Speculations I Minsky

In a contribution to the first conference on physics and computation held at MIT in 1982 [land82b], Minsky considered whether a universe satisfying the following two conditions could exist [minsky82] (1) each volume of space contains a finite amount of information, and (2) over a suitable range of size and speed, the mechanics of the universe are approximately classical. 

Envisioning space-time as a four-dimensional CA lattice, wherein sites take on one of a finite number of values and interact via a local dynamics, Minsky explored various elementary properties of this universe particle (or packet ) size and speed, time contraction, symmetry, and how the notion of field might be made palatable within such a framework. 

The idea that localized partic le-like propagating structures can be defined on a lattice Wcus nothing new. For example, Minsky was well aware of the existence of gliders in Conway s Life rule. Minsky s own pedagogical example was effectively a four-state one-dimensional CA with states a e 0,1,a,/ and rules 4 (cri i,CTi,cri+i) —cr given by  

Using these rules, it is easy to show that value sequences of the form 11.. 11 Q,  

Notice that in this example, the speed of the packet is inversely proportional to the packet s spatial size. While there is certainly nothing unique about this particular representation, it is interesting to speculate, along with Minsky, whether it may be true that, just as the simultaneous information about position and momentum is fundamentally constrained by Heisenberg s uncertainty relation in the physical universe, so too, in a discrete CA universe, there might be a fundamental constraint between the volume of a given packet and the amount of information that can be encoded within it. 

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