On the Continuity of Chance 7 



of turns, each of these again so bent, and so on forever till the 

 number of turns is as "infinitely infinite" as you please. The 

 number of points must then be regarded as at least one degree 

 more highly infinite, and therefore can be put into one-to-one 

 correspondence with the points in infinite «-way space where 

 n is as large as you please. Algebra makes all this even easier 

 by saying, between all the values positive and real of x and 

 X " there is a one-to-one correspondence. 



Does the conception of 9i-way space baffle and confuse you? 

 Drop it. Take only three-way space, but endow each point 

 with movement, with mass, with attraction and repulsion: nay, 

 more; accompany every movement with sensation, thought, 

 and feeling in all the infinite variety that we know. In brief, 

 give life, give a soul to the universe. (If there be not a 

 fourth dimension in space, there is I know not what high di- 

 mension in quality.) Add in the flow of time, and still the 

 one-to-one correspondence can hold, to each point of the line 

 corresponding a distinct point of space with distinct mass, 

 motion, force, with distinct thought and feeling or absence of 

 it, at a distinct instant of time; a history of the universe 

 throughout all time written in the position of points on the 

 inch line. Note, too, that the line itself is a part of that uni- 

 verse with which the correspondence is made. The problem 

 of the position of points on the line becomes, in a way, the 

 problem of science, to state in laws the relations of the posi- 

 tions, movements, and qualities of all this material and spirit- 

 ual universe. There is even mathematical truth in that frag- 

 ment of Tennyson's: 



" Flower in the crannied wall, 



I pluck you out of the crannies; — 



Hold you here, root and all, in my hand, 



Little flower— but if I could understand ^ 



What you are, root and all, and all in all, 



I should know what God and man is." 



Now on our line, remember no law could give all the points. 



137 



