Part ISourceBy Gunnar Tomasson
04-17-2004
In his lead-off post in this thread, Roland Heap writes:
I also do not believe that the physical universe is reducable to simple equations and concepts. Am I alone in this?Comment:
No, you are not alone! – but there are few theoretical physicists who both (a) understand the reason why it is NOT so reducible and (b) have the guts to concede the point.
The reason for (a) is not lack of mathematical brains as distinct from the purely analytical kind with which the intellectually mature Einstein was endowed, as reflected, inter alia, in the implicit distinction which Einstein drew between his mature and immature self in this respect in an exchange between Heisenberg and himself, as reported by the former:
“But you don’t seriously believe,” Einstein protested, “that none but observable magnitudes must go into a physical theory?”
“Isn’t that precisely what you have done with relativity?” I asked in some surprise. “After all, you did stress the fact that it is impermissible to speak of absolute time, simply because absolute time cannot be observed; that only clock readings, be it in the moving reference system or the system at rest, are relevant to the determination of time.”
“Possibly I did use this kind of reasoning,” Einstein admitted, “but it is nonsense all the same. Perhaps I could put it more diplomatically by saying that it may be heuristically useful to keep in mind what one has actually observed. But on principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality, the very opposite happens. It is the theory which decides what we can observe.” (In ‘Physics and Beyond – Encounters and Conversations’, Harper Torchbooks, 1972, p. 63.)
As told in his autobiographical ‘My Philosophical Development’, it was only late in life that Bertrand Russell could bring himself “very reluctantly” to admit that mathematics is a pragmatic human rather than an eternal divine creation – although he still remembered his youthful delight in the contrary belief, he wrote, he now viewed it as nonsense.
Indeed, he was now persuaded that all mathematics is “tautology” as exemplified by the proposition that “a four-footed animal is an animal”. The curious thing about all this is why it took Russell so long to recognize and come to terms with the obvious – or so it had seemed to Wittgenstein as he parted philosophical ways with Russell decades earlier, and so it seemed to me soon after my initial encounter with the epistemological issues involved in the mid-1970s.
In this respect, it is morally certain that Russell was familiar with and must have reflected on the issues raised by Einstein in his 1921 statement on the heart of the matter which Jon Awbrey cited in his ‘All Liar, No Paradox’ thread some time ago as follows:
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. It seems to me,” Einstein added, “that complete clearness as to this state of things first became common property through the new departure in mathematics which is known by the name of mathematical logic or ‘Axiomatics’. The progress achieved by axiomatics consists in its having neatly separated the logical-formal from its objective or intutive content.”
Three years earlier, on the occasion of Max Planck’s sixtieth birthday in 1918, Einstein had emphasized that, in attempting to reduce the physical universe to simple equations and concepts, “the physicist has to limit himself very severely; he must content himself with describing the most simple events which can be brought within the domain of our experience; all events of a more complex order are beyond the power of the human intellect to reconstruct with the subtle accuracy and logical perfection which the theoretical physicist demands. Supreme purity, clarity, and certainty at the cost of completeness. But what can be the attraction of getting to know such a tiny section of nature thoroughly, while one leaves everything subtler and more complex shyly and timidly alone? Does the product of such a modest effort deserve to be called by the proud name of a theory of the universe?” (In ‘Ideas and Opinions’, Dell/Laurel Paperback, 1976, p. 221.)
The modern quest for a Theory Of Everything, I submit, is predicated on (a) the mistaken belief that mathematics is NOT a form of human language and, as such, differs from the verbal kind only in the precision of its tautological propositions, and (b) the identification of “Everything” with that subset of Everything “which can be brought within the domain of our experience” in the manner of experimental science.
A whiff of epistemological clarity would remedy (a) – a prospect which would seem to be alluded to by Prospero in Act IV, Sc. i of Shakespeare’s play, ‘The Tempest’:
“…And, like the baseless fabric of this vision, The cloud-capp’d towers, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve And, like this insubstantial pageant faded, Leave not a rack behind.”
The record shows that the intellectual myopia associated with (a) is not terminal; it is a different matter with the hubris which once made Stephen Hawking proclaim that the object of contemporary physical science was to make Man “master of the universe”.
Gunnar