On Tue, May 13, 2014 at 01:29:58AM -0700, jim bell wrote:
From: Georgi Guninski <guninski@guninski.com>
It is more interesting to me if sqrt(-1), n-dimensional space, etc. are part of nature...
My understanding is that they are part of nature. If you think about it, to hunter-gatherer-level societies, negative numbers could be called "imaginary": There is no such thing as "negative-3 sheep", for instance. Nor is there a third of a (living) sheep. It was easy enough for people to divorce themselves from the idea of integers, or positive numbers. It was much more difficult to deal with "irrational numbers" (numbers which could not be expressed as the ratio of two integers). Square roots were comparatively easy...as long as you were talking a positive number. Computing imaginary roots seems terribly difficult, until you express the number in terms of a real/imaginary graph, and voila, it's trivial again. I think that (e (to the power of (2 times pi times I)) -1) =0 was discovered at least a couple hundred years ago. It's been attributed to Euler, nearly 300 years ago. And the various string theories proposed in the last 20 years require the universe to contain 10 or 11 dimensions, with 6 (or 7) of them wound up tightly, perhaps near a Planck length. (10e(-33)cm). Jim Bell
I am not good at neither math nor physics, but your argument didn't convince me for the relation with physics (the math appears correct). IMHO currently we know little about both math and physics, so the future might tell.