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Gregory Chaitin
7 quotes
“...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!”
Gregory Chaitin (born 1947) first seen 1999 wikiquote, CC BY-SA 4.0 source
Recorded in: 1999 Lecture—"A Century of Controversy over the Foundations of Mathematics" at U. Massachusetts at Lowell, quoted in p. 15
“At first it might seem that quantum mechanics (QM), which began with Einstein's photon as the explanation for the photoelectric effect in 1905, goes further in the direction of discreteness. But the wave-particle duality discovered by de Broglie in 1925 is at the heart of QM, which means that this theory is profoundly ambiguous regarding the question of discreteness vs. continuity. QM can have its cake and eat it too, because discreteness is modeled via standing waves (eigenfunctions) in a continuous medium.”
Gregory Chaitin (born 1947) first seen 2004 wikiquote, CC BY-SA 4.0 source
Recorded in: How real are real numbers? arXiv:math/0411418v3 (2004). p. 12
“Are there mathematical propositions for which there is a considerable amount of computational evidence, evidence that is so persuasive that a physicist would regard them as experimentally verified?”
Gregory Chaitin (born 1947) first seen 2004 wikiquote, CC BY-SA 4.0 source
Recorded in: Thoughts on the Riemann hypothesis The Mathematical Intelligencer (December 2004) vol. 26, issue 1, pp. 4–7, quote on p. 4
“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.”
Gregory Chaitin (born 1947) first seen 2005 wikiquote, CC BY-SA 4.0 source
Recorded in: Epistemology as information theory: From Leibniz to Omega." arXiv preprint math/0506552 (2005). p. 3
“I'm interested in the computer as a new idea, a new and fundamental philosophical concept that changes mathematics, that solves old problems better and suggests new problems, that changes our way of thinking and helps us to understand things better, that gives us radically new insights...”
Gregory Chaitin (born 1947) first seen 2006 wikiquote, CC BY-SA 4.0 source
Recorded in: Meta Maths!: The Quest for Omega. Vintage Books (2006). p. 11
“[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.”
Gregory Chaitin (born 1947) first seen 1932 wikiquote, CC BY-SA 4.0 source
Recorded in: Doing Mathematics Differently" Inference (Feb 2016) Vol. 2, No. 1. Ref: Hermann Weyl, The Open World: Three Lectures on the Metaphysical Implications of Science (1932)
“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.”
Gregory Chaitin (born 1947) wikiquote, CC BY-SA 4.0 source