July 7, 1921] 



NATURE 



579 



not mean that Lord Haldane's exposition has 

 .made either writer easy to understand, but it has 

 :made it possible for anyone who cares to give the 

 .necessary attention and concentration to under- 

 stand them both. Those who have argued a. 

 priori that any exposition of the principle of rela- 

 tivity by Lord Haldane must be defective and 

 inconclusive because he is not a mathematician 

 rand therefore does not use or know how to use 

 the language which enables mathematicians to 

 •express their equations have only shown that they 

 mistake both the purpose and the nature of the 

 a-alue of mathematical methods. It is just because 

 mathematics is restricted to abstract quantitative 

 measurements that its system of symbols is so 

 -effective an instrument. Mathematicians are the 

 'first to acknowledge this. They know it is they 

 -who are handicapped when it comes to laying 

 "bare the metaphysical concept, handicapped by 

 the very ease with which they are able, by 

 the manipulation of symbols, to simplify the 

 ■most complex and complicated quantitative 

 ■equations. 



When we say of anything that it is relative, the 

 •question immediately follows: Relative to what? 

 -Absolute relativity is either a contradiction in 

 ■terms, as if one should say a round square, or 

 it is an expression for that extreme form of scep- 

 ticism which professes to be a universal negation. 

 Now, undoubtedly the first impression we receive 

 •of the general principle of relativity does dispose 

 »us to identify it with the principle of universal 

 •doubt. On this aspect of the great problem Lord 

 Haldane is clear and pronounced from the first 

 rsentence of his preface to the end of his book. 

 To the question, Relative to what? he replies, 

 Relative to knowledge ; and knowledge is not 

 'itself an abstract relation, but a concrete uni- 

 ■versal. In this he is following Hegel, who first 

 "brought to light, in its modern form, the dia- 

 lectical nature of thought. "Knowledge," says. 

 Lord Haldane, "is dynamic. It is an effort to 

 transcend the apparently given. It is always 

 pointing beyond itself " (p. 140). It is from this 

 point of view that the comparison of Whitehead 

 and Einstein is instructive. Both are concerned, 

 ;and concerned only, to present to us a science of 

 Nature. Both reject the absolute : there is neither 

 a space-time system nor a material, depen- 

 ■dent or independent of the observers attached 

 to it, which can serve as a norm by which to 

 regulate the relations of different space-time 

 systems. Both reject the principle of action at 

 -a distance : it is inconceivable as fact and useless 

 :as a principle. An interesting, though perhaps a 

 ffninor, point in which Lord Haldane notes a 

 NO, 2697, VOL. 107] 



difference between them is that, while for White- 

 head the element out of which our concept of 

 Nature is constructed is the event, and the object 

 is a derivative notion, for Einstein the event 

 seems to depend on the notion of object. In this 

 Lord Haldane thinks Whitehead is more faithful 

 than Einstein to the fundamental principle of the 

 four-dimensional space-time continuum-. Apart 

 from this, it is Einstein who has made the 

 greater advance to the full philosophical con- 

 cept. Whitehead halts. He cannot surrender the 

 notion that Nature in its existence is self-con- 

 tained, that it stands for a reality which in the 

 last analysis is closed to mind. Is this concept 

 of a reality closed to mind a necessity of mathe- 

 matical and physical science? Some philosophers 

 would agree with Whitehead in saying, Yes. They 

 are the new realists, and are here criticised from 

 that point of view. On the other hand, Einstein 

 and Eddington seem very definitely to say. No, 

 and to be able to prove it. Lord Haldane sug- 

 gests that Whitehead's own persistent question, 

 in regard to any and every specified point-event 

 — the question. Whose space-time? or, W^hat 

 space-time system? — in its implications is the 

 negation of his own conclusion. This brings out 

 Lord Haldane's foundational fact. Knowledge is 

 a universal within which all distinctions fall. It 

 is not, and cannot be, conceived as an abstract 

 relation between two self-subsistent and existenti- 

 ally exclusive realities, mind and Nature. 



Let us now turn to another question, which is 

 equally pressing as a scientific problem, and 

 equally significant as a philosophical problem — 

 the quantum theory. Lord Haldane makes only 

 a brief reference to it (p. 106), but it is in a 

 certain sense even more relevant to the concept 

 which it is his main purpose to expound, the con- 

 cept of degrees of reality, than the principle of 

 relativity itself. For the quantum theory shows 

 that in scientific explanation, however far we are 

 able to pursue it, we are brought up finally against 

 a fact which positively forces us to appeal to a 

 character of knowledge in plain contradiction of 

 our scientific principle of explanation. 



On p. 114 there is a delightful account of the 

 curious statue erected to Gauss and Weber in 

 Gottingen. It is made the occasion of expounding 

 the work of those mathematicians who, as Lord 

 Haldane says, " nearly three-quarters of a century 

 since, prepared the way for thinkers like Einstein 

 and the interpreters of the doctrine of quantitative 

 relativity." But it is also curious to remember 

 that at the same time there was living in Leipzig 

 another Weber, the philosopher and psychologist 

 who has given his name to the famous law of 



