THE LAW OF MOTION 127 



to Einstein's laws. Einstein's law of motion can be 

 deduced from his law of gravitation. The prediction of 

 the track of a planet although divided into two stages 

 for convenience rests on a single law. 



I should like to show you in a general way how it is 

 possible for a law controlling the curvature of empty 

 space to determine the tracks of particles without being 

 supplemented by any other conditions. Two "particles" in 

 the four-dimensional world are shown in Fig. 5, namely 

 yourself and myself. We are not empty space so there is 



— ^-"^ 



Fig. 5 



no limit to the kind of curvature entering into our com- 

 position; in fact our unusual sort of curvature is what 

 distinguishes us from empty space. We are, so to 

 speak, ridges in the four-dimensional world where it is 

 gathered into a pucker. The pure mathematician in his 

 unflattering language would describe us as "singulari- 

 ties". These two non-empty ridges are joined by empty 

 space, which must be free from those kinds of curva- 

 ture described by the ten principal coefficients. Now 

 it is common experience that if we introduce local 

 puckers into the material of a garment, the remainder 

 has a certain obstinacy and will not lie as smoothly as 



