Engineers From England

"We may define an object to be big when the disturbance accompanying our observation of it may be neglected, and small when the disturbance cannot be neglected... In order to give an absolute meaning to size, such as is required for any theory of the ultimate structure of matter, we have to assume that there is a limit to the fineness of our powers of observation and the smallness of the accompanying disturbance... If the object under observation is such that the unavoidable limiting disturbance is negligible, then the object is big in the absolute sense and we may apply classical mechanics to it. If, on the other hand, the limiting disturbance is not negligible, then the object is small in the absolute sense and we require a new theory for dealing with it."

"The reader.. may argue that a very strange idea has been introduced — the possibility of a photon being partly in each of two states of polarization, or partly in each of two separate beams — but even with the help of this strange idea no satisfying picture of the fundamental single-photon processes has been given... it may be remarked that the main object of physical science is not the provision of pictures, but is the formulation of laws governing phenomena and the application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance. In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word 'picture', by which is meant a model functioning essentially on classical lines. One may, however, extend the meaning of the word 'picture' to include any way of looking at the fundamental laws which makes their self-consistency obvious. With this extension, one may gradually acquire a picture of atomic phenomena by becoming familiar with the laws of the quantum theory."

"... we cannot observe a small system with that amount of detail which classical theory supposes. The limitation in the power of observation puts a limitation on the number of data that can be assigned to a state... A state of a system may be defined as an undisturbed motion that is restricted by as many conditions or data as are theoretically possible without mutual interference or contradiction."

"The nature of the relationships which the superposition principle requires to exist between the states of any system is of a kind that cannot be explained in terms of familiar physical concepts. One cannot in the classical sense picture a system being partly in each of two states and see the equivalence of this to the system being completely in some other state. There is an entirely new idea involved, to which one must get accustomed and in terms of which one must proceed to build up an exact mathematical theory, without having any detailed classical picture."

"... people have tried to establish analogies with systems in classical mechanics, such as vibrating strings or membranes... Such analogies have led to the name 'Wave Mechanics' being sometimes given to quantum mechanics. It is important to remember, however, that the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation. The analogies are thus liable to be misleading."

"{\int _{-\infty }^{\infty }{\delta \left({x}\right){d{x}}}}=1 \delta \left({x}\right)=0 \text{ for } x\not= 0"

"It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory."

"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."

"Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them."

"Perhaps the most distinguished of 'why botherers has been Dirac (1963 Sci. American 208 May 45). He divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second-class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the 'renormalisation' procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise. The first-class difficulties concerned the role of the 'observer', 'measurement', and so on. Dirac thought that these problems were not ripe for solution, and should be left for later. He expected developments in the theory which would make these problems look quite different. It would be a waste of effort to worry overmuch about them now, especially since we get along very well in practice without solving them."

"Dirac was the strangest man who ever visited my institute. […] During one of Dirac’s visits I asked him what he was doing. He replied that he was trying to take the square-root of a matrix, and I thought to myself what a strange thing for such a brilliant man to be doing. Not long afterwards the proof sheets of his article on the equation arrived, and I saw he had not even told me that he had been trying to take the square root of the unit matrix!"

"Regardless of the prophetic value of Dirac’s description [on interference] his was probably the first discussion... including a coherent beam of light. In other words, Dirac wrote the first chapter in laser optics."

"I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful."

"The latest and most successful creation of theoretical physics, namely Quantum Mechanics, is fundamentally different in its principles from the two programmes which we will briefly call Newton's and Maxwell's. For the quantities that appear in its laws make no claim to describe Physical Reality itself, but only the probabilities for the appearances of a particular physical reality on which our attention is fixed. Dirac, to whom, in my opinion, we owe the most logically perfect presentation of this theory, rightly points out that it appears, for example, to be by no means easy to give a theoretical description of a photon that shall contain within it the reasons that determine whether or not the photon will pass a polarizator set obliquely in its path."

"One of the most revered – and strangest – figures in the history of science."

"When I was a young man, Dirac was my hero. He made a breakthrough, a new method of doing physics. He had the courage to simply guess at the form of an equation, the equation we now call the Dirac equation, and to try to interpret it afterwards. Maxwell in his day got his equations, but only in an enormous mass of 'gear wheels' and so forth."

"Before World War II there had been considerable theoretical effort directed towards the question of the self-energy of the electron. However, because of the war, interest had remained dormant. Now, the stimulus of results of Lamb and Retherford the latent interest developed into a major attack by theoretical physicists, and within a few years the problem was solved to the satisfaction of nearly everyone. (To the end of his life, however, Dirac maintained that any theory involving the subtraction of infinities was ugly, unsatisfactory and surely incomplete.)"

