Science and the modern world · Alfred North Whitehead
RELATIVITY
The conception of internal relatedness involves the analysis of the event into two factors, one the underlying substantial activity of individualisation, and the other the complex of aspects—that is to say, the complex of relatednesses as entering into the essence of the given event—which are unified by this individualised activity. In other words, the concept of internal relations requires the concept of substance as the activity synthesising the relationships into its emergent character. The event is what it is, by reason of the unification in itself of a multiplicity of relationships. The general scheme of these mutual relationships is an abstraction which presupposes each event as an independent entity, which it is not, and asks what remnant of these formative relationships is then left in the guise of external relationships. The scheme of relationships as thus impartially expressed becomes the scheme of a complex of events variously related as wholes to parts and as joint parts within some one whole. Even here, the internal relationship forces itself on our attention; for the part evidently is constitutive of the whole. Also an isolated event which has lost its status in any complex of events is equally excluded by the very nature of an event. So the whole is evidently constitutive of the part. Thus the internal character of the relationship really shows through this impartial scheme of abstract external relations.
But this exhibition of the actual universe as extensive and divisible has left out the distinction between space and time. It has in fact left out the process of realisation, which is the adjustment of the synthetic activities by virtue of which the various events become their realised selves. This adjustment is thus the adjustment of the underlying active substances whereby these substances exhibit themselves as the individualisations or modes of Spinoza’s one substance. This adjustment is what introduces temporal process. Thus, in some sense, time, in its character of the adjustment of the process of synthetic realisation, extends beyond the spatio-temporal continuum of nature.[7] There is no necessity that temporal process, in this sense, should be constituted by one single series of linear succession. Accordingly, in order to satisfy the present demands of scientific hypothesis, we introduce the metaphysical hypothesis that this is not the case. We do assume (basing ourselves upon direct observation), however, that temporal process of realisation can be analysed into a group of linear serial processes. Each of these linear series is a space-time system. In support of this assumption of definite serial processes, we appeal: (1) to the immediate presentation through the senses of an extended universe beyond ourselves and _simultaneous_ with ourselves, (2) to the intellectual apprehension of a meaning to the question which asks what is _now immediately happening_ in regions beyond the cognisance of our senses, (3) to the analysis of what is involved in the _endurance_ of emergent objects. This endurance of objects involves the display of a pattern as now realised. This display is the display of a pattern as inherent in an event, but also as exhibiting a temporal slice of nature as lending aspects to eternal objects (or, equally, of eternal objects as lending aspects to events). The pattern is spatialised in a whole duration for the benefit of the event into whose essence the pattern enters. The event is part of the duration, _i.e._, is part of what is exhibited in the aspects inherent in itself; and conversely the duration is the whole of nature simultaneous with the event, in that sense of simultaneity. Thus an event in realising itself displays a pattern, and this pattern requires a definite duration determined by a definite meaning of simultaneity. Each such meaning of simultaneity relates the pattern as thus displayed to one definite space-time system. The actuality of the space-time systems is constituted by the realisation of pattern; but it is inherent in the general scheme of events as constituting its patience for the temporal process of realisation.
Footnote 8: Max Müller’s translation. “I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, _and therefore necessarily preceded by it_.[9] I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, starting from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all the portions of time, and their addition, a definite quantity of time.” Footnote 9: Italics mine, and also in the second passage. The second passage runs thus: “This peculiar property of quantities that no part of them is the smallest possible part (no part indivisible) is called continuity. Time and space are quanta continua, because there is no part of them that is not enclosed between limits (points and moments), _no part that is not itself again a space or a time. Space consists of spaces only, time of times. Points and moments are only limits_, mere places of limitation, and as places _presupposing always_ those intuitions which they are meant to limit or to determine. Mere places or parts that might be given before space or time, could never be compounded into space or time.”
I am in complete agreement with the second extract if ‘time and space’ is the extensive continuum; but it is inconsistent with its predecessor. For Zeno would object that a vicious infinite regress is involved. Every part of time involves some smaller part of itself, and so on. Also this series regresses backwards ultimately to nothing; since the initial moment is without duration and merely marks the relation of contiguity to an earlier time. Thus time is impossible, if the two extracts are both adhered to. I accept the later, and reject the earlier, passage. Realisation is the becoming of time in the field of extension. Extension is the complex of events, _quâ_ their potentialities. In realisation the potentiality becomes actuality. But the potential pattern requires a duration; and the duration must be exhibited as an epochal whole, by the realisation of the pattern. Thus time is the succession of elements in themselves divisible and contiguous. A duration, in becoming temporal, thereby incurs realisation in respect to some enduring object. Temporalisation is realisation. Temporalisation is not another continuous process. It is an atomic succession. Thus time is atomic (_i.e._, epochal), though what is temporalised is divisible. This doctrine follows from the doctrine of events, and of the nature of enduring objects. In the next chapter we must consider its relevance to the quantum theory of recent science.
It is to be noted that this doctrine of the epochal character of time does not depend on the modern doctrine of relativity, and holds equally—and indeed, more simply—if this doctrine be abandoned. It does depend on the analysis of the intrinsic character of an event, considered as the most concrete finite entity. In reviewing this argument, note first that the second quotation from Kant, on which it is based, does not depend on any peculiar Kantian doctrine. The latter of the two is in agreement with Plato as against Aristotle.[10] In the second place, the argument assumes that Zeno understated his argument. He should have urged it against the current notion of time in itself, and not against motion, which involves relations between time and space. For, what becomes has duration. But no duration can become until a smaller duration (part of the former) has antecedently come into being [Kant’s earlier statement]. The same argument applies to this smaller duration, and so on. Also the infinite regress of these durations converges to nothing—and even on the Aristotelian view there is no first moment. Accordingly time would be an irrational notion. Thirdly, in the epochal theory Zeno’s difficulty is met by conceiving temporalisation as the realisation of a complete organism. This organism is an event holding in its essence its spatio-temporal relationships (both within itself, and beyond itself) throughout the spatio-temporal continuum. Footnote 10: _Cf._ ‘Euclid in Greek,’ by Sir T. L. Heath, Camb. Univ. Press, in a note on Points.
Text from Project Gutenberg, public domain in the United States.