A world without constraints would be totally chaotic. The tur-
Bulent river below Niagara might be such a world (though the
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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
Q UA N TI TY O F V AR IE TY
Physicist would still find some constraint here). Our terrestrial
World, to which the living organism is adapted, is far from pre-
Senting such a chaos. Later (S.13/5) it will be suggested that the
Organism can adapt just so far as the real world is constrained, and
No further.
Ex.: Attempt to count, during the next one minute, all the constraints that are
Operating in your surroundings.
Prediction and constraint. That something is “predictable”
Implies that there exists a constraint. If an aircraft, for instance,
Were able to move, second by second, from any one point in the
Sky to any other point, then the best anti-aircraft prediction would
Be helpless and useless. The latter can give useful information only
Because an aircraft cannot so move, but must move subject to sev-
Eral constraints. There is that due to continuity— an aircraft cannot
Suddenly jump, either in position or speed or direction. There is the
Constraint due to the aircraft’s individuality of design, which
Makes this aircraft behave like an A-10 and that one behave like a
Z-20. There is the constraint due to the pilot’s individuality; and so
On. An aircraft’s future position is thus always somewhat con-
Strained, and it is to just this extent that a predictor can be useful.
Machine as constraint. It will now be appreciated that the
Concept of a “machine“, as developed from the inspection of a
Protocol (S.6/5), comes from recognising that the sequence in the
Protocol shows a particular form of constraint. Were the protocol
To show no constraint, the observer would say it was chaotic or
Unpredictable, like a roulette-wheel.
When it shows the characteristic form of constraint, the
Observer can take advantage of the fact. He does this by re-coding
The whole protocol into a more compact form, containing only:
I) a statement of the transformation
And (ii) a statement of the actual input given.
Subsequently, instead of the discussion being conducted in terms
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Of a lengthy protocol, it is conducted compactly in terms of a suc-
Cinct transformation; as we did throughout Part I.
Thus, use of the transformation is one example of how one can
Turn to advantage the characteristic constraint on behaviour
Imposed by its being “machine-like”.
Ex.: If a protocol shows the constraint characteristic of a machine, what does the
Constraint exclude ?
Within the set of determinate machines further constraints
May be applied. Thus the set can be restricted to those that have a
Certain set of states as operands, or to those that have only one
Basin, or to those that are not reducible.
A common and very powerful constraint is that of continuity. It
Is a constraint because whereas the function that changes arbitrar-
Ily can undergo any change, the continuous function can change,
At each step, only to a neighbouring value. Exercise 4 gives but a
Feeble impression of the severity of this constraint.
Ex. 1: The set of closed single-valued transformations (absolute systems) on
Three states a, b, c has 27 members (compare Ex. 7/7/7). How many members
Remain if we add the restriction that the absolute system is to have no state
Of equilibrium?
Ex. 2: (Continued.) Similarly, but the restriction is that there must be only one
Basin.
Ex. 3: (Continued.) Similarly, but the restriction is that the transitions a -> b and
b → c may not occur.
Ex. 4: A vector has ten components, each of which can take one of the values: 1,
How much variety has the set of vectors if (i) the components vary
Independently (S.7/12); (ii) under the rule that no two adjacent components
May differ in value by more than one unit ?
Learning and constraint. For the psychologist, an important
Example of constraint occurs in learning. Pavlov, for instance, in
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One experiment gave both thermal and tactile stimuli, as well as
Reinforcement by meat powder, in the following combinations:
ThermalTactileReinforcement
1+++
2+––
3– ++
4–––
(The fourth combination occurred, of course, in the intervals.)
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