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Whither geometric complexity?

🔗Graham Breed <gbreed@gmail.com>

9/21/2007 12:54:42 AM

I'm bringing this up mainly because Monz says he's updating his encyclopedia again.

Currently there's an entry on geometric complexity that's clearly incomplete. It refers to a "Graham geometric complexity" which isn't listed on its own. And although that had something to do with me I never understood it anyway.

I thought that maybe my new scalar complexity was really geometric complexity in new clothes. On looking back that doesn't seem to be the case. Geometric complexity is octave-equivalent in some way. And I saw a term like

p_i^2 q_i q_j

which, whatever its significance is, would more likely be

p_i p_j q_i q_j

in scalar complexity.

So, my first question is -- do we agree that scalar complexity, however obvious, is original?

Other questions arise.

Can anybody (I'm looking at Gene ;) define geometric complexity in a way we might understand?

Does anybody still care about it?

Should we tell Monz to drop the entry on it?

Should I say anything about it in my prime errors/complexities PDF?

As scalar complexity has a geometric interpretation, how about we rename that geometric complexity?

Graham