或掉落在坚硬的表面上)造成的,虽然会带来不便,但不会危及生命。

这可以通过更换手机来解决,消费者宁愿经常更换手机或购买保险,也不愿提高手机本身的零售价格。

FIGURE

图 10-3 冗余。同时穿着背带和腰带是冗余设计的典型例子。

因此,冗余在其他工程学科中的应用并不均匀,并且是一种资源密集型的可靠性方法,但事实证明它是自然生物系统中相对常见的特征。例如,大多数动物细胞携带两个完整的基因组拷贝,而植物则更进一步,有时携带六到八个基因组拷贝。 活细胞中的冗余对于它们的生存很重要,因为 DNA 可能会被细胞环境中的诱变剂损坏。暴露在阳光或诱变剂下会引起 DNA 序列的变化,使一些遗传指令基本上无法读取。遗传冗余为细胞提供了一些保险。即使其中一个 DNA 拷贝被损坏,另一个 DNA 拷贝也可能保持完整,并且还可以作为修复受损拷贝的模板。细胞必须在能源和原材料方面为这种保险付出高昂的代价,但基因组“额外”副本的成本可以通过其遗传指令的安全性得到补偿。鉴于遗传冗余是大多数多细胞生物的标准特征,进化优势必定超过成本。

合成生物学家可以通过使用特定 DNA 序列的多个副本来设计他们的系统,从而引入遗传冗余。这可以通过用额外的质粒转化细胞或将某些基因的额外拷贝插入细胞的基因组来完成。这些遗传技巧可以通过为细胞提供基因的备份副本来增强基因电路的稳定性,以便在其他副本失败时使用。但令人惊讶的是,它也会破坏系统的稳定性。一些生物体,例如酵母,已经学会识别并去除 DNA 的直接重复序列。基因产物表达过多也存在危险。细胞是极其高效的系统,因此维持和表达额外的遗传物质可能会耗费大量能量,从而增加细胞的代谢负担或破坏工程系统的平衡。有一些方法可以解决这些缺陷,例如像我们在金面包实验中所做的那样,对冗余基因进行密码子改组,或者对冗余基因的表达添加一些调节。然而,成本/效益分析并不容易,而且目前还不清楚在将可靠性设计到生命系统中时应遵循哪些一般规则。

构建强大的系统

FIGURE

我们将在这里讨论的工程可靠性的最终方法是构建一个比严格必要的更强大的系统。例如,在建造一座桥梁时,工程师可以使用能够支撑 60 吨卡车的材料进行设计,因为他们知道大多数州卡车的最大法定重量为 40 吨。同样,他们可以设计一座能够承受里氏 10 级地震的桥梁,因为他们知道有史以来最大的地震是 9.5 级。为了充分设计如此强大的系统,工程师可以使用建模方法来预测其设计和材料对卡车和地震的反应。图片 本章提供有关建模的更多信息,并考虑模型如何为不同压力下的系统提供良好的数据。

设计过于稳健的系统的缺点是相关的成本。例如,建造如此超强桥梁的材料可能比能够承受桥梁实际预期应力的材料贵得多。大多数产品设计师都会理性地选择材料,通常会使用称为阿什比图的工具将可能材料的强度与其成本进行比较。通常,他们还会考虑与设计过于强大的系统相关的额外时间以及该时间的成本。与在足够的系统中构建的标准材料相比,超级材料的构建、采购或维护可能更复杂。亨利·彼得罗斯基(Henry Petroski)的另一本精彩著作《有用事物的演变》在其“小钱变大钱”一章的大部分内容中描述了一个看似平凡的工程项目,即床架上板条的工程。 Pertoski 追溯了为什么板条与框架成直角而不是对角穿过框架的问题(图 10-4)。事实证明,这个看似简单的问题早在亚里士多德就已经提出过,并且在荷马的《奥德赛》中也得到了考虑,当时奥德修斯建造了一张必须固定在橄榄树上并用皮带穿过的新娘床。令人惊讶的是,在大多数有记录的历史中,带有对角板条的床的经济性和维护被认为是不合理的!

FIGURE

图 10-4 平衡稳健性和成本。仅具有水平板条的床(左)不如具有对角板条网格的床(右)坚固,但前者比后者便宜。多年来,工程师在这种情况下一再选择成本较低的设计。

当材料选择扩展到生物系统的设计时会是什么样子?也许“强度”是指系统中不同蛋白质的表达水平,底盘本身的可预测生长,或者用于零件和设备的蛋白质的物理特性。 需要加强的生物系统的相关方面将取决于具体设计及其预期用途。

考虑一个系统,例如生物设计基础章节中的砷传感器,或任何其他与此相关的环境传感器。与使用超强钢建造桥梁的生物学类似,可以设计具有许多蛋白质传感器设备副本的系统,或者使用比严格必要的更灵敏的传感器。通过这些修改,您可以放心,即使是微量的触发化合物也会被传感器检测到并启动您想要的细胞反应。此外,即使基因中的有害突变随着时间的推移而积累,传感器也可以继续发挥作用,因为它的设计功能已经超出了规格。在这种情况下,需要权衡的是触发误报的可能性。高亲和力砷传感器现在可以识别类似的、毒性较小的化合物,甚至在根本不存在任何配体的情况下打开。编码如此高产量的传感器蛋白的系统在代谢上也可能是“昂贵的”,需要大量的细胞能量来维持高产量水平。细胞的许多资源将仅用于设计的系统,而不是细胞保持健康所需的其他基线代谢和修复系统。 使用蜂窝资源来设计可靠性最终可能会对细胞的健康产生负面影响,从而干扰工程系统的功能。事实上,代谢压力可能会减缓细胞的生长并降低工程系统的性能——这与工程师在引入更多传感器副本时试图做的事情恰恰相反。

此外,如果工程细胞处于进化劣势,它们将被生长更快的新突变体所取代,如前所述。根据工程细胞及其突变版本的生长速度,进化之战可能会在短短几代内失败。因此,毫不奇怪,合成生物学家正在采用基因设计原理,使它们的部件“更强”,因为它们不太可能发生突变。例如,由于相同的 DNA 序列经常通过重组被删除,因此通常会避免遗传元件的直接重复。合成生物学家可以利用遗传密码中的简并性来改变冗余 DNA 部分的序列,例如用 TTG 或 CTA 编码亮氨酸。这个技巧使得同一个蛋白质可以由两个不同的 DNA 序列编码,而这两个序列不太容易重组。通过用两个基因编码该功能,可能会使系统表现得更加可靠。您将通过 Golden Bread 工程活动直接测试这个概念。

合成生物学家还拥有一些工具来增强他们使用的底盘,使它们不易受到意外变化的影响(图 10-5)。有些菌株具有改进的 DNA 修复机制。其他基因已被修改,以减少突变诱导过程或丰富有助于蛋白质适当折叠的机制,这可能允许轻微突变的蛋白质正常发挥作用。最后,一些底盘设计有“终止开关”,或一种自毁手段,因此任何变异偏离所需行为的细胞都可以从群体中移除。然而,这些都不是万无一失的。因此,合成生物学的活跃研究领域之一是设计更安全、更可靠的底盘

FIGURE

图 10-5 自校正系统。工程细胞(顶部,蓝色)的分裂可以创建精确的副本(第二行,蓝色),或者可能导致产生可能无法执行所需功能的遗传变体(第二行,绿色)。为了防止这些不需要的变异在群体中持续存在,工程师可以设计组件来杀死这些细胞,如红线所示,以确保系统可靠运行。

“VitaYeast” iGEM 项目的背景

动机

获得足够维生素 A 的唯一方法是通过健康饮食或维生素补充剂。全球有超过 2 亿学龄前儿童无法通过任何一种方式获取维生素 A,他们的维生素 A 缺乏会对他们的视力和整体健康造成重大影响。维生素 A 在体内由 β-胡萝卜素加工而成,是视黄醛的前体,视黄醛是视力所需的化学物质。它也是视黄酸的前体,视黄酸对于健康的免疫系统和发育至关重要。甘薯、胡萝卜、西兰花和绿叶蔬菜中含有丰富的维生素 A,但在这些食物不生长或不生长的地方,维生素 A 缺乏 (VAD) 是一个主要的健康问题经常食用。

世界卫生组织估计,维生素 A 补充剂可以将 5 岁以下儿童的死亡率降低 24% 至 34%。然而,向农村地区分发补充剂可能很困难且成本高昂,因此不是应对这一健康挑战的可持续解决方案。因此,一些研究人员旨在开发一种本身富含维生素A的主食。2000年,一个欧洲研究小组宣布开发出这样一种食品:一种经过基因改造表达β-胡萝卜素的“黄金大米”品种。 。水稻经过改造后能够表达三种酶,这些酶可以从大米中一种名为香叶基香叶基二磷酸的天然化合物中产生β-胡萝卜素。由于β-胡萝卜素的存在,又被称为“维生素A原”,因为它在体内可转化为维生素A(图10-6),使米粒呈现金黄色,因而得名。 “黄金大米”(图10-7)。

FIGURE

图 10-6 维生素 A 合成。人类通过食用富含 β-胡萝卜素的饮食来获取维生素 A,也称为视黄醇,β-胡萝卜素在消化过程中会分解成两个维生素 A 分子。

研究人员希望将浓缩大米分发到大米是当地饮食主要组成部分且 VAD 构成健康挑战的地方。然而,他们遇到了强烈的反对。环保团体和个人担心生物工程食品对该地区个人健康、生态系统和经济的潜在负面影响。黄金大米的反对者限制了它的分发,因此它是否能减少 VAD 死亡的问题没有得到解答。许多这些问题背后的信念和概念可以引发充满活力的课堂讨论,生物伦理学基础章节提供了引导此类讨论的方法。

FIGURE

图 10-7 黄金大米。黄金大米是富含β-胡萝卜素的白米,摄入后会转化为维生素A。

2011 年,约翰·霍普金斯大学的国际基因工程机器 (iGEM) 团队寻求不同的解决方案来打破 VAD/黄金大米的僵局。该团队没有在主要食物来源中添加 β-胡萝卜素并将其颜色改变为不自然的颜色,而是决定使用面包酵母的工程版本,扩展了研究人员 2007 年发表的一些研究成果,这些研究人员对常见菌株酿酒酵母进行了基因改造,除了正常的遗传信息补充外,还表达三个 β-胡萝卜素生物合成基因(图 10-8)。 iGEM 团队的想法是用这种酵母替代标准面包酵母,使用户能够烘焙营养丰富的面包。不需要特殊的烘焙说明。用户只需在他们的标准面包配方中添加一点工程“VitaYeast”即可(图 10-9)。 iGEM 团队希望这一解决方案能够缓解围绕黄金大米引起的一些担忧。工程酵母将是维生素强化面包的次要成分。此外,酵母在面包烘烤过程中会被杀死,所得的面包应呈现自然颜色,而不是合成颜色和令人倒胃口的颜色。

