Lenses and Waves

258 CHAPTER 7
rise to. In this sense Huygens’ mathematics is indeed lowbrow. He was more
fascinated by the frayed fringes of mathematics when it came down to
penetrating the behavior of concrete objects like brass pendulums and glass
lenses, than in developing indisputable foundations or in gaining access to
the truth about nature.
However tempting, it would be too easy to explain the factual character
of his mathematics by some sort of artisanal attitude. True, one can discern
interesting parallels between artisanal practice and Huygens’ mathematics.
The visual reasoning by which his mathematics has been characterized has
also been pointed out to typify the way of thinking of the craftsman and the
engineer. 5 Like a craftsman wants things to work, Huygens first of all wanted
to get the mathematics right. By his propensity for application he had to
reckon with parameters eluding mathematical theory, as a craftsman has to
cope with the imperfections of concrete materials standing in the way of a
perfectly functioning apparatus. In either case this yields a different view of
knowledge as never final and always open to improvement. As said, an
explanation of the character of Huygens’ mathematics along such lines
would be too easy. De Aberratione suggests that he did not fully grasp the
mismatch between mathematical and artisanal knowledge. Yet, he probably
had a clearer few of the gap between science and technology than anybody
else in the seventeenth century, and he came closest to bridging it. In the
end, however, Huygens could not integrate his theoretical and practical
abilities.
Huygens always had a keen eye for useful applications, but these did not
drive his theoretical studies. Moreover, his interest in mathematical theory
went beyond mere instrumentalism, in view of the way he sought to establish
general theories that made possible a rigorous mathematical analysis of the
subject at hand. Even in dioptrics, where the tie between theory and practice
was closest, his practical approach cannot be said to originate in practice.
Tractatus was written prior to his work on lens grinding and his telescopic
observations. At the end of chapter three I have pointed out that, however
strange it may seem, his orientation on telescopes emanated from itself. The
same applies, I believe, to his approach in general. The Huygens I see was
fascinated by figuring out the mathematics of real, tangible things and this
concrete puzzling was to him of intrinsic value.6
All in all, I see quite a lot of coherence in Huygens’ activities before his
move to Paris. First of all, most formed a part of the mathematical sciences. 7
Secondly, he displayed a marked predilection for the elaboration of
mathematical theory, including its application to concrete objects and
5 Bos, “Huygens and mathematics”, 132 and Ferguson, Engineering and the mind’s eye, 1-12.
6 In a way, his tutor Henricus Bruno foresaw this with the fourteen-year old Christiaan, when he wrote
Constantijn sr. that they would have to fear that he might turn into an engineer, given the his fascination
and skill with taking apart clocks. OC1, 552.
7 His work on pumps in 1661 being the most notable exception, but in this his principal interest was in
apparatus rather than vacuum. For an overview see Sparnaay, Adventures in vacuums.