"Here we find a man with an almost miraculous apprehension of the structure of the physical world, coupled with gentle incomprehension of that less logical, messier world, the world of other people."

"Let me backtrack... to the 1920s when quantum mechanics was created. ...[O]ne of the things that the originators of quantum mechanics... were very unhappy about was that quantum mechanics was not compatible with the special theory of relativity. ...Attempts were made to create a theory of the electron that is consistent with relativity, and one person made such a theory, but it was inconsistent with the electron spin. Another person made a theory that was consistent with electron spin, but not consistent with relativity. Until finally... a then young man... Paul Dirac created the theory of an equation that correctly describes the electron, and is relativistic, and also includes the description of spin... [T]hat was the beginning of the marriage that would take place between quantum mechanics and relativity. ...He originally noticed that the equation had too many solutions... He thought the negatively charged solutions would be electrons and the positive charge solutions would be s... He realized that this made no sense and the two things had to have the same , and finally... realized that he was... predicting [the positively charged electron,] the , just shortly before the positron was... independently and serendipitously discovered."

"Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe. He is surely worthy of the memorial in Westminster Abbey. It is just a scandal that it has taken so long."

"Dirac’s relationship with quantum electrodynamics was not an easy one. On the one hand, the theory owes to him much more than to anybody else, especially if one considers the years crucial for its emergence, the late 1920s and early 1930s, when practically all its main concepts, except for that of renormalization, were developed. After this period Dirac also wrote a number of important papers, specifically, on indefinite metrics and quantum dynamics with constraints. On the other hand, since the early 1930s he was an active critic of the theory and tried to develop alternative schemes. He did not become satisfied with the later method of renormalization and regarded it as a mathematical trick rather than a fundamental solution, and died unreconciled with what, to a large extent, was his own brainchild. …"

"In the fight between you and the world, back the world."

"Mr. Herschel ... brought with him the calculations of the computers, and we commenced the tedious process of verification. After a time many discrepancies occurred, and at one point these discordances were so numerous that I exclaimed, "I wish to God these calculations had been executed by steam," to which Herschel replied, "It is quite possible.""

"The Economy of Manufactures established Babbage's position as a political economist and its influence is well attested, particularly on John Stuart Mill and Karl Marx. Babbage's pioneering discussion of the effect of technical development on the size of industrial organizations was followed by Mill and the prediction of the continuing increase in the size of factories, often cited as one of Marx's successful economic predictions, in fact derives from Babbage's analysis... Babbage wrote with many talents: a natural philosopher and mechanical engineer, his knowledge of factory and workshop practice was encyclopaedic; he was well-versed in relevant business practice; and he was without rival as a mathematician among contemporary British political economists."

"Babbage was one of the founders of the Cambridge Analytical Society whose purpose he stated was to advocate "the principles of pure d-ism as opposed to the dof-age of the university."

"We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves."

"Propose to any Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible; if you peel a potato with it before his eyes, he will declare it useless because it will not slice a pineapple. Impart the same principle or show the same machine to an American or to one of our Colonists and you will observe that the whole effort of his mind is to find some new application of the principle, some new use for the instrument."

"Errors using inadequate data are much less than those using no data at all."

"The foundation of all religion is the belief in a God, and that He exists in certain relation with His creatures. Such belief necessarily leads to the consciousness of some obligation towards the Deity ; and this consciousness suggests the duty of worship ; and in the selection of the form of this worship originates the various creeds which distinguish and distract mankind. There is a sort of geography of religion ; and I regret to think that the majority of mankind take their creed from the clime in which they happen to be born ; and that many, and not an inconsiderable portion of mankind, suffer the sacred torch to burn out altogether, in their contact with the world, and then vainly imagine that they can recover the sacred fire by striking a park out of dogmatic theology."

"Miracles may be, for anything we know to the contrary, phenomena of a higher order of God's laws, superior to, and, under certain conditions, controlling the inferior order known to us as the ordinary laws of nature."

"If we define a miracle as an effect of which the cause is unknown to us, then we make our ignorance the source of miracles! and the universe itself would be a standing miracle. A miracle might be perhaps defined more exactly as an effect which is not the consequence or effect of any known laws of nature."

"We must be careful to discriminate between our own incapacity to test truth and the necessary improbability of an event. It is plain that from our ignorance of the remote spheres of God's action we cannot judge of His works removed from our experience; but a fact is not necessarily doubtful because it cannot be reached by our ordinary senses. To recapitulate, we may lay down the following propositions: 1. That there is no real physical distinction between miracles and any other operations of the Divine energy : that we regard them differently is because we are familiar with one order of events and not the other. 2. There is nothing incredible in a miracle, and the credibility of a miraculous event is to be measured only by the evidence which sustains it. And although the extraordinary character of a phenomenon may render the event itself improbable, it does not, therefore, necessarily render it either incredible or untrue."

