Let's Rethink
I've bounced off this project of understanding, well, the universe several times. I keep hitting a wall each approach I try (but getting a little bit further each time). I tend to go through this cycle:
- OK, let's read about quantum field theory!
- I need to learn a lot more basic physics and mathematics before I understand this.
- The way this basic mathematics is done in the standard textbooks is horrible, I want to see a category theoretic version.
- Oh, that would be an actual research project.
- OK, let's sit down and learn the classical version.
- Hmm, the basic textbooks have so little rigour that I can't really fully what's going on, but the rigorous textbooks assume that you've already read the basic textbooks.
In particular I'm feeling the hurt from missing out on vector calculus and topology when I was an undergraduate. I'll probably have to catch up with those sooner or later. But here's how I'm going to do things, in the hope that my completionist brain will accept each one as done once it is done:
I have the following projects. I will switch between them at random, whichever one I feel like advancing at the time. If I hit a wall with one of them, I will make a note of what I need to be able to proceed.
- Read John Baez's reading list.
- Read the references in the Background section of D. J. Myers, H. Sati, U. Schreiber Topological Quantum Gates in Homotopy Type Theory.
- Read the references in the statement of the Yang-Mills problem.
- Write a rigorous treatment of quantum field theory (as much as is possible today) in ZFC.
- Write a mathematically rigorous version of this Wikipedia page.
- Read the Geometry of Physics pages.
- Write a treatment of quantum field theory in Martin-Löf Type Theory.
- Write a treatment of quantum field theory in Homotopy Type Theory.
In the next post, we'll start with project C and see how far we get.
Comments
Post a Comment