Could God create a world with fundamentally different mathematics? Where our calculus and probability theory gave completely innacurate results? Where 2 + 2 = 5? I'm thinking about this because I'm looking at probability in my Artificial Intelligence class. Probability theory is stranger than things like arithmetic and calculus because it is trying to give precise estimates, which seems like it's almost an oxy moron. But even with probability theory, I think that mathemeticians believe it speaks of absolute truths, truths which could not be anything other than what they are. That, I gather, is something that mathemeticians find very alluring about math. It is Truth. It has a purity and unassailability that other disciplines lack. However, for some reason, when I have studied math recently, I've been pestered by the idea that it's a set of rules put together by people because they thought they were interesting or gave good results, and that they were just ideas without substance behind them. In our world, that isn't so, at least for most math. Most math represents the real workings of things. But to really appreciate this, I'd like to explore the question: Could math be different? I cannot understand how it could be different, but I do appreciate that my understanding is very limited. I may not be able to imagine math being different, but I also can't imagine a four-dimensional object particularly well. Just because I don't understand it doesn't mean it couldn't be.
So please, post comments, give me your deep philosophical thoughts! Or brief and pointed jabs. Whatever you think most effective.
P.S. You may notice I've posted on my blog twice this evening. That is because, while I need to work on my AI homework, I am exhausted from strike for the play. I went up and down stairs a lot, and carried heavy things. Apparently, being exhausted leads to more blog posts. Interesting.
