Cone, will allow air to escape, and will cause a fall of the pressure
Z inside B; conversely, a movement up at L will make z rise.
The air pressure in B works in opposition to a heavy weight P,
Which IS continued upwards as a pillar, the whole weight being
Able to move only up or down. The pillar carries two pivots, K and
Fig. 12/21/1
M. M is pivot for a strong bar G, which is fixed at one end, F Thus
If P moves upwards, M must move upwards by the same amount,
And G’s free end H must move upwards by twice the distance.
Now let us see what happens if L is moved. Suppose the opera-
Tor lifts L by one inch. The other end (V) falls at once by one inch
The valve is more obstructed, less air escapes, and more accumu-
Lates in B, sending up the pressure. The increased pressure will lift
P, and thus M and H. Thus H’s movements tend simply to copy
L’s. (We can notice that the upward movement of P (L being fixed
After its one inch rise) will make the valve V open, so the response
Of the whole system to L’s movement will be self-limiting, for the
Feedback is negative; subject to certain quantitative details, which
239
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 ERR O R- CO N TR O LLED REG U LA TO R
Would require exact treatment in any particular embodiment, the
System is thus stable at a state of equilibrium whose position is
Determined by L’s position.)
The whole can thus also be regarded as a stable system that acts
So that, while a movement of, say, one inch at L would tend to
Cause, at V, a movement of one inch also, the reaction of the sys-
Tem annuls this. So the system can also be regarded as one that
Acts so as to keep the position of V constant.
We can now see how it can become a power amplifier, and be
Used as a crane.
The designer takes care to see that the lever J is light, and that
The valve is shaped so that the escaping air, or the pressure z, has
Little effect on the force required at L. He also takes care that B
Shall have a large area of action on P, and that the average work-
Ing pressure z shall be high (with the pressure at A higher still). If
He is successful, a small force at L, raising it through one inch, will
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Be sufficient to evoke a large force at H sufficient to raise a heavy
Mass through the same distance. Thus a force of 1 lb. moving
Through one inch at L may result in a force of 1000 lbs. moving
Through one inch at H. It is thus a work- (or power-) amplifier.
So far it has given merely a simple and clear exemplification of
The principles of regulation and control described earlier. Later
(S.14/1) we shall return to it, for we shall have to be clear about
How we can have, simultaneously, a law saying that energy cannot
Be created, and also a power-amplifier.
Ex. 1: How many degrees of freedom for movement have the three bodies, P,
J, G?
Ex. 2: Modify the arrangement so as to make H move oppositely to L while
Keeping the equilibrium stable.
Ex. 3: Modify the arrangement so that the equilibrium is unstable.
This, for instance, may be the case in wild life when a prey
Attempts to regulate against an attack by a predator, when the
Whole struggle progresses through alternating stages of threat and
Parry. Here the predator’s whole attack consists of a sequence of
actions D1, D2, D3 …, each of which evokes a response, so that the
whole response is also a sequence, R1, R2, R3, …,The whole strug-
Gle thus consists of the double sequence
D1, R1, D2, R2, D3 , R3, …
The outcome will depend on some relation between the predator’s
Whole attack and the prey’s whole response.
We are now considering an even more complex interpretation
Of the basic formulation of S.11/4. It is common enough in the
Biological world however. In its real form it is the Battle of Life;
In its mathematical form it is the Theory of Games and Strategies.
Thus in a game of chess the outcome depends on what particular
Sequence of moves by White and Black
W1, B1, W2, B2, W3 , B3, …
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Has been produced. (What was called a “move” in S.11/4 corre-
Sponds, of course, to a play here.)
This theory, well founded by von Neumann in the ’30s, though
Not yet fully developed, is already too extensive for more than
Mention here. We should, however, take care to notice its close
And exact relation to the subject in this book. It will undoubtedly
Be of great scientific importance in biology; for the inborn char-
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