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
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.
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