FIGURE

图 10-8 β-胡萝卜素生物合成途径。用于改造 VitaYeast 的代谢途径由三种酶(灰色圆圈)组成,它们将磷酸法尼酯(顶部菱形)转化为 β-胡萝卜素(底部菱形)。该途径中的前三种化合物是无色的,后三种化合物分别为黄色、红色和橙色。此处显示的酶功能为 crtE,天然存在于面包酵母中,但由名为 BTS1 的基因编码;另外两种酶 crtYB 和 crtI 是从红色真菌 X. dendrorhous 中作为基因导入的。

FIGURE

图 10-9 富集酵母。有一天,一种市售的“VitaYeast”可以代替面包酵母来解决全球维生素 A 缺乏的问题。

零件级和设备级设计

尽管iGEM团队的“VitaYeast”项目是受黄金大米项目推动并有许多相似之处,但大米和酵母系统的生物学特性却存在重要差异。由于这个原因(也可能是其他原因),VitaYeast 中的基因回路源自真菌,而黄金大米的基因回路则源自植物。 首先开发 VitaYeast 菌株的研究人员引入了一种来自红色酵母 Xanthophyllomyces dendrorhous 的生物合成途径,该酵母天然产生类胡萝卜素化合物,并且具有可用于生产 β-胡萝卜素的酶。相比之下,黄金大米的开发者引入了三种植物基因,将大米中天然存在的香叶基香叶基二磷酸转化为β-胡萝卜素。

与大米一样,面包酵母酿酒酵母可以自然产生二磷酸法呢酯,这是合成 β-胡萝卜素的起始化合物。然而,这些酵母还表达一种由 BTS1 基因编码的酶,可将法呢基二磷酸转化为香叶基香叶基二磷酸。将香叶基香叶基二磷酸转化为 β-胡萝卜素需要两种酶 crtYB 和 crtI 的作用,这两种酶是从红色酵母导入面包酵母的。这些酶中的每一种都有双重作用。 crtYB 酶在合成的早期发挥作用,将香叶基香叶基二磷酸转化为八氢番茄红素,然后在合成的最后一步重新发挥作用,将番茄红素转化为 β-胡萝卜素。 crtYB 催化步骤之间有两个反应,需要 crtI 酶的活性,该酶也从红色真菌导入面包酵母菌株中。该酶首先将八氢番茄红素转化为神经孢子烯,然后转化为番茄红素。

大自然提供了一种简单的方法来检测该途径产生的色素。酵母使β-胡萝卜素变成亮橙色(图10-10)。或者,酵母只使番茄红素像番茄一样变红,番茄红素天然浓度很高。最后,神经孢子烯是该途径中的黄色中间体。然而,颜色编码到此为止,因为该途径中较早的化合物具有少于七个共轭双键,因此是无色的。然而,该途径中的三种有色产物使得更容易确定哪些酶起作用以及哪些菌株产生所需的化合物。

FIGURE

图 10-10 VitaYeast 设计。通过添加合成 β-胡萝卜素(中)的酶途径对面包酵母(左)进行改造,产生了一种可用于烘焙的新型橙色 β-胡萝卜素合成酵母。

当构建 VitaYeast 菌株的研究人员看到它的橙色时,他们可能会欣喜若狂。然而,仔细观察他们所做的事情,他们一定很快意识到,并非所有殖民地的行为都符合他们的预期和希望。尽管事实上它们都来自同一个遗传父母,并且本身的基因应该是相同的,但有些是橙色的,有些是红色的,有些是黄色的,有些是白色的。一种可能的假设是,这些不同颜色的酵母“卡在”生物合成途径的中间步骤。了解这一假设是否确实是五彩酵母的原因并解决问题是 BioBuilder Golden Bread 活动的核心。

设计和构建初始“VitaYeast”菌株的研究人员采用了两种方法来提高其 β-胡萝卜素生产的可靠性。 首先,他们试图建立一个更强大的系统。 特别是,他们停止使用表达红色酵母基因的易于使用的质粒。他们没有使用质粒,而是将 crtYB 和 crtI 基因转移到他们正在构建的面包酵母的染色体中。这些基因的整合副本不太可能丢失,因此菌株应该更可靠地呈现橙色。这种方法的缺点是,当基因位于染色体中时,它们也更难处理,因为遗传物质在实验室中不容易操作,但在这种情况下,研究人员认为系统可靠性的提高将值得在使用它时增加更多的麻烦。

其次,他们尝试通过添加冗余基因来提高β-胡萝卜素的产量,为催化途径第一步的酶添加第二个基因拷贝。最初,他们依靠面包酵母的天然酶 BTS1 将法呢基二磷酸转化为香叶基香叶基二磷酸,但在优化系统的工作中,他们发现,如果他们提供 β-胡萝卜素的产量,就可以增加 β-胡萝卜素的产量。通过在该路径的第一步中引入一些冗余来启动。他们从红色酵母中引入了另一种酶 crtE,以帮助将法尼基二磷酸转化为香叶基香叶基二磷酸。那么,他们的最终系统在一定程度上依赖于冗余来保证可靠性。它包含两个基因:crtE 和 BTS1,尽管它们的 DNA 和蛋白质序列完全不同,但它们都能产生进行 β-胡萝卜素生物合成第一个生化反应的酶。

最后,研究人员通过一项额外的修改改进了系统。他们确定可以通过包含 crtI 基因的第二个拷贝来增加 β-胡萝卜素的产量。在这种情况下,研究人员怀疑额外的 crtI 基因的可靠性增加是由于酶的表达水平增加,而不是我们在前面部分中讨论的冗余的其他优点,例如在第一个情况下有一个额外的副本可用复制失败。

感谢研究人员对这种 VitaYeast 菌株进行的所有巧妙的基因工程,我们现在拥有了一种呈亮橙色的酵母菌株,2011 年霍普金斯大学的 iGEM 团队可以使用它。 然而,令团队非常失望的是,为可靠性而设计的应变仍然不是 100% 的橙色。将这种酵母菌株的单个菌落重新划线到培养皿上会产生橙色菌落,但也会产生一些红色、黄色和白色菌落。 BioBuilder 的 Golden Bread 活动研究了这种不稳定性,并尝试了提高菌株性能的方法。

额外阅读和资源

  • 阿什比,M.F. (1999) 机械设计中的材料选择 [ISBN: 0750643579]。
  • Petroski, H. (1985) 《工程师就是人:失败在成功设计中的作用》[ISBN: 0679734163]。
  • Petroski, H. (1994) 实用物品的演变:日常用品——从叉子和别针到回形针和拉链——是如何形成的。 [ISBN:0679740392]。
  • Verwaal,R. 等人。通过用来自树状叶黄酵母 Appl Environ Microbiol 的胡萝卜素基因连续转化,在酿酒酵母中高水平生产 β-胡萝卜素。 2007;73(13):4342-50。
  • 网站:黄金大米
  • 网站:世界卫生组织,微量营养素缺乏症

FIGURE

金面包实验室

该实验室向学生介绍真核实验生物酿酒酵母,其生长速度和基因操作方法与大肠杆菌不同。出于工程可靠性的目标,该实验试图表征菌株的不稳定性,使用菌落 PCR 评估其可能的遗传来源。通过用含有工程途径中基因之一的合成版本的质粒转化酵母,强调了冗余的工程概念。您可以使用 Golden Bread 实验室程序来教授生物技术技能,例如固态微生物培养和 DNA 电泳。

设计选择

使用单一基因程序构建的单一酵母菌株可以产生多种颜色的酵母,这一事实表明,VitaYeast 菌株无法像生物工程师希望的那样可靠地生产 β-胡萝卜素。为了调查不可靠性的根源,我们首先假设不同的菌落颜色是由遗传不稳定性造成的,即细胞分裂时β-胡萝卜素代谢途径中一个或多个基因的变化。 您将进行实验来量化不可靠性的程度并评估遗传变化发生的位置

在这些活动中,您将特别关注 crtYB 基因,因为它是系统中唯一没有任何已设计到 β-胡萝卜素生产途径中的遗传冗余的部分。然而,重要的是要认识到,这种不可靠性可能还有其他解释,包括主要不参与β-胡萝卜素途径的基因的作用,或完全非遗传的原因,例如生长培养基的差异。尽管我们不会在这里研究这些其他潜在的不可靠性来源,但它们代表了出色的后续实验。

实验问题

我们将研究并尝试使用经过验证的冗余工程策略来修复 VitaYeast 菌株的遗传不稳定性。通过将注意力集中在一个特定基因 crtYB 上,我们有效地将实验问题缩小到一个简单且可测试的问题:向 VitaYeast 菌株中添加合成的 crtYB 基因 crtYB’ 是否会减少或完全消除酵母菌的生长非橙色(即红色、黄色、白色)菌落?

为了解决这个问题,我们需要比较两个值:

  • 添加 crtYB’ 之前,红色、黄色和白色菌落相对于橙色菌落的数量,或非橙色菌落的百分比。
  • 添加 crtYB’ 后非橙色菌落的百分比。

如果百分比下降,我们可以得出结论,冗余实际上减少了系统中的遗传不稳定性。如果百分比保持不变,也许我们应该尝试添加一个或多个不同的基因,或者完全采取另一种方法。如果百分比增加,我们可能会质疑我们用于引入合成基因的程序是否会产生意想不到的副作用。

通过思考实验可能的结果,我们可以更好地设计必要的控制。对于在质粒上引入 crtYB 新副本的转化过程,我们可以想象使用阴性和阳性对照。 转化的阴性对照是我们不希望在我们的选择平板上生长的样品,在这种情况下,平板缺乏必需氨基酸,因为它不包含带有选择标记的质粒,该基因产生相同的必需氨基酸。为了准备该样品,我们需要执行与实验样品相同的所有步骤,但不添加质粒 DNA。如果阴性对照确实生长,与我们的预期相反,我们知道有关程序或平板的某些因素无法有效地将转化细胞与没有质粒 DNA 的细胞分开。

阳性对照可以帮助我们解决有关转化过程中意外副作用的问题。 我们期望阳性对照在选择板上生长,但不希望它包含 crtYB 的额外副本(这将使其与我们的实验样本相同)。因此,对于我们的阳性对照,我们将用包含选择性标记但不含 crtYB 副本的“空”质粒转化酵母。现在,让我们回到我们的“思想”实验:如果遗传不稳定性在转化后增加怎么办?通过与阳性对照进行比较,我们可以确定是否是 crtYB’ 或单独的转化导致了这种意外结果。事实上,转化是一个严酷的过程,可能会导致酵母 DNA 发生意外变化,因此排除这种可能的遗传不稳定来源非常重要。

