ed 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
without getting rid of, but greatly aggravating, the disadvantages of
the existing one. But then, he says, it is absolutely necessary that the
basis of numeration should be a prime number. All other people think it
absolutely necessary that it should not, and regard the present basis as
only objectionable in not being divisible enough. But M. Comte's puerile
predilection for prime numbers almost passes belief. His reason is that
they are the type of irreductibility: each of them is a kind of ultimate
arithmetical fact. This, to any one who knows M. Comte in his later
aspects, is amply sufficient. Nothing can exceed his delight in anything
which says to the human mind, Thus far shalt thou go and no farther. If
prime numbers are precious, doubly prime numbers are doubly so; meaning
those which are not only themselves prime numbers, but the number which
marks their place in the series of prime numbers is a prime number.
Still greater is the dignity of trebly prime numbers; when the number
marking the place of this second number is also prime. The number
thirteen fulfils these conditions: it is a prime number, it is the
seventh prime number, and seven is the fifth prime number. Accordingly
he has an outrageous partiality to the number thirteen. Though one of
the most inconvenient of all small numbers, he insists on introducing it
everywhere.

These strange conceits are connected with a highly characteristic
example of M. Comte's frenzy for regulation. He cannot bear that
anything should be left unregulated: there ought to be no such thing as
hesitation; nothing should remain arbitrary, for _l'arbitraire_ is
always favourable to egoism. Submission to artificial prescriptions is
as indispensable as to natural laws, and he boasts that under the reign
of sentiment, human life may be made equally, and even more, regular
than the courses of the stars. But the great instrument of exact