[Beowulf] core diameter is not really a limit

Eugen Leitl eugen at leitl.org
Thu Jun 13 04:34:33 PDT 2013

I've remembered to check the cluster monkey feed, and

The assumption made here is that every node needs to be able
to talk to every other node within the assembly.

I think there is a large class of problems where direct
long-distance communication is not necessary. E.g. if
you're simulating a 3d system with local interactions,
where long-range interactions emerge by propagating
across computational volume in a wave-like fashion
your relativistic limits are only limited to the
geometry of the node and its direct neighbors.
Further nodes will be reached at next refresh,
assuming a relativistic cut-through fabric present
in each node, or computation where information is
passed implicitly by change of state within
adjacent node.

Such problem classes on such node geometries have
no intrinsic size limit to the number of nodes,
since communication is always limited to overlapping
light cones of subsystems.

Obviously smaller nodes means higher refresh rate,
so the system asymptotically converges towards a 
cellular automaton model, with ~nm sized cells.
It is provably impossible to do classical computing
faster than this. The time domain is rather ~ps
than ~us, and maximally possible refresh rate is 
some ~100 PHz for ~nm sized cells.

Obviously, ability to cool such volumes will limit
such high refresh rates, even if the computation is
reversible (which probably means it has to be
adiabatic, and hence also intrinsically slower).
It also seems that spintronics is not extremely
fast, and spintronics/photonics/plasmonics is
likely to be the modes of computation and 
communication used in such future systems.

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