WHY HYPERCUBE COMPUTER TECHNOLOGY WILL BECOME OBSOLETE

An excerpt from Philip Emeagwali's 1989
Gordon Bell Prize Report

+ p h i l i p e m e a g w a l i +

Why hypercube computer technology will become obsolete

Consider an n-dimensional hypercube of edge length 4
which contains

hyperspheres of unit radius which are tightly-packed so that
two adjacent hyperspheres
touch each other.

A 32-node
binary hypercube network.

The distance from the centers of the

hyperspheres to the center
of the bounding n-dimensional hypercube is

.

Consequently, for
dimensional hypercubes, the
hypersphere tightly-packed into the hole
at the center
of the sphere-packed hypercube will not touch the bounding
hypercube. For n=9, the hypersphere
will touch the bounding hypercube. For
,
the
hypersphere tightly-packed
into the huge hole at the center
of the sphere-packed 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
sphere-packed hypercubes
continuously decreases as the dimensionality increases.

Philip Emeagwali discovered that sphere packing and
hypercube technology are related fields.