"Mill, in speaking of Hume's celebrated principle, "that nothing is credible which is contradictory to experience, or at variance with the laws of nature," calls it a very plain and harmless proposition, being, in effect, nothing more than that whatever is contradictory to a complete induction is incredible. Admit the existence of a Deity, and the possibility of a miracle is the natural consequence. No doubt our examination of the evidence which sustains an unusual phenomenon should be most carefully conducted; but we must not measure the credibility or incredibility of an event by the narrow sphere of our own experience, nor forget that there is a Divine energy which overrides what we familiarly call the laws of nature."

"There is nothing in the nature of a miracle that should render it incredible: its credibility depends upon the nature of the evidence by which it is supported. An event of extreme probability will not necessarily command our belief unless upon a sufficiency of proof; and so an event which we may regard as highly improbable may command our belief if it is sustained by sufficient evidence. So that the credibility or incredibility of an event does not rest upon the nature of the event itself, but depends upon the nature and sufficiency of the proof which sustains it."

"It has always occurred to my mind that many difficulties touching Miracles might be reconciled, if men would only take the trouble to agree upon the nature of the phenomenon which they call Miracle. That writers do not always mean the same thing when treating of miracles is perfectly clear; because what may appear a miracle to the unlearned is to the better instructed only an effect produced by some unknown law hitherto unobserved. So that the idea of miracle is in some respect dependent upon the opinion of man. Much of this confusion has arisen from the definition of Miracle given in Hume's celebrated Essay, namely, that it is the "violation of a law of nature." Now a miracle is not necessarily a violation of any law of nature, and it involves no physical absurdity. As Brown well observes, "the laws of nature surely are not violated when a new antecedent is followed by a new consequent ; they are violated only when the antecedent, being exactly the same, a different consequent is the result;" so that a miracle has nothing in its nature inconsistent with our belief of the uniformity of nature. All that we see in a miracle is an effect which is new to our observation, and whose cause is concealed. The cause may be beyond the sphere of our observation, and would be thus beyond the familiar sphere of nature; but this does not make the event a violation of any law of nature. The limits of man's observation lie within very narrow boundaries, and it would be arrogance to suppose that the reach of man's power is to form the limits of the natural world. The universe offers daily proof of the existence of power of which we know nothing, but whose mighty agency nevertheless manifestly appears in the most familiar works of creation. And shall we deny the existence of this mighty energy simply because it manifests itself in delegated and feeble subordination to God's omnipotence?"

"The true value of the Christian religion rests, not upon speculative views of the Creator, which must necessarily be different in each individual, according to the extent of the knowledge of the finite being, who employs his own feeble powers in contemplating the infinite : but it rests upon those doctrines of kindness and benevolence which that religion claims and enforces, not merely in favour of man himself but of every creature susceptible of pain or of happiness."

"In the course of my inquiries, I met with the work upon the Trinity, by Dr. Samuel Clarke. This I carefully examined, and although very far from being satisfied, I ceased from further inquiry. This change arose probably from my having acquired the much more valuable work of the same author, on the Being and Attributes of God. This I studied, and felt that its doctrine was much more intelligible and satisfactory than that of the former work. I may now state, as the result of a long life spent in studying the works of the Creator, that I am satisfied they afford far more satisfactory and more convincing proofs of the existence of a supreme Being than any evidence transmitted through human testimony can possibly supply."

"In the works of the Creator ever open to our examination, we possess a firm basis on which to raise the superstructure of an enlightened creed. The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws. The works of the Creator, ever present to our senses, give a living and perpetual testimony of his power and goodness far surpassing any evidence transmitted through human testimony. The testimony of man becomes fainter at every stage of transmission, whilst each new inquiry into the works of the Almighty gives to us more exalted views of his wisdom, his goodness, and his power."

"There remains a third source from which we arrive at the knowledge of the existence of a supreme Creator, namely, from an examination of his works. Unlike transmitted testimony, which is weakened at every stage, this evidence derives confirmation from the progress of the individual as well as from the advancement of the knowledge of the race. Almost all thinking men who have studied the laws which govern the animate and the inanimate world around us, agree that the belief in the existence of one Supreme Creator, possessed of infinite wisdom and power, is open to far less difficulties than the supposition of the absence of any cause, or of the existence of a plurality of causes."

"It is difficult to estimate the misery inflicted upon thousands of persons, and the absolute pecuniary penalty imposed upon multitudes of intellectual workers by the loss of their time, destroyed by organ-grinders and other similar nuisances."

