number and figure. Instruments of such power and elasticity could not fail
to be 'a most gracious assistance' to the first efforts of human
intelligence.

There was another reason why numbers had so great an influence over the
minds of early thinkers--they were verified by experience. Every use of
them, even the most trivial, assured men of their truth; they were
everywhere to be found, in the least things and the greatest alike. One,
two, three, counted on the fingers was a 'trivial matter (Rep.), a little
instrument out of which to create a world; but from these and by the help
of these all our knowledge of nature has been developed. They were the
measure of all things, and seemed to give law to all things; nature was
rescued from chaos and confusion by their power; the notes of music, the
motions of the stars, the forms of atoms, the evolution and recurrence of
days, months, years, the military divisions of an army, the civil divisions
of a state, seemed to afford a 'present witness' of them--what would have
become of man or of the world if deprived of number (Rep.)? The mystery of
number and the mystery of music were akin. There was a music of rhythm and
of harmonious motion everywhere; and to the real connexion which existed
between music and number, a fanciful or imaginary relation was superadded.
There was a music of the spheres as well as of the notes of the lyre. If
in all things seen there was number and figure, why should they not also
pervade the unseen world, with which by their wonderful and unchangeable
nature they seemed to hold communion?

Two other points strike us in the use which the ancient philosophers made
of numbers. First, they applied to external nature the relations of them
which they found in their own minds; and where nature seemed to be at
variance with number, as for example in the case of fractions, they
protested against her (Rep.; Arist. Metaph.). Having long meditated on the