To say nothing of the mind

What can we say about how complex systems behave? Systems of sufficient complexity that they are capable of computation. Do they have any specific properties?

No.

By definition, no. They're complex and thus, in general, we can say nothing about what they might do. How can we say nothing? Use a power law! Power laws are "scale invariant", they don't even say at what scale a process might operate. In the absence of any prior information, a power law is about as little as it is possible to assume. Thus the "reason" power laws occur all the time in complex systems is just that there is no specific reason why they should not occur.

As the mind is a complex system, we should expect power laws to crop up all over. Here's a start:

I've previously hypothesized that the way the mind works has something to do with fitting pieces together, and i have a couple of models of this.

Best-fit synthesis. Best-fit synthesis is equivalent to a cellular automata. Cellular automata can perform computation. Therefore, it is not too surprising that best-fit synthesis displays power law behaviour. Best-fit synthesis is especially interesting as a model of memory. Chunks of memory are assembled into a coherent story by working out how they can be connected together best.

(Note: while best-fit synthesis also has a "power" parameter in the form of a choice of norm, i am not sure exactly how this power gets converted into the power parameter of a power law.)

Tiling patterns. Tiling patterns are also (at least) equivalent to cellular automata. The process of putting together tiles may require backtracking following a power law distribution (Ghost Diagrams does this, though i have not yet performed experiments to show if doing so is optimal). Assembly of tiling patterns strikes me as similar to the processes of thinking, designing, and drawing.

The optimal power parameter for the power law will depend on the tile-set. The more "interesting" tile sets require the power be closer to one.

It is interesting to observe how people go about solving tile sets.

The structure of the brain (a thin layer of neurons atop a ball of interconnections) suggests that it has a network structure similar to that of a Distributed Hash-table or hyper-cube. If you work out the lengths of cabling required in proportion to the number of nodes, that's the physical structure you end up with. That is, the connections from each neuron probably follow a scale-free power law distribution.

Power law behaviour should be observable in almost any activity people engage in. It should be fairly easy to measure the power and minimum-value parameters (these corresponding to degree of autism and attention deficit respectively).

People with a low power parameter will tend to compensate by having a lower minimum-value parameter. Otherwise their attention would constantly be shifting wildly. Thus people with autism would display high levels of precision and periods of intense focus, punctuated by abrupt and violent shifts of attention.

A good candidate behaviour to measure would be eye saccade sizes. I think i recall seeing some reasearch that used eye-tracking on autistic and normal people, so the data already exists. If this works, it will be a test that can be applied at a very early age, which is useful.

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