Mathematicians From England

"SPIN... is a... curious axiom. If you take one of these particles and ask it what... it's squared component of spin is, in three... mutually perpendicular directions, it always happens that two of the answers are 1, and one of them is 0. That's most mysterious... and... it's not possible to solve this puzzle. ...[W]e have these 33 directions, and it's not possible to assign 0s and 1s to them, subject to that condition... the 1-0-1 rule. ...[T]he particle is acting somewhat like a little boy ...making up its mind as it goes along. It doesn't stop it from giving answers, but it does stop the answers from being determined ahead of time, and that's the guts of it."

"TWIN... I just described... Even remotely separated particles... a condition in which, if asked the same questions, they will give the same answers. If they're not asked the same questions, all bets are off. ...We call that Twinning the particles ...an instance of ...entanglement."

"[T]he strangest contribution of quantum mechanics to this discussion is the EPR paradox. ...That's an essential contribution to our theorem too. ...Despite the fact that information can't be transmitted faster than the speed of light, ...remotely separated events can be correlated ...and this is the content of our TWIN axiom, you can put two particles into a... singleton state... the angular momentum of the pair of particles is zero... [B]y the conservation of angular momentum... if you measure the angular momentum of this in any direction, then for the angular momentum of the other you get the negative answer, but... we're going to square it, that means... the squared component of spin is the same... [T]hese particles have been sort of hypnotized. If you ask... they will give the same answer... like I and my twin brother... [T]he funny thing is, even though the proves that the answers do not exist ahead of time, the equality of the answers can exist..."

"If I ask this question of this particle, and... my colleague on Mars asks the same question of the other particle, then even though those questions aren't determined, ...they don't exist ahead of time, ...they'll give the same answer. ...It's meaningless to compare the times at which we do it, because time is not an invariant concept. ...[I]f my colleague on Mars has asked the same question, or ...will ask the same question... or if he's now asking the same question... he'll get the same answer. That is the EPR paradox, the fantastic thing that Einstein thought would disprove quantum mechanics. It is... perfectly consistent, but ever since it was discovered people have been trying to explain it away... because it's hard to believe."

"[R]elativity is an important part of the game."

"[Y]ou've probably heard of the theory of relativity. ...Most of us have heard the assertion that you can't transmit information faster than the speed of light. Most of us... hear it on authority only. We don't really understand why not. ...The reason is ...there's no absolute notion of time. Time depends on which coordinate system you're using... on your frame of reference... As seen from one frame of reference, event A can be before event B and as seen from another frame of reference, event B came first. The world [universe] hasn't got a standard definition of time."

"[T]he proof of the Free will theorem... It's ...plausible ...from the start. ...Let's see ...the axioms SPIN, FIN and TWIN."

"Don't think... I believe unreservedly in quantum mechanics, but I'm not going to change my mind before there's some reason..."

"I have a very simple way of explaining relativity theory... and if you follow that you'll understand how... it's impossible to... transmit information faster than the speed of light. The reason is, if you could, then seen from another person's point of view, you'd transmit information backward in time... [W]e would know the result of somebody's experiment before they performed it, and if they have free will... you'd know the result of their choice before they've made it, and they're free to make another one."

"[S]uppose I had a twin brother... [M]y sisters would have had a much better chance... [T]hey could... interrogate us separately... Then we can't change the object. ...Without transmitting information ...we couldn't win... [T]hat's what manages to happen in the particle case. ...[T]his ...Simon also thought of a long time ago.... but he didn't... deduce the ."

"The Free Will Theorem [s]ays roughly, that "if... humans have free will, then so do the elementary particles outside us. Uses three axioms SPIN, FIN, (or MIN) and TWIN." I only mean this in a very restrictive sense. I don't suppose much free will. The supposition is only that the human can choose which one of 33 buttons he want to press. ...[T]his choice affects the future history of the world in a minor way. ...We know that button was pressed ...before it was pressed we didn't know which one it was and ...a human experimenter has that much free will. That's the only amount of free will I suppose. We suppose nothing about these deep questions of moral responsibility and so on."

"[T]his Kochen-Specker paradox ...what it does ...[T]here's a problem in physics ...the measurement problem ...that's a wrong description. There's ...measuring the squared spin of a spin one particle. ...Let's say "measuring the spin" or measuring the [squared] component of spin ...of a spin one particle in a certain direction."

