M. Comte finds the
means of accomplishing it. His plan is, to make Space also an object of
adoration, under the name of the Grand Milieu, and consider it as the
representative of Fatality in general. "The final _unity_ disposes us to
cultivate sympathy by developing our gratitude to whatever serves the
Grand Etre. It must dispose us to venerate the Fatality on which reposes
the whole aggregate of our existence." We should conceive this Fatality
as having a fixed seat, and that seat must be considered to be Space,
which should be conceived as possessing feeling, but not activity or
intelligence. And in our abstract speculations we should imagine all our
conceptions as located in free Space. Our images of all sorts, down to
our geometrical diagrams, and even our ciphers and algebraic symbols,
should always be figured to ourselves as written in space, and not on
paper or any other material substance. M. Comte adds that they should be
conceived as green on a white ground.

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 sacres_: 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
follow