192 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1941 



SYMBOLISM 



Whether we agree to this postulational so-called simplicity, we 

 can have no doubt of the existence and efficacy of symbolism in both 

 mathematics and the sciences. The desire for constructibility, so 

 ably championed by Knonecker, has found its way into our search 

 for an understanding of the nature of matter. We hear Lord Kelvin 

 exclaim that he "can understand nothing of which he cannot make a 

 mechanical model." To meet this desire we have the dynamic Euth- 

 erford-Bohr model of the atom and the static Lewis-Langmuir model. 

 But we are told these are too simple and definite to be regarded as 

 other than intellectual conveniences. The ether is symbolized for 

 us as a jellylike mass with remarkable properties. We are warned, 

 however, that the universe is not completely picturable in a graphical 

 sense. Radiation and gravitation elude such a mechanical descrip- 

 tion. We speak of particles and waves as describing the behavior 

 of light and radiation, but we are reminded that the electron is 

 only a symbol for convenience of speech. Eddington tells us that 

 matter and all else in the physical world has been reduced to a 

 "shadowy symbolism." When we ask what the symbols stand 

 for, the reply is that it doesn't matter. (One is reminded of the 

 story that is told of Professor Lefevre, of the University of Vir- 

 ginia. He is said to have greeted his philosophy class one fine morn- 

 ing with the startling pronouncement, "What is mind? No matter. 

 What is matter? Never mind.") "Physics," continues Eddington, 

 "has no means of probing beneath the symbolism. Nor does one 

 have to understand the symbols. What we have to understand are 

 the conditions to which the symbols are subjected." The symbols 

 themselves are dummies. Any other would do as well. 



The mathematician is thoroughly in accord with this use of sym- 

 bolism. He has likened his subject to a game of chess. The rules 

 of the game play the role of postulates. In such a game Bell tells 

 us there is no question of "truth"; there is merely a question as to 

 whether the rules have been complied with. To Hilbert mathematics 

 is "a game played according to certain simple rules with meaningless 

 marks on paper." 



PREDICTION 



We have heard of old that a prophet is not without honor. For 

 the man in the street the ability of science to predict the future 

 holds a particular fascination. He is thrilled by the story of an 

 Adams and a Leverrier working apart, each computing from the 

 perturbing influences of an unknown source on Uranus, the position 

 of a new planet, Neptune, just 52 minutes from where Galle later 

 found it. He reads of the electromagnetic waves predicted by Faraday 



