December 29, 1922] 



SCIENCE 



753 



speeulatiaig on these possibilities inasmuch as thej' 

 shed light on the philosophical problem of cosmic 

 and phenomenal time. Although paradoxes of this 

 kind appear, nowhere do we find any real contra- 

 diction to the facts directly presented to us in 

 experience. 



Now I 'have two favors to ask: 



First, that any reader who is dnterested com- 

 pare my little skit on "Tangling Up tihe Time 

 Line" with this and see wheither I have made 

 any serious misuse of the text. 



Second, that Dr. Humphrej''s put tiiis same 

 idea into five hundred words so that mathema- 

 ticians would approve of it and editors accept 

 it. I am proposing this, not 'because I think 

 that Dr. Humphreys can't do it, but ibeoause I 

 know he can. I greaifly admire^ and have often 

 benefited by, his power of clear exposition and 

 I want him to apply it in this case. I will not 

 only thank him for it but I will pay him for it. 



Somebody must do ithis job of translating 

 Einstein and it ought to be done by thorough 

 mathematicians like Dr. Humphreys rather than 

 'by outsidere like myself. I realize thait trans- 

 lating mathemati'cs is like transd'ating music. 

 StiU I suppose that even the most complicated 

 equation could be put into ordinai'y language 

 though it would be so wordy and involved that 

 nobody would read it. All th'at can 'be done 

 is to give by illustratio.ns and analogies some 

 notion of the conception. I may say that, ac- 

 cording to my custom, I submitted my version 

 to a professor of nmthematics in one of oui- 

 leading universities, who specializes in Einstein 

 ■and I reworked the wording twice in accordance 

 wiith his suggestions although I will not in- 

 criminate him by mentioning his name. 



Most of the "long list of absurdities" ithat 

 Dr. Humphi-eys mentions are not in 'the article 

 he criticizes; for instance, gravitation. I know 

 that Einstein has not eliminated gravitation 

 from the universe, for if he had I should have 

 felt a sense of relief amounting to 187 pounds. 

 What he has done is well expressed by Lord 

 Haldane, in 'his "Eeign of Eelativity," when he 

 says that Einstein's doctrine "has banished out 

 of physics the necessity of attributing en ob- 

 jective character to gravitation," and he adds 

 "a time may arrive when even the good old 



name gravitation will not be diseovera:ble in any 

 respectable textbook." The way Weyl puts it 

 is: (p. 226). 



We shall find actually that the planets pursue 

 tie courses mapped out for them by the guiding 

 field, and that we need not have recourse to a 

 special "force of gravitation," as did Newton, 

 to account for the influence which diverts the 

 planets from their paths as prescribed 'by Galilei's 

 Principle (or Newton's first law of motion). 



Is not Weyl to ibe taken literally when he 

 makes such a statement as the following: (p. 

 278)? 



We conclude that space is closed and hence 

 finite. If this were nod; the case, it would scarcely 

 be possible to imagine how a state of statistical 

 equilibrium could come about. If the world is 

 closed, spatially, it becomes possible for an ob- 

 server to see several pictures of one and the same 

 star. These depict the star ait epochs separated 

 by enormous intervals of time (during which light 

 travels once entirely round the world). 



Professor Ed'dimgton of Cam'bridge, who 

 'Started the Einstein boom by his report of the 

 British eolipse expeditions of 1919, puts this 

 point still more plainly and literally in "Space, 

 Time and Gravitation": (p. 161) 



Perhaps one or more of the many spiral nebula; 

 are really phantoms of our own stellar system. 

 Or it may be that only a proportion of the stars 

 are substantial bodies; the remainder are optical 

 ghosts revisiting tiheir old haunts. It is, however, 

 unlikely that the light rays after their long jour- 

 ney would converge with the accuracy which this 

 tlieory would require. 



Both Weyl and Eddington are careful to 

 state that what is theoretieaUy possible may be 

 a practieail impossibility and I imitated their 

 caution wihen I said: 



Such a thing (as the influence of tlie future on 

 the present) is conceivable in the generalized 

 theory of relativity, though, like most conceivable 

 things, it does not occur, or is never known to 

 occur, in reality. 



I submit tlhat this is a fair warning to the 

 reader as to the speculative nature of these de- 

 duetions and a fair translation of Weyl's 

 wtords : 



In actual fact the very considerable fluctuations 



