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"But what would you propose instead of mathematics?" It's not that we shouldn't use math, but I suggest that when using Math we are predisposed to want clean,

• Jach 10y ago
  Maxwell's equations can be written as one equation with geometric algebra, □A =J/(c є0) If the math comes out ugly we can just macro our way to prettier math and stick complicated things behind simple looking symbols. I don't think this is a predisposition in the initial search as much as aesthetics on making the form of work pleasant regardless of what you start with. But then, maybe it's even more than aesthetics, truth and reality seem to have an (unreasonable?) simplicity to them, so maybe there's objective beauty in simplicity; I don't see the point in intentionally seeking out ugly formalisms for ugly's sake especially when we've had so much success with simple and elegant.
• chriswarbo 10y ago
  I think it's mostly a matter of Occam's Razor, Kolmogorov Complexity, the pigeonhole principle, etc. There aren't many clean, simple equations (relatively speaking), compared to long, ugly ones. Each time you make an equation longer, you have a huge variety of choices for the new bits; if we take "ugliness" to include things like asymmetry, arbitrary constants, lack of relationships between the parts, etc. then there are more ugly equations than beautiful ones. It's more practical to look for simple, pretty laws since there are far fewer of them to try. Once we've exhausted them, we can try making things a little uglier, and seeing if that works; and keep incrementing. After all, if you have enough epicycles you can explain any motion you like (since you're basically taking a fourier transform)