In a system. It may well happen that the view taken when the mat-
Ter is examined in the small is quite different from that taken in the
Large. Thus suppose it is asked whether the brewing industry in
England is localised. The Exciseman, knowing of every building
In his district whether it is or is not part of the brewing trade, will
Say that brewing is undoubtedly “localised”. On the other hand,
The map-maker of England, being unable to mark any particular
County as being the seat of brewing, will say that it is not local-
Ised. Each, of course, is correct. What allows the contradiction is
That when the range of size is great, what is true at one end of the
Scale may be false at the other.
Another example showing how contradictory may be the proper-
Ties in the small and the large is given by an ordinary piece of elas-
Tic. For years physical chemists searched for what made the
Molecule contractile. They have since discovered that they were
Making exactly the mistake that this section is attempting to pre-
Vent. It is now known that the rubber molecule has no inherent con-
tractility: stretch one out and let it go, and nothing happens! Why
Then does rubber contract ? The point is that “stretching rubber” is
not “stretching one…”; the molecules, when there are more than
One, jostle each other and thereby force the majority to take lengths
Less than their maxima. The result is that a shortening occurs, just as
If, on a crowded beach, a rope fifty feet long is drawn out straight:
after a few minutes the ends will be less than fifty feet apart!
Further examples are hardly necessary, for the point to be made
Is the merely negative one that in a large system there is no a priori
Necessity for the properties of the whole to be a simple copy of
Those of the parts. (S.7/3 adds some further examples.)
As the system becomes larger, so does the fundamental
Method of study (S.6/3) become more laborious in application.
Eventually the amount of labour necessary becomes prohibitive.
What then is the observer to do? The question is of great impor-
Tance in the biological sciences, whether zoological or sociologi-
Cal, for the size and complexity of the systems is great indeed.
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The same difficulty has occurred in other sciences. Thus
112
Although the Newtonian theory has, in principle, solved all gravi-
Tational problems, yet its application to three bodies is most com-
Plex, and its application to half a dozen is prohibitively laborious.
Yet astrophysicists want to ask questions about the behaviour of
star clusters with 20,000 members! What is to be done?
Experience has shown that in such cases the scientist must be
Very careful about what questions he asks. He must ask for what
He really wants to know, and not for what he thinks he wants. Thus
The beginner will say simply that he wants to know what the clus-
Ter will do, i.e. he wants the trajectories of the components. If this
Knowledge, however, could be given to him, it would take the
Form of many volumes filled with numerical tables, and he would
Then realise that he did not really want all that. In fact, it usually
Happens that the significant question is something simple, such as
“will the cluster contract to a ball, or will it spread out into a disc?”
The physicists, led originally by Poincare, have now a well
Developed method for dealing with such matters— that of topol-
Ogy. By its means, unambiguous answers can be given to simple
Questions, so that the intricacies that would overwhelm the
Observer are never encountered.
A similar method, applied to complicated differential equa-
Tions, enables the main important features of the solutions to be
Deduced in cases where the full solutions would be unmanageably
Complicated. This is the so-called “stability” theory of these equa-
Tions.
What is important for us here is that these methods exist. They
Suggest that if a Black Box (such as a brain) has far too many var-
Iables for a study in every detail to be practical then it should be
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Possible for the cybernetically-minded psychologist to devise a
“topological” approach that shall enable him to get what informa-
tion he really wants (not what he thinks he wants!) without his
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