In regards to yesterday's comic: can you build a math without commutativity? I think you can, but I haven't done it. Allison sent T-Rex a great proof that addition is commutative, based on Peano Axioms, which are almost as cute as they sound. Peano Axioms are some simple axioms that we all agree are true and that can be used as a basis for a mathematical system. They're things like, "For all x, x equals x". It is hard to argue these axioms... but what if we could?
You have to imagine that I take off my glasses with a flourish when I say that.
I still feel like it should be possible to build a system of math where addition isn't commutative. It may mean rejecting some of these axioms, and maybe redefining how equality operates, but that could be pretty neat! Maybe? Unfortunately it's been a while since I did anything approaching this, so if someone wanted to take up the challege I would be more than happy to post the results here!
To be clear, this doesn't mean that math is capital-t True. Math can be consistent, or complete (but not both!), and it does seem to reflect the world we're in - but that's because we've built it that way. There are alternatives! If you're looking for ULTRA ACCURATE INDISPUTABLE PHILOSOPHICAL TRUTH, all in caps like that, I don't think you're going to be able to dance around the "reality is an illusion" problem with math.
Okay! So here's something neat but it needs some explanation. There's a forum for the comics, right? And this forum started a wiki because everyone likes to gossip about other people in a big group. And on this wiki there's a page called Dinosaur Comics Timeline, created by an anonymous IP that edited that page and only a few others and then disappeared forever. It is amazing. The author has taken all the "YEARS LATER:" and "FIFTEEN YEARS EARLIER:" stuff I do and flattened it out and fit it all together in a way that's fun AND entertaining. Also, there's references for every event. So, yeah! Thanks, anonymous person!