"[Robert Nozick]: Philosophical Explanations "...it would be foolhardy ...to place ...significant weight upon the necessity or even truth of SR. ...Moreover theorems show that any theory that retains certain features of Quantum Mechanics also will not satisfye SR." SR is Leibniz's . ...[T]here's a reference to the Kochen-Specker paper ...in which Kochen, my co-author, and Specker ...both logicians, not physicists ...prove this ...From our point of view this is not enough. The is not as strong as the new theorem."

"[S]omebody said, ..."We have to believe in free will. There's no choice." That's a nice ...sort of paradox ..."

"Dennis Overbye ...says ~everything we know of science convinces me ...that the world is deterministic, nevertheless I cling to the illusion of free will.~ (I'm not quoting his exact words.) ..~I can't run my life without this illusion.~ Some people have described it as a necessary illusion. We don't think it's an illusion ...It's not ...We think we have free will."

"The rise of determinism, it's just a consequence of the fact, science advanced tremendously, as a result mostly of... Newton and people like Laplace. They could determine things, but it's only the large scale science that ...seems ...deterministic. This century it's not been so."

"[T]he arguments that suggest that we have free will can't be turned into logical deductive proofs. There's nothing wrong with that. If you argue in a court of law... we ...conclude, although we haven't got a proof, that probably the culprit was Mr. X."

"There isn't anything really, in the last resort that isn't inductive. Even the laws of deductive logic have been established only by induction. ...We can't use deductive logic ..."

"The consistency of determinism doesn't mean that it's true. Mathematicians are accustomed to have consistency proofs. They say nothing about truth. They just say something about what might be true."

"Here's a particle, and I... direct my finger at it... and ask... What's it's spin in that direction? ...This particle is quantized. ...[I]t can only give two answers ...1 and 0. If I hadn't put that word squared in it could give three answers, 1, -1 and 0 ...Initially, it was... obvious... to believe that this concept existed before you measured it, but that was found not to be so. ...[W]hat the says is that it can't exist before you measure it... because there's no consistent set of answers to every question."

"One consequence of the ... plus the assumption we actually have free will, is that even in the... inanimate world of particles, it's not true, this . A particle does one thing or another, and there's no reason... There's nothing in the previous history of the universe which tells it what to do."

"Laplace... wrote Mécanique céleste discussing the motion of the planets. ...[O]ne ...reason why ...determinacy got its ...impetus from the development of science, was that Newton's theory of gravitation ...was entirely deterministic. It left no room for freedom. ...Laplace, who did a lot of work on Newtonian ...theory says ...An intellect ...[or] intelligence, which knew ...where all the particles were at some moment and how fast they were moving, and so on, that every single thing could be known to that intelligence, provided a ...good calculator. ...It could reason out exactly what was going to happen in the future. ...It's the strongest ...assertion of determinism in the scientific literature. I don't believe it for one moment..!"

"The philosophical consequences of the General Theory of Relativity are perhaps more striking than the experimental tests. As Bishop Barnes has reminded us, "The astonishing thing about Einstein's equations is that they appear to have come out of nothing." We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates and also that the geometry of space-time is Riemannian. From this exiguous basis, formulae of gravitation more accurate than those of Newton have been derived. As Barnes points out..."

"In general, Protestants of that era [late 1930s] did not object to state involvement in reproductive control; indeed, some of the Protestant Churches had originated as extensions of state power in the first place. Many protestants embraced eugenics as part of a broader trend towards acceptance of the secularization of modern societies. ...Many Protestant theologians were outspoken eugenicists, and some even supported eugenic sterilization: in Britain, William Ralph Inge, the dean of St. Paul's and Ernest William Barnes, the Bishop of Birmingham; in Germany, Hans Harmsen... in Romania, Alfred Csallner... Such direct involvement with eugenics demonstrates that a religiously sanctioned programme of human improvement was possible."

"With a view to recalling Clausen's identity, we begin by introducing the generalized Gaussian and Clausenian hypergeometric function defined, in the notations of Leo Pochhammer and Ernest William Barnes... as already pointed out by Barnes, the generalized hypergeometric function pFq originated with Clausen and was studied, among others, by Johannes Karl Thomae, Édouard Jean-Baptiste Goursat, and Pochhammer whose voluminous work on the subject provides a detailed development of the theory."

