[Edu-sig] quantum instance?
ajsiegel at optonline.net
Sun Sep 11 21:34:57 CEST 2005
Kirby Urner wrote:
>In Fuller's synergetic geometry, circles don't become infinite lines, but
>just bigger and bigger circles. Lines that appear locally straight are just
>that: local. Clearly we're starting with different assumptions than those
>of Euclidean greek metaphysics. More from Democritus. Lines aren't
>perfectly straight either -- zoom in and they become zig-zaggy/wavilinear.
>Zoom out, and all you get are curves and great circles.
FWIW, I am working with (as in studying and implementing some tools in
PyGeo to enliven that study of) the geometry of complex numbers. And
doing so in such a way that all fundamental elements are defined by its
2X2 hermitian matrix. So I am getting fairly abstract - a "line" has
hermitian == 0, else I am looking at a "point" or a "circle".
Drawing the damn things is a lot less abstract - and as hermitian
approaches 0, a line makes a better represetantion - is all. And since
things are dynamic, I need my iinstances to think on their feet as to
what makes a better representation. If/else is really all I need - but
I was playing in my head with trying something more "dramatic".
Fredrk Lundh - the fbot and author of PIL - posted a blog entry a few
months ago about working with complex numbers to do basic image
manipulation. With Numeric in play, I can imagine a lot of efficiency
gains by working with it and the Python built_in complex numbers- via
Hermitian matrixes and 2X2 mobius transformation matrixes - to
accomplish a lot of the kind of image transformation effects that I
imagine are normally done otherwise. I expect that experimentation
along these lines is going to eventually get me more into playing with
bitmap graphics, whereas until now I have been a vector graphics kind of
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