"As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise — by what course of calculation can these results be arrived at by the machine in the shortest time?"

"The whole of arithmetic now appeared within the grasp of mechanism."

"On two occasions I have been asked, — "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" In one case a member of the Upper, and in the other a member of the Lower, House put this question. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."

"But a much graver charge attaches itself, if not to our clergy, certainly to those who have the distribution of ecclesiastical patronage. The richest Church in the world maintains that its funds are quite insufficient for the purposes of religion and that our working clergy are ill-paid, and church accommodation insufficient. It calls therefore upon the nation to endow it with larger funds, and yet, while reluctant to sacrifice its own superfluities, it approves of its rich sinecures being given to reward, — not the professional service of its indefatigable parochial clergy, but those of its members who, having devoted the greater part of their time to scientific researches, have political or private interest enough to obtain such advancement. But this mode of rewarding merit is neither creditable to the Church nor advantageous to science. It tempts into the Church talents which some of its distinguished members maintain to be naturally of a disqualifying, if not of an antagonistic nature to the pursuits of religion; whilst, on the other hand, it makes a most unjust and arbitrary distinction amongst men of science themselves. It precludes those who cannot conscientiously subscribe to Articles, at once conflicting and incomprehensible, from the acquisition of that preferment and that position in society, which thus in many cases, must be conferred on less scrupulous, and certainly less distinguished inquirers into the works of nature. As the honorary distinctions of orders of knight hood are not usually bestowed on the clerical profession, its members generally profess to entertain a great contempt for them, and pronounce them unfit for the recognition of scientific merit."

"The Church has been reproached with endeavouring to appropriate to itself all those professorships in our Universities which are connected with science: it is however certain that the larger portion of these ill-remunerated offices have been filled by clergymen."

"It is difficult to pronounce on the opinion of the ministers of our Church as a body: one portion of them, by far the least informed, protests against anything which can advance the honour and the interests of science, because, in their limited and mistaken view, science is adverse to religion. This is not the place to argue that great question. It is sufficient to remark, that the best-informed and most enlightened men of all creeds and pursuits, agree that truth can never damage truth, and that every truth is allied indissolubly by chains more or less circuitous with all other truths; whilst error, at every step we make in its diffusion, becomes not only wider apart and more discordant from all truths, but has also the additional chance of destruction from all rival errors."

"It is not uninteresting to observe in society the opinions of its different classes respecting honours conferred on science. Military and naval men, especially the most eminent, feel that genius is limited by no profession, and themselves sympathizing with it, would gladly hail as brothers in the same distinction, the philosopher and the poet. With lawyers the case is reversed ; genius dwells not in their courts : industry and acuteness, monopolised by one absorbing professional subject, exclude larger views; and ribbons not being amongst the honoraria of their own profession, they reprobate their application to science. To this there are, however, some noble exceptions. Amongst the brightest ornaments, of their own profession, men are to be found of larger experience and more extended views than it often produces, who are themselves qualified to have become discoverers in other sciences. It is much to be regretted when such powers are applied to the mere administration, instead of to the reformation, of the laws of their country."

"The successful construction of all machinery depends on the perfection of the tools employed; and whoever is a master in the arts of tool-making possesses the key to the construction of all machines... The contrivance and construction of tools must therefore ever stand at the head of the ."

"Machinery of a very beautiful kind has been contrived for copying accurately, on a reduced or an enlarged scale, both medals and statues. The itself could not be justly excluded from a purely industrial exhibition, if, placed in the centre of a series diminishing on the one side to a statuette of a foot high, and increasing on the other to a figure double her own height. Such a series, though fairly introduced as an illustration of industrial art, would, indeed, itself be highly interesting to the fine arts, as exhibiting the effect of change of magnitude, when the proportions remain identical."

"In the making both of lace and of statues, the to the artists can only be reduced by producing a larger number of them through more extended education. The expense of the raw material is small in both. The expense of labour in lacemaking is very large, and it is perhaps considerable also in sculpture. The discovery of more convenient localities yielding marble, may make some diminution in its cost; and the improved manufacture of thread may slightly reduce the price of lace. A reduction in the price of labour may to a very moderate extent reduce the cost of the raw material of both. But it is evident that any very great reduction is not to be expected. Let us now contrast this possible reduction with the past history of some industrial art. The plain made at , called patent net, will supply us with a good example. In the year 1813 that lace was sold in the piece at the rate of 218. a-yard. At the present time lace of the same kind, but of a better quality, is sold under the same circumstances at 3d. per yard. Thus, in less than forty years the price of the industrial produce has diminished to one eighty-fourth part of its original price."