put whatever it be, there it is—exhibiting to us a certain region of external space. If we are gazing at a nebula, a thousand light-years away, we are not looking backward through a thousand years. Such ways of speaking are interpretative phrases, diverting attention from the pri- mary fact of direct experience, observing the illumination of a contemporary patch of the heavens. In philosophy, it is of the utmost importance to beware of the interpre- tative vagaries of language. Further, the extent of the patch illuminated will depend entirely upon the magni- fying power of the telescope used. The correlation of the patch, thus seen through the telescope, with a smaller patch, defined by direct ‘projection’ from the observer, is again a question of scientific interpretation. This smaller patch is what we are said to have seen ‘magnified’ by the use of the telescope. What we do see is the bigger patch, and we correlate it with the smaller patch by theoretical calculation. The scientific explanation neglects the tele- scope and the larger patch really seen, and considers them as merely instrumental intermediaries. It concentrates on the contemporary smaller patch, and finally deserts aven that patch in favour of another region a thousand years in the past. This explanation is only one illustra- tion of the way in which so-called statements of direct observation are, through and through, merely interpreta- tive statements of simple direct experience. When we say that we have seen a man, we may mean that we have seen a patch which we believe to be a man. In this case, our total relevant experience may be more than that of bare sight. In Descartes’ phraseology, our experience of the external world embraces not only an ‘inspectio’ of the ‘realitas objectiva’ in the prehensions in question, but also a ‘judicium’ which calls into play the totality of our experience beyond those prehensions. The objection to this doctrine of ‘presentational immediacy’—that it pre- supposes a definition of straight lines, freed from depend- ence on external actualities—has been removed by the production of such a definition in the previous chapter.
496 Process and Reality
Of course the point of the definition is to demonstrate
that the extensive continuum, apart from the particular
actualities into which it is atomized, includes in its sys-
tematic structure the relationships of regions expressed
by straight lines. These relationships are there for
perception.
The Cartesian doctrine of the ‘realitas objectiva’ at- taching to presentational immediacy is entirely denied by the modern doctrine of private psychological fields. Locke’s doctrine of ‘secondary qualities’ is a halfway house to the modern position, and indeed so is Descartes’ own position considered as a whole. Descartes’ doctrine on this point is obscure, and is interpretable as according with that of the philosophy of organism. But Locke conceives the sensa as purely mental additions to the facts of physical nature. Both philosophers conceive the phys- ical world as in essential independence of the mental world, though the two worlds have ill-defined accidental relationships. According to the philosophy of organism, physical and mental operations are inextricably inter- twined; also we find the sensa functioning as forms par- ticipating in the vector prehensions of one occasion by another; and finally in tracing the origin of presenta- tional immediacy, we find mental operations transmuting the functions of sensa so as to transfer them from being participants in causal prehensions into participants in presentation prehensions. But throughout the whole story, the sensa are participating in nature as much as anything else. It is the function of mentality to modify the physical participation of eternal objects: the case of presentational prehensions is only one conspicuous exam- ple. The whole doctrine of mentality—from the case of God downwards—is that it is a modifying agency. But Descartes and Locke abandon the ‘realitas objectiva’ so far as sensa are concerned (but for Descartes, cf. Medita- tion I, “It is certain all the same that the colours of
Measurement 497
which this is composed are necessarily real”), and hope to save it so far as extensive relations are concerned. This is an impossible compromise. It was easily swept aside by Berkeley and Hume. (Cf. Enquiry, Part I, Sect. XII. Hume with obvious truth, refers to Berkeley as the origi- nator of this train of argument.) The modern doctrine of ‘private psychological fields’ is the logical result of Hume’s doctrine, though it is a result which Hume ‘as an agent’ refused to accept. This modern doctrine raises a great difficulty in the interpretation of modern science. For all exact observation is made in these private psycho- logical fields. It is then no use talking about instruments and laboratories and physical energy. What is really being observed are narrow bands of colour-sensa in the private psychological space of colour-vision. The impres- sions of sensation which collectively form this entirely private experience ‘arise in the soul from unknown causes.’ The spectroscope is a myth, the radiant energy is a myth, the observer’s eye is a myth, the observer’s brain is a myth, and the observer’s record of his experi- ment on a sheet of paper is a myth. When some months later, he reads his notes to a learned society, he has a new visual experience of black marks on a white back- ground in a new private psychological field. And again, these experiences arise in his soul ‘from unknown causes.’ It is merely ‘custom’ which leads him to connect his earlier with his later experiences.
All exact measurements are, on this theory, observa- tions in such private psychological fields.
Hume himself ‘as an agent’ refused to accept this doc-
trine. The conclusion is that Hume’s account of experi-
ence is unduly simplified. This is the conclusion adopted
by the philosophy of organism.
But one important fact does emerge from the discus-
sion: that all exact measurements concern perceptions
in the mode of presentational immediacy; and that such
observations purely concern the systematic geometric
forms of the environment, forms defined by projectors
498 Process and Reality
from the ‘seat? of the strain and irrespective of the actu- alities which constitute the environment. The contem- porary actualities of the world are irrelevant to these observations. All scientific measurements merely con- cern the systematic real potentiality out of which these actualities arise. This is the meaning of the doctrine that physical science is solely concerned with the mathe- matical relations of the world.
