[next] [prev] [up] Date: Mon, 28 Mar 88 15:54:07 -0500 (EST)
[next] [prev] [up] From: Peter Beck <pbeck@ARDEC.ARPA >
~~~ ~~~ [up] Subject: magic polyhedra

a puzzle fool's view of plate tectonics
by peter beck april 1, 1988

what follows is an unfounded speculation of how "magig polyhedra" can be used to
understand the manifistations of plate tectonics. my imagination was piqued
while manipulating the "megaminx" (a dodecahedron with flat pentagon shaped
faces, marketed in the usa by tomy) because the puzzle locks up when an attempt
is made to turn too many faces simultaneously. this causes the surface to
distort and when too much force is excerted the puzzle comes apart in an
explosive fashion.

i, impusively concluded that the geometric principles governing this explosion
are analogous to what happens when the surface plates of the earth are rotated
by the forces behind plate tectonics. this analogy is useful because it
provides a macro model with physical parity constraints to study plate
tectonics, eg, by helping forecasters tie together observable events around the
world a better understanding of individual events could be obtained. another
area of study could be the parity constraints on the motion of the plates, ie,
the directions of plate rotation are constrained by their neighbors, because
each plate does not move independently (see fig. 465.10 in fuller's book
"synergetics"). [it should be noted that other dodecahedron magic polyhedra
may be more appropriate for the study of plate tectonics; ie, the "impossiball"
or 'alexander's star".]

now that my fantasizing is in high gear i will expand my speculation to consider
the engine that drives plate tectonics. i have decided that if one knew some
physics it could probably be shown that a rotating sphere with a liquid center
would develop 12 local circulations which the surface plates would float on.
thus, plate tectonics can on a macro scale be reduced to a simple problem of
fluid dynamics and some geometric parity constraints which can be displayed with
magic polyhedra.

the future is puzzling, but cubing is forever !!


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