CHAPTER V.
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
| 960 | 958
| ||||||
| A | B | A | B | A | B | |||||||
| (2) | 16 | 15
| 15
| 15
| ||||||||
| C | D | C | D | |||||||||
| (3) | 16 | 15
| ||||||||||
| E | F | |||||||||||
| (4) | 2 | 1
| 1
| |||||||||
| (5) | 0 |
|
| |||||||||
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, 994881000, 9916801000, |
| 88 |
| 1000 |
| 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.