56 THEORETICAL BIOLOGY 



first arithmetic lesson. By doing so, we succeed in making a 

 connecting-link between the magnitudes of time and those of 

 space, and we call this connecting-link " number." For just 

 as the beat consists in the alternation of accented with un- 

 accented moment-signs, so the row of strokes consists likewise 

 of accented and unaccented local signs. The series of Roman 

 numerals approaches the original type most nearly, except that 

 in it every fifth stroke has a special shape, so as to facilitate 

 by group-formation a rapid comprehensive survey. The series 

 of Arabic numerals has a special sign for each stroke from i to 

 9, and thereby offers important advantages for group-forma- 

 tion. For each Arabic numeral signifies not merely a certain 

 stroke in the series, but also the whole group beginning with 

 the first and ending with the stroke in question. 



It is interesting to find that, at first, group-forming by 

 writing lingered behind group-forming by special words for 

 the numbers ; for spoken Latin, unlike written, possessed ten 

 different designations for the numbers from i to lo. 



The method often employed for giving children an idea of 

 number by beginning with objects is really too circuitous. If 

 one tries to teach a child that 3 apples and i pear together 

 are 4 fruits, that may only lead to confusion ; for what the 

 child really ought to learn — namely, to combine in groups its 

 own regularly recurrent activity — is made more difiictilt for 

 it by having its attention turned from the subjective beat to 

 objective things. 



The following will help us to a more profound under- 

 standing of the processes described. 



If you consider the numerical series represented by any 

 long row of strokes as the symbol for a series of beats which 

 can be extended at will, it becomes evident that the making 

 of numbers even in this elementary form requires very great 

 abstraction. 



Let us inquire how this abstraction is effected. On the 



