Academics From The United Kingdom

"In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, "How many arbitrary parameters did you use for your calculations?" I thought for a moment about our cut-off procedures and said, "Four." He said, "I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." With that, the conversation was over."

"The laws of nature are constructed in such a way as to make the universe as interesting as possible."

"Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists."

"The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design."

"The public has a distorted view of science, because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries. (New York Review of Books, 2011)"

"As we look out into the Universe and identify the many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the Universe must in some sense have known that we were coming."

"I have felt it myself. The glitter of nuclear weapons. It is irresistible if you come to them as a scientist. To feel it's there in your hands, to release this energy that fuels the stars, to let it do your bidding. To perform these miracles, to lift a million tons of rock into the sky. It is something that gives people an illusion of illimitable power, and it is, in some ways, responsible for all our troubles — this, what you might call technical arrogance, that overcomes people when they see what they can do with their minds."

"Thirty-one years ago [1948], Dick Feynman told me about his "sum over histories" version of quantum mechanics. "The electron does anything it likes," he said. "It just goes in any direction at any speed, forward or backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function." I said to him, "You're crazy." But he wasn't."

"I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce."

"It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex."

"The whole point of science is that most of it is uncertain. That's why science is exciting--because we don't know. Science is all about things we don't understand. The public, of course, imagines science is just a set of facts. But it's not. Science is a process of exploring, which is always partial. We explore, and we find out things that we understand. We find out things we thought we understood were wrong. That's how it makes progress. (2014 interview)"

"There is an imperialism that deserves all honor and respect — an imperialism of service in the discharge of great duties. But with too many it is the sense of domination and aggrandisement, the glorification of power. The price of peace is eternal vigilance."

": These have often been attributed to Thomas Jefferson, but also to Thomas Paine, Abraham Lincoln, and many others; Lord Denning in The Road to Justice (1988) states that the phrase originated in a statement of Irish orator John Philpot Curran in 1790: "It is the common fate of the indolent to see their rights become a prey to the active. The condition upon which God hath given liberty to man is eternal vigilance.""

"It is true— it has been already admitted— that the picture will not be universally recognized; but it has been suggested that the failure of recognition lies rather in the degeneracy of the faculty of seeing than in the misrepresentation of the vision to be seen. It may be also confessed that life often survives all the perversities of training. We cannot absolutely nullify the prodigality of nature, try as hard as we may. In spite of most careful management, untractable growths survive in the most provoking way, and intrude themselves into fields believed to be kept free from their presence. And sometimes it happens that the poor party managers have to accommodate themselves to the genius they curse."

"As for life within a Legislature,— who can tell how warped and bent and twisted, and accommodated to the exigencies of party struggle become the faculties of belief? Strong and courageous natures know it, and remain strong and courageous in spite of knowledge and practice; but the pliancy of man is beyond admiration, and is nowhere better seen than under the schooling of Parliament."

"What an education follows! It is really a fine comedy, though the players rarely know it. I am but a clumsy performer myself, and have to confess to incurable defects of training, so that I sometimes wonder I have not been hissed off the stage; still I have seen the performance through more than once or twice, and know something about it. Such tender and delicate adjustments and readjustments of convictions to keep the party balance sure! Such abundance of spoonmeat on the one hand, and such careful economy on the other of truths that may prove too strong for weak digestions! Such avowals of readiness to consider seriously any opinion, however obviously absurd, broached by a possible supporter! Such prompt denunciations of all the devices of an irreconcilable opponent!"

"The young man who is moved in any way to contemplate an entry into public life, whose creed is not in absolute inheritance from his fathers, learns first of all to understand that there are two great political organizations, with one of which he must associate himself, learning and echoing its catch-words, accepting its leadership, and steeping himself in the belief that in it are wisdom and truth while the other party is void of both. It is not everyone whose ductile mind takes him through this training, and a goodly number of up-growing men of not the worst promise for the future have to step aside."

