14 Chapter 1
which all the other numbers came. For Philolaus, the One was cosmologically as well
as metaphysically central: “ The first thing fitted together, the One, in the middle of the
sphere, is called the hearth, ” the central fire around which all else revolves. Aristotle
noted that, though “ most people say that [the Earth] lies in the center, ” as he himself
held, “ the people in Italy who are called Pythagoreans speak in opposition to this. For
they say that at the center is fire, while the Earth is one of the stars, and by traveling in
a circle around the center makes night and day. ”^13 We will return to this Pythagorean
notion in the following chapters.
Recounting Philolaus ’ s views, Plato presents the same harmonia governing soul and
body as regulates the cosmos. In his Timaeus , Plato asserts that the soul and the cosmos
are both made of music , which explains why we are so moved by the primal cosmic har-
monies: in them, we recognize the same numerical concords that ground our own being.^14
Archytas took Philolaus ’ s ideas as the basis of what he called the four math ē mata , literally
“ learnable things ” : astronomy, geometry, “ numbers ” (arithmetic), and music. These four
are united because “ their concern is with the two primary forms of what is, which are
sisters themselves, ” by which Archytas may have meant the realms of the visible and the
audible.^15 In his Republic , Plato put these four at the center of the education that leads to
what he called “ philosophy, ” which he depicted as a journey from the shadowy illusions
of perception to the full light of reality that shines beyond the dark cave we call “ the
world. ” This quest requires harmony in both body and soul, for which Plato prescribes the
combined practice of mousik ē and gymnastik ē , which is not merely acrobatics or calisthen-
ics but the living embodiment of mousik ē in the moving body. He uses the expression “ to
rhythmize ” as a synonym for education.^16
Children learn these musical skills “ by habit, not knowledge, imparting a kind of tune-
fulness by mode and gracefulness by rhythm, ” but those who aspire to guide and guard
the human commonwealth must go further. To pass from habit to knowledge, they need
“ to learn to count, ” an ability (Socrates notes) even the famous warlord Agamemnon
lacked, “ that little matter of distinguishing one and two and three. ”^17 With his usual irony,
Socrates may allude to the famous catalog of ships, which Homer includes as if the war
chief were incapable of numbering his vast host, or may allude to Agamemnon ’ s failure
to understand the need to unite his army, rather than divide it by angering Achilles. In
more senses than one, Agamemnon did not know what really counts.
Numbering here unites a basic sense of counting off with the larger judgment of what
objects count as sufficiently separate to merit enumeration, which depends on context:
Agamemnon and Achilles are two separate men, at odds whether or in what way they
should constitute a single larger whole as allied Hellenes. Then too, in an era before
widespread literacy, knowledge of calculation was far less widespread; the Greek notation
for numbers lacked a zero and used the alphabet in ways that made numerical knowledge
depend on basic literacy.^18 Plato takes these numerical foundations as important because
they rely on fundamental distinctions between what is the same and what is other, what