thought for the day/ Barry Mazur's "Imagining Numbers: in particular the square root of -15/ Permisability

ESA/NASA Hubble Space Telescope image

I haven't read the entire book yet; I just got it.  I wasn't sure if i'd even like the book. But, I've found the more I read it the more interesting things are said.  I still don't think it will ultimately be correct.  I'm thinking Barry Mazur's use of the word 'imagination' is much like other vague words like beauty, good, 'having fun/party.'  I should explain that last part about 'having fun/party.'  I find that people, generaly non-intellectuals, often say they just want to have fun.  And, 'we like to party.'  Well, define these things.  And just when you're about to ask them to define what they mean, they're running off.  Life is just this fast paced social nothing fun.  What party really means is go to some meeting place and bullshit one another.  You drink to have fun because otherwise you're pissing each other off. "Having fun" means going to a party.  "Having fun" never means adventure of exploration - exploration of anything; whether art, sports, or some kind of science.  Working hard it not fun, but some kind of thrill ride is.  I like roller coasters to, but why bungy jumping?  Enough of that soapbox, how about another?  This should be called the soapbox post!

I should say that asking the question of what do you mean by having fun is not permissible.

Barry Mazur suggests that in mathematics, one overcomes permisability in old ways of thought. I completely agree. Most life evolves to adapt to a certain environement.  They're suppose to go through their lives in certain ways.  Homo Sapiens for some reason have reached a certain stage of consciousness, where we overcome what we're suppose to do.  Homo Erectus was the first animal to spread to so many different environments. No animal is suppose to look up at the heavens; but, Homo Sapiens eventually did.

Mr Mazur even decodes invention and discovery from this permisability concept.  One major philosophical debate amongst mathematicians is whether mathematics is invented or discovered.  Barry Mazur relates the two to permisability; he says that when mathematics seems unpermissable, we say mathematics is discovered.  When someone shows us how to do mathematics in a new way(such as Descartes coordinate geometry for instance), mathematics is pure invention!