Comments by "Lepi Doptera" (@lepidoptera9337) on "Numberphile2" channel.

  1. If it allows them to calculate the low energy string spectrum, then yes. It does not necessarily lead to a practical result because of the string landscape. Unless it allows us to pick one specific version of the theory out of the 10^500 (or whatever) possible ones, the spectrum is still not uniquely determined. That problem will most likely not go away anymore than the equivalent problem in quantum field theory. Why is the low energy spectrum in QFT U(1)xSU(2)xSU(3) and not something else? We don't know. Well, actually, it's not even that if you are precise. You, as in your body, are a peak in the low energy spectrum of QFT. So is a water molecule, a goat, third avenue in New York and the star Beta Orionis. "Every possible thing" in physics is such a peak. We aren't calculating any of these solutions from first principles. We are happy to stop at the em field, electrons, muons, neutrinos, quarks etc., so we are basically cutting ourselves off at one massless and one solution that is a fraction of an eV (the neutrinos). And technically we can't calculate the locations of any of these peaks in QFT, either. We a simply fitting measurements to them. So it's not like that string theory can't so something that QFT can. They are pretty much equally "powerless" at the moment, it just gets misrepresented in the public discussion. (And no, I don't think string theory is the correct approach, either, I am just trying to qualify a little better what "theory" means in this sector.).
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  2.  @Muhahahahaz  I have a felling that might be the catch. The verification of that process might be harder than the original proof. Maybe my intuition here is wrong, but the constructions seems to classify all theorems and proofs into an infinite set of equivalence classes. What we are given is the equivalence class but not which particular proof in that class it is. Since the number of proofs in each equivalence class is infinite, knowing the class is useless.
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  3. What does? String theory? What do you mean by "mathematical foundations"? That one can't give an axiomatization? Of course one can. At the end of the day all of these things flow back to Kolmogorov and partitions of unity. This one supposedly obeys general relativity in the low energy limit, whereas quantum field theory is only required to obey special relativity.
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  4. It's simple but not efficient. He said that the map might be humongous (as in have a larger number of countries than the number of atoms in the observable universe).
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  5. Would it surprise you if string theory turns out to be an effective field theory? It would not surprise me.
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