我们的实验样品将包含 VitaYeast 和包含选择性标记和 crtYB 基因的质粒。我们将比较转化后非橙色菌落与阳性对照平板上的菌落的百分比。这将提供最直接的同类比较,并使我们能够将任何颜色变化归因于 crtYB’ 基因本身,而不是任何其他混杂因素。

入门

您将收到一种已经含有工程化 β-胡萝卜素途径的酵母菌株。您将首先进行自己的简单实验,通过重新划线橙色酵母并计算橙色、红色、黄色和白色菌落的数量来测量 β-胡萝卜素生产的可靠性。

然后,您将开始处理一个或多个非橙色菌落。您将进行 PCR 实验以确定 crtYB 基因是否仍然存在。回想一下,crtYB 是系统中唯一没有冗余副本的基因。我们将提供用于扩增 crtYB 的引物,但您也可以自己为该基因或途径中的其他基因设计引物。

我们还将为您提供一个含有 crtYB 基因冗余但合成副本的质粒,我们将其称为 crtYB’。该基因产生与原始 crtYB 基因相同的蛋白质产物,但用密码子改组的 DNA 序列对其进行编码。由于遗传密码的简并性,基因的重新编码得以发生。与 PCR 实验一样,您也可以自行设计这个冗余副本。您将把这个多余的 crtYB 副本转化为红色、橙色、黄色或白色酵母。转化方案与转化大肠杆菌的方案略有不同,但基本原理是相同的。将转化反应铺板并使菌株生长 2 天后,您将计算不同颜色的菌落数量,以评估引入这种冗余是否使系统运行更可靠。

本实验的酵母菌株含有整合到其染色体 DNA 中的产生 β-胡萝卜素的遗传电路。酵母将以“刺”或“斜”的形式到达,即在倾斜介质上装有少量酵母的试管。

  1. 使用无菌牙签或接种环将酵母划线到培养皿上:从牙签或接种环上的刺处收集少量细胞,并将细胞转移到含有酵母提取物蛋白胨葡萄糖培养基 (YPD) 的培养皿中琼脂。
  2. 将这些培养皿培养基面朝上放入 30°C 培养箱中 36-48 小时。平板也可以在室温下孵育,但细胞生长会更慢。

实验室协议

这是实验室协议的缩写版本,仅包括转化活动。 BioBuilder 网站上提供了菌落 PCR 和设计冗余合成基因的说明。

这些说明使用酵母转化试剂盒来制备感受态细胞。该试剂盒的内容是专有的,但如果您在谷歌上搜索化学感受态酵母细胞,很可能会找到这些内容。

改造 VitaYeast

  1. 对于您想要执行的每个转化(阳性对照、阴性对照、实验),给微量离心管贴上标签。然后加入 500 微升水,并用牙签在每个试管中摇动装满产生维生素 A 的酵母。
  2. 在微量离心机中旋转试管 30 秒,收获酵母。
  3. 将每个颗粒的上清液吸出或移入装有 10% 漂白剂的废烧杯中,以除去上清液。您不必除去每一滴上清液。
  4. 将每个细胞沉淀重悬于试剂盒中的 500 μl“洗涤溶液”或“溶液 1”(很可能只是无菌水!)中进行洗涤。
  5. 在微量离心机中全速旋转 30 秒收获细胞。
  6. 如前所述吸出或除去上清液。
  7. 将每个沉淀重悬于 50 μl 的“感受态溶液”或“溶液 2”(最有可能是醋酸锂和 DTT,它通过未知机制使酵母透化)。与化学感受态细菌不同,感受态酵母在这种状态下并不“脆弱”,并且可以保持在室温下。
  8. 在阴性对照管中加入 5 μl 水。轻弹管子以混合内容物。该试管不含 DNA。
  9. 将 5 µl pRS414 DNA (50 ng) 添加到阳性对照管中。轻弹管子以混合内容物。该质粒带有酵母复制起点和 TRP1 基因,可作为转化的阳性对照。
  10. 将 5 µl pRS414+crtYB’ DNA (50 ng) 添加到实验样品管中。轻弹管子以混合内容物。
  11. 向每个试管中添加 500 µl“转化溶液”或“溶液 3”到细胞中。这种材料很可能是聚乙二醇(“PEG”又名防冻剂),粘稠且粘稠,包含在转化方案中以帮助将 DNA 传递到酵母中。使用 P1000 将溶液与酵母一起上下移液,然后轻轻涡旋试管以形成均匀的悬浮液。
  12. 将管子与等量的 -TRP 板一起在 30°C 下孵育约 1 小时,盖子半开,以蒸发其表面上的水分。在这一小时内,您可以定期“轻弹”试管以混合内容物;这将有助于防止细胞沉降到底部。
  13. 至少一小时后,轻弹试管以混合内容物,然后将 250 μl 每种混合物涂在适当标记的 -TRP 板上。
  14. 将培养皿介质面朝上,在室温下或在 30°C 培养箱中培养两天。
  15. 返回收集数据后,确定每个培养皿上菌落的数量和颜色。

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2024-05-15
多么丰富多彩的世界

第9章 多么丰富多彩的世界

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多么丰富多彩的世界强调设计-构建-测试周期的“构建”阶段。您将在此 BioBuilder 实验室活动中构建的合成生命系统是用紫色颜料或绿色颜料着色的细胞,具体取决于您选择运行的遗传程序。然而,颜色的强度很难提前预测。细胞会是苍白的还是军绿色的?深紫色还是浅紫色?让事情变得更加复杂的是,我们认识到每个基因回路可能会产生不同数量的颜色,具体取决于运行它的细菌菌株。组合组件产生的这种意想不到的、古怪的结果的正式术语是紧急行为。

如果你倾向于像科学家一样思考,这种突发行为可能会让你问:“如何解释我观察到的结果?”如果您倾向于像工程师一样思考,这些行为可能会让您觉得“呃”,然后开始定义优化系统性能的最佳方法,希望避免此类意外行为。这两种方法都有优点,并且科学和工程方法共同应该在未来带来更可靠的设计,并最大限度地减少我们在构建新的生命系统时看到的令人惊讶的行为数量。

在这个实验室中,生成紫色或绿色色素的 DNA 程序已经为您编写和组装,但您将通过将编码程序的 DNA 插入到一些不同的细菌底盘中来完成最终的构建步骤。 DNA 程序来自 2009 年国际基因工程机器 (iGEM) 项目,名为“E. chromi”,剑桥大学的学生设计并改造了大肠杆菌来生产一系列颜料。 您将构建多个颜色生成系统,以探索底盘如何影响设计的遗传程序的输出。由于颜料是肉眼可见的,因此您可以轻松确定机箱之间的颜色输出是否不同。

不过,在详细介绍实验之前,我们将对底盘设计和决策进行一般性讨论,并且我们将逐步介绍 E. chromi 项目,为您的调查提供一些背景信息。

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机箱简介

正如汽车制造商在设计发动机时必须考虑整个汽车一样,合成生物学家也必须考虑他们正在构建的整个系统,包括他们设计的基因程序将在其中执行的细胞环境。就像路上有各种各样的汽车一样,细胞的大小、形状、细胞器和基本代谢功能也有很大差异。因此,为任何工程遗传程序选择最好的宿主细胞或底盘是设计过程中的重要一步。许多参数都会影响底盘的选择,包括特定于某些应用的一些考虑因素。然而,普遍关注的是实用性和安全性,我们将在以下几节中对此进行探讨。

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实用程序以及如何设计它

在为合成生物学应用选择底盘时,研究人员会考虑通用实用性和利基实用性。一般效用是指具有普遍帮助性的品质;例如,在实验室环境中的快速增长。此外,普遍有用的底盘应该相对容易使用,这解释了为什么科学家依赖的许多常见模型生物(大肠杆菌、酿酒酵母等)对合成生物学家来说都是有吸引力的底盘。这些细胞拥有强大的工具,可以以合理且相当可靠的方式设计和操纵它们。

另一方面,利基效用是指使单元适合特定应用的品质。利基效用的一个例子是 BioBuilder 的 Eau That Smell 基因程序的细菌宿主。如果您熟悉这个实验装置,您会记得该项目的合成生物学家希望让细菌散发出香蕉或冬青的宜人香气。为了实现这一目标,他们通过从细胞色氨酸生物合成途径中删除一个基因,消除了所使用的大肠杆菌宿主产生的自然臭味,从而产生了一个“无臭”底盘来运行其产生气味的基因程序。

有两种互补的方法可以为每个可以想象的目的找到合适的底盘。在第一种方法中,我们可以称之为“最近的野生型生物”方法(见图 9-1),底盘是根据其执行类似于合成生物学家想要完成的任务的能力从自然界中识别出来的。一个新的系统。野生型生物体具有其自然界中物种最典型的特征,在这种方法中,野生型细胞的自然功能得到改进,使现有细胞越来越接近新系统中所需的行为。为了说明这种最接近野生型生物的方法,请考虑劳伦斯伯克利国家实验室辛格研究小组的工作。该小组的目标是改造富养罗尔斯通氏菌(Ralstonia eutropica),以生产丁醇和烯烃等生物燃料,有朝一日可能会取代石油基化学燃料。富养罗氏菌自然地将二氧化碳转化为储能聚合物,因此这些工程师认为这是一个有吸引力的底盘,并正在实验性地修改其自然途径,以便细胞产生生物燃料,而不是它们通常制造的聚合物。

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图 9-1 底盘选择的“最近野生型生物体”方法。野生型生物体1可以被改造为相对相似的工程化生物体1,其具有与亲本生物体相同的整体形状和多个鞭毛。类似地,野生型生物体 N 的形状与野生型生物体 1 略有不同,并且没有鞭毛,可以修改为工程生物体 N。对于新的野生型生物体中的每个实质性差异,都需要重复此过程。工程生物体所需的特性。

底盘设计的第二种方法从我们所说的“标准底盘”开始。在这种方法中,如图 9-2 所示,合成生物学家可能会选择更通用的底盘,该底盘要么具有最少数量的天然成分,要么易于理解且高度可工程化。简单的底盘本质上为合成生物学家提供了一块空白画布,并且至少在理论上可以成为具有完全不同的所需输出的各种工程系统的理想底盘。 Ginkgo Bioworks 的研究人员采用标准底盘方法,使用工程大肠杆菌来制造生物燃料。与我们之前考虑的例子不同,在该例子中,生物燃料生产是从天然聚合物工厂 R. eutropica 开始的,而大肠杆菌没有现有的人才可以推荐它们进行生物燃料生产。然而,大肠杆菌是该领域最接近标准细菌底盘的生物体。因此,Ginkgo Bioworks 的研究人员认为大肠杆菌是一个具有多种用途的有吸引力的平台,包括将二氧化碳和电能转化为异辛烷,异辛烷是一种非常适合美国现有运输燃料基础设施的液体燃料。

