350 THE POPULAR SCIENCE MONTHLY. 



are far simpler subjects, and far less involved in sublime mysteries, 

 than are mathematics. All subjects were studied, or at least specu- 

 lated upon, in no other order than that of their apparent nearness to 

 human interests and that of the obviousness of their phenomena.* 



Exactly the same is true for every individual mind, whose percep- 

 tions are not regularly successive, but simultaneous, and are as liable 

 to be attracted toward infinitely complex objects as toward the sim- 

 plest details. It is true, as has been pointed out in the " Experiment," 

 that a child's first perceptions are necessarily of form and color, and 

 the ideas of form belong to mathematics. But color is a physical 

 property of bodies, and therefore the subject of a science which is, 

 according to the Comtist measure of simi^licity, two degrees removed 

 from mathematics. Ou the other hand, the property of number, 

 although like forms, mathematical, is not grasped till much after color 

 and many other physical properties have been appreciated. 



Other properties of bodies become known in direct proportion to 

 their obviousness, and to their accidental impact on the senses, or to 

 their association with the personal experience of the child. These may 

 be mathematical, physical, biological, or even social. The mind of 

 the child, like that of the race, looks over the surface of all things at 

 once ; its progress is not from the simple toward the complex, but 

 from the superficial and obvious toward the profound and hidden. 

 The mutual aid rendered by sciences, w^hen, to use Herbert Spencer's 

 expression, they become arts to one another, is only required after the 

 observation and registration of accessible facts are completed, and 

 when analysis is required to bring to light new facts or to explain 

 others. But the child's mind does not reach this stage, and it is either 

 illusory or fatal to attempt to force it prematurely. 



It is very interesting to notice, by study of the actual evolution of 

 knowledge, what a large amount of knowledge was obtained simul- 

 taneously in each department by independent observation, and before 

 the necessity for mutual help, other than that derived from element- 

 ary mathematics, had been perceived. During this period the advance 

 was made in each science, not by deductions from some simpler science, 

 but by observations and methods peculiar to itself. Thus, as already 

 stated, the germs of mathematics, physics, biology, and sociology, 

 are all found coexisting at what seem to us the opening periods of 

 Greek thought ; nor was their degree of development at all propor- 

 tioned to their degree of simplicity. If some truths of geometry and 

 arithmetic were really established, so, in spite of the obscurity sur- 

 rounding biological laws, were many phenomena of living beings also 

 observed. The pulse Avas known, if the circulation was not, and nu- 

 merous are the clinical observations of Hippocrates which still hold 



* " Tlie broad distinction between the two orders of knowledge [the ordinary and the 

 scientific] is not in their nature, but in their remoteness from perception."— Spencke, 

 ioc. cit. 



