
Why hypercube computer technology will become obsolete
Consider an ndimensional hypercube of edge length 4
which contains
hyperspheres of unit radius which are tightlypacked so that
two adjacent hyperspheres
touch each other.
A 32node
binary hypercube network.
The distance from the centers of the
hyperspheres to the center
of the bounding ndimensional hypercube is
.
Consequently, for
dimensional hypercubes, the
hypersphere tightlypacked into the hole
at the center
of the spherepacked hypercube will not touch the bounding
hypercube. For n=9, the hypersphere
will touch the bounding hypercube. For
,
the
hypersphere tightlypacked
into the huge hole at the center
of the spherepacked hypercube will protrude outside the
bounding hypercube.
The 2048 processing nodes of the Connection Machine are
interconnected in a hypercube topology with each node containing 32 processing elements.
Click
on photograph.
The latter results demonstrate that the packing density of
spherepacked hypercubes
continuously decreases as the dimensionality increases.
Philip Emeagwali discovered that sphere packing and
hypercube technology are related fields.
Click on emeagwali.com for more information.
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