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图 9-2 “标准机箱”方法。标准起始底盘简单且易于设计,因此合成生物学家可以将其用作工程有机体 1、工程有机体 N 以及介于两者之间的所有产品的先驱。

最近的野生型生物和标准底盘方法都有优点和缺点。例如,如果仅需要对现有生物体进行微小的改变即可获得所需的结果,则使用最接近的野生型生物体方法可能相对容易。然而,这种策略可能难以扩展,因为对于每个新的设计规范,设计人员都需要找到新的底盘。此外,使用现有生物体作为底盘可能会出乎意料地复杂,因为所有生物体都有自己的代谢途径和需求,其中任何一个都可能以令人惊讶的方式干扰所需的输出。

标准底盘方法避免了使用复杂生物体构建合成生命系统时出现的一些并发症。这种方法也比最接近的野生型生物方法更具可扩展性,因为它为设计者提供了一个通用的起点。借助通用的标准化机箱,设计人员可以将一种设计的工具重复用于另一种设计,至少在某种程度上是这样。天上掉馅饼的希望是“空白画布”细胞可以通过编程来生产药物、食品、组织或生物燃料,但目前这种希望相当牵强。目前,细胞还不能被抽象成一个不可知的画布来运行 DNA 程序。

然而,合成生物学家对计算机编程的成功感到鼓舞,因为这种跨平台工具确实存在。例如,Java等软件平台定义了“虚拟机”,使程序可以在任何操作系统上运行。 Java 虚拟机采用 Java 字节码,以便无论操作系统如何,它都以相同的方式工作。在这个类比中,Java 字节码类似于 DNA 序列,我们可以将 Java 虚拟机(加上操作系统)视为将该代码转换为操作的细胞机器。换句话说,我们可以将合成生物学的标准底盘视为生物学的Java虚拟机。

然而,想象每个合成生物学应用都有一个标准底盘还不现实,因此在最近的野生型和标准底盘方法之间达成了妥协。在这种妥协中,一个小的底盘菜单将作为合成生物学家的起点,他们可以为任何给定的应用领域从几种不同的细胞类型中进行选择。在这种情况下,可能存在一两个用于细菌应用的可靠标准底盘,以及另外一两个用于在哺乳动物细胞中运行的遗传程序的标准底盘。尽管该技术仍在开发中,但这种细胞底盘工程的混合方法也许更有可能为合成生物学家在短期内取得成功提供可用的工具。

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安全性以及如何设计它

在选择用于运行工程 DNA 程序的机箱时,您必须始终考虑安全性。具体来说,研究人员必须考虑他们在使用合成生命系统时的个人安全、实验室环境的安全,以及如果他们的工程生物体进入更广阔的世界可能发生的任何伤害。

现有的指南和法规在很大程度上保护了研究人员及其工作所在实验室社区的人身安全。随着重组 DNA 技术的出现,这些法规于 20 世纪 70 年代开始实施。它们通常被认为是成功的,但当时引起了激烈的争论,这些争论为今天的合成生物学提供了许多相关的教训。有关指南及其发展的更详细说明,请参阅生物伦理学基础章节。

除了从基因工程领域继承的监管工作之外,合成生物学家还必须仔细考虑将合成生命系统安全地引入我们复杂的环境中。理想情况下,应该有一种通用方法来最大限度地减少和遏制可能逃逸或故意部署到实验室外环境中的生物体造成的任何潜在损害。由于它们携带额外的遗传负担,大多数合成生物体相对于其天然竞争者来说适应性下降,这已经降低了工程生物体在野外持续存在或造成重大损害的可能性。然而,依赖这种不平等似乎是不明智的,并且在合成生物学家规划他们的系统时正在设计额外的安全措施。

相反,合成生物学家正在尝试进行安全设计。 “设计安全”的一个根本例子是合成生物学研究,以设计与天然存在的 DNA 不同的解码方式的正交 DNA。由于DNA可以在生物体之间转移,而且这种转移相对常见,因此人们担心如果工程生物体从自然存在的生物体中获取DNA,反之亦然,可能会产生潜在的后果。然而,如果工程生物体表达的正交 DNA 无法在原始宿主之外正确解码,那么这些可能的危险就会最小化。任何使用改变的遗传密码的底盘都无法实现从外部环境获得的新的且具有潜在危险的遗传功能,并且如果将来自工程生物体的基因转移到自然存在的环境中,则无法实现它们有机体。

合成生物学家仍处于此类研究的早期阶段,但 2011 年《科学》杂志上发表的一篇论文显示了一些有希望的结果。由哈佛大学 George Church 博士实验室领导的研究小组通过用同义 TAA 终止密码子替换他们在 460 万个碱基对基因组中发现的所有 TAG 终止密码子,对大肠杆菌进行了“重新编码”,如图 9 所示-3。将这组看似“无声”的变化结合起来是一项技术杰作,促使团队开发出新的、非常有用的基因组操作工具,称为“MAGE”和“CAGE”。然而,与本次讨论更相关的是,与天然菌株相比,所得底盘具有两个安全优势。首先,新菌株中的所有编码序列仍然可以转录和翻译,但因为它们都没有使用 TAG 密码子,所以可以重新调整该密码子,将替代氨基酸添加到新的 DNA 程序中。 然后可以通过使其依赖于研究人员提供的一些非天然氨基酸(而不是自然提供的)来设计新生物体以确保安全。其次,TAG密码子不再在重新编码的大肠杆菌中充当终止密码子。因为Church研究小组还删除了在任何TAG处终止翻译的释放因素。因此,如果重新设计的细菌拾取任何使用 TAG 终止密码子的外部 DNA,所得的多肽链将失去功能,因为核糖体将继续读取超过终止密码子的内容。 必须做进一步的工作才能使工程 DNA 真正成为现实。与自然发生的遗传物质正交,但“安全设计”的早期成功是一个值得考虑的很好的模型,随着努力的推进。

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图 9-3 一种生成正交 DNA 的方法。左侧天然存在的 DNA 序列编码四个氨基酸,由序列上方的蓝色和绿色球表示,以 TAG 终止密码子结尾。通过将 DNA 天然存在的 TAG 终止密码子(左)转换为 TAA 终止密码子(右),蛋白质产物不会发生变化,但表达该遗传密码的细胞可以通过将 TAG 密码子重新分配给非天然氨基酸来重新设计成正交基因组。

E. chromi iGEM 项目的背景

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剑桥大学团队在 2009 年的 iGEM 项目中设计、指定并构建了一套生物传感器,团队将其称为 E. chromi。鉴于生活世界中存在各种各样的自然颜色(橙色胡萝卜、紫色花朵等),该团队决定使用颜色作为其系统的输出。它还决定为特定金属化合物制造传感器,包括砷、汞和其他重金属,这些金属在一些国家一直是污染问题。 这些环境污染物输入将触发肉眼可见的基于颜料的输出,以便轻松、立即部署。该设计是对之前使用 pH、电导和荧光等输出的 iGEM 生物传感器项目的改进,因此需要额外的步骤来检测输出信号。这些颜料还提供了视觉多样性,激励团队构建一种活的“量油尺”,可以用一个样本拭子以彩色方式报告多种污染物,如图 9-4 所示。

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图 9-4 检测单个水样中多种污染物的量油尺。量油尺上会发现表达不同基因程序的细菌,这些基因程序能够感知污染物并产生颜色响应。当暴露在没有任何诱导剂的水中时(左),不会产生颜色。当暴露于含有两种污染物的混合物(中心)的水中时,会产生两种相应的颜色。如果水中含有四种污染物(右),就会产生四种颜色。

除了检测特定污染物的存在之外,研究小组认为估算每种污染物的浓度也很有用。 通过开发一系列控制系统灵敏度的“调谐器”设备,该团队可以生成每个颜色生成系统的变体,以便系统仅当污染物存在于特定浓度范围内时才会改变颜色。砷浓度低的水样只会触发低灵敏度调谐器,并将信号传递到该变体中的颜色生成装置。含有高浓度砷的水样将触发低、中、高灵敏度调谐器,并触发所有三种变体的颜色。通过最终的系统(图 9-5),该团队可以将其收集的变体暴露于水样中,并根据哪些变体产生颜色、哪些不产生颜色,确定存在哪些污染物以及浓度。

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图 9-5 活体生物传感器的系统级设计。用于检测环境污染物并报告其浓度的电池的黑盒设计理念。

关于他们的设备

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为了找到编码鲜艳颜色的 DNA 序列,iGEM 团队挖掘了文献,最终确定了三种能够产生独特色素的自然存在的细菌系统。这些系统如表 9-1 所示。

表 9-1 产生生动色彩的天然来源

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由于该团队想要多种颜色,因此他们将所有这些来源作为潜在的设备,并发现其中一些更适合某些应用。例如,黑色素由单个基因编码,这使得通过已建立的基因调控方法相对容易控制输出,但该系统还需要在培养基中添加铜和酪氨酸,从而使菌株的生长条件变得复杂表达这种颜色。另外两个色素家族是通过多个基因产物的作用产生的,这使得它们的调节更加复杂,但产生这些色素的细胞更容易生长,因为颜色是在生长培养基中没有任何不寻常的化合物的情况下产生的。

为了部署系统的设备,iGEM 团队还必须考虑用于生产紫罗兰素和类胡萝卜素色素的不同机制。类胡萝卜素装置首先使用一种途径产生红色素,然后使用下游酶将红色素的一部分转化为橙色素。相比之下,紫罗兰素装置依靠分支代谢途径来产生绿色和紫色,如图 9-6 所示。

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图 9-6 色素生成代谢途径。左侧显示类胡萝卜素途径,右侧显示紫罗兰素途径。菱形代表不同的细胞中间体,圆圈代表负责化学反应的酶。有色化合物以其近似颜色表示。

零件和设备

BioBuilder 多彩世界活动使用紫罗兰素系统的成分,根据相对较小的基因变化,可以产生绿色或紫色色素。通常,该色素生成系统的输入是氨基酸色氨酸,通过五种酶(VioA、VioB、VioC、VioD 和 VioE,但不是按此顺序!)的作用,产生一种称为紫罗兰素的紫色色素。然而,当 vioC 基因被去除时,该途径分支被阻断,最终无法转化为紫草素,因此系统的终点反而变成了原紫草酸,一种深绿色的色素。 您可以通过检查代谢途径来推断去除 vioC 基因的效果(图 9-6)。这种行为也可以使用逻辑门和真值表的工程形式来说明,如图 9-7 所示。

