i 4 8 GRAVITATION— THE EXPLANATION 



We have already had three versions of what the earth 

 is trying to do when it describes its elliptic orbit around 

 the sun. 



(i) It is trying to go in a straight line but it is 

 roughly pulled away by a tug emanating from the sun. 



(2) It is taking the longest possible route through 

 the curved space-time around the sun. 



(3) It is accommodating its track so as to avoid 

 causing any illegal kind of curvature in the empty space 

 around it. 



We now add a fourth version. 



(4) The earth goes anyhow it likes. 



It is not a long step from the third version to the 

 fourth now that we have seen that the mathematical 

 picture of empty space containing "illegal" curvature 

 is a sheer impossibility in a world surveyed from within. 

 For if illegal curvature is a sheer impossibility the earth 

 will not have to take any special precautions to avoid 

 causing it, and can do anything it likes. And yet the 

 non-occurrence of this impossible curvature is the law 

 (of gravitation) by which we calculate the track of the 

 earth! 



The key to the paradox is that we ourselves, our 

 conventions, the kind of thing that attracts our interest, 

 are much more concerned than we realise in any account 

 we give of how the objects of the physical world are 

 behaving. And so an object which, viewed through our 

 frame of conventions, anay seem to be behaving in a 

 very special and remarkable way may, viewed according 

 to another set of conventions, be doing nothing to excite 

 particular comment. This will be clearer if we consider 

 a practical illustration, and at the same time defend 

 version (4). 



