Ashby Theorems - Revision history

Admin: Reverted edits by Eboxytezi (Talk) to last version by Jfromm

2011-02-11T21:40:53Z

Reverted edits by Eboxytezi (Talk) to last version by Jfromm

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	There are a few laws and theorems about [[Basic_System_Theory\|system theory]] proposed by		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		Cybernetics pioneer W. Ross Ashby. If is doubtful if they
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	The principle has to be taken with care, because one can easy state		The principle has to be taken with care, because one can easy state
-	the contrary ~~"~~black box~~"~~ principle that ~~"~~even though a system is	+	the contrary "black box" principle that "even though a system is
-	not completely known, it can be managed effectively~~"~~. It is obvious	+	not completely known, it can be managed effectively". It is obvious
	that one can control and regulate a system better if one understands		that one can control and regulate a system better if one understands
	it well, and a model can certainly ease understanding.		it well, and a model can certainly ease understanding.
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	Only variety in a system itself can successfully counter a variety of disturbances in the environment		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~~"~~.	+	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.	+	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.

Eboxytezi at 02:48, 24 November 2010

2010-11-24T02:48:10Z

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		+	=[http://otyxemydu.co.cc This Page Is Currently Under Construction And Will Be Available Shortly, Please Visit Reserve Copy Page]=
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		+	=[http://otyxemydu.co.cc CLICK HERE]=
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		+	</div>
	There are a few laws and theorems about [[Basic_System_Theory\|system theory]] proposed by		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		Cybernetics pioneer W. Ross Ashby. If is doubtful if they
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	The principle has to be taken with care, because one can easy state		The principle has to be taken with care, because one can easy state
-	the contrary "black box" principle that "even though a system is	+	the contrary "black box" principle that "even though a system is
-	not completely known, it can be managed effectively". It is obvious	+	not completely known, it can be managed effectively". It is obvious
	that one can control and regulate a system better if one understands		that one can control and regulate a system better if one understands
	it well, and a model can certainly ease understanding.		it well, and a model can certainly ease understanding.
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	Only variety in a system itself can successfully counter a variety of disturbances in the environment		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".	+	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.	+	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.

Jfromm: New page: 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 ...

2008-08-30T11:38:17Z

New page: 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 ...

New page

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.