286 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



concerned. As Newton said, "time flows equably," and it 

 makes no difference whether the individual is busy or idle, 

 amused or bored. Though the last mile may seem the longest, 

 abstract distances are always the same. 



Isotropy. Some difficulty arises in connection with the 

 concept of isotropy, due to the ambiguity in the notion of 

 "direction." By the isotropy of space is meant its sameness 

 in all directions. Poincare describes space as isotropic in that 

 " all straights which pass through the same point are identical 

 with one another." 1 This suggests that by isotropy is meant 

 the similarity in all dimensions. If this is the correct in- 

 terpretation no question arises with regard to time, for 

 time is one-dimensional. But by "direction" is also meant 

 the asymmetry of a relation; for example, Chicago is in a 

 different direction from New York than New Y ork is from 

 Chicago, and the direction of time from 1936 to 1937 is 

 different from the direction from 1937 to 1936. In this sense 

 time may or may not be isotropic; but since there are two 

 possible "directions" for time the question becomes at least 

 relevant. One may call the former sense of isotropy its 

 dimensional interpretation, and the latter its directional in- 

 terpretation. Separate discussions of space and time are 

 then necessary. 



According to the dimensional interpretation Euclidean 

 space is isotropic. By this is meant that the up-down, 

 right-left, and here-there dimensions of space are identical. 

 Since one's movements in the first of these dimensions are 

 somewhat restricted, he tends to assign to that dimension a 

 peculiar place in space; but this individual character must 

 be seen to be merely relative to the observer, and hence 

 not a feature of space as such. So far as space itself is con- 

 cerned, rotation of objects makes no difference, i.e., an 

 object is not compelled to suffer a deformation merely by 

 virtue of rotation through ninety degrees. According to 

 the directional interpretation Euclidean space is also iso- 

 tropic. By this is meant that the up-down direction is the 



1 Foundations of Science, p. 67. 



