are far simpler subjects, and far less involved in sublime mysteries, than are mathematics. All subjects were studied, or at least speculated upon, in no other order than that of their apparent nearness to human interests and that of the obviousness of their phenomena.[1]
Exactly the same is true for every individual mind, whose perceptions are not regularly successive, but simultaneous, and are as liable to be attracted toward infinitely complex objects as toward the simplest 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 simplicity, two degrees removed from mathematics. On 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, when, 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 simultaneously in each department by independent observation, and before the necessity for mutual help, other than that derived from elementary 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 proportioned to their degree of simplicity. If some truths of geometry and arithmetic were really established, so, in spite of the obscurity surrounding biological laws, were many phenomena of living beings also observed. The pulse was known, if the circulation was not, and numerous are the clinical observations of Hippocrates which still hold
- ↑ "The broad distinction between the two orders of knowledge [the ordinary and the scientific] is not in their nature, but in their remoteness from perception."—Spencer, loc. at.