"[L]ots of philosophical discussions about free will are concerned with the question of assigning moral responsibility. ...If the judge is a determinist, I might argue it was all determined. I just had to do it. I'm not responsible. ...We're not concerned with assigning moral responsibility... I want you to think of free whim..."

"Barnes was notorious for delivering what the press called his "guerilla sermons," in which he pointed out the need for the church to be honest in admitting how much of its traditional dogma would have to be abandoned if evolution theory was accepted. Even a progressionist, teleological evolutionism required a reinterpretation of the doctrine of original sin. To begin with, Barnes said little about the actual process of evolution, but he seems to have assumed that it was purposeful and aimed at the production of higher mental states. In 1930, though, he obtained a copy of R. A. Fisher's Genetical Theory of Natural Selection and began a correspondence with Fisher, who had studied under him while a student at Cambridge. Barnes was one of the few clergymen who could actually understand Fisher's mathematics (although even he admitted that it was hard going)... He did not concede that the selection theory offered a complete explanation, and he continued to believe that evolution was intended to produce beings with higher mental and spiritual qualities, but he was now aware that the more simpleminded forms of teleology were unacceptable."

"We see in man three elements; the material body, the life principle and the element of human personality. The last has only slowly reached its present complexity and is still far from the power and perfection that we can imagine it will some day possess."

"Man is what he is, because a spiritual element has entered into, and taken possession of, animal consciousness. This spiritual element is not, according to Christian teaching, divine: but it is capable of entering into relations with God. It can perceive Him: in thought, it can reason as to His nature and actions: in will and feeling, it can serve and love Him, or disobey and fear Him. Such activity shows itself in what we call the working of conscience."

"There has been the assumption that men are finite spirits. They are, that is to say, not only animals with a brief terrestrial existence, but in them is an element which comes from, and belongs to, the spiritual world. This world we postulate to be the world of eternal reality, of God; and we assume that in it whatever is of God, the things that are good, beautiful and true, will exist for ever with Him. We have then, to justify our belief that, because such God-like qualities exist in human personality, that personality will survive the destruction of the body."

"The Roman Catholics were already prominent in the debate on abortion in Britain in the 1930s. It is notable, for example, that only two religious groups were keen to give evidence before the Inter-Departmental Committee in Abortion between 1937 and 1939 or sent written statements to the Committee. One was the Modern Churchmen's Union, and in particular its most prominent supporter, though not a member, Ernest William Barnes, the Anglican Bishop of Birmingham, which was concerned to advance the cause of abortion on eugenic grounds, and the other was the Roman Catholics... No representatives of the Protestant Nonconformist Churches took part or made statements (Report of the Inter-Departmental Committee 1939)"

"I believe, and most people believe until they are educated out of this belief, that we are... free."

"Revelation can be supplemented by reason. Christ Himself gave reasons for His belief, and put in modern form, these reasons are, to my mind, conclusive. You remember the passage in the earliest Gospel: "But as touching the dead, that they are raised; have ye not read in the book of Moses, in the place concerning the bush, how God spake unto him, saying, I am the God of Abraham, and the God of Isaac, and the God of Jacob? He is not the God of the dead, but of the living: ye do greatly err" (Mark xii, 26 R.V.) Herein, in a form adapted to Jewish thought is "the one great argument which has made most sincere believers in God believers in Immortality also."

"[P]articles making choices... seems to involve deliberation. ...We are not pretending particles are conscious..."

"The conclusion seems to be irresistible that such laws of nature as the principle of conservation of energy, the principle of conservation of momentum and the law of gravitation are necessary consequences of our modes of measurement. They are, in fact, elaborately disguised identities which could have been predicted a priori by a being of sufficiently powerful analytical insight who fully understood all that is implied in the way we measure space-time intervals."

"The astonishing thing about Einstein's equations is that they appear to have come out of nothing."

"Our own attitude to intercourse with "spirits" must be determined not by the authority of great teachers of the 13th or any other century, but by our examination in the light of the best secular knowledge of our time of the revelation of spiritual truth given by Christ."

