Process and Reality — the Gifford Lectures, 1929

Given a family of straight lines, expressing a system of relatedness in a ‘geometric’ society, the notion of ‘congruence’ and thence of ‘measurement’ is now determinable in a systematic way throughout the society. But again in this case there certainly are competing systems of measurement. Hence in connection with each family of straight lines—allowing there be more than one such family—there are alternative systems ** of metrical geometry, no one system being more fundamental than the other. Our present cosmic epoch is formed by an ‘electromagnetic’ society, which is a more special society contained within the geometric society. In this society yet more special defining characteristics obtain. These characteristics presuppose those of the two wider societies within which the ‘electromagnetic’ society is contained. But in the ‘electromagnetic’ society the ambiguity as to the relative importance of competing families of straight lines (if there be such competing families), and the ambiguity as to the relative importance of competing definitions of congruence, are determined in favour of one family and one ** congruence-definition. This determination is effected by an additional set of physical relationships throughout the society. But this set has lost

18 The existence of alternative systems was demonstrated by Cayley in his Sizth Memoir on Quantities in R. S., Trans. 13859. ;

14The transformations into an indefinite variety of coordinates, to which the ‘tensor theory’ refers, all presuppose one congruence definition. The invariance of the Einsteinian ‘ds’ expresses this fact.

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its merely systematic character because it constitutes our neighbourhood. ‘These relationships involve components expressive of certain individual diversities, and identities between the occasions which are the members of the nexus. But these diversities and identities are correlated according to a systematic law expressible in terms of the systematic measurements derived from the geometric nexus. We here arrive at the notion of physical quantities which vary from individual to individual; this is the notion of the systematization of individual differences, the notion of ‘Law.’

It is the ideal of mathematical physicists to formulate this systematic law in its complete generality for our epoch. It is sufficient for our purposes to indicate the presumed character of this law by naming the members of the society ‘electromagnetic occasions.’ Thus our present epoch is dominated by a society of electromagnetic occasions. In so far as this dominance approaches completeness, the systematic law which physics seeks is absolutely dominant. In so far as the dominance is incomplete, the obedience is a statistical fact with its corresponding lapses.

The electromagnetic society exhibits the physical electromagnetic field which is the topic of physical science. The members of this nexus are the electromagnetic occasions.

But in its turn, this electromagnetic society would provide no adequate order for the production of individual occasions realizing peculiar ‘intensities’ of experience unless it were pervaded by more special societies, vehicles of such order. The physical world exhibits a bewildering complexity of such societies, favouring each other, competing with each other.

The most general examples of such societies are the regular trains of waves, individual electrons, protons, individual molecules, societies of molecules such as inorganic bodies, living cells, and societies of cells such as vegetable and animal bodies.

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SECTION V

It is obvious that the simple classification (cf. Part I, Ch. III, Sect. II) of societies into ‘enduring objects,’ ‘corpuscular societies,’ and ‘non-corpuscular societies’ requires amplification. The notion of a society which includes subordinate societies and nextis with a definite pattern of structural inter-relations, must be introduced. Such societies will be termed ‘structured.’

A structured society as a whole provides a favourable environment for the subordinate societies which it harbours within itself. Also the whole society must be set in a wider environment permissive of its continuance. Some of the component groups of occasions in a structured society can be termed ‘subordinate societies.’ But other such groups must be given the wider designation of ‘subordinate nexis.’ The distinction arises because in some instances a group of occasions, such as, for example, a particular enduring entity, could have retained the dominant features of its defining characteristic in the general environment, apart from the structured society. It would have lost some features; in other words, the analogous sort of enduring entity in the general environment is, in its mode of definiteness, not quite identical with the enduring entity within the structured environment. But, abstracting such additional details from the generalized defining characteristic, the enduring object with that generalized characteristic may be conceived as independent of the structured society within which it finds it. For example, we speak of a molecule within a living cell, because its general molecular features are independent of the environment of the cell. Thus a molecule is a subordinate society in the structured society which we call the ‘living cell.’

But there may be other nexiis included in a structured society which, excepting the general systematic characteristics of the external environment, present no features capable of genetically sustaining themselves apart fromp. 152 the special environment provided by that structured society. It is misleading, therefore, to term such a nexus a ‘society’ when it is being considered in abstraction from the whole structured society. In such an abstraction it can be assigned no ‘social’ features. Recurring to the example of a living cell, it will be argued that the occasions composing the ‘empty’ space within the cell exhibit special features which analogous occasions outside the cell are devoid of. Thus the nexus, which is the empty space within a living cell, is called a ‘subordinate nexus,’ but not a ‘subordinate society.’

Molecules are structured societies, and so in all probability are separate electrons and protons. Crystals are structured societies. But gases are not structured societies in any important sense of that term; although their individual molecules are structured societies.