Mutual Support Domains

In a large set of control systems if one loop of mutual support can form, so can others. It is quite probable that several independent loops of mutual support may develop. The members of a loop support one another in the same way as do members of a spin-glass domain.

Mutual Support loops as "Domains"

If one of the members of a loop changes its perceptual vector or its action vector, it changes the way it interacts with the other members of the loop, and the control performance of all members of the loop is likely to get worse. Reorganization is therefore likely to restore the loop--or to create another more effective one.This is what makes it like a spin-glass domain.

Or else the loop effectively ceases to exist, leaving its members to "fly solo." Solo control systems may not control well in the environment of the disturbances induced by the actions of the other control systems, and their perceptual or action vectors may be changed by reorganization.

How likely is it that two domains will be orthogonal?

Environmental Resource Limitation

The perceptual vector of a single control unit projects onto a single dimension of environmental space, in which it defines the Controlled Environmental Variable of the control unit. The output projects onto another dimension of the environment--meaning that it affects aspects of the environement other than those of which the perceptual vector is composed. If the control system is efficient, its output vector correlates well with its perceptual vector, but nevertheless, the two vectors will almost certainly not be identical. Each individual control system therefore spans two dimensions of the environmental space.

The 2-D subspace of the environment spanned by the vectors of one control system will probably be nearly orthogonal to those spanned by another control system under two conditions: that the environment has enough dimensions (degrees of freedom) and that the two systems have reorganized together long enough to allow orthogonalization to happen.

In a mutual support domain, the individual control units are as orthogonal as are any other units. Participating in the same loop of mutual support does not mean that two control units are likely to have correlated vectors. If anything, the converse is true, since having correlated vectors would mean that the actions of one control unit would disturb the other's perceptual signal. So, if anything, the vectors of two units in a mutual support domain are more likely to be orthogonal than are those of two randomly chosen control units.

In a loop consisting of N units, the loop as a whole spans 2N dimensions of the environmental space in which perceptions and actions are made manifest. But one has to ask how many dimensions the environment has available. If there are L loops, is it reasonable to expect 2N*L dimensions to be available, so that all the N*L control units can avoid interfering with each other's attempts to control?

This is a question about resource limitation.