Proteinness of the other. Thus what usually happens is that the two
Systems, biological and model, are so related that a homomor-
Phism of the one is isomorphic with a homomorphism of the
Other. (This relation is symmetric, so either may justifiably be said
To be a “model” of the other.) The higher the homomorphisms are
On their lattices, the better or more realistic will be the model.
At this point this Introduction must leave the subject of Homo-
Morphisms. Enough has been said to show the foundations of the
Subject and to indicate the main lines for its development. But
These developments belong to the future.
Ex. 1: What would be the case when it was the two top-most elements of the two
Lattices that were isomorphic?
Ex. 2: To what degree is the Rock of Gibraltar a model of the brain?
Ex. 3: To what extent can the machine
p q r ↓ q r r
Provide models for the system of Ex. 6/13/2?
4
6
5
This diagram is of a type known as a lattice— a structure much
Studied in modern mathematics. What is of interest in this Intro-
Duction is that this ordering makes precise many ideas about sys-
Tems, ideas that have hitherto been considered only intuitively.
Every lattice has a single element at the top (like 1) and a single
Element at the bottom (like 6). When the lattice represents the pos-
Sible simplifications of a machine, the element at the top corre-
Sponds to the machine with every state distinguished; it
Corresponds to the knowledge of the experimenter who takes note
Of every distinction available in its states. The element at the bot-
Tom corresponds to a machine with every state merged; if this
State is called Z the machine has as transformation only
↓
Z
Z
This transformation is closed, so something persists (S.10/4), and
The observer who sees only at this level of discrimination can say
Of the machine: “it persists”, and can say no more. This persist-
Ence is, of course, the most rudimentary property of a machine,
Distinguishing it from the merely evanescent. (The importance of
“closure”, emphasised in the early chapters, can now be appreci-
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Ated — it corresponds to the intuitive idea that, to be a machine, an
Entity must at least persist.)
Between these extremes lie the various simplifications, in their
Natural and exact order. Near the top lie those that differ from the
Full truth only in some trifling matter. Those that lie near the bot-
Tom are the simplifications of the grossest type. Near the bottom
Lies such a simplification as would reduce a whole economic sys-
108
T HE VE RY L ARGE B OX
The previous sections have shown how the properties that are
Usually ascribed to machines can also be ascribed to Black Boxes.
109
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 BL AC K B O X
We do in fact work, in our daily lives, much more with Black
Boxes than we are apt to think. At first we are apt to think, for
Instance, that a bicycle is not a Black Box, for we can see every
Connecting link. We delude ourselves, however. The ultimate links
Between pedal and wheel are those interatomic forces that hold the
Particles of metal together; of these we see nothing, and the child
Who learns to ride can become competent merely with the knowl-
Edge that pressure on the pedals makes the wheels go round.
To emphasise that the theory of Black Boxes is practically
Coextensive with that of everyday life, let us notice that if a set of
Black Boxes has been studied by an observer, he is in a position
To couple them together to form designed machinery. The method
Is straightforward: as the examination of each Box has given its
Canonical representation (S.6/5), so can they be coupled, inputs to
Outputs, to form new systems exactly as described in S.4/8.
What is being suggested now is not that Black Boxes behave
Somewhat like real objects but that the real objects are in fact all
Black Boxes, and that we have in fact been operating with Black
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Boxes all our lives. The theory of the Black Box is merely the the-
Ory of real objects or systems, when close attention is given to the
Question, relating object and observer, about what information
Comes from the object, and how it is obtained. Thus the theory of
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