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Mathematicians are coming up with s that they use in their actual mathematical research. And these, like , I think is the name of one of them ... the… - Gregory Chaitin
" "Mathematicians are coming up with s that they use in their actual mathematical research. And these, like , I think is the name of one of them ... these are actually like s that have been engineered in a way that they can actually be used by working mathematicians to check the work they're doing.
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About Gregory Chaitin
Gregory Chaitin (born 25 June 1947) is an Argentine-American mathematician, computer scientist, and author. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem.
Also Known As
Alternative Names:
Gregory J. Chaitin
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Chaitin
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Gregory John Chaitin
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Additional quotes by Gregory Chaitin
Why do I think that Turing's paper "On computable numbers" is so important? Well, in my opinion it's a paper on epistemology, because we only understand something if we can program it, as I will explain in more detail later. And it's a paper on physics, because what we can actually compute depends on the laws of physics in our particular universe and distinguishes it from other possible universes. And it's a paper on ontology, because it shows that some real numbers are uncomputable, which I shall argue calls into question their very existence, their mathematical and physical existence.
[A]ccording to Weyl, complexity is essential in understanding the concept of a law of nature. If laws of nature may be arbitrarily complex, he argued, the very concept... becomes vacuous. What difference would remain... if the laws meant to explain them were as complex as the phenomena they are meant to explain?
Laws of nature must be simple.
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...Once you entomb mathematics in an artificial language à la Hilbert, once you set up a completely formal axiomatic system, then you can forget that it has any meaning and just look at it as a game that you play with marks on paper that enable you to deduce theorems from axioms. You can forget about the meaning of the game, the game of mathematical reasoning, it's just combinatorial play with symbols! There are certain rules, and you can study these rules and forget that they have any meaning!
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