Re: Epistemology 201: The Science of Science
From: Albert (albertwagner_at_cox.net)
Date: 02/27/05
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Date: Sun, 27 Feb 2005 17:40:22 -0600
Wolf Kirchmeir wrote:
> Albert wrote:
<snip>
>> I can visualize 4 identical spheres in closest packing, i.e. their
>> centers representing point locations and forming the vertices of a
>> tetrahedron, expanding as you describe. However, I cannot envision
>> this for spheres of different sizes, especially the situation where 4
>> identical spheres in closest packing have at the center of the
>> tetrahedron a much smaller sphere touching each of the four larger
>> spheres. Perhaps you can help me.
>
> Um, how about thinking of the spheres' centres instead.
I was not thinking of spheres apart from their centers, as I
think my statement makes clear.
> you will
> visual8se a lattice. Expand the tetrahedron, ie, increase the lines
> connecting the tetrahedron's vertices at some constant rate. The lines
> connecting those vertices to the central sphere's center will also
> expand. Etc. Is that good enough?
Almost.
> BTW, by introducing that central sphere you've cut the original regular
> tetrahedron into four similar irregular ones. Can you visualise that?
Of course. Visualization of static things is relatively easy.
Visualization of proportional growth of different sized spheres
that keeps them in their original relative positions and relative
sizes is a little harder.
-- "Mercifully free of the ravages of intelligence" -- Time Bandits
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