FIGURE

图 9-7 紫罗兰素相关系统的不同表示。逻辑门表示(左上)显示输入 X(VioA、B、D 和 E)和输入 Y (VioC) 必须如何存在才能生成紫色输出 Z。修改后的真值表(左下)显示输入 X单独可以创建绿色输出,而单独输入 Y 不会生成输出,输入 X 和输入 Y 生成紫色输出。右侧的遗传示意图显示,绿色生成装置(由 VioA、B、D 和 E 组成)上游的启动子产生绿色色素,紫色生成装置(由 VioA、B、D 和 E 组成)上游的启动子产生绿色色素。 B、C、D 和 E,产生紫色颜料。

额外阅读和资源

  • Changhao, B. 等人开发用于富养罗尔斯通氏菌的广泛宿主合成生物学工具箱及其在工程碳氢化合物生物燃料生产中的应用。微生物细胞工厂 2013;12:107。
  • Ginkgo Bioworks Foundry (http://ginkgobioworks.com/foundry/ )。
  • 拉乔伊,MJ。等人。基因组重新编码的生物体扩展了生物功能。科学2013;342(6156):357-60。
  • E. chromi 网站 (http://www.echromi.com/ )。

FIGURE

多么丰富多彩的世界实验室

在本实验室中,将使用细菌转化技术将一些质粒 DNA 引入两种细胞类型。通过比较两种不同大肠杆菌菌株中相同基因程序的功能,探索了底盘的工程概念。无菌技术和固态微生物培养是本实验室强调的生物技术技能。

设计选择

在我们对 E. chromi 项目的讨论中,我们看到 iGEM 团队对系统的性能做出了一些假设。特别是,团队成员推测,当暴露于给定浓度的金属污染物时,颜色生成设备将可预测地生成可见的调色板。然而,研究小组意识到,每种色素生成装置都有其特殊性。例如,黑色素需要补充介质。为了解决这些特性,它对多种细菌菌株进行了实验,旨在找到运行每台设备的“最佳”菌株。

在本实验中,您将了解 iGEM 团队项目的这方面内容。 您将比较两个不同机箱中的两个颜色生成设备,以研究是否可以获得可靠的颜色输出。

实验问题

您将在两种常见的实验室大肠杆菌菌株(K12 菌株和 B 菌株)中测试紫色和绿色颜色生成装置。这两种菌株通常用于研究细菌细胞的行为和执行分子生物学技术。它们在实验室环境中存在了很长时间,以至于它们的许多基因发生了突变,这些突变不再是它们在狭窄的条件下生存所必需的。结果,它们几乎失去了在实验室环境之外茁壮成长的能力。鉴于对这些细胞的描述,它们似乎为细菌合成生物学的标准底盘提供了开端,至少在安全方面是这样。在本实验室中,您将通过测试它们是否产生可靠、可重复的行为来调查它们是否也接近实现标准机箱的“实用”要求。

要进行此实验,您需要将携带紫色和绿色颜色生成装置的基因程序转换到每种细菌菌株中(图 9-8)。这个过程涉及的步骤包括修补菌株以培养您需要的细胞,然后用盐溶液处理细胞,以便它们能够吸收 DNA。您将感受态大肠杆菌菌株与编码颜色生成装置的 DNA 混合,然后将细胞暴露在高温下一小段时间。这种热休克有助于细胞从环境中吸收 DNA。在最后的实验步骤中,您将在转化混合物中添加一些新鲜培养基以帮助细胞恢复,然后将转化的细胞铺板到装有琼脂固化培养基的培养皿上,其中还含有抗生素氨苄青霉素。编码颜色生成装置的 DNA 也编码氨苄青霉素抗性基因,因此唯一可以在平板上生长的细胞是那些具有颜色生成装置的细胞。

FIGURE

图 9-8 不同机箱中的颜色生成设备。您将把相同的设备插入不同的机箱(左与右)并研究它们的行为。

作为阴性对照,您将在转化过程中加入不含质粒的样品。该阴性对照预计不会在含有氨苄青霉素的平板上生长,因为它不包含氨苄青霉素抗性基因。如果观察到生长,您就知道您的程序或材料存在某些问题,无法仅选择已成功用质粒转化的细胞。一个潜在的原因可能是平板中的氨苄青霉素随着时间的推移而降解。包含对照对于良好的实验设计至关重要,因为它使您可以隔离变量,并可以为以后尝试解决实验中遇到的问题提供信息。

您收集的数据将基于对板的目视检查——您的眼睛是您需要的唯一精美的检测设备。经过一晚的生长,每个在转化和抗生素暴露中幸存下来的细胞都有时间生长成肉眼可见的细胞集落。您将对菌落进行计数以确定转化效率,并且您将记录不同板上菌落的颜色、形状和大小,以确定选择作为底盘的菌株是否会影响系统的输出。

入门

表 9-2 详细介绍了“多彩世界”实验中比较的两种质粒。

表 9-2 多么丰富多彩的世界质粒和菌株描述

质粒   注册质粒#   质粒描述
pPRL   BBa_K274002   pUC18 质粒骨架,AmpR
pGRN   BBa_K274004   pSB1A2 质粒骨架,AmpR

4-1: NEB 大肠杆菌 K12 ER2738:F’proA+B+ lacIq Δ(lacZ)M15 zzf::Tn10(TetR)/ fhuA2 glnV Δ(lac-proAB) thi-1 Δ(hsdS-mcrB )5

4-2: NEB 大肠杆菌 BL21 C2523:fhuA2 [lon] ompT gal sulA11 R(mcr-73::miniTn10– TetS)2 [dcm] R(zgb-210::Tn10–TetS) endA1 Δ(mcrC-mrr)114::IS10

该实验室需要两种大肠杆菌菌株:4-1(K-12 型)和 4-2(B 型)。为了获得足够数量的细菌来进行转化,您需要将这些菌落重新接种为补片。每个贴片将为一个实验室小组提供足够的细菌,一个平板上最多可容纳六个贴片。

  1. 使用无菌接种环或牙签,将细菌菌落从其中一个培养皿转移到新的 Luria Broth (LB) 琼脂(非 LB+amp)培养皿中,为每种菌株绘制 1 cm x 1 cm 的正方形。以这种方式绘制的每个正方形都会产生足够的细胞来用两个质粒进行转化。
  2. 对转化实验室所需的每种菌株重复上述步骤。
  3. 将培养皿置于 37°C 培养箱中过夜。

实验室协议

  1. 将两个小微量离心管标记为“4-1”和“4-2”。
  2. 将 200 μl CaCl_2 转化溶液移入每个管中,然后将管置于冰上。
  3. 使用无菌木钉或接种环刮起一整块标有“4-1”的细胞(不包括它们生长的琼脂!),然后将细胞旋入装有冷 CaCl_2 的管中少量琼脂可能会被转移,而不会影响您的实验。如果您有涡旋,您可以通过涡旋一分钟来使细胞重新悬浮。如果没有涡流,轻轻弹动并翻转管子。
  4. 重复,使用不同的无菌木钉刮掉标记为“4-2”的细胞块。如果可能的话,短暂涡旋。一些细胞团保留在该溶液中是可以的。
  5. 在准备用于转化的 DNA 时,将这些感受态细胞置于冰上。
  6. 在每个质粒的微量离心管中取出两等份,总共四个样品(2x 紫色生成装置质粒,pPRL,2x 绿色生成装置质粒,pGRN)。每个等份含有 5 ul DNA。 DNA 的浓度为 0.04 μg/μl。当您在实验结束时计算转化效率时,您将需要这些值。
  7. 将其中一支 pPRL 管标记为“4-1”。将另一个 pPRL 管标记为“4-2”。确保标签可读。将管子放入冰桶中。
  8. 将其中一支 pGRN 管标记为“4-1”。将另一个 pGRN 管标记为“4-2”。确保标签可读。将管子放入冰桶中。
  9. 用感受态 4-1 菌株轻弹试管,然后将 100 μl 细菌移入标有“pPRL, 4-1”的试管中,再将 100 µl 细菌移入标有“pGRN, 4-1”的试管中。轻弹以混合管子并将其放回冰中。将剩余的少量 4-1 菌株保存在冰上。
  10. 用感受态 4-2 菌株轻弹试管,然后将 100 μl 移液至标有“pPRL, 4-2”的试管中,再将 100 μl 移入标有“pGRN, 4-2”的试管中。轻弹混合并将它们以及剩余体积的感受态细胞储存在冰上。
  11. 将 DNA 和细胞置于冰上 5 分钟。
  12. 当您的 DNA 和细胞孵化时,您可以标记您需要的六个培养皿的底部(介质侧)。标签应标明您使用的菌株(“4-1”或“4-2”)以及转化它们所用的 DNA(“pPRL”、“pGRN”或“无 DNA 对照”)。
  13. 将试管置于 42° 温度下精确热激 90 秒(使用计时器)。
  14. 90 秒结束时,将管子移至室温下的架子上。
  15. 将 0.5 ml 室温 LB 添加至试管中。盖上盖子,翻转试管以混合内容物。
  16. 使用无菌涂布器或无菌珠子,将 200–250 μl 转化混合物涂布到 LB+氨苄青霉素琼脂培养皿的表面。
  17. 盖上盘子并放置一分钟。然后,将盘子翻过来。培养皿将倒置存放,以防止冷凝水滴到细菌上。
  18. 将培养皿琼脂面朝上,在 37°C 下孵育过夜。

FIGURE

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2024-05-15
想象一下这个

第8章 想象一下这个

FIGURE

BioBuilder 的图片 该活动强调设计-构建-测试周期的“设计”阶段。图片 这使用了 2004 年国际基因工程机器 (iGEM) 团队开发的系统,该系统改变了大肠杆菌对光的敏感性,使该菌株可用于“细菌摄影”。研究小组将这些细胞改造为既能感光又能产生颜色,并将这些遗传功能相互连接起来(图 8-1)。由这些细胞组成的草坪能够通过充当照相像素来复制打印在掩模上的图像,从而在黑暗中“打开”细胞的颜色生成遗传电路,在光线中“关闭”细胞。

iGEM 团队经过大量的试验和错误以及良好的运气,才成功设计和构建了产生这种摄影行为的复杂遗传电路。未来,当合成生物学家设计出更加复杂的生命系统时,他们将需要依赖其他工程学科可以使用的关键工具:数学和物理建模。当可靠的建模工具可用时,合成生物学家将能够在开始使用实际细胞和 DNA 之前进行计算模拟和实验来测试他们的系统。他们不会通过构建生命系统来启动项目,而是从模型中收集信息来预测细胞的一些行为,这将帮助这些合成生物学家做出设计选择。这些模型可能无法完全代表真实系统的行为方式(毕竟它们只是模型),但它们应该提供一个强大的起点和一个出色的工具来提出以其他方式探索很难或耗时的问题。计算机程序员和数学建模者开发这些模拟工具在合成生物学领域占有重要地位。

