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134 First Steps to Jainism
Ps will reach a maximum for some value of n and then decline. For example if p=.6, q=.3, r=.1, P, reaches its maximum value of .5184 when n=4.
I have dealt with a case which arises when the question asked is as simple as possible. Human judgements are generally more complicated. We may attend to the data of several different senses, and of our memories. Thus we arrive at one conclusion from one set of data, and another from another set. We say that wood is hard when compared with clay, soft when compared with iron, indeterminate when compared with similar wood.
The close analysis of vision with a dark adapted eye shows that in this case at least. Mahalanobis was correct in regarding the saptabhanginaya as foreshadowing modern statistical theory. It appears that when dark adaptation is complete, about five quanta of radiation must arrive within a short time in a small area of the retina before light is reported. Whether they will do so with a given intensity of illumination can only be stated as a probability. It is probable, though not by any means certain, that more complicated judgements depend on similar probabilities of events within the central nervous system.
Whatever philosophers of other schools may think, a Jaina can hardly object to regarding human predication as a special kind of animal behaviour. In this he agree with followers of Darwin, such as myself. Attempts at a logical classification of animal behaviours frequently lead to a separation of 2"-1 types, where however n may exceed 3. Thus Haldane (1953) classified the possible results of learning in an animal as follows. In any situation an animal will, or will not, give a certain response R, say eating a particular type of food within a minute of its presentation, or lifting its leg within ten seconds after an auditory signal is given.
If we compare the set of possible situations in which an animal may be placed before and after an experience E, they fall into four categories, r r, rR, R r, and RR. A situation rr is one in which the response is not given before or after experience. A situation r R is one which it is given after E, but not before E, and so on. All situations may be r r. For example no-one has taught a dog to write. Some may be r r and some rr. For example a dog which did not previously bring objects from the water to his master can learn
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