December 11, 2017

The brain as a probability calculator

If a bridge player is to maximize his chances of winning he must be able to calculate the most probable distribution of the cards yet to be played among the three other players. Similar probability calculations are required on the part of all gamblers if they are to maximize their chances of success. A little reflection will reveal that this must apply to all behavioural processes. In each case, the hypothesis that is postulated, and on which a behavioural response is based, must be the one that has the highest probability. The fact that this is not evident at first sight, as it is in a game of chance, is because what constitutes the most probable hypothesis to explain a given situation will be different in each case, since the information in terms of which probabilities must be calculated will, like Heraclitus’s river, be modified with each experience.

Are we not over-estimating the capacity of biological organisms in suggesting that they are capable of making such precise calculations? I do not think so. The ability of relatively simple organisms to perform mathematical feats which would test the capacity of the most able mathematician has been clearly demonstrated. For instance, experiments with the lesser white-throated warbler have revealed that they are guided by the stars during their migrations. The skill with which they are able to do this is quite surprising. Sauer writes:

“Warblers have a remarkable hereditary mechanism for orientating themselves by the stars, a detailed image of the starry configuration in the sky, coupled with a precise time sense which relates the heavenly canopy to the geography of the earth at every time and season. At their very first glimpse of the sky, the birds automatically know the right direction. Without the benefit of previous experience, with no key except the stars, the birds are able to locate themselves in time and space, and to find their way to their destined post . . .

“Not only does this ‘Time-sense’ allow them to take account of the sun’s motion across the sky, but it must also be able to make adjustments to astronomical evolution, for, in the course of time, the pattern of constellations in the sky is slowly but constantly changing.”

It is clear that these birds are in possession of an advanced piece of measuring equipment, which our best engineers would have difficulty in designing.

Another example is provided by a little fish (Gymnarchus niloticus) that lives in the Nile. It is capable of darting in muddy water after the small fish on which it feeds, and never bumps into anything, in spite of the fact that its eyes are quite degenerate and only sensitive to extremely bright light. Liss-man, who spent 12 years experimenting with this fish, found that it owed its capacity for finding its way around so skilfully to its ability to discriminate between minute differences in the conductivity of the objects in its immediate environment. This skill is so developed that the Gymnarchus can tell the difference between mixtures of different proportions of tap water and distilled water entirely on the basis of their different conductivity. If salts or acids are added to the distilled water so that its electrical conductivity matches that of the tap water, it can no longer discriminate between them. Here again a complicated calculation must be made. To give an dea of the precision involved, Lissmann worked out:

“. . . that the Gymnarchus can respond to a continuous direct-current stimulus of about 0.15 microvolt per centimetre, a value that agrees reasonably well with the calculated sensitivity required to recognise a glass rod 2 millimetres in diameter. This means that an individual sense organ should be able to convey information about a current change as small as 0.003 micro-microampere. Extended over the integration time of 25 milliseconds, this tiny current corresponds to a movement of some 1,000 univalent, or singly charged ions.”

Similarly, Noel-Martin noted the extraordinary mathematical ability of bees:

“Honeycombs are built according to maximum efficiency principles. Being hexagonal, the cells make use of available space in the most economic and symmetrical way possible, and the angle between adjoining cells is such that the smallest possible amount of wax is required for their construction.”

It may be thought that these examples are simply curiosities of Nature. However, if our thesis be correct, they are but striking examples of a principle in terms of which we must explain “perception” and “thought” at all levels of organisation.

Thus, when I look out of my window and see a tree, a road, and people walking about, I am in fact formulating that hypothesis as to the nature of the environmental data isolated by my detecting mechanisms that has the highest probability in the light of my model of the environment. The same is true when I identify one of the passers-by as John Smith, and also when I assume that he is going home for dinner. And so it is when I guess that his dinner will consist of shepherd’s pie and bananas and custard.

In each case, I am formulating that hypothesis which, in the light of my model of the environment, has the highest probability, though there may be a reduction in the degree of the probability involved as we proceed from the first case to the last.


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