The method is simple in principle: he must specify broadly, and
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Must specify a general method by which the details shall be spec-
Ified by some source other than himself. In the examples above, it
Was a pack of cards that made the final decision. A final, unique
System can thus be arrived at provided his specification is supple-
Mented. (The subject is developed more thoroughly in S.13/18.)
Ex. 1: Define a method (using dice, cards, random numbers, etc.) that will bring
The closed single-valued transformation T:
S S S S S ST: ↓ ?1 ?2 ?3 ?4 ?5 ?6
To some particular form, so that the final particular form is selected by the
Method and not by the reader.
Ex. 2: (Continued.) Define a method so that the transformation shall be one-one,
But not otherwise restricted.
Ex. 3: (Continued.) Define a method so that no even-numbered state shall trans-
Form to an odd-numbered state.
Ex. 4: (Continued.) Define a method so that any state shall transform only to a
State adjacent to it in number.
Ex. 5: Define a method to imitate the network that would be obtained if parts
Were coupled by the following rule: In two dimensions, with the parts placed
M a regular pattern thus:
0 0 0
0 0 0
0 0 0
Extending indefinitely in all directions in the plane, each part either has an
Immediate effect on its neighbour directly above it or does not, with equal
Probability; and similarly for its three neighbours to right and left and below.
Construct a sample network.
Richness of connexion. The simplest system of given large-
Ness is one whose parts are all identical, mere replicates of one
Another, and between whose parts the couplings are of zero degree
(e.g. Ex. 4/1/6). Such parts are in fact independent of each other
Which makes the whole a “system” only in a nominal sense, for it
Is totally reducible. Nevertheless this type of system must be con-
Sidered seriously, for it provides an important basic form from
Which modifications can be made in various ways. Approximate
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Examples of this type of system are the gas whose atoms collide
Only rarely, the neurons in the deeply narcotised cortex (if they
Can be assumed to be approximately similar to one another) and a
Species of animals when the density of population is so low that
They hardly ever meet or compete. In most cases the properties of
This basic type of system are fairly easily deducible.
The first modification to be considered is obviously that by
Which a small amount of coupling is allowed between the parts,
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A N I N T R O D UC T I O N T O C Y B E R NE T I C S
TH E MA C HI N E WI TH I N PUT
So that some coherence is introduced into the whole. Suppose then
That into the system’s diagram of immediate effects some actions,
I.e. some arrows, are added, but only enough to give coherency to
The set of parts. The least possible number of arrows, if there are
N parts, is n– 1; but this gives only a simple long chain. A small
Amount of coupling would occur if the number of arrows were
Rather more than this but not so many as n2– n (which would give
Every part an immediate effect on every other part).
Smallness of the amount of interaction may thus be due to
Smallness in the number of immediate effects. Another way,
Important because of its commonness, occurs when one part or
Variable affects another only under certain conditions, so that the
Immediate effect is present for much of the time only in a nominal
Sense. Such temporary and conditional couplings occur if the vari-
Able, for any reason, spends an appreciable proportion of its time
Not varying (the “part-function”). One common cause of this is the
Existence of a threshold, so that the variable shows no change
Except when the disturbance coming to it exceeds some definite
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