TIME AND MOTION 61 



together constitute the order of the possibilities 

 of a whole universe." This is a remarkable 

 prophecy whose fulfillment w^as heralded in the 

 ringing words of Minkowski,^ "From this time 

 on, space in itself and time in itself shall sink 

 to shadows, and only a kind of union of the two 

 shall retain independence." 



It has become the habit of scientists to em- 

 ploy the Cartesian method of diagrams when- 

 ever they wish to show graphically the depend- 

 ence of one quantity upon another. Thus Fig- 

 ure 10 shows how the volume of a given amount 

 of w^ater changes with the temperature. We say 

 that the volume is "plotted" vertically and the 

 temperature horizontally. So, too, our auto- 

 matic recording instruments give us similar 

 diagrams; a recording thermometer shows the 

 variation of temperature with the time. 



In the same way we may record the motion 

 of bodies by sho^^ng their positions at different 

 times. Suppose that we have a straight string 

 with a knot at either end, and three beads lying 

 between these knots. We take an instantaneous 

 photograph, showTi by the lowest line in Figure 



2 Minkowski, Rmim und Zeit (collected papers). The 

 same qualitative idea was clearly set forth nearly a century 

 ago in an almost forgotten essay by Fechner, Der Raum 

 hat Vier Dimensionen (Kleine Schriften). 



