# Ashby Theorems

### From CasGroup

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.