^{page 215 note 1} Process and Reality, p. 134Google Scholar.

^{page 217 note 1} It may seem strange to assert that mathematical relations belong as much to the natures of the percipient as to the external world, but that this is the case is shown by the Organic Philosophy in the exposition of an interesting topic called ‘strain feelings.’ Here is a brief summary of Whitehead's discussion of this topic (Process and Reality, pp. 439–465Google Scholar): First of all it must be remembered that any present perception is strictly inherited from antecedent bodily functioning: A “strain feeling” felt by an actual entity is one in which the ‘forms’ exemplified in the datum presented to it for novel synthesis, concern ‘geometrical, straight and flat loci.’ In a datum characterized by these geometrical forms, certain other elements express themselves as ‘qualities’ implicated in these forms. These additional qualities are the forms of simpler feelings (i.e. sensations) associated with the ‘geometrical seat’ of the strain in the actual entity in process of creation. The geometrical seat of a strain feeling is composed of certain sets of points, and these points belong to the volume defining the standpoint of the experient subject of the actual entity in question. But the strain feeling, when analysed, is seen to involve a geometrical region as part of itself called the ‘focal’ region beyond its own regional standpoint. This ‘focal’ region is a region of dense occurrences of straight lines defined by the ‘seat.’ These lines have a twofold function as determinants of the strain feeling of the actual entity in question. In the first place they define the ‘strain’ of the feeler; and in the second place they define the ‘focal’ region which they thus relate to the feeler. The pattern or eternal object involved in a strain feeling, thus relates the subject of an actual entity (via the ‘seat’ in its volume) to a definite spatial ‘focal’ region external to itself. This definite contemporary focal region is a nexus which is part of the objective datum of the novel concrescing actual entity. Thus the actual entity's feeling of efficacy in its concrescence is the feeling of the sense datum as implicated in the whole region, viz. of (i) antecedent ‘seats’ of earlier occasions from which it has sprung and (ii) the ‘focal’ region geometrically defined by its inherited strain. This patterned region, illustrated by the sense datum, is peculiarly dominated by the ‘final’ seat in the body of the feeler, and by the final focal region external to the perceiver. In other words the sense datum has a general spatial relation in which two spatial regions are dominant. Strain feelings are inherited by many strands from the antecedent bodily nerves, but it can be said generally that these many strands of transmission of bodily efficacy converge upon the same ‘focal’ region picked out by the many bodily strains, and that the ‘strain’ in the final percipient actual entity defines the ‘seat’ and the ‘focal’ region, the intermediate regions and more vaguely the whole of a ‘presented’ space.

It is important to emphasize that all exact measurements concerning perceptions of the immediate present world (‘Presentational Immediacy’), concern the systematic ‘forms’ of the environment. These forms are defined by projectors from the ‘seat’ of the strain and are irrespective of the actualities which constitute the environment. The ‘strain-locus’ is defined by the projectors which penetrate any one finite region within it. Such a locus is a systematic whole, and is also independent of the actualities which may atomize it. This means that a strain-locus depends merely upon its geometrical content. It is therefore to be distinguished from a ‘duration,’ which does depend upon its physical content.

The consideration of ‘strains’ in an actual entity compels us therefore to assert that mathematical relations are at once public fact and private experience. Concerning strains generally. Whitehead says: “It is obvious that important feelings of strain involve complex processes of concrescence. They are accordingly only to be found in comparatively high-grade actual entities. They do not in any respect necessarily involve consciousness or even that approach to consciousness which we associate with life. But the behaviour of enduring physical objects is only explicable by reference to the peculiarities of their strains.… The growth of ordered physical complexity is dependent on the growth of order relationships among strains. Fundamental equations in mathematical physics, such as Maxwell's electro-magnetic equations, are expressions of the ordering of strains throughout the physical universe.”