Word: formalisms
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Dates: during 1990-1999
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...dawned on a few insightful souls, Godel foremost among them, that this way of looking at things opened up a brand-new branch of mathematics--namely, metamathematics. The familiar methods of mathematical analysis could be brought to bear on the very pattern-sprouting processes that formed the essence of formal systems--of which mathematics itself was supposed to be the primary example. Thus mathematics twists back on itself, like a self-eating snake...
...thinking of theorems as patterns of symbols, Godel discovered that it is possible for a statement in a formal system not only to talk about itself, but also to deny its own theoremhood. The consequences of this unexpected tangle lurking inside mathematics were rich, mind-boggling and--rather oddly--very sad for the Martians. Why sad? Because the Martians--like Russell and Whitehead--had hoped with all their hearts that their formal system would capture all true statements of mathematics. If Godel's statement is true, it is not a theorem in their textbooks and will never, ever show...
...upshot of all this is that the cherished goal of formalization is revealed as chimerical. All formal systems--at least ones that are powerful enough to be of interest--turn out to be incomplete because they are able to express statements that say of themselves that they are unprovable. And that, in a nutshell, is what is meant when it is said that Godel in 1931 demonstrated the "incompleteness of mathematics." It's not really math itself that is incomplete, but any formal system that attempts to capture all the truths of mathematics in its finite set of axioms...
...later years Godel grew paranoid about the spread of germs, and he became notorious for compulsively cleaning his eating utensils and wearing ski masks with eye holes wherever he went. He died at age 72 in a Princeton hospital, essentially because he refused to eat. Much as formal systems, thanks to their very power, are doomed to incompleteness, so living beings, thanks to their complexity, are doomed to perish, each in its own unique manner...
...Shockley left the electronics industry and accepted an appointment at Stanford. There he became interested in the origins of human intelligence. Although he had no formal training in genetics or psychology, he began to formulate a theory of what he called dysgenics. Using data from the U.S. Army's crude pre-induction IQ tests, he concluded that African Americans were inherently less intelligent than Caucasians--an analysis that stirred wide controversy among laymen and experts in the field alike...