ARE SPACE AND TIME INFINITE? 81 



the circle, but the line forming its circumference. This 

 is a finite but endless line. Next think of a sphere — the 

 surface of a sphere — that also is a region which is 

 finite but unbounded. The surface of this earth never 

 comes to a boundary; there is always some country 

 beyond the point you have reached; all the same there 

 is not an infinite amount of room on the earth. Now go 

 one dimension more; circle, sphere — the next thing. 

 Got that? Now for the real difficulty. Keep a tight hold 

 of the skin of this hypersphere and imagine that the 

 inside is not there at all — that the skin exists without 

 the inside. That is finite but unbounded space. 



No; I don't think you have quite kept hold of the 

 conception. You overbalanced just at the end. It was 

 not the adding of one more dimension that was the real 

 difficulty; it was the final taking away of a dimension 

 that did it. I will tell you what is stopping you. You 

 are using a conception of space which must have 

 originated many million years ago and has become 

 rather firmly embedded in human thought. But the 

 space of physics ought not to be dominated by this 

 creation of the dawning mind of an enterprising ape. 

 Space is not necessarily like this conception; it is like — 

 whatever we find from experiment it is like. Now the 

 features of space which we discover by experiment are 

 extensions, i.e. lengths and distances. So space is like 

 a network of distances. Distances are linkages whose 

 intrinsic nature is inscrutable; we do not deny the 

 inscrutability when we apply measure numbers to them 

 — 2 yards, 5 miles, etc. — as a kind of code distinction. 

 We cannot predict out of our inner consciousness the 

 laws by which code-numbers are distributed among the 

 different linkages of the network, any more than we 

 can predict how the code-numbers for electromagnetic 