FIGURE

图 8-1 细菌摄影系统级设计。细菌摄影系统以光作为输入并产生彩色像素作为输出。

在BioBuilder的图片这个活动中,你可以为细菌摄影系统建立两种模型:计算模型和电子模型。 在实践中,工程师会在构建实际系统之前构建模型,但在这里,我们以相反的顺序工作。通过这种方式,我们可以首先揭示构建模型的一般效用。 正如您将看到的,这两种模型都有优点和缺点,但每种模型都可以提供对遗传系统行为的宝贵见解。在本章中,我们首先考虑不同类型的模型,包括它们的优点和缺点。然后我们更详细地了解 iGEM 团队的细菌摄影系统。

建模简介

建筑师可能需要数月甚至数年的精心规划才能设计一座摩天大楼,使其具有正确的形式和结构健全。在此期间,建筑师的设计过程将包括各种建模方法,其中一些方法有助于可视化建筑物完工后的外观,另一些方法则用于预测建筑物的行为方式。这些模型是一项投资,如果在摩天大楼本身之前建造,可以节省时间和金钱。

您应该使用哪种模型? 根据项目的性质,建筑师可能会绘制二维蓝图,使用轻木构建三维微型模型,或者运行计算机模拟(图 8-3 )来测试结构如何应对地震。这些模型中的每一个都有不同的优点。例如,轻木模型可以帮助设计师评估建筑物的美观性,计算机模型可以确认建筑物不会在自然灾害中倒塌。通过使用各种建模技术,可以快速考虑不同的设计选项,直到找到满足建筑师规范和需求的设计选项。这样,建模可以帮助在构建阶段开始之前推动设计过程(图 8-2)。

FIGURE

图 8-2 说明了建模在设计-构建-测试周期中的作用。建模(此处象征性地描绘为左上角的小齿轮)可以帮助推动设计过程。

FIGURE

图 8-3 某些类型的模型。模型可以采用多种不同的形式。使用我们的架构示例,一些有用的模型包括蓝图(左)、三维物理模型(中)和计算模型(右)。

当然,没有任何模型,甚至模型集合,可以完全捕捉最终设计的所有方面。每个使用建模技术的人,无论是建筑师还是合成生物学家,都必须在每个模型的限制范围内工作。在大多数情况下,人们使用不同建模技术的组合来形成关于系统可能如何运行的相对完整的想法。但是,使用更多模型并不会自动生成更好的数据,因为并非所有模型都是好模型。使用不适当的计算模型或构建歪曲系统的物理模型可能会将工作引向错误的方向。了解模型是如何构建的以正确解释其提供的结果至关重要。

计算建模

计算建模(图 8-4)是指使用计算机来模拟特定设计的行为。 为了构建合成生物学的计算模型,工程师输入有关其生物系统各个组件的信息,包括方程当所有组件都放在一个单元中时,计算机可以使用这些算法来计算系统的预期行为。这些方程可能非常接近生物系统的实际行为,但不太可能完美地再现它。例如,许多描述反应速度和程度的方程最初是由在试管中单独研究单个酶的科学家推导出来的,这比细胞的复杂环境要简单得多。在细胞中,多种酶可以竞争相同的反应物,或者一种酶的产物可能抑制另一种酶的活性。事实上,我们还没有完全理解为什么我们的方程不能完全捕捉细胞行为,但我们可以对分子行为做出某些假设来近似不同的条件。例如,该模型可能会简化反应速率,使它们都是恒定的;因此,该模型适用于某些情况,但并非所有情况。

FIGURE

图 8-4 细胞过程的计算建模。可以收集每个相关反应的数据(左)并通过计算机(中)进行整合,以构建细胞行为的工作模型并预测不同化合物的浓度将如何随时间变化(右)。如果模型的输出与设计规范不匹配,则可以适当调整模型或收集更多数据,并且可以根据需要多次重新运行仿真。这样,计算建模是“测试”设计的快速方法。

尽管有其局限性,计算模型还是有用的,因为它们可以快速、精确地求解集成多个过程的方程。该模型的输出可能无法完美地反映自然,但即使模型的缺陷也可以教会我们一些关于我们正在使用的系统的新知识。通过构建计算模型,我们实际上是在测试我们理解的极限,并且可能会发现系统的重要新方面,需要将这些方面纳入模型中以反映可观察到的内容。

计算模型的另一个好处是它们可以模拟复杂系统在暴露于各种条件下时的行为。使用一组起始条件,计算模型可以计算系统状态将如何随时间变化。回到建筑示例,可以使用模拟来确定建筑物如何应对强风。模型的输入可能包括钢材强度、其对温度变化的响应以及该地区的预期风速等因素。建筑师可以对不同的摩天大楼高度、风速(如图 8-5 所示)或建筑材料进行模拟。一个好的计算模型将充分预测不同设计选项的行为,并帮助建筑师确定设计的物理限制。

FIGURE

图 8-5 模拟风对建筑物周围压力的影响。计算模型可以预测在盛行风况(左)和相反风况(右)下压力将如何变化,红色表示高风压,蓝色表示低压。

模型从两个基本来源获取信息:其内置知识库和用户输入的新信息。例如,建筑师的建模软件可能包含有关各种材料如何响应不同温度或风速的信息。这种公共信息已经内置到模型中。使用模型的建筑师可以指定要使用的钢材类型,然后运行模拟(有时称为建模实验),看看它是否足够坚固。如果结果表明钢材不足,则可以轻松运行另一个模拟,输入不同类型钢材的信息。这种方法被称为计算机辅助设计 (CAD),显然比建造一整座摩天大楼、发现其强度不足以抵御风并被迫重建更高效、更安全。

合成生物学项目也受益于计算建模。研究人员对各种细胞系统进行了建模,根据模型的复杂程度、优缺点,取得了不同程度的成功。正如建筑师的模型包含特定材料如何响应风的内置信息一样,生物系统的计算模型包含有关蛋白质和其他生物分子动态行为的信息。每个组件的信息越具体和准确。系统越好,得到的模型就越好。这就是合成生物学家测量各个部件的行为并开发通过标准化数据表相互共享信息的方法的原因之一,如 iTune 设备一章中所述。由于各个部分可以通过实验得到更好的表征,因此可以将所得信息包含在模型中,以提高其准确性和生物相关性。

建立模型并运行一次(或两次或三次)模拟后,就可以从计算机回到实验室工作台了。 我们可以将“湿实验室”实验的结果与计算模拟的结果进行比较,然后,理想情况下,结果用于进一步完善计算模型。通过计算和实验室工作的组合和迭代方法,尽管各自存在固有的限制和假设,但它们都得到了改进。

物理建模

物理建模是计算建模的补充。例如,建筑师可能会创建一个微型物理结构,以帮助可视化超出计算机模拟所能揭示的建筑项目。对于微观的细胞来说,尚不清楚物理模型可能揭示什么。因此,合成生物学家通常不会建立结构模型来说明他们的生命系统实际上是什么样子。然而,通过生命系统的信息流的物理模型可能是一个好处。

我们可以使用电子元件来实现这一目标,因为它们提供了有形且易于理解的物理模型,可以说明和探索遗传电路的设计和功能。合成生物学家已经将机械和电气工程成熟领域的术语和逻辑原理应用到生命系统的设计过程中,这在生物设计基础章节中进行了探讨。电气元件还为遗传系统的物理建模提供了有用的工具。

生物系统的电气模型有很多好处,其中最引人注目的是电气工程师创建系统原型的速度。工程师可以快速构建和测试电气系统,只需正确连接电线、电阻器和其他电子元件即可。相比之下,建立一个生物系统非常耗时,而且其结果也不太确定。此外,当它不起作用时,故障排除过程可能会非常缓慢。在生物学中,细胞不会给出任何错误消息(除了生长失败!),也没有方便的电压表或其他测量设备来评估系统内各个模块的正常功能。最后,生物模块本身在很大程度上并不是由随处可用且每次都能工作的标准化现成部件制成。因此,不受任何这些并发症影响的电子设备可以提供遗传电路和生物系统的良好有形表示,用于测试和故障排除。这种类型的物理模型可以帮助设计人员更深入地了解他们正在构建的系统,并可能识别其他表示中不明显的问题。

当然,电子模型在某些方面无法充分代表系统的电路。图 8-6 说明了一个限制是电子器件的数字行为——组件要么“开”,要么“关”。 另一方面,生物成分往往以模拟方式表现,具有完全“开启”和完全“关闭”之间的一系列行为。

FIGURE

图 8-6 数字信号与模拟信号。数字信号显示出明显的开/关行为(红色虚线)。低输入不产生任何输出。当输入超过某个阈值时,输出跳至其最大值。另一方面,模拟信号在关闭和打开之间显示出更加渐进的过渡(蓝色实线)。因此,低于数字阈值的输入仍然可以生成一些输出,而高于数字阈值的输入可以生成小于最大值的输出,即使数字和模拟组件的完全“关闭”和完全“打开”值也是相同的。

数字和模拟行为都需要。例如,数字电子行为就像打开或关闭灯泡的电灯开关,而模拟行为就像允许中间亮度的调光开关。鉴于数字电路不易受到输入信号(“噪声”)轻微波动的影响,合成生物学家花费了大量的时间和精力来表征和设计生物系统,使其尽可能“数字化”。 不过,大多数自然系统都是模拟系统,随着输入信号的微小变化,输出会逐渐增加。合成生物学家使用一些巧妙的技术在细胞中实现更多的数字行为,例如构建多层模拟调节并对信号进行分层,以使输出看起来要么打开要么关闭。使用电子元件进行生物电路建模的第二个限制是电子面包板允许电线、电阻器和其他元件的物理分离。然而,在细胞内部,各种成分不断混合,因此单个事件很难隔离和建模。尽管存在缺陷,良好的电子模型可以提供对系统设计和工程细胞行为的深入了解,正如 BioBuilder 的图片此活动所示。

来自“Coliroid”iGEM 项目的灵感

FIGURE

该团队的设计目标乍一看似乎很学术,但实际上识别明暗边界的能力揭示了图像的轮廓。该团队设想的成功的一些积极成果包括改善基因表达的光控制、化学产品的精细空间控制、信号转导途径的合理设计以及有用的细胞间通讯电路。图像处理器(包括面部识别软件等系统)可以通过仅检测边缘来快速处理复杂图像,边缘由可捕获的数据的可管理子集来描述。这一挑战对于一个夏天来说是一项雄心勃勃的挑战,事实上,完整的边缘检测系统又花了几年的研究和开发才能完成。在 2004 年的 iGEM 项目中,由德克萨斯大学奥斯汀分校和加州大学旧金山分校的成员组成的团队构建了一种光检测和颜色生成的大肠杆菌菌株,可用于“然而,该团队在细菌摄影系统方面取得了巨大的进步,即使作为实现更大目标的中间站,其工程生命系统也是我们可以继续探索并从中学习的系统。处理整个图像中的数据会降低软件的速度,因为数据集非常大。细菌摄影。”通过将这种系统构建到细菌草坪中,iGEM 团队并不打算取代人脸识别软件或人工智能程序中的电子边缘检测器。该团队的最初目标是构建边缘检测器的实时版本,这是一种检测对比度的数学图像处理方法。相反,它认为设计这个生命系统是一项艰巨的挑战,如果解决了,可能会推动合成生物学领域的多项基础性工作。

