TH E MA C HI N E WI TH I N PUT
In this case the whole is less richly connected internally, for one
Of the actions, or channels, is now missing.
The lessening can continue. We may find that the diagram of
Immediate effects is simply
PQ
So that the whole consists really of two parts that are functionally
Independent. In this case the whole is said to be reducible. The
Importance of this concept will be referred to later (S.13/21).
Ex.: Of the systems in Ex. 4/12/1, which are reducible?
At this minute of writing, the Laughter and Singing are
Troth sounding. Please tell me what manipulations of
Incense and organ I should make to get the house quiet, and
To keep it so.
(Hint: Compare Ex. 4/1/4.)
Ex. 2: (Continued.) Does the Singing have an immediate effect on the Laughter ?
Ex. 3: (Continued.) Does the incense have an immediate effect on the Singing ?
Ex. 4: (Continued.) Deduce the diagram of immediate effects of this machine
With input (with two parameters and two variables).
Materiality. The reader may now like to test the methods of
This chapter as an aid to solving the problem set by the following
Letter. It justifies the statement made in S.1/2 that cybernetics is not
Bound to the properties found in terrestrial matter, nor does it draw
Its laws from them. What is important in cybernetics is the extent
To which the observed behaviour is regular and reproducible.
“Graveside”
Wit’s End
Haunts.
Dear Friend,
Some time ago I bought this old house, but found it to be
Haunted by two ghostly noises— a ribald Singing and a sar-
Donic Laughter. As a result it is hardly habitable. There is
Hope, however, for by actual testing I have found that their
Behaviour is subject to certain laws, obscure but infallible,
And that they can be affected by my playing the organ or
Burning incense.
In each minute, each noise is either sounding or silent—
They show no degrees. What each will do during the ensu-
Ing minute depends, in the following exact way, on what
Has been happening during the preceding minute:
The Singing, in the succeeding minute, will go on as it was
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During the preceding minute (sounding or silent) unless there
Was organ-playing with no Laughter, in which case it will
Change to the opposite (sounding to silent, or vice versa).
As for the Laughter, if there was incense burning, then it
Will sound or not according as the Singing was sounding or
Not (so that the Laughter copies the Singing a minute later).
If however there was no incense burning, the Laughter will
Do the opposite of what the Singing did.
60
T HE VER Y LAR GE S YS TE M
Up till now, the systems considered have all seemed fairly
Simple, and it has been assumed that at all times we have under-
Stood them in all detail. Cybernetics, however, looks forward to
Being able to handle systems of vastly greater complexity— com-
Puting machines, nervous systems, societies. Let us, then, con-
Sider how the methods developed so far are to be used or modified
When the system is very large.
What is meant by its “size” needs clarification, for we are
Not here concerned with mere mass. The sun and the earth form
Only a “small” system to us, for astronomically they have only
Twelve degrees of freedom. Rather, we refer to the system’s com-
Plexity. But what does that mean here ? If our dynamic system
Were a native family of five persons, would we regard it as made
Of 5 parts, and therefore simple, or as of 1025 atoms, and therefore
Very complex ?
In the concepts of cybernetics, a system’s “largeness” must
Refer to the number of distinctions made: either to the number of
States available or, if its states are defined by a vector, to the num-
Ber of components in the vector (i.e. to the number of its variables
Or of its degrees of freedom, S.7/13). The two measures are corre-
Lated, for if other things are equal, the addition of extra variables
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Will make possible extra states. A system may also be made larger
From our functional point of view if, the number of variables
Being fixed, each is measured more precisely, so as to make it
Show more distinguishable states. We shall not, however, be
Much interested in any exact measure of largeness on some par-
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