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Wretched as this is, it is singularly characteristic of M. Comte's later mode of thought. A writer might be excused for introducing into an avowed work of fancy this dance of the planets, and conception of an animated Earth. If finely executed, he might even be admired for it. No one blames a poet for ascribing feelings, purposes, and human propensities to flowers. Because a conception might be interesting, and perhaps edifying, in a poem, M. Comte would have it imprinted on the inmost texture of every human mind in ordinary prose. If the imagination were not taught its prescribed lesson equally with the reason, where would be Unity? "It is important that the domain of fiction should become as systematic as that of demonstration, in order that their mutual harmony may be conformable to their respective destinations, both equally directed towards the continual increase of unity, personal and social."[26]

Nor is it enough to have created the Grand Fétiche (so he actually proposes to call the Earth), and to be able to include it and all concrete existence in our adoration along with the Grand Etre. It is necessary also to extend Positivist Fetishism to purely abstract existence; to "animate" the laws as well as the facts of nature. It is not sufficient to have made physics sentimental, mathematics must be made so too. This does not at first seem easy; but 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 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 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 regulation for the details of life is numbers: fixed numbers, therefore, should be introduced into all our conduct. M. Comte's first application of this system was to the correction of his own literary style. Complaint had been made, not undeservedly, that in his first great work, especially in the latter part of it, the sentences and paragraphs were long, clumsy, and involved. To correct this fault, of which he was aware, he imposed on himself the following rules. No sentence was to exceed two lines of his manuscript, equivalent to five of print. No paragraph was to consist of more than seven sentences. He further applied to his prose writing the rule of French versification which forbids a hiatus(the concourse of two vowels), not allowing it to himself even at the break between two sentences or two paragraphs; nor did he permit himself ever to use the same word twice, either in the same sentence or in two consecutive sentences, though belonging to different paragraphs: with the exception of the monosyllabic auxiliaries.[27] All this is well enough, especially the first two precepts, and a good way of breaking through a bad habit. But M. Comte persuaded himself that any arbitrary restriction, though in no way emanating from, and therefore necessarily disturbing, the natural order and proportion of the thoughts, is a benefit in itself, and tends to improve style. If it renders composition vastly more difficult, he rejoices at it, as tending to confine writing to superior minds. Accordingly, in the Synthèse Subjective, he institutes the following "plan for all compositions of importance." "Every volume really capable of forming a distinct treatise" should consist of "seven chapters, besides the introduction and the conclusion; and each of these should be composed of three parts." Each third part of a chapter should be divided into "seven sections, each composed of seven groups of sentences, separated by the usual break of line. Normally formed, the section offers a central group of seven sentences, preceded and followed by three groups of five: the first section of each part reduces to three sentences three of its groups, symmetrically placed; the last section gives seven sentences to each of its extreme groups. These rules of composition make prose approach to the regularity of poetry, when combined with my previous reduction of the maximum length of a sentence to two manuscript or five printed lines, that is, 250 letters." "Normally constructed, great poems consist of thirteen cantos, decomposed into parts, sections, and groups like my chapters, saving the complete equality of the groups and of the sections." "This difference of structure between volumes of poetry and of philosophy is more apparent than real, for the introduction and the conclusion of a poem should comprehend six of its thirteen cantos," leaving, therefore, the cabalistic numeber seven for the body of the poem. And all this regulation not being sufficiently meaningless, fantastic, and oppressive, he invents an elaborate system for compelling each of his sections and groups to begin with a letter of the alphabet, determined beforehand, the letters being selected so as to compose words having "a synthetic or sympathetic signification," and as close a relation as possible to the section or part to which they are appropriated.