WHICH SCIENCE FINDS DISQUIETING IT IGNORES (via Ed Bush):

Gödel and Einstein: Friendship and Relativity (PALLE YOURGRAU, 12/17/04, Chronicle of Higher Education)

Washed up onto America's shores by the storm of Nazism that raged in Europe in the 1930s, the two men awakened to find themselves stranded in the same hushed academic retreat, the Institute for Advanced Study, the most exclusive intellectual club in the world, whose members had only one assigned duty: to think. But Gödel and Einstein already belonged to an even more exclusive club. Together with another German-speaking theorist, Werner Heisenberg, they were the authors of the three most fundamental scientific results of the century.

Each man's discovery, moreover, established a profound and disturbing limitation. Einstein's theory of relativity set a limit -- the speed of light -- to the flow of any information-bearing signal. And by defining time in terms of its measurement with clocks, he set a limit to time itself. It was no longer absolute but henceforth limited or relative to a frame of measurement. Heisenberg's uncertainty principle in quantum mechanics set a limit on our simultaneous knowledge of the position and momentum of the fundamental particles of matter. This was not just a restriction on what we can know: For Heisenberg it signified a limit to reality. Finally, Gödel's incompleteness theorem -- "the most significant mathematical truth of the century," as it would soon be described in a ceremony at Harvard University -- set a permanent limit on our knowledge of the basic truths of mathematics: The complete set of mathematical truths will never be captured by any finite or recursive list of axioms that is fully formal. Thus, no mechanical device, no computer, will ever be able to exhaust the truths of mathematics. It follows immediately, as Gödel was quick to point out, that if we are able somehow to grasp the complete truth in this domain, then we, or our minds, are not machines or computers. (Enthusiasts of artificial intelligence were not amused.)

Einstein, Gödel, Heisenberg: three men whose fundamental scientific results opened up new horizons, paradoxically, by setting limits to thought or reality. Together they embodied the zeitgeist, the spirit of the age. Mysteriously, each had reached an ontological conclusion about reality through the employment of an epistemic principle concerning knowledge. The dance or dialectic of knowledge and reality -- of limit and limitlessness -- would become a dominant theme of the 20th century. Yet Gödel's and Einstein's relation to their century was more uneasy than Heisenberg's.

The zeitgeist took root most famously in quantum mechanics. Here Gödel and Einstein would find themselves in lonely opposition to Heisenberg, who, on the wrong side in the war of nations, chose the winning team in the wars of physics. Heisenberg was champion of the school of positivism, known in quantum physics as the Copenhagen interpretation, in deference to Heisenberg's mentor, Niels Bohr. What had been a mere heuristic principle in Einstein's special relativity -- deducing the nature of reality from limitations on what can be known -- became for Heisenberg a kind of religion, a religion Gödel and Einstein had no wish to join. Some, however, claimed to see in Gödel's theorem itself an echo of Heisenberg's uncertainty principle. The group did not include Gödel. [...]

If Einstein succeeded in transforming time into space, Gödel would perform a trick yet more magical: He would make time disappear. Having already rocked the mathematical world to its foundations with his incompleteness theorem, Gödel now took aim at Einstein and relativity. Wasting no time, he announced in short order his discovery of new and unsuspected cosmological solutions to the field equations of general relativity, solutions in which time would undergo a shocking transformation. The mathematics, the physics, and the philosophy of Gödel's results were all new. In the possible worlds governed by these new cosmological solutions, the so-called "rotating" or "Gödel universes," it turned out that the space-time structure is so greatly warped or curved by the distribution of matter that there exist timelike, future-directed paths by which a spaceship, if it travels fast enough -- and Gödel worked out the precise speed and fuel requirements, omitting only the lunch menu -- can penetrate into any region of the past, present, or future.

Gödel, the union of Einstein and Kafka, had for the first time in human history proved, from the equations of relativity, that time travel was not a philosopher's fantasy but a scientific possibility. Yet again he had somehow contrived, from within the very heart of mathematics, to drop a bomb into the laps of the philosophers. The fallout, however, from this mathematical bomb was even more perilous than that from the incompleteness theorem. Gödel was quick to point out that if we can revisit the past, then it never really "passed." But a time that fails to "pass" is no time at all.

Einstein saw at once that if Gödel was right, he had not merely domesticated time: He had killed it. Time, "that mysterious and seemingly self-contradictory being," as Gödel put it, "which, on the other hand, seems to form the basis of the world's and our own existence," turned out in the end to be the world's greatest illusion. In a word, if Einstein's relativity theory was real, time itself was merely ideal. The father of relativity was shocked. Though he praised Gödel for his great contribution to the theory of relativity, he was fully aware that time, that elusive prey, had once again slipped his net.

But now something truly amazing took place: nothing. Although in the immediate aftermath of Gödel's discoveries a few physicists bestirred themselves to refute him and, when this failed, tried to generalize and explore his results, this brief flurry of interest soon died down. Within a few years the deep footprints in intellectual history traced by Gödel and Einstein in their long walks home had disappeared, dispersed by the harsh winds of fashion and philosophical prejudice. A conspiracy of silence descended on the Einstein-Gödel friendship and its scientific consequences. [...]

Only in the last few years has this child, the Gödel universe, received any glimmer of recognition. This comes from the redoubtable Stephen Hawking. Revisiting the rotating Gödel universe, Hawking was moved to deliver the highest of compliments. So threatening did he find Gödel's results to the worldview of sober physicists that he put forward what amounts to an anti-Gödel postulate. If accepted, Hawking's famous chronology-protection conjecture would precisely negate Gödel's contribution to relativity. So physically unacceptable did Hawking find conclusions like Gödel's that he felt compelled to propose what looks like an ad hoc modification of the laws of nature that would have the effect of ruling out the Gödel universe as a genuine physical possibility.

Hawking's attempt to neutralize the Gödel universe shows how dangerous it is to break the conspiracy of silence that has shrouded the Gödel-Einstein connection. Not only does this mysterious silence hide from the world one of the most moving and consequential friendships in the history of science, it also keeps the world from realizing the true implications of the Einstein revolution. It is one thing to overturn, as Einstein did, Newton's centuries-old conception of the absoluteness and independence of space and time. It is quite another to demonstrate that time is not just relative but ideal.

Yesterday, on NPR Morning Edition Saturday, there was an amusing discussion of the concept of infinity with the mathematician Keith Devlin, in which he mentioned, just in passing, that String Theory is an attempt to banish infinity from physics. If the Einstein/Godel relationship is ignored, that's nothing compared to the ferocity with which the implications of Heisenberg's insight is denied. And, of course, Rationalists run like Frenchmen from the implications of the totality of science and the application of reason to Reason.

Posted by Orrin Judd at December 19, 2004 10:49 AM