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I skimmed it in a bit less than an hour, like reading every second paragraph. If you are not a mathematician and physicist, it will probably take you weeks or m

I skimmed it in a bit less than an hour, like reading every second paragraph. If you are not a mathematician and physicist, it will probably take you weeks or months to follow the argument in any detail and even then you will still be far away from really understanding it. That is some seriously advanced stuff and it touches on a quite broad spectrum of ideas. I also tend to question what devereaux thinks is the essence of it. I would say it is mostly a presentation of the evolution of mathematical ideas with some focus on ideas applicable to physics. I did not notice any new physical ideas, at best new mathematical ideas applied to existing physical theories and even that only on the last couple of pages. Also to the best of my knowledge our current physical theories are heavily constrained by very general principles, at times up to uniqueness. As a simple example, the Poincaré group of special relativity is the unique solution if you make some quite basic assumptions like homogeneity and isotropy of space. That conflicts with saying that quantum theory is not special. Also the sentence mentioning renormalization does not really sound like it was written with an understanding of what renormalization in this context means. I hope I do not sound to harsh, I am far from an expert myself, but that TL;DR seems way of in my opinion.

devereaux 9y ago
It is not hash, I welcome criticism! This is how we improve!! And yes, my TLDR is mostly based on the last pages. The rest just seems to present the ideas that helped reach this conclusion. Regarding renormalization, there are many things I (wrongly?) call a renormalization - even doing a PCA and dropping the components that add little to the variance of the data. This destructs some signal, unless you believe that is just noise and the data should only be analyzed along say the first 3 PCs. I'd call that a renormalization in a 3d space. Maybe this is an improper use of the word in this context?
- auntienomen 9y ago
  In QFT, renormalization is a way of mapping the behavior of a QFT at one distance scale onto its behavior at a different distance scale. Long story short, there's an equivalence between changing distance scales and changing the coupling constants in the theory. Once you get this mapping right, you discover the infinities present in the naive computations have vanished. (There is actually a quantity which has its normalization reset in this mapping, but that's actually the least interesting part of the story. It's somewhat odd that it's become the name for the whole mapping.)

devereaux 9y ago

It is not hash, I welcome criticism! This is how we improve!! And yes, my TLDR is mostly based on the last pages. The rest just seems to present the ideas that helped reach this conclusion. Regarding renormalization, there are many things I (wrongly?) call a renormalization - even doing a PCA and dropping the components that add little to the variance of the data. This destructs some signal, unless you believe that is just noise and the data should only be analyzed along say the first 3 PCs. I'd call that a renormalization in a 3d space. Maybe this is an improper use of the word in this context?

auntienomen 9y ago
In QFT, renormalization is a way of mapping the behavior of a QFT at one distance scale onto its behavior at a different distance scale. Long story short, there's an equivalence between changing distance scales and changing the coupling constants in the theory. Once you get this mapping right, you discover the infinities present in the naive computations have vanished. (There is actually a quantity which has its normalization reset in this mapping, but that's actually the least interesting part of the story. It's somewhat odd that it's become the name for the whole mapping.)