i 4 2 SCIENCE PROGRESS 



Levy-Bruhl, do not distinguish clearly between the number and the numbered 

 object. Numbers excited the Pythagorean world partly because they were 

 distinguished as independent objects of thought and observed to enter into 

 striking mathematical relations. But the old feeling that numbers are remarkable 

 because they belong to, or are confounded with, remarkable things continued to 

 pervade the Greek mind. Almost every small number has been regarded as 

 mystical and peculiarly sacred by some people. Different numbers, remarks 

 Levy-Bruhl, have supreme mystical quality among different peoples. The number 

 seven was charged with significance for the Babylonian and the Hebrew, probably 

 becauses the phases of the moon divide time into periods of seven days. Seven 

 has not yet lost its mystical import, for modern Theosophy divided the universe 

 into seven planes and each plane into seven grades. 



Numbers probably, in part at any rate, first excited the human mind because 

 they were one of its mental conquests. Man was not born with a sense of 

 number. The Pythagorean definition of man as the numbering animal would 

 probably exclude from the class of men all those " missing links " that modern 

 anthropology has discovered. The ability to count is exceedingly defective 

 among most primitive peoples : the savages who can count at all are often unable 

 to proceed beyond five, and frequently stop at two or three. Very often they 

 reckon by comparing objects with their fingers, and this method may be devoid 

 of any real ability to number in the real sense of the word. Primitive feebleness 

 in reckoning by numbers was known long before the modern science of anthro- 

 pology. "The Tououpinambos," writes Locke, "had no names for numbers 

 beyond five ; any number beyond that they made out by showing their fingers, 

 and the fingers of those who were present." The art of numbering, when it was 

 attained, probably brought a sense of mastery that was one of the first sources of 

 the excitement produced by numbers. Numbering or counting is one mode 

 of mental mastery. The most primitive men probably knew whether all the 

 members of their group were present by realising whether particular individuals 

 were missing or not, as a dog probably knows that the tale of sheep is complete. 

 When men learned to count their fish or their head of game or their cattle or 

 the members of their tribe they simplified enormously their control over their 

 collections. This sense of control is perhaps reflected in the primitive fear of 

 being counted. The Bakonga believe, according to Weeks, that evil spirits will 

 snatch away a woman's children if she deliberately counts them ; the people 

 dislike being counted, and fear a census. Census superstitions are constantly 

 encountered in the life and records of peoples. The familiar story of the pestilence 

 sent by Jehovah upon the Hebrews when they were numbered by King David 

 doubtless originated in the belief that it was dangerous to be counted. 

 Numbering was a source of power for man over his collections, enabling him to 

 check their items without the labour of identifying each separately ; demons 

 obtained similar powers if numbers became known to them. There was probably 

 a sense of identity between a number and the individuals or objects it denoted — 

 a notion that because a number denoted a certain group of individuals it gave a 

 grip over them. The number does give a mental grip which seems to have been 

 confounded, in true primitive fashion, with power of a more concrete kind. 

 Through this sense of identity numbers participated in the qualities of the objects 

 they denoted. The four cardinal points made the number four significant. A 

 mystic quality attached to the number six when the zenith and the nadir were 

 collected into a group with the four primary points of the compass. The seven 

 days of the week made seven a magic number. Thus the way was prepared for 



