Thread: Theoretical Disaster

Fucking Christ! That was tedious.

Originally Posted by Xei

Simple algebra cannot be equivalent to geometry, geometry is consistent and complete whereas algebra is not.

Could you elaborate on that? Specifically, what do you mean by algebra? I'm sure you're aware that R^n is a model of Euclidean geometry and that all Theorems of Euclidean geometry can be derived purely from that relationship. So you must mean something other than what I think you mean. There's also the possibility that you temporarily caught a slight case of stupidity (perfectly understandable given the vast amount of it flying around at high velocities on this thread)

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Well, it is my understanding that Euclidean geometry is known to be simple enough that it is complete and consistent, whereas Godel's incompleteness theorem applies to arithmetic. I can't really remember what inane point was originally being made here, but I was basically indicating that the two aren't equivalent.

Originally Posted by Xei

Well, it is my understanding that Euclidean geometry is known to be simple enough that it is complete and consistent, whereas Godel's incompleteness theorem applies to arithmetic.

You're right. Tarski formulated it as complete. If you include the ability to measure angles (which I always assumed, not being incredibly interested in it), then it is powerful enough to describe arithmetic and then Godel applies.

Hey I read through the debate between you guys, and I just couldn't
understand what was the argument about. So can someone tell me
what was the "main" topic about? It looks interesting but I just seem not
to understand.

Thanks,

P.S. : If you can direct me to a website to understand theses kind of stuff
that will be grate thanks.