Ashby Theorems

There are a few laws and theorems about [[Basic_System_Theory|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.