These mathematical relations belong to the systematic
order of extensiveness which characterizes the cosmic
epoch in which we live. The societies of enduring ob-
jects—electrons, protons, molecules, material bodies—at
once sustain that order and arise out of it. The mathe-
matical relations involved in presentational immediacy
thus belong equally to the world perceived and to the
natures of the percipient. They are, at the same time,
public fact and private experience.
The perceptive mode of presentational immediacy is
in one sense barren. So far as—apart from symbolic
transference—it discloses the contemporary world, that
world, thus objectified, is devoid of all elements consti-
tutive of subjective form, elements emotional, apprecia-
tive, purposive. The bonds of the objectified nexus only
exhibit the definiteness of mathematical relations.
But in another sense this perceptive mode has over- whelming significance. It exhibits that complex of sys- tematic mathematical relations which participate in all the next of our cosmic epoch, in the widest meaning of that term. These relations only characterize the epoch by reason of their foundation in the immediate experi- ence of the society of occasions dominating that epoch. Thus we find a special application of the doctrine of the interaction between societies of occasions and the laws of nature. The perceptive mode in presentational imme- diacy is one of the defining characteristics of the societies which constitute the nextis termed material bodies. Also in some fainter intensity it belongs to the electromagnetic occasions in empty space. From the point of view of a
Measurement 499
single experient, that mode discloses systematic relations
which dominate the environment. But the environment
is dominated by these relationships by reason of the
experiences of the individual occasions constituting the
societies.
It is by reason of this disclosure of ultimate system that an intellectual comprehension of the physical uni- verse is possible. There is a systematic framework per- meating all relevant fact. By reference to this frame- work the variant, various, vagrant, evanescent details of the abundant world can have their mutual relations ex- hibited by their correlation to the common terms of a universal system. Sounds differ qualitatively among themselves, sounds differ qualitatively from colours, colours differ qualitatively from the rhythmic throbs of emotion and of pain; yet all alike are periodic and have their spatial relations and their wave-lengths. The dis- covery of the true relevance of the mathematical relations disclosed in presentational immediacy was the first step in the intellectual conquest of nature. Accurate science was then born. Apart from these relations as facts in nature, such science is meaningless, a tale told by an idiot and credited by fools. For example, the conjecture by an eminent astronomer, based on measurements of photo- graphic plates, that the period of the revolution of our galaxy of stars is about three hundred million years can only derive its meaning from the systematic geometrical relations which permeate the epoch. But he would have required the same reference to system, if he had made an analogous statement about the period of revolution of a child’s top. Also the two periods are comparable in terms of the system.
Measurement depends upon counting and upon per-
manence. The question is, what is counted, and what is
permanent? The things that are counted are the inches
on a straight metal rod, a yard-measure. Also the thing
500 Process and Reality
that is permanent is this yard-measure in respect both to its internal relations and in respect to some of its extensive relations to the geometry of the world. In the first place, the rod is straight. Thus the measurement depends on the straightness and not the straightness upon the measurement. The modern answer to this statement is that the measurement is a comparison of infinitesimals, or of an approximation to infinitesimals. The answer to this answer is that there are no infinitesimals, and that therefore there can be no approximation to them. In- mathematics, all phraseology about infinitesimals is merely disguised statement about a class of finites. This doctrine has been conclusive mathematical theory since the time of Weierstrass in the middle of the nineteenth century. Also all the contortions of curvature are pos- sible for a segment between any end-points.
Of course, in all measurement there is approximation
in our suppositions as to the yard measure. But it is
approximation to straightness. Also having regard to the
systematic geometry of straight lines, and to the type
of approximation exhibited by the rod, the smaller the
portion used, the more negligible are the percentage
errors introduced by the defects from straightness. But
unless the notion of straightness has a definite meaning
in reference to the extensive relations, this whole pro-
cedure in practical measurement is meaningless. There
is nothing to distinguish one contorted segment between
end-points from another contorted segment between
those end-points. One is no straighter than another.
Also any percentage differences between their lengths.
can exist.
Again, the inches are counted because they are con-
gruent and are end-on along the straight rod. No one
counts coincident inches. The counting essentially is
concerned with non-coincident straight segments. The
numerical measure of length is the indication of the fact
that the yard measure is a straight rod divisible into.
thirty-six congruent inch-long segments.
Measurement 501
There is a modern doctrine that ‘congruence’ means the possibility of coincidence. If this be the case, then the importance of congruence would arise when the pos- sibility is realized. Alternatively, the possibility could be of importance as a lure entering into the subjective aim. If the latter alternative were true, congruence would play its part in the form of a tendency of con- gruent bodies to coalesce, or to resist. coalescence. In fact, there would be adversion to, or aversion from coales- cence. Of course the suggestion is fantastic. Recurring to the former alternative, the importance of the thirty- six inches along the yard-measure depends on the fact that they are not coincident and, until the destruction of the rod, never will be coincident. There is a realized property of the rod that it is thirty-six inches in length. Thus although ‘coincidence’ is used as a test of congru- ence, it is not the meaning of congruence.
We must now consider the use of ‘coincidence’ as a test.
Congruence is tested either by the transference of a steel
yard-measure from coincidence with one body to coin-
cidence with another body, or by some optical means
dependent on the use of an optical instrument and on
the congruence of successive wave lengths in a train of
waves, or by some other vibratory device dependent on
analogous principles.