November 25, 2017

How hypotheses are formed

Appendix 9 of The Stable Society: its structure and control: Towards a Social Cybernetics, Wadebridge Ecological Centre, UK, 1978

Models or hypotheses are postulated. However, this does not convey very much information on the actual process involved; no more, in fact, than to say that they are simply reached by ‘intuition’.

Postulation cannot just occur at random. Some mechanism must be involved, and it must be possible to determine and formulate the principles underlying it.

The obvious question to ask is what must be the relationship of the hypothesis postulated to all other hypotheses that might be postulated? The equally obvious answer is that it must have the highest probability in terms of the system’s model. Thus, if a bridge-player is to maximise his chances of winning over a period, his model must provide him with 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 maximise 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 in order to give rise to adaptive responses 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 probably because what constitutes the most probable hypothesis to explain a situation will be different in the case of each different act, since the model 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 simple organisms in suggesting that they are capable of making such precise calculations? I do not think so. The ability of certain organisms to perform mathematical feats which would test the capacity of the most able mathematician has been clearly demonstrated.

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:153

“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 conservation 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.

The Nile fish gymnarcus niloticus darts among rocks 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. Lissmann,154 who spent twelve 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 was so developed that it could 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 were added to the distilled water so that its electrical conductivity matched that of the tap water, it could no longer discriminate between them. Here again, a complicated calculation must be made. To give an idea of the precision involved, Lissmann154 worked out:

“. . . that Gymnarcus can respond to a continuous direct-current electric stimulus of about .15 microvolt per centimeter, a value that agrees reasonably well with the calculated sensitivity required to recognize a glass rod two millimeters in diameter. This means that an individual sense organ should be able to convey information about a current change as small as .003 micromicroampere. 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 Martin93 notes the extraordinary mathematical ability of spiders:

“Spiders act as if they had the brain of first-class mathematicians. For them, space has properties which make its structure quite unique. Moreover, these properties are dynamic. Each time a spider spins a web, it must cope with changing conditions, for the construction of a web involves such variable factors as wind direction, weather protection, exposure to sunlight, and the abundance of prey. The web itself is a masterpiece of construction. It has all the ideal properties which engineers look for—maximum resistance and maximum efficiency, combined with minimum use of material.

“. . . The bee is another insect which seems to have great mathematical gifts. 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.”

Even more illustrative of an organism’s capacity to calculate probabilities on the basis of its model of the system is the behaviour of the didiera in Madagascar and the baobob trees in Africa, which are capable of filling the cells of their trunks with water during the rainy season. Many other plants, such as cacti, can do the same thing. Certain of these are capable of storing water in their cells over long periods. The more water they store in their cells, the slower is their metabolism, which can almost come to a halt if they are saturated. On the other hand, the more water they can store, the greater is the period they can last without rain. In order to be able to store up the optimum amount of water in their cells, which must correspond to the minimum amount which they require to see them through a drought, they have perfected a method of forecasting the amount of rain that there will be in the succeeding months. Researchers from The Massachussetts Institute of Technology have studied such cacti in the Mohave desert in South California for four years. They discovered that if after rainfall the cacti filled their cells to one-third or one-half of their capacity, it would invariably rain during the next two or three months. On one occasion they found that the plants had filled their cells to full capacity. It did not rain at all for the next 685 days. It is evident that to maximise their chance of survival, the amount of water they must store is the minimum necessary for their requirements. This can only be calculated by predicting with the maximum degree of probability what the rainfall is likely to be in the following months, a calculation which they appear to perform with astonishing precision.

Again, it may be thought that these examples are simply curiosities of nature. On the contrary, if our thesis is correct, they are but striking examples of a principle in terms of which must be regarded perception and thought processes at all levels of complexity.

Thus, when I look out of my window and see a tree, a road, and people walking to and fro, I am in fact formulating a hypothesis as to the nature of the environmental data isolated by my detecting mechanisms that has the highest probability in the light of my systemic model. 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, even though there may be a reduction in the degree of probability involved as we proceed from the first case to the last.


93. Charles Noel-Martin, The Role of Perception in Science Hutchinson, London, 1963.

153. E.G.F. Sauer, ‘Celestial Navigation of Birds’ Scientific American August, 1958.

154. H.W. Lissman, ‘Electric Location by Fishes’ Scientific American March, 1963.

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