We cannot go on any longer with this. In spite of it all, the volume on
mathematics is full of profound thoughts, and will be very suggestive to
those who take up the subject after M. Comte. What deep meaning there
is, for example, in the idea that the infinitesimal calculus is a
conception analogous to the corpuscular hypothesis in physics; which
last M. Comte has always considered as a logical artifice; not an
opinion respecting matters of fact. The assimilation, as it seems to us,
throws a flood of light on both conceptions; on the physical one still
more than the mathematical. We might extract many ideas of similar,
though none perhaps of equal, suggestiveness. But mixed with these, what
pitiable _niaiseries_! One of his great points is the importance of the
"moral and intellectual properties of numbers." He cultivates a
superstitious reverence for some of them. The first three are sacred,
_les nombres sacrés_: One being the type of all Synthesis, Two of all
Combination, which he now says _is_ always binary (in his first treatise
he only said that we may usefully represent it to ourselves as being
so), and Three of all Progression, which not only requires three terms,
but as he now maintains, never ought to have any more. To these sacred
numbers all our mental operations must be made, as far as possible, to
adjust themselves. Next to them, he has a great partiality for the
number seven; for these whimsical reasons: "Composed of two progressions
followed by a synthesis, or of one progression between two couples, the
number seven, coming next after the sum of the three sacred numbers,
determines the largest group which we can distinctly imagine.
Reciprocally, it marks the limit of the divisions which we can directly
conceive in a magnitude of any kind." The number seven, therefore, must
be foisted in wherever possible, and among other things, is to be made
the basis of numeration, which is hereafter to be septimal instead of
decimal: producing all the inconvenience of a change of system, not only