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WHY HYPERCUBE COMPUTER TECHNOLOGY WILL BECOME OBSOLETE


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

[Philip 
Emeagwali]

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




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