It is now the place in which to give a clear account of the king’s
activity, and explain how he maintained the varied life of the valley.
And the best plan is to take a typical instance, and to adopt the Arabic
method of description. By the Arabic method of description is meant the
same method which the Arabs used for the description of numerical
quantities. For instance, in the Arabic notation, if we are asked the
number of days in the year, we answer first 300, which is a false
answer, but gives the nearest approximation in hundreds; then we say
sixty, which is a correction; last of all we say five, which makes the
answer a correct one, namely, 365. In this simple case the description
is given so quickly that we are hardly conscious of the nature of the
system employed. But the same method when applied to more difficult
subjects presents the following characteristics. Firstly, a certain
statement is made about the subject to be described, and is impressed
upon the reader as if it were true. Then, when that has been grasped,
another statement is made, generally somewhat contradictory, and the
first notion formed has to be corrected. But these two statements taken
together are given as truth. Then when this idea has been formed in the
mind of the reader, another statement is made which must likewise be
received as a correction, and so on, until by successive statements and
contradictions, or corrections, the idea produced corresponds to the
facts, as the describer knows them.
Thus the activity of the king will be here described by a series of
statements, and the truth will be obtained by the whole of the
statements and the corrections which they successively bring in.
When the king wished to start a being on the train of activity he
divided its apathy into pleasure and pain. The pleasure he connected
with one act which we will call A. The pain he associated with another
act which we will call B.
These two “acts,” A and B, which together form what we call an “action,”
were of such a nature that the doing of A first and then of B was a
process used in the organization of the life in the valley.
Thus the act A may be represented by moving the right foot, B by moving
the left foot, then AB will be the action of taking a step. This however
is but a superficial illustration, for the acts which we represent by A
and B were fundamental acts, of which great numbers were combined
together in any single outward act which could be observed or described.
Suppose for the present that there is only one creature in the valley.
The king separates his apathy with regard to the action AB. Let us say
he separates his apathy into 1000 pleasure and 1000 pain. Of the
pleasure he lets the being experience the whole, of the pain he bears an
amount which we will represent by 2. Thus the being has 1000 pleasure
and 998 of pain, and the action is completed. His sensation is measured
by the number 1000 in the first act, and by 998 in the second act.
But the king did not choose to make the fundamental actions of this
limited and finishing kind. As the type of the fundamental activity, he
chose an action, and made the being go through it again and again. Thus
the being would go through the act A, then the act B. When the action AB
was complete it would go through an act of the kind A again, then
through an act of the kind B. Thus the creature would be engaged in a
routine of this kind, AB, AB, AB, and so on.
And if the creature had been alone, and this had been the sole activity
in which it was concerned, the king would have gone on bearing 2 of pain
in each of these actions. The king would have kept the routine going on
steadily, the creature bearing 1000 of pleasure in each A, and 998 of
pain in each B.
At this point it may be asked that an example should be given of one of
these elementary routines which the king set going. And this seems a
reasonable request, and yet it is somewhat too peremptory. For in the
world we may know of what nature the movements of the atoms are without
being able to say exactly what the motion of any one is. In such a case
a type is the only possible presentation. Again, take the example of a
crystal. We know that a crystal has a definite law of shape, and however
much we divide it we find that its parts present the same conformation.
We cannot isolate the ultimate crystalline elements, but we infer that
they must be such as to produce the crystal by their combination.
Now life on the valley was such in its main features as would be
produced by a combination of routines of the kind explained. There were
changes and abrupt transitions, but the general and prevailing plan of
life was that of a routine of alternating acts of a pleasurable and a
painful kind. It was just such as would be built up out of elementary
routines, on which the king could count, and which, unless he modified
their combinations, tended to produce rhythmic processes of a larger
kind. And even the changes and abruptnesses had a recurrent nature about
them, for if any routine in the valley altered suddenly, it was found
that there were cases of other routines altering in like manner, when
the conditions under which they came were similar. Thus the fundamental
type of the action which the king instituted was that of a routine AB,
AB, as described above. But there were two circumstances which caused a
variation, so that this simple routine was modified.
Firstly, there was not one being only but many.
Secondly, the king wished to have some of his pain-bearing power set
free from time to time. He did not wish to have to be continually
spending it all in maintaining the routines he had started at first, and
those immediately connected with them.
When he first began to organize the life of the beings he did not
consciously keep back any of his pain-bearing power, but threw it all in
the activities which he started. Still from time to time he wished to
start new activities quite unconnected with the old, and for this reason
he withdrew some of his pain-bearing power, as will be shown afterwards.
There were many beings. The king chose that the type of activity in each
should be a routine. In that way he could calculate on the activity, and
hold it in his mind as a settled process on whose operation he could
count. But as the routines of the beings proceeded they came into
contact with one another, and made, even by their simple co-existence,
something different from what a routine by itself was. They interwove in
various ways. Then, in order to take advantage of the combinations of
these routines, or to modify them, it was necessary to set going other
routines.
In order to be able to originate these connected routines the king
adopted the following plan.
In the first action AB he separated the creatures’ apathy into 1000
pleasure and 1000 pain, bearing 2 of the pain himself. The creature thus
went through 1000 of pleasure and 998 of pain. In the next action AB he
did not separate the beings’ apathy up into so much pleasure and pain.
He separated it up into 980 pleasure and 980 pain, that is, each moment
of feeling was 20 less in sensation than the moments of feeling were in
the first action.
Now it is obvious that if the bearing 2 of pain will make it worth while
for a being to go through 1000 pleasure and 998 pain, then the bearing
on the king’s part of 1 of pain would make it worth while for the being
to go through 500 pleasure and 499 of pain.