设备级设计

FIGURE

为了构建其系统,该团队决定使用两个设备:一个光检测设备和一个颜色生成设备,如图 8-7 所示。光检测设备旨在检测光的存在或不存在,然后将适当的信号发送到第二个设备。信号的确切性质尚未定义,至少在最初是这样。将系统抽象为两个设备,使团队能够根据出现的系统详细信息以及可用的部件来完善项目。例如,该团队希望在大肠杆菌中构建系统,因为大肠杆菌没有天然存在的光检测装置,因此需要从另一种生物体中识别候选光敏蛋白以用于设计。光检测设备和颜色生成设备之间的通信将取决于该光传感器的身份及其可以生成的信号。同样,颜色生成装置旨在提供可见输出,但最初并未定义具体的颜色或化合物。通过在设备级别进行抽象工作,团队不必遵守其系统的任何特定规范,并且可以考虑多种变体来开始工作。通过在这个抽象级别上工作,可以依次考虑关键决策,而不是立即规划从最具体的 DNA 序列细节到最一般的系统功能的所有方面。

FIGURE

图 8-7 细菌摄影设备级设计。细菌摄影系统将光作为其光探测器的输入。然后,第一设备的输出确定颜色生成器是否处于活动状态并产生其颜色输出。连接两个设备的线路并不意味着 DNA 的物理连接;相反,它显示从一个设备到另一设备的信息流。

零件级设计

FIGURE

当需要根据遗传部分来指定系统的颜色生成装置时,团队决定使用一种经过充分表征的酶,β-半乳糖苷酶 (β-gal)。该酶是 lacZ 基因的产物,通常是 lac 操纵子的几个基因之一。该酶将二糖(乳糖)转化为细胞更容易代谢的两种单糖。该酶还对天然底物以外的多种底物起作用。许多非天然底物的化学结构与乳糖相似,但当酶裂解它们时,它们会产生有色产物。例如,当 β-gal 裂解 X-gal 时,一种产物呈蓝色。当 β-gal 裂解 ONPG(如 BioBuilder iTune 设备活动中所用)时,一种产物呈黄色。在进行细菌摄影系统的部件级设计时,团队选择使用 β-gal 作为颜色生成装置,因为该酶在裂解其底物 S-gal 时可以产生黑色。 β-gal 裂解 S-gal 形成稳定的不溶性沉淀物,沉积到介质中,类似于显影过程中沉积到相纸上的银粒。

合成生物学视觉记者

为了设计细菌摄影系统,iGEM 团队需要肉眼可见的输出,因此选择了 β-gal。原则上,该团队可以从许多替代的颜色生成装置中进行选择,例如荧光蛋白。 β-gal 是一个方便的选择,因为它是一种特性良好且用途广泛的酶,您可能已经从它在 BioBuilder 活动中的重复使用中猜到了。有趣的是,BioBuilder 的 iTune 设备活动也使用 β-gal,但在这种情况下,该酶用于报告基因设计的功效,因此并不严格要求可见的输出。视觉产品,或者更通用的名称,提供了易于检测的输出。它们也很容易相互交换。在大多数情况下,一个报告器可以替换任何其他报告器,根据应用情况进行交换。例如,如果您正在为色盲或视力受损的人设计一个系统,那么基于气味的报告器(例如使用 BioBuilder 的 Eau That Smell 活动的报告器)可能更合适。

对于其细菌摄影系统,团队需要找到一种方法将信号(在本例中为光)的存在或不存在与 β-gal 活性联系起来。对于这种联系,该团队做出了明智的设计选择,并利用了细菌通常用来感知环境信号的共同途径。细菌的信号传感通路统称为两部分信号通路。通常,这些途径的一个组件是环境因素的传感器,另一个组件是响应器。在许多情况下,应答者调节基因或基因家族的转录。在构建细菌摄影系统时,iGEM 团队修改了由名为 EnvZ 的传感器和名为 OmpR 的响应器组成的信号系统(图 8-8)。

FIGURE

图 8-8 打开黑盒设备的包装。为了检测大肠杆菌中的光,iGEM 团队将来自蓝藻的光敏蛋白 Cph1 的一部分与大肠杆菌蛋白的一部分进行基因融合,创造出一种新的蛋白 Cph8(粉色圆圈),它可以磷酸化 OmpR(橙色圆圈)。 Cph8/OmpR 组合可以感应光作为输入,然后生成 PomplacZ 颜色生成设备可以理解的输出信号。

EnvZ 通常通过添加磷酸盐将有关细胞外盐浓度的信息传递给 OmpR。然后,磷酸化的 OmpR 可以结合特定启动子序列上游的 DNA,并增加该启动子下游基因的转录。在自然界中,受磷酸化 OmpR 调节的基因编码膜孔,允许或多或少的盐从环境中进入细胞。 在设计细菌照相系统时,iGEM 团队对 DNA 进行了改造,使磷酸化的 OmpR 能够调节 β-gal 的表达。研究小组只是将 OmpR 调节的启动子置于 lacZ 基因的上游,这样 OmpR 就会像调节膜孔的基因一样调节 lacZ(图 8-9)。

现在您可能会想,“等一下……这种排列不是会响应细胞环境中盐分的变化而产生颜色吗?”目标是感知光。 大肠杆菌中没有天然的光敏蛋白,所以在这里,iGEM团队再次巧妙地利用了一些天然遗传元素。蓝藻是一种对光有反应的微生物,iGEM团队决定修改来自蓝细菌的光传感蛋白,用于报告其大肠杆菌系统中的光输入。该团队进行了基因融合,从光敏蛋白 Cph1 的基因开始,到大肠杆菌 EnvZ 与 OmpR 通讯的部分结束。知道蛋白质将它们所做的工作划分为离散的模块域后,iGEM 团队相信这种融合蛋白能够发挥作用,并且能够像希望的那样感知光并与 OmpR 进行通信。

FIGURE

图 8-9 制作颜色生成装置。 lac 操纵子(顶部)被截短(左下)并用 OmpR 敏感启动子(橙色箭头)进行修饰,以生成对 OmpR 蛋白敏感的颜色生成装置。

为了构建其系统,该团队依靠遗传学和分子生物学(以及大量的努力工作和一定程度的好运),并找到了一种可以完成设计所需的所有功能的变体。该团队将这种融合蛋白命名为 Cph8(图 8-10)。与 Cph1 蛋白一样,Cph8 对特定波长的红光敏感。 然而,为了使其发挥作用,团队需要一些来自蓝细菌的“辅助”发色团,因此系统再次进行了修改。在这个新版本中,研究小组表达了蓝藻基因 ho1 和 pcyA,它们合成了 Cph8 所需的辅助因子。

FIGURE

图 8-10 光敏 Cph8 融合蛋白。来自蓝藻的光敏蛋白 Cph1 与磷酸化 OmpR 的大肠杆菌蛋白 EnvZ 部分融合,产生一种新蛋白 Cph8,它以光作为输入并输出 Pomp 可以理解的信号。 -lacZ颜色发生装置。

当这些最终修饰到位时,当细胞在黑暗中生长时,所得系统可以表达β-gal。红光源抑制 OmpR 的磷酸化,导致 LacZ 的转录减少,从而导致 β-gal 酶的转录减少。通过在打印在透明胶片上并用胶带粘在培养皿上的图像后面生长细胞,可以遮蔽细菌菌苔的区域。在掩模的黑暗部分后面生长的细胞可以使它们周围的介质变黑(图8-11)。暴露在红光下的细胞使介质保持自然颜色,使得掩模上的图像在 24 小时的生长期后能够在介质本身中再现。

FIGURE

图 8-11 通过细菌摄影系统的信息流。光探测器由 Cph8 融合蛋白(粉色圆圈)和细胞的 OmpR 天然副本(橙色圆圈)组成,Cph8 会激活 OmpR。在上图中,激活的 OmpR 然后可以与颜色生成器设备中的 Pomp 运算符(橙色弯曲箭头)结合,从而产生 lacZ 表达(蓝色飞镖)。在下图中,当光线照射到系统上时,OmpR 与 Pomp 的这种相互作用被阻止(平头箭头)。

额外阅读和资源

  • Deepak, C.、Bergmann, F.T.、Suaro, H.M. TinkerCell:用于合成生物学的模块化 CAD 工具。生物工程杂志。 2009;3:19。网站:http://www.tinkercell.com/.
  • Levskaya,A. 等人。合成生物学:改造大肠杆菌以见光。自然 2005;438(7067):441-2。
  • Stock, A.M.、Robinson, V.L.、Goudreau, P.N.二元信号转导。生物化学年度评论 2000;69:183-215。
  • 网站:Mouser Electronics 网站上的 BioBuilder“项目”页面,您可以在其中购买每个电子部件。 (http://bit.ly/biobuilder_mouser )。

描绘这个实验室

BioBuilder 的图片 该实验室通过分析改进的双组分传感系统,介绍了复杂的生物学概念,例如信号转导和细胞动力学。它强调通过对工程细胞进行计算机模拟并通过构建类似于细胞遗传电路的电子电路来进行抽象和建模的工程概念。

设计选择

在这里,我们使用两种方法来理解细菌摄影系统:使用名为 TinkerCell 的程序进行计算建模,以及使用标准电气组件进行物理建模。与其他 BioBuilder 活动相比,该实验室专注于开发实验问题,而不是直接提出问题。这两种互补的建模方法提供了对生命系统行为不同方面的洞察,并说明了我们当前生物学建模工作的优势和缺点。

尽管该活动目前没有“湿实验室”部分,但支持机构可以使用您选择的图像来制作由工程菌株制成的细菌照片。请务必检查 BioBuilder 网站以获取此活动的更新并查找提交指南。下节简要描述了细菌照片显影的方案。

FIGURE

细菌照片

为了准备细菌照片,工程菌株在适当的抗生素存在下生长,这些抗生素选择用于光检测装置、颜色生成装置以及使光传感器 (Cph8) 在大肠杆菌中发挥作用的辅助组件。大肠杆菌。然后,您可以将过夜培养物与熔化的琼脂、抗生素和指示剂化合物 S-gal 混合,并将其倒入培养皿中,将细菌包埋在培养介质中。您可以将带有黑白图像的透明胶片粘贴到培养皿背面,然后在红光下孵育过夜,为细菌在黑暗中生长提供时间以产生 β-gal 酶。由于这种介质的 S-gal 成分非常昂贵(约 600 美元/克),并且曝光这些照片的光波长不是标准的,因此 BioBuilder 教室冲洗照片的最常见方式是发送透明胶片或 .jpg 文件的图像的要开发。

