4 ms·

You have definitely intrigued me enough that I want to read it too. May I ask how long it took you to read it? It's 36 pages not including the references, and i

You have definitely intrigued me enough that I want to read it too. May I ask how long it took you to read it? It's 36 pages not including the references, and it's only been up on Hacker News for a short time. As a non-mathematician were you able to read that quickly? It doesn't look dense with proofs but it does look like something I'd print out and read over coffee for several hours. I guess I'm surprised that some people can read (and understand/appreciate) math and physics papers so quickly.

devereaux 9y ago
I am happy I intrigued you enough that you decided to read it too! That's exactly why I posted a TLDR. I usually skim through comments before reading long articles, to check whether the article is interesting and worth my time. There was no comment so I made a bet and gave the article a try, as a payback to all the times other HN comments guided me to very interesting reads. About the time it took me to read the article, I read it during a break while working on some R code this afternoon. Based on the time of my commits, I can tell you it took me about 20 minutes. But I just went through the reasoning. I did not go into it very deeply or check the equations because mathematics is not my domain. I am in economics and IT (but going into statistics as it just seems more fun) I will also try to go over this article in more detail with a coffee in a few days as I found it very inspiring. Hopefully there will be more comments here to share some insights and act as a guide. Like, maybe a mathematician can spot errors in my summary, and suggest us something to read before this article to understand it better?
danbruc 9y ago
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

I am happy I intrigued you enough that you decided to read it too! That's exactly why I posted a TLDR. I usually skim through comments before reading long articles, to check whether the article is interesting and worth my time. There was no comment so I made a bet and gave the article a try, as a payback to all the times other HN comments guided me to very interesting reads. About the time it took me to read the article, I read it during a break while working on some R code this afternoon. Based on the time of my commits, I can tell you it took me about 20 minutes. But I just went through the reasoning. I did not go into it very deeply or check the equations because mathematics is not my domain. I am in economics and IT (but going into statistics as it just seems more fun) I will also try to go over this article in more detail with a coffee in a few days as I found it very inspiring. Hopefully there will be more comments here to share some insights and act as a guide. Like, maybe a mathematician can spot errors in my summary, and suggest us something to read before this article to understand it better?

danbruc 9y ago

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.)