246 MAN AND THE WORLD. 



problem of life must be at once abandoned ; for to 

 an infinite environment there can be no adaptation 

 (cp. ch. iv. § 4). Hence to admit the infinity of 

 Space and Time is to give up all hope of tran- 

 scending Pessimism, and it is necessary to subject 

 this doctrine to careful criticism. 



§ 2. It is necessary, in the first place, to determine 

 the proper sense of infinity. 



First of all we must reject the popular and poeti- 

 cal use in which infinity is vaguely used as the 

 equivalent of any extremely large quantity, and 

 indicates merely the point at which the intelligent 

 appreciation of magnitude ceases. This limit, of 

 course, varies immensely with times and seasons 

 and stages of civilization. Thus the Greeks, as 

 their language shows, at one time regarded 10,000 

 as an infinitely large number ; the Romans con- 

 tented themselves with 600, while to many savages 

 everything above two or three is ''many," and 

 *' infinity " begins before five has been reached. So, 

 too, the sands of the seashore, the hairs of the head, 

 and even the stars of heaven have all been popular 

 representatives of infinity. Yet an exact computa- 

 tion shows that a luxuriant head of hair does not 

 contain much over 100,000, and that the stars 

 visible to the naked eye at any one time amount 

 to less than 3,000. And the number of grains of 

 sand on a definite piece of shore, though it may be 

 indefinitely large, is not infinite. 



The popular usage, in short, means very little : 

 infinity is merely a big word which impresses 

 people because they do not understand it. And 

 how little they understand its proper meaning is 

 shown by the history of allied words like " endless,' 

 ''immense," "incalculable," "immeasurable," "in- 



