Lenses and Waves

LENSES & WAVES 261
other part of physical optics in which experiment was used as a heuristic tool
for exploring new phenomena of light and establishing their mathematical
properties. In this way he had extended the mathematical science of optics to
the quality of color. Huygens had extended it to the mechanistic causes of
the laws of optics. By applying Galileo’s science of motion to the motions of
ethereal particles, he had invented the most complete form of mathematical
physics in the seventeenth century.
Huygens and Descartes
Traité de la Lumière gave a new form to mechanistic science, the first
‘thoroughly Cartesian’ theory of light. Yet – and this is the gist of my
argument – it was not the outcome of some program in mechanistic, or even
Cartesian, science. A careful reconstruction of what exactly were the leading
questions for Huygens, juxtaposed with comparable pursuits of other
protagonists of seventeenth-century optics, reveals that Huygens’ wave
theory was the outcome of his typically rigorous and tenacious approach to a
problem raised in the context of geometrical optics. As was his wont, he first
of all wanted to get the mathematics of his solution right. He wanted the
explanations of the various laws to be mathematical derivations that were
mutually consistent. As a result of the particular character of the ‘matter’ of
geometrical optics – light rays, which had come to be seen as being of a
mechanistic nature – he got involved in mechanistic questions. He did so in a
deliberately mathematical way, intending to stick to the rigor of mathematics
he missed in the reasonings of his fellows at the Académie. He believed in
the power of mathematical reasoning and did not content himself with illdefined
mechanisms.
This reaction to the Parisian Cartesians can be seen as a continuation of
what I regard as Huygens’ lifelong reaction to Descartes. Much of his oeuvre
was a direct response to what Descartes had said on impact, circular motion,
curves, lenses, light, halos, etc. He did so in a clearly mechanistic context,
accepting fundamental concepts and drawing inspiration from some of
Descartes’ ideas. In his theories of gravity and light he also considered the
conceptualization of the mechanistic nature of things. Discours was induced
by the – in his view – obscurities vented on the Parisian scene. Pardies may
have inspired his thinking on the nature of light and the intellectual climate
at the Académie, but strange refraction – together with the problem of
caustics – may well have been the sole occasion for Huygens’ consideration
of the mechanics of light propagation.
As an adolescent, Huygens had soaked up Principia Philosophiae and its
clarity of reasoning had made an indelible impression on him. The idea that
nature ultimately consists of passive matter in motion was always at the back
of his mind. But this does not turn Huygens into a Cartesian. Mechanistic
philosophy was merely a tacitly assumed background of his thinking.
Huygens quite consistently confined himself to the mathematics of these