And a similar relation would hold for different amounts of pleasure and
pain. Thus clearly for the being to go through 980 of pleasure and the
corresponding amount of pain, it would not be necessary for the king to
bear so much as when the being went through 1000 of pleasure and the
corresponding amount of pain.
Consequently when the king divided the beings’ apathy into 980 pleasure
and 980 pain, it would not be necessary for him to bear 2 of pain to
make it worth the beings’ while to go through the action. The king would
not bear so much as 2 of pain, and thus he would have some of his
pain-bearing power set free. He would have exactly as much as would
enable him to make it worth a being’s while to go through an action with
the moments of 20 of pleasure and 20 of pain.
And this—with a correction which will come later—is what the king did.
He employed the pain-bearing power thus set free in starting other
routines. Thus in the routine AB, AB, AB there would be first of all the
action AB. Then along with the second action AB, the king (with the
pain-bearing power set free) started an action CD—the beginning of a
routine CD, CD, CD. Thus as the first routine went on and came into
connection with other routines, new and supplementary routines sprang up
which regulated and took advantage of the combinations of the old
routines.
The amount of the moments of pleasure in the routine CD, was (with a
slight correction explained below) measured in sensation, equal to 20.
Thus the moment of pleasure in the first A being 1000, the moment of
pleasure in the second A was 980, the moment of pleasure in the first C
was 20 (subject to the correction spoken of). Thus the total amount of
sensation in the second A and the associated act C, taken together (but
for a small correction) was equal to the sensation in the first A. Hence
the three points which were characteristic of the activity of the beings
in the valley are obvious enough.
1. There is as fundamental type a routine AB, AB, AB, the sensation
involved in which goes on diminishing.
2. There are routines CD, CD, &c., connected with AB, AB, in which the
sensation which disappears in the routine AB, AB seems to reappear.
3. In the action AB itself there is a disappearance of sensation. The
sensation connected with A is 1000, that connected with B is 998. Thus 2
of sensation seems to have disappeared. This 2 of sensation is of course
the pain which the king bore, and which was the means whereby the
creature was induced to go through the action at all. But looked at from
the point of view of sensation, it seems like a diminution of amount.
This diminution of amount, owing to the correction spoken of above, was
to be found regularly all through the routine.
And now, with the exception of the final correction, the theory of the
king’s activity is complete. There are certain mathematical difficulties
which render an exhaustive account somewhat obscure in expression. When
we take a general survey of a theory we want to see roughly how it all
hangs together; but if we mean to adopt it, the exactitude of the
numerical relations becomes a matter of vital importance.
It must be added that the numbers taken above were taken simply for
purposes of illustration. In reality the pain born by the king was less
in proportion.
The exhaustive account which follows deals with small numerical
quantities. It had better be omitted for the present, and turned to
later on for reference.
EXHAUSTIVE ACCOUNT.
We keep for the time being to the numbers used above. When the king had
enough pain-bearing power set free in the second action of the routine
AB, AB to start another routine CD, of 20 pleasure 20 pain, he did not
use it all. He only used enough of it to set a routine going the moments
of pleasure and pain in which were 16 in sensation. The routine CD was
made up of acts with 16 of pleasure and 16 of pain.
The sensation in the first A was 1000, in the first B it was 998, giving
a disappearance of 2. In the second A it was 980, and in C, which starts
concurrently with the second A, it was not 20 as might have been
expected, but 16, giving a loss of 4. The second A is less than the
first A by 20. Searching for that 20 we find 16 in C. But there has been
a disappearance of 4.
Looking now at the successive acts in the series we have in A 1000
sensation, in B 998 sensation, in A and C together 996 sensation.
The cause of the loss between A and B has already been explained. That
between B and the second A with C remains to be accounted for.
It has been already said that the king withdrew some of his pain-bearing
power from the routine AB and all routines connected with it, thus he
was enabled to start activities altogether unconnected with those which
he had originated, and was with regard to the products of his own
activity as he had been at first, with regard to the beings in the
valley before he started them on the path of life. And it was in
consequence of his withdrawal of his pain-bearing power that the amount
of sensation in C was not 20 but was less. This loss of 4 of sensation
to the being corresponded to a setting free of a certain portion of
pain-bearing power on the part of the king. And thus as the process went
on, a portion of his power was continually being returned to him.
In the table below the first line of figures contains the amount of
sensation in the actions AB, AB. The second line of figures contains the
amount of sensation in the actions CD, CD. The third line of figures
relates to another connected routine EF, EF, which originates in a
manner similar to CD. The fourth line of figures represents the amount
of pain borne by the king, the fifth line represents his pain-bearing
power set free.
(1) 1000 998 980 978-40/1000 960 958-80/1000
A B A B A B
(2) 16 15-998/1000 15-630/1000 15-658640/1000000
C D C D
(3) 16 15-998/1000
E F
(4) 2 1-992/1000 1-991/1000
+
360/1000000
(5) 0 8/1000 8/1000 +
640/1000000
If the total amount of sensation which is experienced by the being in
the original routine and the connected routines in the consecutive
stages be summed up, it will be found to be
1000, 998, 996, 994-88/1000, 991-680/1000,
and so on.
Finally, the proportion of pain borne by the king was so small compared
with the sensation experienced by the being, that A and B were
apparently equal in sensation. Thus the sensation in the second A and in
C together becomes apparently equal to that in B. And instead of the
sensation diminishing quickly as shown above, it was only after a great
many acts of the primary and connected routines had been gone through
that any diminution of sensation in the form which the being could
experience it was to be detected. Thus, as before stated, there was:
1. A routine of continually diminishing sensation.
2. Connected routines the sensation in which was apparently equal to
that lost in A.
3. There was a continuous disappearance of sensation from the experience
of the beings accompanying every step of the routine. The sensation
which they could experience was less in every subsequent step and
connected steps than in any one in which it was measured.