Lenses and Waves

Chapter 7
Conclusion: Lenses & Waves
A sketch of Huygens in the light of his optics
This study has been aimed at finding out the coming into being of Traité de la
Lumière. How did Huygens’ work in optics develop into the wave theory of
light, a new way of doing optics in which the laws of optics are derived from
an experimentally confirmed, mathematized theory of the mechanistic nature
of light?
Huygens’ work in optics comprises in the first place his dioptrical studies,
but these have hardly been taken into account by historians. Dioptrica has
very little been studied historically and its potential relevance for
understanding Traité de la Lumière has not been considered previously.
Huygens’ optics tends to be identified with his wave theory and the
mechanistic reasoning in it is often taken as a natural part of his science. Yet,
little in Huygens’ work in optics prior to 1672 gives reason to suspect that he
would have given a new form to mechanistic science by 1679. Taking
Dioptrica into account while discussing the development of Huygens’ optics
raises a historical problem. The kind of theorizing pursued in Traité de la
Lumière is completely absent from Dioptrica. Generally speaking, Huygens
does not appear to have had a particular interest in mechanistic topics prior
to the 1670s. The Huygens of Dioptrica was a seventeenth-century
mathematician who does not at all resemble the alleged, ‘first thoroughgoing
Cartesian’ of Traité de la Lumière.
What I wish to do now, is to forget about Huygens’ Cartesianism for a
while and focus on the Huygens of Dioptrica. By comparing his pursuits in
dioptrics to those of his precursors and contemporaries a picture has arisen
of a mathematician with an idiosyncratic approach to questions of
mathematical theory. I shall generalize this picture to include his pursuits in
other fields and make a sketch of his scientific persona. Only then shall I ask
how Traité de la Lumière may fit in and how we should assess his alleged
Cartesianism.
A seventeenth-century Archimedes
The Huygens who went to Paris in 1666 pursued the various branches of the
mathematical sciences: geometry, arithmetic, statics, optics, harmonics, some
astronomy, and the study of motions. He pursued these brilliantly, and
marked himself off by a particular sense of practical possibilities. Huygens’
orientation on instruments in Dioptrica was unique for its day, having his
theoretical investigations guided by questions of practical relevance.