That’s such a great development. Cool.

]]>When I was young, I really wanted to understand *everything* about the universe—and especially the most basic, fundamental things. So, I wanted to start by learning the laws of physics, since these govern everything. As I went further, I realized that the laws of physics are written in the language of mathematics, so I got interested in that.

I also discovered that profound questions like “what is true?” and “how do we know anything?” led people to develop logic. Thanks to a book my dad checked out of the public library, I learned that in the 20th century Gödel and others proved theorems in logic that put limits on what we can prove. So I got interested in logic, which nowadays is another branch of mathematics.

Nowadays I feel I know enough math and physics to start thinking about other things, like global warming, biology, and a general theory of networks. But occasionally I want to work on pure math, so I do projects like this one on topological crystals.

]]>Good puzzle! You can work it out yourself using the formulas on page 18 here.

]]>Interesting…Tropical mathematics as “low T limit of mathematics”. I will reread your winter 2007 seminar…I had almost forgotten it completely! And what about the high temperature limit?

]]>Thanks! I love it when people catch my typos.

Next time I’ll give tons of examples. All this was just to define the construction and prove it gives a “crystal” embedded in a vector space.

]]>OH, I did not remember that! You have been so prolific than I forgot your QG seminar touching this fascinating topic. What about a p-adic/tropical geometry dictionary? Does it exist if any? It is interesting your comment about tropical math as the “classical” limit of quantum math. Low temperature physics is purely quantum at nature (e.g., see the BEC phase transition!). Tropical mathematics is yet a young branch but I am sure physisics will face with it much more in the near future.

]]>You can combine ideas in many ways, but throwing them together at random is rarely opimtal. Tropical mathematics is really the ‘classical limit’ or ‘low-temperature limit’ of mathematics using complex numbers. I discussed this in weeks 11, 12 and 13 of my Winter 2007 seminar: you can read the notes. I also recommend this:

• Grigori L. Litvinov, The Maslov dequantization, idempotent and tropical mathematics: a very brief introduction.

I think this is the most promising way to apply tropical mathematics to physics.

]]>To go beyond: What about tropical spacetime physics or tropical Quantum Mechanics? What about a polycrystalline tropically quantum spacetime?

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