Visualizing Calabi-Yau spaces?

[bearly]

rant he says. you sure are used to being around people who worship you. i know they don't teach this in the "hard" sciences, but one of the common uses of the word "know" is to indicate one has made a judgement. i have clearly had bad experiences you say. pure genius, i just told you of one. "enjoy these things? you have gone off the track. in case you don't know this, a few bad experiences don't make a person feel inadequate. perhaps you rely on peoples bad experiences w/ you to intimidate them. that just makes you a bully boy. are you a bully, gal? your manner sounds like the kind of intellectual bullying that is common in the academic world. and you know it "scarred" me. it didn't, it taught me. perhaps you might benefit from realizing there are many things you could learn. i try my best on these forums. people w/out humility are very hard to reach, especially when young. btw, how do you know what "anyone" thinks? if a person doesn't take me seriously, i have either gone about it wrong, or it is their loss. another one of those sticky judgements to make. regarding your last sentence: a smirk and a snicker never made anyone feel better, save maybe the perpetrator. sleep tight in galway............b

[Galwegian]

Your bitterness is too much for me. I give up

[bearly]

your self-adoration and smugness are a bit much for me. glad you gave up...............b

[bearly]

as always, my highest hopes that you will have a peaceful life..........b

[prosellis]

If you were to picture existence as proposed by M-theory you would begin by picturing a great empty space (p-dimension) and in that space you picture a three dimensional space representing our universe (x,y,z). Zoom in really far to some very specific coordinates in this space. At those coordinates picture another three dimesnional shape, but when you picture it give it a different orientation than the original three dimensions. Now curve the axis so that the positive and negative poles of each form closed loops.

You wind up with what looks like a three dimensional object, but when you consider movement you can begin to see how these extra dimensions work. You move up-down, back-forth, and across the first three dimensions until you find this object. When you reach the object you can move through it by moving along the original x,y,z axis, but to move around the object you have to follow one of the curved axis to do it.

I hope that helps. I think it's impossible to picture higher dimensional shapes and graphs without considering movement. The dimensional bundles in M-theory also have more than three axis each, which makes my theory of visualization pointless outside of maybe helping the discussion.

[Mickey Brausch]

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CNN

MADRID, Spain (AP) -- A reclusive Russian won an academic prize Tuesday, the Fields Medal which was announced at the International Congress of Mathematicians, for work toward solving one of history's toughest math problems. Grigory Perelman, a 40-year-old native of St. Petersburg, was praised for work in the field known as topology, which studies shapes, and for a breakthrough that might help scientists figure out nothing less than the shape of the universe.
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The riddle Perelman tackled is called the Poincaré conjecture, which essentially says that in three dimensions, a doughnut shape cannot be transformed into a sphere without ripping it, although any shape without a hole can be stretched or shrunk into a sphere.

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CUNY article: Hamilton, Perelman and the Poincaré Conjecture