228 THE MECHANISM OF LIFE 



of mobility, and time is our duration as conscious, remembering 

 individuals. What we know and deal with intellectually are 

 points in space and instants in time. There is nothing between 

 the space points but a mathematical relation and the intuition 

 of a possible actual or virtual bodily movement, and between the 

 time instants there is a similar relation and duration, which is, 

 perhaps, the " stufi " of our intuition. 



Proceed a little further, and note that in "reading the baro- 

 meter" we observe a space-time coincidence. There is an instant 

 at which the top of the mercury column coincides with a mark 

 on the adjoining scale. That instant itself is a coincidence of 

 the hand of the clock with a mark on the scale or dial. There is, 

 therefore, a double space coincidence. In the barometric reading 

 we define a point y^ in reference to another point = ?/o, the scale 

 zero. In the time measurement we find an arc by defining a 

 point X, y in reference to the " zero " of the dial — ^its centre. This 

 latter point we, however, call ^, the time. Thus our measure- 

 ments are defined by reference to some co-ordinate system, and 

 their statement is always an arbitrary or conventional one, and 

 depends on the choice of the scale zeros or co-ordinate systems. 



Proceed with such an analysis in relation to any transforma- 

 tion, or event, or object, or phenomenon whatever. The 

 " elements " of our knowledge — the perceptions with which we 

 construct the universe — ^are space-time coincidences. In any such 

 perception we generally observe the coincidences of four points 

 (three space points and one time instant), x^^ lyi, Zj, ^i, with other 

 four, 352, y^i ^ii ti- Let us state this in a quite dogmatic way (for 

 it can be amply demonstrated, if necessary) — all the data of our 

 knowledge of nature are space-time coincidences and the relations 

 of such. 



Nature a System of Relations. — ^We do not deal with even the 

 space and time points, for these have no meaning except with 

 relation to a " frame of reference," or co-ordinate system. The 

 latter is always an arbitrary (though convenient) one, and obvi- 

 ously the position of any point depends on the zero from which 

 it is measured. We take as an illustration (for a clear under- 

 standing of the matter is very desirable) the trajectory of a 

 material body falling freely in vacuo. 



We do not deal with " spaces " and " times " here, but with 

 " differentials," ds and dt. The symbol ds is not an infinitesi- 

 mally small space, but the limit to a space that becomes smaller 

 and smaller without ever becoming zero. It can be so small that 

 the error involved in regarding it as zero will be less than any 



