Ashby Theorems

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There are a few laws and theorems about system theory proposed by Cybernetics pioneer W. Ross Ashby. If is doubtful if they deserve to be called theorems, because a theorem can be proved. Ashby's theorems are very general and cannot be proved with mathematical rigor. They may seem obvious, but nevertheless there is some truth in them.

Conant-Ashby Theorem

The Conant-Ashby theorem states that

Every good regulator of a system must have a model of that system

The principle has to be taken with care, because one can easy state the contrary "black box" principle that "even though a system is not completely known, it can be managed effectively". It is obvious that one can control and regulate a system better if one understands it well, and a model can certainly ease understanding.

Conant, R. C./Ashby, W. R., Every Good Regulator of a System Must be a Model of that System, in: International Journal of System Science, Vol. 1 No 2 (1970) 89-97

The Law of Requisite Variety

The law of indispensable or requisite variety from William Ross Ashby states simply that any effective control system must be as complex as the system it controls: a wide variety of available responses and actions is indispensable in order to ensure that a system which aims to maintain itself in a certain state can actually adapt itself satisfactorily if it is confronted with a wide variety of pertubations from the outside.

Only variety in a system itself can successfully counter a variety of disturbances in the environment 

This may seem obvious, because a flexible system with many options is of course better able to cope with change and changing conditions. In other words, "the larger the variety of actions available to a control system, the larger the variety of perturbations it is able to compensate".

It is also clear that sufficient "requisite variety" is already available in systems with a small numbers of elements, as soon as those elements can interact in arbitrary ways we get a combinatorial explosion. Thus the law might say nothing, but nevertheless there is some truth in it.

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