当细胞在明显的光亮或黑暗中生长时,就会产生最引人注目的细菌照片。如果图像的黑白部分高度混合(例如,图像具有非常细的线条),则光线会在边缘周围反射并使生成的照片模糊。一般来说,最好是深色背景和浅色图像,而不是相反。为了使图像的深色部分变暗,通常在两张透明胶片上打印相同的图像,然后将两份副本重叠,使用它们来遮盖培养皿。培养皿的直径小于 3 英寸,因此选择的图像必须小于此直径或进行调整以适合。

TinkerCell 建模

您可以从 TinkerCell 主页下载 TinkerCell。您可以在 TinkerCell 平台中找到构建细菌摄影系统的详细说明以及 BioBuilder 网站上建议的模拟。

TinkerCell 活动分为两个阶段:细菌摄影电路的重绘和其行为的模拟。作为重绘阶段的第一步,您可以从可用部件菜单中选择设备的 DNA 电路组件并将其拖放到建模画布上。在TinkerCell中,这些部分按照其功能进行分类;例如,“激活剂结合位点”、“RBS”、“启动子”、“编码”、“转录因子”或“受体”。以下是细菌摄影系统建模所需的组件列表:

  • 颜色发生器装置的组件:
    • 激活剂结合位点
    • ompC 启动子
    • 核糖体结合位点 (RBS)
    • 编码区域
    • β-半乳糖苷酶
  • 光检测装置的组件:
    • Cph8 光受体
    • OmpR转录因子
  • 三个“小分子”:
    • S-gal
    • 颜色
  • 1个蜂窝底盘

该模型强调了我们最感兴趣的系统方面,即 β-gal 酶的转录控制。这就是为什么系统的某些元件(例如 OmpR)被作为预先存在的蛋白质而不是转录基因表达盒放入模型中。当然,我们作为蛋白质放入的元素存在转录控制和翻译控制,但这里的模型假设这些步骤可以简化,并且暂时可以忽略对它们的控制。这种简化是抽象的另一个例子,抽象是一种在生物设计基础章节中广泛讨论的工程工具。我们在这里使用抽象来保持计算负载的可控性。

选择进入模型的组件后,下一步是显式定义它们的关系。以下是细菌摄影系统建模组件之间的关系列表:

  • Cph8 可以激活或抑制 OmpR 的磷酸化(请注意,根据您的选择,您需要调整光是激活还是抑制 Cph8)。
  • 磷酸化的 OmpR 可以与报告基因的激活剂结合位点结合。
  • 报告基因可以产生β-gal酶。
  • β-gal可以将“S-gal”小分子作为输入,并可以产生“彩色”小分子作为输出。

最后,将底盘添加到画布上。你必须排列现有的组件,使“轻”的小分子位于细胞外,Cph8 蛋白位于细胞膜中,而其他所有成分都位于细胞内(图 8-12)。

TinkerCell 活动的下一阶段是运行系统行为的模拟。由于系统被设计为对光敏感,因此模型的输出将保持不变,除非光输入量发生变化。如果灯光在整个模拟过程中保持打开或关闭状态不变,则模型的输出不会改变。您可以使用 TinkerCell 菜单选项中的阶跃函数指定光输入何时以及如何变化,然后您可以运行模拟以查看系统如何响应不同的光照水平。

FIGURE

图 8-12 TinkerCell 建模界面的屏幕截图。细菌摄影系统的计算模型包含模拟系统在各种条件下的行为所需的所有遗传和生物组件。

TinkerCell 提供称为起始条件的默认值,用于确定模型组件的起始浓度和反应效率。酶效率给出了一个值,RBS 的强度、启动子、激活、抑制以及天然存在的 OmpR 和 S-gal 的量也给出了一个值。运行模拟时,您可以使用默认值,也可以更改它们以查看模型如何预测细胞的响应。例如,如果磷酸化的 OmpR 蛋白多 10 倍怎么办?如果结合 DNA 的磷酸化 OmpR 的量受到限制,则增加会导致更多的 lacZ 转录,从而产生更多的 β-gal 酶。如果酶对 S-gal 产生颜色的催化作用有限,这种变化反过来会增加在有限时间内形成的颜色量。

因此,即使 TinkerCell 对模型的组件做出了许多假设,您也可以调整这些参数来探索系统如何响应。您会发现这些模拟实验比湿实验室版本花费的时间要少得多;因此,如果模型设置得当,它可以节省您在工作台上的很多时间,并且您在那里工作时可以采取明智的实验方法。

电子电路建模

在 Picture This 的物理建模组件中,您将构建细菌摄影菌株的电子版本。回想一下本章前面的建筑示例,计算机辅助设计工具可以帮助建筑师在各种环境条件下评估和测试设计。架构师还可以进行补充形式的建模,即物理模型,以帮助设想设计并识别所需但缺失的组件。对于合成生物学家来说,细胞的物理模型可能不会提供太多附加信息,但说明通过遗传电路的信息流的物理模型可以提供丰富的信息,然后您可以使用它来对电路进行测试预测。随着遗传电路变得越来越复杂,对通过它们的信息流进行建模可能变得异常困难。然而,细菌摄影系统具有相当简单的逻辑,因此我们可以用它来说明物理模型的价值,该模型使用电子元件来“替代”生物模型,如图 8-13 所示。

本章前面第 155 页的“其他阅读材料和资源”部分包含指向 Mouser Electronics 网站上 BioBuilder“项目”页面的链接,您可以在其中找到此活动的电子部件。表 8-1 列出了本 BioBuilder 活动中专门使用的组件。

在电子系统中,开关控制进入电路的电流,因此类似于膜结合光传感器蛋白 (Cph8) 所扮演的角色,它检测光并启动或抑制激酶反应。发光二极管 (LED) 的行为模仿细菌摄影系统的输出,根据电路的“光检测”开关组件的状态打开或关闭。面包板、电线和电阻器传播来自开关的信号并指定系统的逻辑,按下开关时关闭输出,关闭开关时打开输出。该电阻器还对系统的灵敏度进行建模,调节流经系统的信息量。

FIGURE

图 8-13 细菌摄影系统电气模型的示意图。光传感器(左)是光电二极管或开关,相当于光检测装置。可见光输出(右)是 LED(发光二极管),对应于颜色生成设备。多种组件可以连接光检测器和 LED,以模拟细胞内发生的信号传播。

表 8-1 电路元件

电子零件:   生命系统中的相应组件   贸泽电子零件编号
瞬时开关 Cph8光检测系统 611-8551MZQE3
显色LED β-gal + S-gal显色反应 607-5102H5-12V
电池和卡扣式夹子 为电池提供电力的新陈代谢 9V和534-235
电线和电阻器 信息流的通路和调节 510-WK-3 和 71-CCF0720K0JKE36
面包板 E.大肠杆菌底盘 510-GS-400

在面包板上构建电路 面包板是用于快速制作电子电路原型的平台。您可以将电线插入面包板塑料盖上的孔中,以轻松进行电子连接并测试多种电路配置。但这些孔如何将组件连接在一起呢?面包板有两条轨道,每侧一条,它们是标有红色或蓝色线以及加号或减号的长柱。它还具有按五个一排排列的内部孔。沿侧面的导轨是电路连接电源和电源接地的地方。接地本质上是一种将电流返回到起点的方法,也称为闭合或完成电路(对于北美以外的交流供电系统,您可能会看到术语“接地”代替“接地”)。如果电路不接地,电流就无法流动,电路将无法工作。面包板上的两个导轨在功能上是相同的,因此电路的方向是通过将一个导轨连接到电源、将另一个导轨连接到接地来确定的。

如果您剥开面包板后面的盖子,您会看到位于塑料面包板孔后面的金属条(图 8-14)。金属连接每个导轨的整个长度,因此您可以沿着导轨的任何位置连接电源和接地,然后整个导轨提供电源或接地。更多的金属条也位于每排中的五个孔的后面,因此它们彼此连接,但它们不连接到下一排中的孔或向下延伸的凹槽或沟槽另一侧的孔面包板的中间。任何插入同一排孔中的电子元件都是电气连接的,并且电流可以在它们之间流动(请参见http://bit.ly/building_circuits。)

FIGURE

图 8-14 电子面包板。面包板的塑料顶部(左)和其背板被移除(右)以显示导电金属的配置。左侧的绿色轮廓对应于金属片的方向,如右侧所示,因此反映了电子元件的连接性。

在电子领域,传统上用红色表示正极,用黑色表示负极。电路需要电池等能源,可以通过接线柱连接到面包板。对于此 BioBuilder 活动,面包板通过将 9V 电池引线的红线连接到其中一个红色 (+) 导轨,并将电池引线的黑线连接到面包板另一侧的蓝色 (–) 导轨来供电。木板。

电子建模活动

如果您手头有构建细菌摄影电路的电子元件,您可以尝试以下操作。

首先,通过将 9V 电池的接地连接到面包板的蓝色 (–) 导轨,并将电池的正极连接到面包板另一侧的红色 (+) 导轨,为面包板供电。接下来,使用两根小电线将电源连接到面包板的中心部分(其中有五个孔的行)。最后,将 LED 的红线连接到面包板上与红色导轨相连的孔,并将 LED 的另一根线连接到面包板的接地侧,为 LED 供电。

对于这个简单的电路,拔掉引线是改变系统输出的唯一方法。要构建更容易更改的系统,您可以将 LED 上的地线移至新行,然后将开关连接到接地行和带有 LED 地线的行之间,从而在电路中添加一个开关。这是一个很好的时刻,可以注意到电路元件重新接线是多么容易,以及它们如何可靠地连接以相互通信。这也是注意到我们使用的开关是数字的(它要么完全打开,要么完全关闭)的好时机,因此输出无法“调整”。

为了修改系统的输出,电子电路还包括一个电阻器。尽管该电路仍然表现出类似开关的行为,但您可以通过进一步分离 LED 和开关之间的连接并在它们之间插入一个电阻来改变输出的强度。使用您观察到的行为来思考遗传电路和可能影响每个信息流的点。

在过去教授此活动时,我们注意到一些事情可能会对您第一次尝试此活动有所帮助。当电子设备未按预期运行时,检查是否已按照说明进行所有连接非常有用。大多数情况下,面包板上的电线会被错放。当接线完全正确但电路仍然无法工作时,将零件逐一更换为工作设置会有所帮助。我们曾因电池没电、LED 烧坏和面包板故障而感到沮丧,但您可以通过在故障设置和工作设置之间系统地更换零件来识别和解决每个问题。

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