Shelburne Essays, Third Series

by Paul Elmer More

From the days of the old Greek Heraclitus, who built up his theory of the world on the axiom of eternal flux and change, the Doctrine of Motion as a distinct enunciation has lingered on in the world well-nigh unnoticed and buried from sight in the bulk of suppositions and guesses that have made up the passing systems of philosophy. Now and then some lonely thinker took up the doctrine, but only to let it drop back into obscurity; until during the great burst of scientific enquiry in the fifteenth and sixteenth centuries it assumed new significance and began to grow. From that time to this its progress in acceptance as the basis of phenomena may be regarded as a measure of scientific advance.

By a strange fatality Kant, who had been so efficient as an iconoclast in metaphysics, was perhaps with his nebular hypothesis, followed later by the work of Goethe on animal and plant variations, the one most largely responsible for the new hope that in science at last was to be found an answer to the riddle of existence which had baffled the search of pure reason. The achievement of Kant both destructive and constructive is well known, if vaguely understood, by the world at large; but it is not so well known that a contemporary of Kant did precisely for science what the sage of Königsberg accomplished in metaphysics. In the very decade in which The Critique of Pure Reason saw the light, Lagrange, a scholar of France, published a work which carried the analytic method, or the method of motion, to its farthest limit. In this work, the Mécanique Analytique, Lagrange develops an equation from which it can be proved conclusively that to explain any group of phenomena measured by energy an infinite number of hypotheses may be employed. So, for instance, if we establish any one theory which will sufficiently account for the known phenomena of light, such as reflection, refraction, polarisation, etc., there will yet remain an infinite number of other hypotheses equally capable of explaining the same group of phenomena. Or to use the words of Poincaré: "If then we can give one complete mechanical explanation of a phenomenon, there will also be possible an infinite number of others which will account equally well for all the particulars revealed by experiment." That is to say, no experimentum crucis can be imagined which will reveal the truth or error of any given theory. This restriction on the finality of our knowledge is borne out in all physical reasoning,—and I venture also to say in the other sciences; thus in optics we can perform no experiment which will establish as finally true the theory that light is caused by the motion of corpuscles of matter emitted from a luminous body, or that it is due to vibrations propagated through a medium by a wave motion, or that it is generated by certain disturbances in the electrical state of bodies. Each of these hypotheses has its advantages and disadvantages; and in our choice we merely adopt that theory which explains the greater number of phenomena in the simplest way.

If any one should here ask: Granted that from phenomena expressed in terms of energy no ultimate law can be educed, yet may not some other view of phenomena lead to other results? We answer that no other view is possible. Not that the system of the universe, if we may use such an expression, is necessarily constructed on what we call energy, but that our minds can conceive it only in terms of energy. An analysis of the concepts which enter into the idea of energy must make it evident that in our understanding of nature we cannot go beyond this point.

There is an agreement among philosophers and scientists that the concept of space is not derived from external experience, but is inherently intuitive. As stated by Kant:

The representation of space cannot be borrowed through experience from relations of external phenomena, but, on the contrary, those external phenomena become possible only by means of the representation of space. Space is a necessary representation, a priori, forming the very foundation of external intuitions. It is impossible to imagine that there should be no space, though it is possible to imagine space without objects to fill it.

The concept of space therefore makes possible the intuition of external phenomena; but these phenomena to be realised must appeal to one of our senses, and this connecting link between the outer world and our consciousness is the concept which we call time. Quoting again from Kant:

Time is the formal condition, a priori, of all phenomena whatsoever. But, as all representations, whether they have for their objects external things or not, belong by themselves, as determinations of the mind, to our inner state;... therefore, if I am able to say, a priori, that all external phenomena are in space, I can, according to the principle of the internal sense, make the general assertion that all phenomena, that is, all objects of the senses, are in time, and stand necessarily in relations of time.

It follows, then, that our simplest possible expression for phenomena will be in terms of space and time, and that beyond this the human mind cannot go.

Turning here from metaphysical to scientific language, we speak of space and time as the fundamental units from which we deduce the laws of the external world. The fact that space appeals to us only through time furnishes us with our concept or unit of motion, which is the ratio of space to time. The external phenomena so revealed to us we call the manifestations of mass or energy, thus providing ourselves with a second unit. It must be observed, however, that mass or energy is not a new concept, but bears precisely the same relation to motion as Kant's Ding-an-sich bears to space and time: it is the unknowable cause of motion—or more properly speaking it is the ability residing in an object to change the motion of another object and is measured by the degree of change it can produce. And I say mass or energy, advisedly, for the two are merely different names or different views of the same thing; we cannot conceive of matter without energy or of energy without matter. Our choice between the two depends solely on the simplicity and convenience with which deductions may be made from one or the other. From a physical standpoint the concept energy is rather the simpler, but mathematically our deductions flow more readily from the concept mass.