[Edu-sig] quantum instance?

Arthur 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][0] == 0, else I am looking at a "point" or a "circle".  
Drawing the damn things is a lot less abstract - and as hermitian[0][0] 
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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