46 Lehoux
that philosophers will ever be agreed about them!” But mathematics!—
now there is a subject to inspire the mind:Only mathematics can provide sure and unshakeable knowledge to its
devotees, provided one approaches it rigorously... Hence we were drawn to
the investigation of that part of theoretical philosophy, to all of it insofar as
that is possible, but especially to the theory concerning divine and heavenly
things, for that alone is devoted to the investigation of the eternally un-
changing... It is also the best science to help theology along its way, for it is
the only one that can speculate about that action that is unmoved and apart,
because mathematics is familiar both with perceptible bodies... as well as
with what is eternal and unchanging.^20If theology by itself has problems with certainty, Ptolemy could now
offer a remedy: applied mathematics as a tool for a more certain under-
standing of the eternal divinity—a divinity that is best accessed by the
science of astronomy which studies divine and unchangeable motions in
the heavens themselves. What better tool than mathematics to access this
eternal divinity through consideration of its tangible effects? For math-
ematics is situated exactly between the material world, where the effects
of the divine cause ripples ever outwards, and the world of the eternal
and unchanging.
Or so runs the argument. But Ptolemy did not himself pursue this
theological project beyond the mere framing of his inquiry in his preface.
Instead, it is the mathematical analysis of sensory data that he was inter-
ested in. In the Almagest, the mathematical work of systematizing and
modeling the planetary motions, as well as the provision of more accurate
calculating devices (tables) seems to be an end in itself, although he said
in the Tetrabiblos that such accuracy benefi ts the much more useful sci-
ence of astrology. In the Optics and the Harmonics, he used mathematics
not only to systematize his discoveries in nature and to compare phenom-
ena with each other, but also—and this is a theme that recurs again and
again in his works in very sophisticated ways—as a means of using reason
to correct for the vagaries of the senses and their ever- changing objects.^21
Through mathematics as one of its primary tools, reason allows us to un-
derstand the world better, to know it more accurately than the bare senses
would or could permit. Mathematics provides certainty and accuracy in
our understanding of the perceptible world.
But notice the problem sets: Ptolemy did not try to colonize any new
territory, did not geometrize biology, did not mathematize medicine or
alchemy. Instead he chose to work in fi elds where mathematization was