Word: turn
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Dates: during 1990-1999
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...imagine that we wanted to talk about the general nature of all theorems of mathematics. If we look in the Martians' textbooks, all such theorems will look to our eyes like mere numbers. And so we might develop an elaborate theory about which numbers could turn up in Martian textbooks and which numbers would never turn up there. Of course we would not really be talking about numbers, but rather about strings of symbols that to us look like numbers. And yet, might it not be easier for us to forget about what these strings of symbols mean...
...trick is to imagine studying what might be called "Martian-producible numbers" (those numbers that are in fact theorems in the Martian textbooks), and to ask questions such as, "Is or is not the number 8030974 Martian-producible (M.P., for short)?" This question means, Will the statement '8030974' ever turn up in a Martian textbook...
...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...
...they shared a certain wanderlust, an indifference to boundaries. Crick had migrated from physics into chemistry and biology, fascinated by the line "between the living and the nonliving." Watson had studied ornithology, then forsook birds for viruses, and then, doing postdoctoral work in Europe, took another sharp career turn...
...sham science of "racial hygiene." In 1943 he became medical chief at Auschwitz-Birkenau, where he sent more than 400,000 non-Aryan prisoners to the gas chambers. On the side, he engaged in all manner of experimental butchery--dripping chemicals into prisoners' eyes to see if he could turn them a more Reich-pleasing blue, exposing others to infectious diseases to watch how different races respond to pathogens...