THE FOUR-DIMENSIONAL WORLD 53 



The supposed planes of structure represented bj 

 Now lines separated one dimension from the other 

 three; but the cones of structure given by the hour- 

 glass figures keep the four dimensions firmly pinned 

 together.* 



We are accustomed to think of a man apart from his 

 duration. When I portrayed "Myself" in Fig. 2, you 

 were for the moment surprised that I should include 

 my boyhood and old age. But to think of a man without 

 his duration is just as abstract as to think of a man 

 without his inside. Abstractions are useful, and a man 

 without his inside (that is to say, a surface) is a well- 

 known geometrical conception. But we ought to realise 

 what is an abstraction and what is not. The "four- 

 dimensional worms" introduced in this chapter seem to 

 many people terribly abstract. Not at all; they are un- 

 familiar conceptions but not abstract conceptions. It is 

 the section of the worm (the man Now) which is an 

 abstraction. And as sections may be taken in somewhat 

 different directions, the abstraction is made differently 

 by different observers who accordingly attribute different 

 FitzGerald contractions to it. The non-abstract man 

 enduring through time is the common source from which 

 the different abstractions are made. 



The appearance of a four-dimensional world in this 

 subject is due to Minkowski. Einstein showed the rela- 

 tivity of the familiar quantities of physics; Minkowski 

 showed how to recover the absolute by going back to 

 their four-dimensional origin and searching more deeply. 



* In Fig. 4 the scale is such that a second of time corresponds to 

 70,000 miles of space. If we take a more ordinary scale of experience, 

 say a second to a yard, the Seen-Now lines become almost horizontal; 

 and it will easily be understood why the cones which pin the four 

 dimensions together have generally been mistaken for sections separating 

 them. 



