Lenses and Waves

1655-1672 - DE ABERRATIONE 99
extending it to problems the latter had ignored. 207 As with his studies of
dioptrics and circular motion, Huygens’ study of consonance did not develop
in an empirical vacuum. He rejected Stevin’s theory, as purely mathematical
and ignoring the demands of sense perception. But he also rejected systems
that lacked theoretical foundation. 208 His aim was to develop a sound
mathematical theory that explained and founded his musical preferences.
Mean tone temperament therefore was his natural starting point, and the 31tone
division seems a natural outcome of his analysis of its mathematical
properties as it conformed to both his theoretical and practical preferences.
Like his studies of circular motion and consonance, Huygens’ study of
spherical aberration, and this is almost a truism, was predominantly
mathematical. Huygens fruitfully explored and rigorously examined
mathematical theory. More revealing in the context of the present study is
the relationship between mathematics and observation. Huygens was not
blind for the empirical facts. On the contrary, they constituted the main
directive of his investigation in such diverse ways as the measure of gravity,
pleasing temperament and workable lens-shapes. Huygens knew how to
check his theoretical conclusions empirically and he was not easily satisfied.
Exploratory observation of phenomena was not the way Huygens
approached a subject. In modern terms: he did not employ experiment
heuristically. In the case of gravity, he had soon found out that mere
observation did not yield reliable knowledge. The result proved him right:
the analysis of the mathematical properties of circular motion gave him a
better theory as well as a better means of measurement. Huygens successfully
extended the Galilean, mathematical approach to gravity and circular motion.
Newton likewise was a mathematician with a Galilean spirit, but in his
study of colors he linked it with the experimental approach of Baconianism.
Although he was favorably disposed to Bacon’s program for the organization
of science (see below), Huygens did not regard the experimental collecting of
data as a source for new theories, let alone a trustworthy basis for
mathematical derivation. He explored the underlying mathematical structure
of a phenomenon the results of which could be verified to see whether the
supposed structure was real. In the case of consonance, the empirical
foundation of the theory had already been established. In the case of
spherical aberration, however, such preliminary work had not yet been done,
unfortunately. It turned out that not all effects of lenses depended upon the
known mathematical properties of lenses.
Suppose he had pursued his idea that colors were related to the
inclination of the sides of a lens. He might have taken some objective lenses,
covered their center (instead of their circumference as was customary) and
207 Cohen, Quantifying music, 209. It should be noted that, unlike his predecessors, Huygens possessed
logarithms and was therefore readily able to calculate, for example, a 4 1
5
.
208
Cohen, “Huygens and consonance”, 293-294.