Will be still at b. At the second step, a half of those still at b will
Move over to a and a half (i.e. a quarter of the whole) will remain at
B. By continuing in this way we find that, of those that were started
At b,
Reach a after 1 step
1/4 ,, ,, ,, 2 ,,
1/8 ,, ,, ,, 3 ,,
And so on. The average time taken to get from b to a is thus
1 ⁄ 2 × 1+1 ⁄ 4 × 2+1 ⁄ 8 × 3+…
---------------------------------------------------------------------------------- = 2 steps.-
1 ⁄ 2+1 ⁄ 4+1 ⁄ 8+…
Some of the trajectories will be much longer than 2 steps.
As is now well known, a system around a state of equilibrium
Behaves as if “goal-seeking”, the state being the goal. A corre-
Sponding phenomenon appears in the Markovian case. Here,
Instead of the system going determinately to the goal, it seems to
Wander, indeterminately, among the states, consistently moving to
Another when not at the state of equilibrium and equally consist-
Ently stopping there when it chances upon that state. The state still
Appears to have the relation of “goal” to the system, but the system
Seems to get there by trying a random sequence of states and then
Moving or sticking according to the state it has arrived at. Thus, the
Objective properties of getting success by trial and error are shown
When a Markovian machine moves to a state of equilibrium.
At this point it may be worth saying that the common name of
“trial and error” is about as misleading as it can be. “Trial” is in
The singular, whereas the essence of the method is that the
Attempts go on and on. “Error” is also ill-chosen, for the important
Element is the success at the end. “Hunt and stick” seems to
Describe the process both more vividly and more accurately. I
Shall use it in preference to the other.
230
Movement to a goal by the process of hunt and stick is thus
Homologous, by S.12/8, to movement by a determinate trajectory
For both are the movement of a machine to a state of equilibrium.
With caution, we can apply the same set of principles and argu-
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Ments to both.
Ex. 1: What states of equilibrium has the system of Ex. 12/10/l ?
Ex. 2: A Markovian machine has matrix
↓
a
b
c
d
e
f
a
b
c
.
.
.
1
.
.
d
.
.
.
.
1
.
e
.
.
.
.
.
1
f
.
.
.
.
.
1
1/3 1/3
1/3 1/3
1/3 1/3
..
..
..
It is started at a on many occasions; how would its behaviour be described
In the language of rat-maze psychology ?
M AR KOVI AN RE GULAT ION
The progression of a single Markovian machine to a state of
Equilibrium is much less orderly than that of a determinate machine,
So the Markovian type is little used in the regulators of industry. In
Comparison with the smooth and direct regulation of an ordinary
Servo- mechanism it must seem fumbling indeed. Nevertheless, liv-
Ing organisms use this more general method freely, for a machine
That uses it is, on the whole, much more easily constructed and
Maintained; for the same reason it tends to be less upset by minor
Injuries. It is in fact often used for many simple regulations where
Speed and efficiency are not of importance.
A first example occurs when the occupant of a room wishes to
Regulate the number of flies in the room at, or near, zero. Putting
A flypaper at a suitable site causes no determinate change in the
Number of flies. Nevertheless, the only state of equilibrium for
Each fly is now “on the paper”, and the state of equilibrium for
“number of flies not on the paper” is zero. The method is primitive
But it has the great virtues of demanding little and of working suf-
Ficiently well in practice.
A similar method of regulation is that often used by the golfer
Who is looking for a lost ball in an area known to contain it. The
States are his positions in the area, and his rule is, for all the states
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But one, “go on wandering”; for one however it is “stop the wan-
Dering”. Though not perhaps ideal, the method is none the less
Capable of giving a simple regulation.
231
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
Another example of regulation, of a low order of efficiency,
Would be shown by a rat with serious brain damage who cannot
Remember anything of a maze, but who can recognise food when
Encountered and who then stops to eat. (Contrast his behaviour
With that of a rat who does not stop at the food.) His progression
Would be largely at random, probably with some errors repeated;
Nevertheless his behaviour shows a rudimentary form of regula-
Tion, for having found the food he will stop to eat it, and will live,
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