1 The Birth of Science - MSRI

126 5. Medicine and Other Empirical Sciences
case, Herophilus’ familiarity with the terminology of the more advanced
material in Euclid’s Elements is impressive. Herophilus also applied to the
theory of heartbeats musical and metrical terms, with which he names
various cardiac rhythms. This interest in music, too, was shared by Ctesibius,
who invented the water organ. Probably it was not just results and
instruments of exact science that found use in medicine, but also the other
way around.
We know that the only bodily organ about which Herophilus wrote a
specific book was the eye. Since all his anatomical interests seem to be directed
toward an understanding of physiology, he was probably interested
in the fundamentals of physiological optics. This interest would be contemporaneous
with the development of optical science in Alexandria. The page 167
assumption of a close connection between Alexandrian physicians and
the founders of optics may help understand certain parts of Euclid’s Optics
that have remained obscure since the imperial age. 15 We have seen, for
example, that Herophilus knew the “weblike” structure of the retina, as
implied by the name he gave it. This knowledge, plus the knowledge of
the function of sensory nerves, could easily have suggested the existence
of a discrete set of photoreceptors. To construct a mathematical model of
vision, then, it is natural to consider a discrete set of “visual rays”, one for
each sensory element of the retina, and that is exactly what Euclid does.
The resulting theory can explain quantitatively the resolving power of the
human eye. In real life, distant objects appear not only smaller but also
fuzzier, because the amount of information provided by the nerve endings
decreases with the portion of the retina involved. This loss of detail
is not easily explained within a continuous theory of vision; in Euclid’s
model, by contrast, visual rays form a discrete set and are separated by
at least some minimum angle, 16 so the loss derives from fewer visual rays
intercepting the object. Modern scholars, no longer recognizing in classical
optics a mathematical model of the physiological act of vision — in
part because of the total absence, for the next two thousand years at least,
15 The close connection between optics and ophthalmology is also suggested by the passage in
the Arenarius where Archimedes deals with the measurement of the apparent size of the sun: one
preliminary step is the measurement of the pupil’s diameter ([Archimedes/Mugler], vol. II, p. 139).
16 Euclid, Optics. This is already clear at the beginning of the work, in “definitions” 1 and 7 and in
proposition 1. (In the Optics, “definitions” () is the term used for what are in fact the assumptions
underlying the theory.) Definition 7 says that the sharpness with which an object is perceived
depends on the number of incident visual rays, showing that the choice of a discrete model is due
to the need to explain the eye’s limited resolution power. Definition 7 can be regarded as a consequence
of definition 3, which says that a thing is seen if and only if it is reached by visual rays. It
follows that what is reached by more visual rays is seen in greater detail, and what is far enough
is not seen at all (proposition 3) because it falls between adjacent visual rays. According to Euclid,
the impression that we see a continuous image arises from rapid eye movements.
Revision: 1.9 Date: 2002/09/14 19:12:01