The Concept of Nature Part 12

This theory accords no peculiar character to light beyond that accorded to other physical phenomena such as sound. There is no ground for such a differentiation. Some objects we know by sight only, and other objects we know by sound only, and other objects we observe neither by light nor by sound but by touch or smell or otherwise. The velocity of light varies according to its medium and so does that of sound. Light moves in curved paths under certain conditions and so does sound. Both light and sound are waves of disturbance in the physical characters of events; and (as has been stated above, p. 188) the actual course of the light is of no more importance for perception than is the actual course of the sound. To base the whole philosophy of nature upon light is a baseless a.s.sumption. The Michelson-Morley and a.n.a.logous experiments show that within the limits of our inexact.i.tude of observation the velocity of light is an approximation to the critical velocity 'c' which expresses the relation between our s.p.a.ce and time units. It is provable that the a.s.sumption as to light by which these experiments and the influence of the gravitational field on the light-rays are explained is deducible _as an approximation_ from the equations of the electromagnetic field. This completely disposes of any necessity for differentiating light from other physical phenomena as possessing any peculiar fundamental character.

It is to be observed that the measurement of extended nature by means of extended objects is meaningless apart from some observed fact of simultaneity inherent in nature and not merely a play of thought.

Otherwise there is no meaning to the concept of one presentation of your extended measuring rod AB. Why not AB' where B' is the end B five minutes later? Measurement presupposes for its possibility nature as a simultaneity, and an observed object present then and present now.

In other words, measurement of extended nature requires some inherent character in nature affording a rule of presentation of events.

Furthermore congruence cannot be defined by the permanence of the measuring rod. The permanence is itself meaningless apart from some immediate judgment of self-congruence. Otherwise how is an elastic string differentiated from a rigid measuring rod? Each remains the same self-identical object. Why is one a possible measuring rod and the other not so? The meaning of congruence lies beyond the self-ident.i.ty of the object. In other words measurement presupposes the measurable, and the theory of the measurable is the theory of congruence.

Furthermore the admission of stratifications of nature bears on the formulation of the laws of nature. It has been laid down that these laws are to be expressed in differential equations which, as expressed in any general system of measurement, should bear no reference to any other particular measure-system. This requirement is purely arbitrary. For a measure-system measures something inherent in nature; otherwise it has no connexion with nature at all. And that something which is measured by a particular measure-system may have a special relation to the phenomenon whose law is being formulated. For example the gravitational field due to a material object at rest in a certain time-system may be expected to exhibit in its formulation particular reference to spatial and temporal quant.i.ties of that time-system. The field can of course be expressed in any measure-systems, but the particular reference will remain as the simple physical explanation.

NOTE: ON THE GREEK CONCEPT OF A POINT

The preceding pages had been pa.s.sed for press before I had the pleasure of seeing Sir T. L. Heath's _Euclid in Greek_[14]. In the original Euclid's first definition is

s?e??? est??, ?? e??? ???e?.

I have quoted it on p. 86 in the expanded form taught to me in childhood, 'without parts and without magnitude.' I should have consulted Heath's English edition--a cla.s.sic from the moment of its issue--before committing myself to a statement about Euclid. This is however a trivial correction not affecting sense and not worth a note. I wish here to draw attention to Heath's own note to this definition in his _Euclid in Greek_. He summarises Greek thought on the nature of a point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My a.n.a.lysis of the requisite character of a point on pp. 89 and 90 is in complete agreement with the outcome of the Greek discussion.

[14] Camb. Univ. Press, 1920.

NOTE: ON SIGNIFICANCE AND INFINITE EVENTS

The theory of significance has been expanded and made more definite in the present volume. It had already been introduced in the _Principles of Natural Knowledge_ (cf. subarticles 3.3 to 3.8 and 16.1, 16.2, 19.4, and articles 20, 21). In reading over the proofs of the present volume, I come to the conclusion that in the light of this development my limitation of infinite events to durations is untenable. This limitation is stated in article 33 of the _Principles_ and at the beginning of Chapter IV (p. 74) of this book. There is not only a significance of the discerned events embracing the whole present duration, but there is a significance of a cogredient event involving its extension through a whole time-system backwards and forwards. In other words the essential 'beyond' in nature is a definite beyond in time as well as in s.p.a.ce [cf.

pp. 53, 194]. This follows from my whole thesis as to the a.s.similation of time and s.p.a.ce and their origin in extension. It also has the same basis in the a.n.a.lysis of the character of our knowledge of nature. It follows from this admission that it is possible to define point-tracks [_i.e._ the points of timeless s.p.a.ces] as abstractive elements. This is a great improvement as restoring the balance between moments and points.

I still hold however to the statement in subarticle 35.4 of the _Principles_ that the intersection of a pair of non-parallel durations does not present itself to us as one event. This correction does not affect any of the subsequent reasoning in the two books.

I may take this opportunity of pointing out that the 'stationary events'

of article 57 of the _Principles_ are merely cogredient events got at from an abstract mathematical point of view.