Wednesday, December 13, 2006


Another random thought:

I got curious, what would be the minimum abstraction needed to describe communication between agents. One obvious solution would be bitstreams (streams of booleans). On the other hand, it is not the minimal one - if one thinks about computer networks, at the electrical level they do not use streams of bits. Superficially, setting potential on the line to either low or high can be thought as sending a bit, but actually the bitstreams sent this way are very limited - namely only streams with alternating bits can be encoded this way. And informational difference between all streams of units and those streams of bits where bits alternate is very small - just one bit per whole stream! By that I mean that a timestamped sequence of units [(), (), ()] corresponds to one of the two timestamped sequences of bits: either [0, 1, 0] or [1, 0, 1]. This difference is so negligeble, I believe it can be ignored, so we can pretend that computers communicate to each other using unitstreams (at least at some level). It is very crucial that units in these streams are timestamped, otherwise they cannot carry enough information. Networks rely on the fact that peers are usually not moving fast enough relatively to each other, so their local clocks are good enough to recover timestamps that are not sent explicitly. An interesting question would be whether it is beneficial to model clocks as unitstreams as well, then instead of timestamping units in the stream we instead relate them to units in some other stream (but probably need to ground this induction somewhere - or make it coinduction :) ).

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