"A perfectly evil human society is unthinkable: it would be self-destructive. We therefore deny that any society of absolutely evil spirits could be permanent. Evil in short, cannot be a unifying spiritual principle: to put it colloquially, there must be some good in the Devil or he must ultimately destroy himself. It is certain that the Devil cannot be the creative source of evil in the same way that God is the creative source of good."

"[W]hen... non-predictivity of quantum mechanics was discovered, it came as a great surprise. People tried to explain it away. ...Many ...invented larger theories. ...Nobody has succeeded in making one of these theories relativistically invariant, and physics appears to be relativistically invariant. ...Physicists have believed ...in the result that we're proving for a long time. It's no surprise. "I knew all that," they say. However, what they didn't know was that it can be deduced in this very precise, logical fashion, from so little information... that is not at all contentious. ...[T]hese 3 axioms ...they're routine, they're accepted ...They follow from quantum mechanics and relativity. There's nothing dubious about them ...and that's all we need... [T]he original deductions... [of] quantum mechanics... used more. They used all sorts... and some... were... pretty poorly understood..."

"He is Archimedes, Mick Jagger, Salvador Dalí, and Richard Feynman, all rolled into one. He is one of the greatest living mathematicians, with a sly sense of humour, a polymath’s promiscuous curiosity, and a compulsion to explain everything about the world to everyone in it."

"There are many varieties of . ...It says that there's nothing incompatible about determinism... and free will. ...This is from a dispute between Hobbes and.... Archbishop Bramhall... "A man was free, in those things... were in his power, to follow his will, but... he was not free to will..." The will was determinate, but that he was free. ...It's not contradictory, although it looks it at first sight..."

"[T]he last lecture is going to be about the consequence of our ... Descartes'... disconnected determinism won't work. ...That's it. It's gone. Leibniz's won't work. It's gone."

"Descartes... his type of determinism is only partial. I call it disconnected... that the physical world and... our bodies, but not our minds operate mechanically... We're robots, but the mind is different... that "The will is by its nature so free that it can never be constrained." This is normally called Descartes' dualism... mind, soul or spirit, and matter... [M]atter operates according to one set of laws, and mind or spirit... to another."

"Physicists... have seen lots of instances of people... without... qualifications in physics, and presenting some... loony theory... and they don't read it. ...[W]e had this thing in mathematics once. People... thought they'd proved Fermat's Last Theorem... Eventually somebody did, but he was a... distinguished... high-powered mathematician. I'm... prepared for the fact... that physicists, especially ones that don't read our paper, don't believe it. They think it's just another... of those strange things. However, it's... better than that. ...I hope that the physicists stay and... learn something..."

"I'm going to present arguments... to strongly support... that we do... have free will, but not... to prove it at the deductive level."

"Descartes' dualism... is explicitly contradicted by our theorem."

"Human experience has pronounced "black magic" a delusion. Its practice is criminal folly: criminal because its objective is evil, folly because the means employed are futile."

"In many respects, this is not in any way an unorthodox opinion. ...Physicists have lived with these paradoxes ...for 80 years now. They have been accustomed to the fact that quantum mechanics is not a totally predictive theory, and they've proved long ago that no extension of quantum mechanics can be. This is not a defect... It's not a temporary defect, anyway. No extension of quantum mechanics can recover... total predictivity. From our point of view that's... obvious. ...[N]o correct theory can predict what the particle is going to do before it's made its decision... while it's still free to do something else. ...[I]t's not to be seen as a defect in quantum mechanics that it doesn't predict. It's a merit. ...You shouldn't expect to be able to predict things."

"Although he was trained in mathematics and was not a biblical scholar... Barnes, undertook to write a book about the origins of the Christian religion. Published in 1947, The Rise of Christianity caused a stir because it was so frankly dismissive of traditional Christian dogma, especially the miraculous. In this book, for example, Barnes calls the birth stories "edifying legend." He observes that the roots of the story of the Virgin Birth are "pagan." He questions the dogma of the Logos—the eternal word incarnate in this man, Jesus—set forth in the first chapter of John's Gospel. And he denies the bodily resurrection of Christ. Like Thomas Jefferson, he admires Jesus' character and teaching."

"He'd been working with... Jim Ax for two decades on a theory that is now contradicted by... [our] . ...I admire Simon tremendously."