Wednesday, May 20, 2009

Mathematizing Minsky, general approach

Severe restructuring, asymmetry and how to model it. DeLong worries about this, I got as far as this general approach, and no further.

I always start with the idea that things are restricted such that their positions are known to a fixed uncertainty, neither more nor less. Don't ask me why.

Then I add that things are optimal when organized as a sort of bell shape in distribution (maximum variation in minimal space).

These two assumptions get me fixed dimensionality. Specifically, if I break my measurments into orthogal functions, the number of functions I need is fixed, determined my my uncertainty constant.

Having assumed very little, then, I get to a conclusion that large groups of things that must know about its neighbors will organize into fixed spanning trees, with information moving as in a directed graph, and the dimensionality of the tree fixed at N. If the number of things grows, then the system must spawn sub spanning trees, and pick orthoganl functions so the hierarchy of things gets back to a composite of N ranked spanning trees.

This latter process describes a severe restructuring.

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