ITERATED SYSTEMS 12/5 



to see cars go past with the final digits 0,1, 2, 3, 4, 5, 6, 7, 8, 9, in 

 that order. If we insist that the ten cars shall pass consecutively, 

 then on the average we shall have to wait till about 10,000,000,000 

 cars have passed : for practical purposes such an event is impos- 

 sible. But if we allow success to be achieved by first finding a 

 1 ', then finding a 4 1 ', and so on until a l 9 ' is seen, then the 

 number of cars which must pass will be about fifty, and this 

 number makes 4 success ' easily achievable. 



12/5. A well-known physical example illustrating the difference 

 is the crystallisation of a solid from solution. When in solution, 

 the molecules of the solute move at random so that in any given 

 interval of time there is a definite probability that a given molecule 

 will possess a motion and position suitable for its adherence to 

 the crystal. Now the smallest visible crystal contains billions of 

 molecules : if a visible crystal could form only when all its mole- 

 cules happened simultaneously to be properly related in position 

 and motion to one another, then crystallisation could never occur : 

 it would be too improbable. But in fact crystallisation can occur 

 by succession, for once a crystal has begun to form, a single 

 molecule which happens to possess the right position and motion 

 can join the crystal regardless of the positions and motions of the 

 other molecules in the solution. So the crystallisation can pro- 

 ceed by stages, and the time taken resembles T 2 rather than 2\. 

 We may draw, then, the following conclusion. A compound 

 event that is impossible if the components have to occur simul- 

 taneously may be readily achievable if they can occur in sequence 

 or independently. 



Reference 



Parker, G. The evolution of man. New Haven, 1922. 



143 



