236 WORLD BUILDING 



with those who think it a blemish on the theory that 

 the lumber should ever have appeared in it. 



By adding together certain of the measures of struc- 

 ture in a symmetrical manner and by ignoring others 

 we reduce the really important measures to 16.* These 

 can be divided into 10 forming a symmetrical scheme 

 and 6 forming an antisymmetrical scheme. This is the 

 great point of bifurcation of the world. 



Symmetrical coefficients (10). Out of these we find it 

 possible to construct Geometry and Mechanics. They 

 are the ten potentials of Einstein (g,J). We derive 

 from them space, time, and the world-curvatures re- 

 presenting the mechanical properties of matter, viz. 

 momentum, energy, stress, etc. 



Antisymmetrical coefficients (6). Out of these we con- 

 struct Electromagnetism. They are the three com- 

 ponents of electric intensity and three components of 

 magnetic force. We derive electric and magnetic 

 potential, electric charge and current, light and other 

 electric waves. 



We do not derive the laws and phenomena of 

 atomicity. Our building operation has somehow been 

 too coarse to furnish the microscopic structure of the 

 world, so that atoms, electrons and quanta are at present 

 beyond our skill. 



But in regard to what is called field-physics the 

 construction is reasonably complete. The metrical, 

 gravitational and electromagnetic fields are all included. 

 We build the quantities enumerated above; and they 

 obey the great laws of field-physics in virtue of the way 

 in which they have been built. That is the special fea- 

 ture; the field laws — conservation of energy, mass, mo- 



* Mathematically we contract the original tensor of the fourth rank 

 to one of the second rank. 



