MODERN CONCEPTS IN PHYSICS — LANGMUIR 227 



the diameter of a tree or of the length of the waves during a storm 

 at sea. 



Perhaps the strongest reason for the general belief in the existence 

 of an absolute space lay in the apparently perfect agreement between 

 our measurements of lengtli and the theorems of Euclidian geome- 

 try. During the last century, however, mathematicians began more 

 and more to realize that Euclidian geometry was only one out of 

 many possible logical geometries, and since all of these were based 

 solely on certain axioms or postulates none of them had any real or 

 necessary connection with physics. The apparent agreement between 

 our physical observations and Euclidian geometry, therefore, does 

 not prove that space must have the properties postulated in Euclid's 

 axioms. 



MODELS 



As chemists we are all more or less familiar with various models of 

 atoms and molecules that have been proposed within recent years. 

 The structural formulas which the organic chemists have used for 

 a good part of a century are another example of an extremely useful 

 type of model. I want to discuss later some of the models which the 

 physicists have used in giving more concrete forms to their theories. 

 Logically, I believe, we should regard Euclidian geometry as a model 

 devised primarily to help us '' explain " natural phenomena. 



Observation of nature reveals great complexity. We receive enor- 

 mous numbers of impressions simultaneously and if we are to make 

 progress in understanding phenomena we must concentrate on certain 

 aspects of the things we see about us and thus discard the less im- 

 portant features. This involves a process of replacing the natural 

 world by a set of abstractions which we have become very skilful in 

 choosing in such a way as to aid us in classifying and understanding 

 phenomena. Thus it was found useful to develop concepts or ab- 

 stractions such as shape, position, distance, etc., and separate these 

 characteristics of the phenomena from others such as color, hard- 

 ness, etc Euclidian geometry was found useful in correlating these 

 concepts of shape, position, etc. 



Physicists and chemists have usually felt that they understood a 

 phenomenon best when they could explain it in terms of a model or 

 concrete picture. The chemist explained the law of multiple com- 

 bining proportions in terms of atoms which combine together to form 

 molecules. The heat conductivity, viscosity, etc., of gases was ex- 

 plained in terms of the kinetic theory, with molecules making elastic 

 collisions with one another according to the law of probability. 



When we use the atomic or molecular theories to explain phenom- 

 ena in this way, we assign to the atoms and molecules only those 

 properties which seem needed to accomplish the desired result; we 



