It is easy to see, therefore, that, provided the same change is made
To all, change of parameter-value to the whole set cannot increase
The set’s variety. This is true, of course, whether D and E are states
Of equilibrium or not. Now let the system continue under P2. The
Two groups, once resting apart at D and E, will now both come to
B; here all will have the same state, and the variety will fall to
Zero. Thus, change of parameter-value makes possible a fall to a
New, and lower, minimum.
The condition that the change P1 -> P2 may lead to a further fall
In variety is clearly that two or more of P1’s states of equilibrium
Lie in the same P2 basin. Since this will often happen we can make
The looser, but more vivid, statement that a uniform change at the
Inputs of a set of transducers tends to drive the set’s variety down.
As the variety falls, so does the set change so that all its mem-
Bers tend, at each moment, to be at the same state. In other words,
Changes at the input of a transducer tend to make the system’s
State (at a given moment) less dependent on the transducer’s indi-
Vidual initial state and more dependent on the particular sequence
Of parameter-values used as input.
The same fact can be looked at from another point of view. In
The argument just given, “the set” was taken, for clarity, to be a set
Of replicates of one transducer, all behaving simultaneously. The
Theorem is equally applicable to one transducer on a series of
Occasions, provided the various initial times are brought into
138
Proper correspondence. This point of view would be more appro-
Priate if we were studying some very complex transducer, making
Fresh experiments on it each day. If it contained great numbers of
Rather inaccessible parts, there might be difficulty in bringing it
Each morning back to some standardised state ready for the next
Experiment. The theorem says that if its input is taken, in the early
Morning, through some standardised routine, then the longer the
Routine, the more certain is it that the machine will be brought,
Ready for the experimenter, to some standard state. The experi-
Menter may not be able to name the state, but he can be confident
|
|
|
That it tends to be reproducible.
It should be noticed that mere equality of the set’s parameter at
Each step of the sequence is not sufficient; if the effect is to be
More than merely nominal (i.e. null) the parameters must undergo
Actual, non- zero, change.
The theorem is in no way dependent for its truth on the size of
The system. Very large systems are exactly as subject to it as small,
And may often be expected to show the effect more smoothly and
Regularly (by the statistical effect of largeness). It may therefore
Be usefully applicable to the brain and to the social and economic
System.
Examples that may correspond to this process are very com-
Mon. Perhaps something of this sort occurs when it is found that
A number of boys of marked individuality, having all been through
The same school, develop ways that are more characteristic of the
School they attended than of their original individualities. The
Extent to which this tendency to uniformity in behaviour is due to
This property of transducers must be left for further research.
Some name is necessary by which this phenomenon can be
Referred to. I shall call it the law of Experience. It can be
Described more vividly by the statement that information put in by
Change at a parameter tends to destroy and replace information
About the system’s initial state.
139
T RA N SMISSI O N O F VA R IE TY
Chapter
8
Brief account mentions no less than sixteen major transformations
Through all of which something has been preserved, though the
Superficial appearances have changed almost out of recognition.
Complexity of coding. When considering such repeated cod-
Ings the observer may easily over-estimate the amount of com-
Plexity that has been introduced. It not uncommonly happens that
|
|
|
The amount of complexity is nothing like as large as a first impres-
Sion might suggest.
A simple example, showing how a complex coding may have
Hidden simplicities, occurs when a simple one-one coding of the al-
Дата добавления: 2019-11-16; просмотров: 217; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!