ON THE NATURE OF LIFE 205 



cyclic order, such that the most probable phases are those in 

 which entropy tends towards its maximum value, and the least 

 probable ones are those in which entropy tends towards its 

 minimum value. As such it is a permanent universe, self- 

 sufficient, without beginning and without end. Throughout its 

 greater extent nothing happens, and this condition we call the 

 normal one. Here and there, however, and for infinitesimally 

 small periods of duration, there is physical activity, and this 

 condition we call the abnormal one. The probability that any- 

 where and at any time there is such physical activity is of the 

 same order of magnitude as that calculated by Boltzmann for 

 the reversal of direction of motion of all the molecules contained 

 in a small volume of gas. 



A Digression on Orders of Magnitude and Duration. The 



principal difficulty in appreciating the force of such an argument 

 as the above one lies in the reluctance with which we apprehend 

 extremely small and extremely large magnitudes. We refer all 

 measures, space, and time to those spatial and temporal values 

 that limit our bodily activities, and if something is very great 

 compared with these we are apt to say that it is " infinite," 

 while if it is very small we say that it is " practically zero." 

 Now a magnitude that we can estimate is always finite, no 

 matter how big or how small it may be, and greatness and small- 

 ness are always relative to something or other. The same 

 magnitude may be extremely small compared with some other 

 one, but extremely great when compared with yet another. 

 Thus the radius of the earth (4,000 miles) is to us a fairly familiar 

 magnitude, being a distance that we might traverse during a 

 few weeks by means of a steamship. A micron, however that 

 is> TTiVo millimetre, the microscopist's unit of length is a 

 magnitude that is about I/ 6378X10 8 of the earth's radius, and 

 we may call it an infinitesimal of the first order of smallness.* 

 But, again, a molecule of hydrogen is about 2-17X10' 8 mm. 

 in diameter, so that it is an infinitesimal of the first order when 

 compared with a micron, but of the second order when compared 

 with the radius of the earth. f Starting now with our standard 

 magnitude that is, the earth's radius we may compare it with 

 others that are " infinitely great "; thus it is about one-millionth 



* It is about i -billionth part of the earth's radius. 



2-17 

 t 2-17 x 10 - 9 mm. = mm., say 1 thousand millionth mm. 



