Since I spend most of my time these days thinking about designing and
programming massively parallel computers, it occured to me to think about
applying such machines to exploring the Cube's Group. Here are some
When we say "massively parallel" we are talking at least a quarter million
simple processors. This is enough processors to give all of the positions
5 or fewer quarter twists away from home their own processor. A million
processors would be enough to get up to 6 Qs, but lets not push our luck.
Given a machine like the MIT Connection Machine we could set up a database
in which every processor representing a configuration knew the addresses ot
the 12 other processors representing its 12 closest neighbors, in almost no
time at all. (Processors 5 Qs away from home would have null pointers for
their unrepresented 6 Q neighbors.) A conservative statement would be
that operations like generating a list of all identities of length 10 or
less (which has previously taken us hours to accomplish) could be done so
fast that the machine could generate output faster than you could read it.
Since this is all so absurdly easy, there must be ways to go beyond this to
generate significant new results using this (promised) new kind of
hardware. Perhaps Dave Christman, who is both a cube hacker, and a
designer of algorithms for massively parallel machines, could be persuaded
to devote some spare cycles to figuring out ways to brute-force the Cube
using such a machine.