Stated primarily only for two given states, which must have the
Same values in their x, y, and z-components and must differ in
Their u-components. For an immediate effect at one pair of states
Does not, in general, restrict the possibilities at another pair of
States. Thus, the transformation mentioned above gives the transi-
Tions:
(0,0,0,0) → ( , ,0, )
(1,0,0,0) → ( , ,0, )
(0,0,1,0) → ( , ,0, )
(1,0,1,0) → ( , ,2, )
(where irrelevant values have been omitted). The first two show
That in one region of space u does not have an immediate effect on
Y, and the second two show that in another region it does. Strictly,
Therefore, the question “what is the immediate effect of u on y?”
Can be answered only for a given pair of states. Often, in simple
Systems, the same answer is given over the whole phase space; if
This should happen we can then describe the immediate effect of
U on y unconditionally. Thus in the example above, u has an
Immediate effect on y at all points but a particular few.
This test, for u’s immediate effect on y, simply does in symbols
What the experimenter does when he wishes to test whether one
Variable has an immediate effect on another: he fixes all variables
Except this pair, and compares how one behaves when the other
Has a value u1 with how it behaves when the other has the value u2.
The same method is, in fact, used generally in everyday life.
Thus, if we go into a strange room and wish to turn on the light,
And find switches, our problem is to find which switches are and
Which are not having an effect on the light’s behaviour. We
Change one of the switches and observe whether this is followed
By a change in the light’s behaviour. In this way we discover on
Which switch the light is dependent.
The test thus accords with common sense and has the advantage
Of being applicable and interpretable even when we know nothing
Of the real physical or other factors at work. It should be noticed
That the test requires no knowledge of extraneous factors: the
|
|
|
Result is deduced directly from the system’s observed behaviour,
And depends only on what the system does, not on why it does it.
It was noticed above that a transducer may show any degree of
56
Arbitrariness in the distribution of the immediate effects over the
Phase space. Often, however, the distribution shows continuity, so
That over some appreciable region, the variable u, say, has an
Immediate effect on y while over the same region x has none.
When this occurs, a diagram can often usefully be drawn showing
These relations as they hold over the region (which may some-
Times be the whole phase-space). An arrow is drawn from u to y
If and only if u has an immediate effect on y. Such a diagram will
Be called the diagram of immediate effects.
Such diagrams are already of common occurrence. They are
Often used in physiology to show how a related set of variables
(such as blood pressure, pulse rate, secretion of adrenaline, and
Activity at the carotid sinus) act on one another. In the design of
Computing machines and servomechanisms they are known as
“control-flow charts”. They are also used in some large busi-
Nesses to show the relations of control and information existing
Between the various departments.
The arrow used in such a diagram is, of course, profoundly dif-
Ferent in meaning from the arrow used to show change in a tran-
Sition (S.2/2). In the latter case it means simply that one state
Changes to another; but the arrow in the diagram of immediate
Effects has a much more complex meaning. In this case, an arrow
From A to B says that if, over a series of tests, A has a variety of
Different values— B and all other conditions starting with the same
Value throughout— then the values that B changes to over the
Series will also be found to show variety. We shall see later (S.8/
|
|
|
That this is simply to say that a channel of communication goes
From A to B.
When a transducer is given, either in algebraic or real material
Form, we can examine the immediate effects within the system
And thus deduce something of its internal organisation and struc-
Ture. In this study we must distinguish carefully between “imme-
Diate” and “ultimate” effects. In the test given above, the effect of
Дата добавления: 2019-11-16; просмотров: 239; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!