Lenses and Waves

260 CHAPTER 7
mathematical description and physical explanation. That had not been
Bartholinus’ problem, who sought only a correct mathematical description of
the phenomenon. As a matter of fact, few students of optics made a problem
of the coherence of physical explanation and mathematical laws. Kepler,
Descartes, Newton, and possibly Pardies were likely to recognize the
problem. The first two, who did not know strange refraction, did not solve
the problem of ordinary refraction in a satisfactorily coherent manner.
Pardies saw strange refraction as a problem of the crystal, not as a problem
of waves. And Newton … With respect to strange refraction he avoided the
problem by proposing a law of strangely refracted rays without even
suggesting, whether in print or in private, a possible explanation in terms of
light particles. This law happened to be identical with the first stab Huygens
had made at the problem of strange refraction but had failed to solve it. With
a surefootedness that can only be called astonishing Huygens had taken
precisely this problem of reconciling mathematical description and physical
explanation seriously and brought it to a fortunate conclusion. Posing the
problem in this way was, however, not a matter of course, nor was the
eventual solution.
Huygens did not realize that he was doing something new in a broader
sense. In his view, he had merely solved the problem of strange refraction.
And in a sense he was right. He had set his teeth in another challenging
mathematical problem: reconciling waves and strange refraction. Just as he
did not content himself with rough answers about pendulums and lenses, he
wanted to get the mathematics of wave propagation right. Given the
conscientiousness with which he handled all problems, it is quite natural that
Huygens ended up with a coherent and thoroughly mathematical answer. In
his attack on the problem we see the same versatility in applying his
mathematical skills to concrete objects. In this case, however, these concrete
objects were invisible waves of light. As if it went without saying, he had
approached unobservable particles in the same Archimedean way he
approached the tangible objects of his earlier mathematical studies. He had
mathematized the mechanistic causes of the behavior of light rays. Huygens
was therefore wrong as well. He had not just solved the problem of strange
refraction. In effect he had invented a new way of doing optics.
Within the limited scope of reflected and refracted rays, Huygens had
invented that part of physical optics in which mathematics fruitfully
integrated the nature of light and its observed behavior. Kepler had realized
that the mathematical description of light rays also ought to reflect its
physical nature, but had not succeeded in deriving the ‘measure’ of refraction
from its ‘cause’. Descartes had proclaimed the mechanistic nature of light
but, by seeking mathematics in the ontology of matter rather than its
motions, had not succeeded in mathematizing his picture. Newton could
mathematize the motions of particles of light, but he would not allow this to
be integrated with his experimentally established theory of the mathematical
behavior of colored rays. Parallel to Huygens, Newton had developed that