Free Republic

If you travel two hours southeast of Fairfield County and 70 years back in time, you may come upon two old scientists taking a leisurely walk home from the Institute for Advanced Study in Princeton. You'd instantly recognize the one with the bushy mustache, suspenders and wild white hair — that's Albert Einstein. But who is that impeccably dressed, clean-shaven gentleman with the wire-rimmed glasses next to him? That's mathematician and philosopher Kurt Gödel. In Einstein's later years, he once confided to a friend that his own research "no longer meant much" and that he came into work only "to...

The Incomplete Gödel Gregory H. Moore Incompleteness: The Proof and Paradox of Kurt Gödel. Rebecca Goldstein. 296 pp. W. W. Norton, 2005. $22.95.A World Without Time: The Forgotten Legacy of Gödel and Einstein. Palle Yourgrau. x + 210 pp. Basic Books, 2005. $24.Such eminent 20th-century physicists as Albert Einstein, Niels Bohr and Werner Heisenberg are well known to almost all scientists, whether or not they happen to be physicists. Yet most scientists are unfamiliar with eminent mathematicians from the same period, such as David Hilbert (Germany) and Oswald Veblen (United States). A rare exception is John von Neumann (Hungary...

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...

A few weeks ago, I attended a philosophical debate on the merits of abortion. Shortly after the discussion began, I pointed out that this act destroyed a human person. "Do you have proof of that?" asked several members of the panel simultaneously. "Of course," I replied, "proof that cannot be controverted." "What proof would that be?" "The declaration of the dogma of the Immaculate Conception," I replied. "That's not proof!" they shouted. "Oh, but it is," said I, and proceeded to demonstrate how. In 1931, a Czech mathematician named Kurt Godel demonstrated that any logical system as advanced as arithmetic...

The Future According to Professor Paul Davies "Scientists have no doubt whatever that it is possible to build a time machine to visit the future". Since the publication of Einstein’s Special Theory of Relativity in 1905, few, if any, scientists would dispute that time travel to the future is perfectly possible. According to this theory, time runs slower for a moving person than for someone who is stationary. This has been proven by experiments using very accurate atomic clocks. In theory, a traveller on a super high-speed rocket ship could fly far out into the Universe and then come back...