RELA'l'l V1TY
The Origin, Nature and Influence of Relativity. By tileorge David Birkhoff. (Macmillan and Co. Ss. M. net.)
St IENCE never seems more worthy of admiration than when it suddenly gives a new shock to lethargic minds and shows again that the universe is not so easy to understand, not esen so easy to describe, as we are apt to imagine. It happens, unfortunately, that our minds soon seek their repose again. A scientific concept becomes a word ; the word becomes a commonplace ; because we can refer to a problem we think we have solved it. Something of this sort came over Newton's theory of gravitation. Most people, when once they had accommodated themselves to the new word, felt that they knew something more than anyone had known before. They could say that a stone falls through gravitation ; and, though they -really meant no more than - that a stone falls because things fall, they imagined that they had given a perfectly good explanation of the whole process. Similarly it has often been pointed out that the theory of Evolution by Natural Selection, in its commonest expression -- -" the survival of the fittest " -- adds nothing at all to our comprehension. The phrase, if it is analysed, means only " the survival of the survivors." The fittest for what ? Obviously, the fittest for survival. But this carries us no further towards an understanding of principles. We know nothing new of the causes of trams- limitation. We have only ayerred that at each moment the world is the only possible world ; which is to say that it each moment the world is the only actual world at that moment ; which is to say nothing at all. Of interaction if events, of process in the world, of causation, of reason. of purpose, of anything intelligible, we are as ignorant as ever. But the slogan has made a great number of people :mitent to be ignorant ; indeed, it has made them offensively proud of their ignorance.
If only we could come to a conception of the world with heads unencumbered by dead. words, if we .could place ourselves anew before our problems each time we considered them, the process of learning would be by no means so difficult or painful. But, as it is, we build up barriers of pretended knowledge that have to be knocked down with some violence when they prove inefficient. Anyone during :he past century who could treat the Newtonian. physics as iseful in results, yet refuse to accept them as necessarily true in fact, would have been thought log-headed or obstinate. Anyone who opposed to the theory of a universally spread, timelessly propagated gravitation in space a theory of movement through vortical stresses (and such heroes existed) was automatically a crank. His theory would not as com- pletely fit the known. facts, and its a priori conceptual possibility was no recommendation. Another instance may he given, which may seem to some degree a vindication of Newton. Ills own theory of light was that it was corpus- cular. The theory had given way by the end of last 7entury to the undulatory theory, and it was regarded as ultimately fixed that light consisted of waves in the ether, was in no sense composed of quanta, or packets of energy. It becomes necessary, now, to reintroduce the corpuscular ,heory within certain limitations. The good solid ground )1' prejudice is assaulted. We find ourselves in a very mobile world, demanding the utmost adaptability of mind if we arc to gain any clear sight of it at all. And it will be a long time still before it becomes obvious that all a priori con- eeptions which are rigorously consistent are true in their awn territory. if the time arrives when this is an established And common-sense point of view, we shall be very near !o having a rational and thorough scheme of the sciences. We shall then possess the morphology, or relativity, of seientific truths.
Meanwhile it is not much to anyone's discredit if he finds Einstein's theory of relativity ineotnprehensible. Most 'xPositions are quite muddled. Einstein himself is not above making blunders in logic and illustrating his thesis wrongly. And a source of difficulty rises through the fact that illustrations, on the whole, must be made by means of, and across, the ordinary Euclidean preconceptions. We arc told from the beginning that the true substrate of the world is a space-time eontinutme that to separate space and time brings error into our minds. A horde of complications
ensues. One of the chief of them, for logical thought. is this : we are told that the velocity of light is constant ; what is velocity in a space-time continuum ? By Imlinary thinking, velocity is a relation between space and time ; what mysterious thing is this uneompounded velocity ? Whatever the constant velocity of light in Einstein's theory of relativity may be, we are obviously Mistaken if we regard it primarily and expressly as 1811.000 miles per second.
The same difficulty recurs in the smallest details : we are obviously always doing what the strictest theory of relativity would forbid us to do. Mr. Clement V. Durell's exposition. very gaily and clearly written, is perpetually engaged in making things quite clear by pleasant little Euclidean diagrams, and then turning round suddenly and introducing the necessary correction. The same trouble was apparent in non-Enclidean geometries. Our diagrams gave us triangles which were plainly not triangles at ail, and parallel straight lines which were obviously destined to meet. half an inch off the margin of the page. Or if we had a triangle which looked like a triangle, it had to be scrapped Si oner or later. Diagramniatie thinking became lima "■S Ode. and yet diagrams were needed to give us the starting-point for thought. Mr. Dwell, however. has done his task N.ery well. Ilis book is not logically water-tight. but it gives a good deal of the gist and implications of the Einstein theory without any seveir mathematics. It helps the reader, also, to make sure that he is following the orpiment by setting hint comparatively simple mathematic exercises at the end of' each chapter.
Professor 13irkhoff's lectures are more important ; for he shows a very clear cona.iolsness of the imperfections of previous expositions and he really succeeds in clearing up much of the conceptual baekground of the theory. It is MI admirable book, a little stillly written in plmtscology, but easy to follow if the reader has concentration and persistence at his control.
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