284 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



is a three-dimensional continuum of points, and time is a 

 one-dimensional continuum of instants, each of which series 

 is capable of correlation with the series of real numbers. 

 The applications of this correlation to measurement are 

 obvious. 



According to the third meaning of "continuity' space 

 and time may be said to be continuous in the sense that 

 they exhibit no gaps. There is no time when time does not 

 pass, and there is no extent where there is no space. It is 

 obvious that the notion of a gap in time would be incon- 

 ceivable without the conception of another time stream by 

 which the gap could be defined; for the notion of a gap in 

 time implies a separation of two instants in time, and this 

 would be possible only with reference to a background which 

 would itself be a time stream. Another way of expressing 

 this same feature is to say that at no point in the temporal 

 series could one make a cut which would produce an ele- 

 ment outside of time. Similar remarks apply with reference 

 to the notion of a gap in space. 



Infinity. By the infinity of space and time is meant the 

 impossibility of designating any element as the end-element 

 (either first, or last, or both). It is intimately tied up with 

 the notion of order, and therefore requires reference to the 

 dimensionality of space and time. Space is three-dimensional 

 and time is one-dimensional. By this is meant simply that 

 in order to locate an event in space three independent bits 

 of information are required, while in order to locate an 

 event in time only one is required. The notion of dimension 

 is technically defined in terms of a cut. 1 Roughly, a series 

 is n-dimensional when in order to cut it a series of (n — 1) 

 dimensions is required; for example, a plane must be cut 

 by a line, and a line must be cut by a point. Space may 

 then be considered as constituted by three intersecting 

 linear series, while time is simply a single linear series. 

 By the infinity of space and time is meant the absence of 

 first and last points in each of the spatial series and the 



1 H. Poincare, Foundations of Science, pp. 240-241, 256-257. 