"We may blunder on in spite of repeated miscalculations of the popular will. More penetrating and pernicious is the influence our ill-devised machinery has upon the character of our national life. It eats in and into it. It degrades candidates and electors alike. It does its worst to reduce to sterility of influence many of the best of the component elements of the people. The individuals survive, but with their political activity dead or dying, no opportunities of life and growth being afforded them. Finally it presents as an embodiment of the nation an assembly or assemblies into which none can enter who have not been clipped, and pared, and trimmed, and stretched out of natural shape and likeness to slip along the grooves of supply. A free press, free pulpits, and a free people outside help to correct what would otherwise become intolerable but press, pulpits and people, free as they are, work and live in strict limits of relation to the machinery established among them. The world revolves on its axis subject to the Constitution of the United States, and the most Radical newspaper man in London, if such there be, never lets his imagination range out of hearing of the Clock Tower."

"What a jolly awakening there will be some few years hence, when the inevitable argument of experience will show us a nation contradicting itself through the voices of its chosen representatives! The stupidest politician will sit up, rubbing his eyes. After all, facts are facts, and although we may quote one to another with a chuckle the words of the Wise Statesman, "Lies — damned lies — and statistics," still there are some easy figures the simplest must understand, and the astutest cannot wriggle out of. So we may be led to the serious consideration of change by the evolution of materials of conviction which those who run may read, though some who read may wish to run away from them."

"Alan Turing was the first to make a careful analysis of the potential capabilities of machines, inventing his famous "Turing machines" for the purpose. He argued that if any machine could perform a computation, then some Turing machine could perform it. The argument focuses on the assertion that any machine's operations could be simulated, one step at a time, by certain simple operations, and that Turing machines were capable of those simple operations. Turing's first fame resulted from applying this analysis to a problem posed earlier by Hilbert, which concerned the possibility of mechanizing mathematics. Turing showed that in a certain sense, it is impossible to mechanize mathematics: We shall never be able to build an "oracle" machine that can correctly answer all mathematical questions presented to it with a "yes" or "no" answer. In another famous paper Turing went on to consider the somewhat different question, "Can machines think?." It is a different question, because perhaps machines can think, but they might not be any better at mathematics than humans are; or perhaps they might be better at mathematics than humans are, but not by thinking, just by brute-force calculation power. These two papers of Turing lie near the roots of the subjects today known as automated deduction and artificial intelligence."

"It is customary... to offer a grain of comfort, in the form of a statement that some peculiarly human characteristic could never be imitated by a machine. ... I cannot offer any such comfort, for I believe that no such bounds can be set."

"We can only see a short distance ahead, but we can see plenty there that needs to be done."

"Presumably the child-brain is something like a note-book as one buys it from the stationer's. Rather little mechanism, and lots of blank sheets."

"Another simile would be an atomic pile of less than critical size: an injected idea is to correspond to a neutron entering the pile from without. Each such neutron will cause a certain disturbance which eventually dies away. If, however, the size of the pile is sufficiently increased, the disturbance caused by such an incoming neutron will very likely go on and on increasing until the whole pile is destroyed. Is there a corresponding phenomenon for minds, and is there one for machines? There does seem to be one for the human mind. The majority of them seem to be "sub-critical," i.e., to correspond in this analogy to piles of sub-critical size. An idea presented to such a mind will on average give rise to less than one idea in reply. A smallish proportion are super-critical. An idea presented to such a mind may give rise to a whole "theory" consisting of secondary, tertiary and more remote ideas. Animals minds seem to be very definitely sub-critical. Adhering to this analogy we ask, "Can a machine be made to be super-critical?""

"The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles."

"Machines take me by surprise with great frequency."

"I am not very impressed with theological arguments whatever they may be used to support. Such arguments have often been found unsatisfactory in the past. In the time of Galileo it was argued that the texts, "And the sun stood still... and hasted not to go down about a whole day" (Joshua x. 13) and "He laid the foundations of the earth, that it should not move at any time" (Psalm cv. 5) were an adequate refutation of the Copernican theory."

