June 09, 2005
A Talk with Rebecca Goldstein About Kurt GÖDEL
From Edge.org:
Gödel mistrusted our ability to communicate. Natural language, he thought, was imprecise, and we usually don't understand each other. Gödel wanted to prove a mathematical theorem that would have all the precision of mathematics—the only language with any claims to precision—but with the sweep of philosophy. He wanted a mathematical theorem that would speak to the issues of meta-mathematics. And two extraordinary things happened. One is that he actually did produce such a theorem. The other is that it was interpreted by the jazzier parts of the intellectual culture as saying, philosophically exactly the opposite of what he had been intending to say with it.
More here.
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Gödel mistrusted our ability to communicate. Natural language, he thought, was imprecise, and we usually don't understand each other. Gödel wanted to prove a mathematical theorem that would have all the precision of mathematics—the only language wi... [Read More]
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Comments
It is interesting that Kodel would have such a limited view of what can be expressed by language when a typical Webster's dictionary has about 100,000 entries, and most normal exposition likely does not use 10% of them. One wonders if his reservations were due to his own lack of vocabulary, a problem which hinders all of us. Another interesting question comes to mind upon reading this piece. Suppose only a single person in the world understands the proof of a theorem. Or suppose only 10 people in the world claim to "understand" a certain proof of some claims; or even 100 such people in the world. Does this then constitute proof even in a mathematical sense? And as a corollary, suppose it took a lifetime to "prove" that the square root of 2 is irrational; i.e., cannot be expressed as the ration of two integers. How many mathematicians or others would be willing to spend a lifetime "understanding" this? Would it be in mathematics textbooks, which would run to thousands or hundreds of thousands of pages? Obviously, not.
Isn't it a little like the person who claimed to have communicated with the dead? He said, upon being questioned about this, "Yes, I did communicate with them, but I am still waiting for the reply."
Here is a more mundane contribution professor Goldstein could make in a future novel: She could write a new novel, tangentially explaining in a "simple" way, the fairly recent "proof" of Fermat's Last Theorem, presumably "understood" by only a handful of people in the world, if that many. This is the theorem which went unsolved for centuries, that no solution to the equation exists in integers where x(n)+ y(n)= z(n), where x(n) means x to the nth power, and n is an integer greater than 2. Prizes had been offered for a solution. Most people believed this statement, made in the margin of Fermat's notebook, with the claim he had a "beautiful proof" but no room for it in the margin. In recent times, the claim had been subjected to thousands of numerical trials with no counterexample, but, of course, to mathematicians, this is not a proof.
Only physicists are "satisfied" with a few examples as "proof", as the few experiments purportedly "proving" the existence of quarks, hypothetical elementary particles with fractional electric charge, although no particles with fractional charge have every been documented, no quarks have been observed directly, which is the reason some physicists cooked up the concept of "quark confinement", to explain "why" they could not be observed and had not been observed after many serious attempts by various experimental physicists over the years, and finally, that no proton, neutron, or other meson, which are hypothetically "made" of quarks has been calculated convincingly from first principles, with some form of relativistic quantum mechanics, some form of force law for the quarks (which is not known) and the masses and properties of the mythological quarks themselves. In fact, much effort in this field has been made in the direction away from inventing more "elementary" objects the details of which are not understood and may never be understood, so that they act more like free parameters with esoteric names, like quarks. In fact, if in fact they do exist, as a number of the orthodox physicists working in government laboratories claim, what are they made of? That is a problem for another day.
Incidentially, Albert Einstein was also a close friend of Otto Warburg and sought to persuade Warburg not to participate in World War I. It was at a dinner with Otto Warburg and Albert Einstein in about 1925, that a young, unemployed, M.D. by the name of Hans Krebs, obtained, purely by "accident" a position in Warburg's laboratory in Germany, a position which would change his life forever, and he attributed it all to Otto Warburg; his later Nobel prize in medicine and his many years in England on the National Research Council. This would be another suggested subject for professor Goldstein to take up in another novel; i.e., the prejudice of the orthodoxy against Otto Warburg for NOT leaving Germany.
Posted by: Winfield J. Abbe | Jun 9, 2005 11:30:32 PM
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