As opposed to minimally parallel, one must suppose. 

No, that would be maximally parallel. Massively parallel, of hardware architectures, means that there are many, many processing elements, rather than just a few. A ConnectionMachine is massively parallel. A dual-processor server isn't.

''I suppose it's like the distinction between a WorkStation and a PeeCee, then: A moving target that slides to be just a bit "better" than what is on your desktop right now.''

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See Also: CheapMassivelyParallelSequentialSearch