that there was order in the universe. And so there began to be
a real sympathy between the world within and the world without. The
numbers and figures which were present to the mind's eye became visible
to the eye of sense; the truth of nature was mathematics; the other
properties of objects seemed to reappear only in the light of number.
Law and morality also found a natural expression in 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 properties of 1:2:4:8, or 1:3:9:27, or of 3, 4, 5, they discovered
in them many curious correspondences and were disposed to fi