Gödel and physics
"A logical paradox at the heart of mathematics and computer science turns out to have implications for the real world, making a basic question about matter fundamentally unanswerable."
I just love this sentence, published in "Nature". It raises (and somehow exposes the author's intuition about) one of the deepest questions in science: how are mathematics, logic, computer science, i.e. the formal sciences, on the one side, and the "real world" on the other side, related? What is the connection between math and reality? The author seems genuinely surprised that logic has "implications for the real world" (never mind that "implication" is a logical term), and seems to struggle with the idea that a counter-intuitive theorem by Gödel, which has been studied and scrutinized for 85 years, would also apply to equations in physics.
Unfortunately the fundamental question does not really get tackled: the work described here, as fascinating as it is, was an intentional, many year effort to find a place in the mathematical models used in physics where Gödel can be applied. They are not really discussing the relation between maths and reality, but between pure mathematics and mathematics applied in physics. The original deep question remains unsolved and will befuddle students of math and the natural sciences for the next coming years, and probably decades (besides Stephen Wolfram, who beieves to have it all solved in NKS, but that's another story).
Nature: Paradox at the heart of mathematics makes physics problem unanswerable
Phys.org: Quantum physics problem proved unsolvable: Godel and Turing enter quantum physics
AI is coming, and it will be boring
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