"I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted."

"If one wants to make a machine mimic the behaviour of the human computer in some complex operation one has to ask him how it is done, and then translate the answer into the form of an instruction table. Constructing instruction tables is usually described as "programming.""

"Suppose Mother wants Tommy to call at the cobbler's every morning on his way to school to see if her shoes are done, she can ask him afresh every morning. Alternatively she can stick up a notice once and for all in the hall which he will see when he leaves for school and which tells him to call for the shoes, and also to destroy the notice when he comes back if he has the shoes with him."

"A digital computer can usually be regarded as consisting of three parts: (i) Store. (ii) Executive unit. (iii) Control. ...The executive unit is the part which carries out the various individual operations involved in a calculation. ...It is the duty of the control to see that...[the table of] instructions are obeyed correctly and in the right order. ...A typical instruction might say—"Add the number stored in position 6809 to that in 4302 and put the result back into the latter storage position." Needless to say it would not occur in the machine expressed in English. It would more likely be coded in a form such as 6809430217. Here 17 says which of various possible operations [add] is to be performed on the two numbers. ...It will be noticed that the instruction takes up 10 digits and so forms one packet of information..."

"The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer."

"We are not asking whether all digital computers would do well in the game nor whether the computers at present available would do well, but whether there are imaginable computers which would do well."

"May not machines carry out something which ought to be described as thinking but which is very different from what a man does?"

"We do not wish to penalise the machine for its inability to shine in beauty competitions, nor to penalise a man for losing in a race against an aeroplane. The conditions of our game make these disabilities irrelevant."

"Can machines think?"... The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B... We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?"

"It is possible to invent a single machine which can be used to compute any computable sequence. If this machine \mathcal{U} is supplied with a tape on the beginning of which is written the S.D of some computing machine \mathcal{M}, then \mathcal{U} will compute the same sequence as \mathcal{M}."

"To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable."

"It will be useful to put... tables into a... standard form. ...The lines of the table are... of form m-config. | Symbol | Operations | Final m-config. In this way we obtain a complete description of the machine. ...This new description of the machine may be called the standard description (S.D). ...[W]e shall have a description of the machine in the form of an arabic numeral. The integer represented by this numeral may be called a description number (D.N) of the machine. The D.N determine the S.D and the structure of the machine uniquely. The machine whose D.N is n may be described as \mathcal{M}(n)."

"If an ɑ-machine prints two kinds of symbols, of which the first kind (called figures) consists entirely of 0 and 1 (the others being called symbols of the second kind), then the machine will be called a computing machine."

"In this paper I deal only with automatic machines, and will therefore often omit the prefix ɑ-."

"For some purposes we might use machines (choice... or c-machines) whose motion is only partially determined by the configuration... When such a machine reaches... ambiguous configurations, it cannot go on until some arbitrary choice has been made by an external operator. This would be the case if we were using machines to deal with axiomatic systems."

"[T]hese operations include all those which are used in the computation..."

"Some of the symbols written down will form the sequence of figures which is the decimal of the real number... being computed. The others are just rough notes to "assist the memory ". ...[O]nly ...these rough notes ...will be liable to erasure."

"[T]he m-configuration may be changed."

"The machine may also change the square which is being scanned, but only by shifting it one place to right or left."

"In some of the configurations in which the scanned square is blank... the machine writes down a new symbol on the scanned square: in other configurations it erases the scanned symbol."

"The "scanned symbol" is the only one of which the machine is... "directly aware". However, by altering its m-configuration the machine can effectively remember some of the symbols which it has "seen" (scanned) previously."

"The machine is supplied with a "tape" (the analogue of paper) running through it, and divided into sections (called "squares") each capable of bearing a "symbol"."

"We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q1, q2, ..., qK which will be called " m-configurations "."