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 find in them the secret
of the universe. Secondly, they applied number and figure equally to those
parts of physics, such as astronomy or mechanics, in which the modern
philosopher expects to find them, and to those in which he would never
think of looking for them, such as physiology and psychology. For the
sciences were not yet divided, and there was nothing really irrational in
arguing that the same laws which regulated the heavenly bodies were
partially applied to the erring limbs or brain of man. Astrology was the
form which the lively fancy of ancient thinkers almost necessarily gave to
astronomy. The observation that the lower principle, e.g. mechanics, is
always seen in the higher, e.g. in the phenomena of life, further tended to
perplex them. Plato's doctrine of the same and the other ruling the
courses of the heavens and of the human body is not a mere vagary, but is a
natural result of the state of knowledge and thought at which he had
arrived.

When in modern times we contemplate the heavens, a certain amount of
scientific truth imperceptibly blends, even with the cursory glance of an
unscientific person. He knows that the earth is revolving round the sun,
and not the sun around the earth. He does not imagine the earth to be the
centre of the universe, and he has some conception of chemistry and the
cognate sciences. A very different aspect of nature would have been
present to the mind of the early Greek philosopher. He would have beheld
the earth a surface only, not mirrored, however faintly, in the glass of
science, but indissolubly connected with some theory of one, two, or more
elements. He would have seen the world pervaded by number and figure,
animated by a principle of motion, immanent in a principle of rest. He
would have tried to construct the universe on a quantitative principle,
seeming to find in endless combinations of geometrical figures or in the