QUANTITY OF VARIETY 7/17 



Science looks for laws; it is therefore much concerned with looking 

 for constraints. (Here the larger set is composed of what might 

 happen if the behaviour were free and chaotic, and the smaller set 

 is composed of what does actually happen.) 



This point of view, it will be noticed, conforms to what was 

 said in S.1/5. Cybernetics looks at the totality, in all its possible 

 richness, and then asks why the actualities should be restricted to 

 some portion of the total possibilities. 



Ex. 1 : How is the chemist's Law of Simple Proportions a constraint? 

 Ex. 2: How is the Law of Conservation of Energy a constraint? 



7/16. Object as constraint. Constraints are exceedingly common 

 in the world around us, and many of our basic concepts make use 

 of it in an essential way. Consider as example the basic concept 

 of a "thing" or "object", as something handled in daily life. A 

 chair is a thing because it has coherence, because we can put it on 

 this side of a table or that, because we can carry it around or sit 

 on it. The chair is also a collection of parts. 



Now any free object in our three dimensional world has six 

 degrees of freedom for movement. Were the parts of the chair 

 unconnected each would have its own six degrees of freedom ; and 

 this is in fact the amount of mobility available to the parts in the 

 workshop before they are assembled. Thus the four legs, when 

 separate, have 24 degrees of freedom. After they are joined, how- 

 ever, they have only the six degrees of freedom of the single object. 

 That there is a constraint is obvious when one realises that if the 

 positions of three legs of an assembled chair are known, then that 

 of the fourth follows necessarily — it has no freedom. 



Thus the change from four separate and free legs to one chair 

 corresponds precisely to the change from the set's having 24 degrees 

 of freedom to its having only 6. Thus the essence of the chair's 

 being a "thing", a unity, rather than a collection of independent 

 parts corresponds to the presence of the constraint. 



7/17. Seen from this point of view, the world around us is extremely 

 rich in constraints. We are so familiar with them that we take 

 most of them for granted, and are often not even aware that they 

 exist. To see what the world would be hke without its usual 

 constraints we have to turn to fairy tales or to a "crazy" film, and 

 even these remove only a fraction of all the constraints. 



A world without constraints would be totally chaotic. The 

 turbulent river below Niagara might be such a world (though the 



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