Wednesday, February 8, 2006

Ideal forms

Ideas are most mysterious as they start to be understood. I just took in another lecture. This one was on curved space-time. I've been familiar with it for some time but now to hear it explained in a way that makes it accessible is wonderful.. and scary.

I'll try not to get in to details but the essence of curved space is that Euclid is wrong. Or rather that it can be demonstrated that Euclidean geometry (read: geometry) doesn't work. We don't yet have the tools to measure accurately enough to show we do not live in Euclidean space but I would be surprised if the deviations predicted by Einstein were not there when we have such tools.

I'm now wondering what would have happened had Euclid's detractors had access to such tools. See, Euclid's book, The Elements, was written to describe the space we live in. Now through some rational worm hole it has been taken to describe ideal space (though it still works for all practical applications [except programing GPS satellites in case you have the pleasure]). Had it been demonstrated that it didn't describe our space we would likely not have the elaborate theorems we have now for ideal space, and thus have little reference for this idea of curved space.

I'm drifting, aren't I? I guess the question I'm raising is about ideal forms. How many times in the past have we dismissed rationalized ideas because of discrepancies with practice. How many times will we do this again without taking the opportunity to find what the discrepancies can teach us about practice and the world we live in?

I think you get to ask questions like this when you have just accepted that you are traveling at the speed of light in the direction of time.


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