Saturday, January 8, 2011

Combinatorial Explosion, Simulation Argument and Roundworms

Caenorhabditis elegans is a roundworm which has exactly 302 neurons. For this reason it is used as a simple model for neuroscience. Simple is a relaive term. Assuming neurons have only two states (firing or not), this means that the "simple" C. elegans nervous system as a whole has 8.15 x 10^90 states. That is, even if there has been an immortal C. elegans living since the Big Bang, and it can change states once per Planck time (the fundamental time resolution limit of reality), it wouldn't yet have come close to cycling through all possible states of its nervous system.

At first I thought there might be implications here for the simulation argument, based on the economy of simulating so many systems with so many possible states, but this isn't an easy way out. 1) The states of neurons follow lawfully from external object/events and from each other and in this way are like any other type of object, so they are not additional information sources that increase the simulation's computational requirements. 2) If we're being simulated, we can't trust that our experience is actually related to what appear to be neurons anyway. This does however suggest an interesting thought experiment: if we're simulated and can't believe that what feels and looks like our brain and our sense organs are producing the experience, we can still make basic logical and mathematical guesses about the minimum number of interactions or computations you would need to produce the experience that we have.

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