6. Understanding the ‘scientific revolution’
1. Introduction
Philosophy is written in that vast book which stands forever open before our eyes, I mean the universe; but it cannot
be read until we have learnt the language and become familiar with the characters in which it is written. It is
written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which
means it is humanly impossible to comprehend a single word. (Galileo,Il Saggiatore (The Assayer), tr. in Drake 1960,
pp. 183–4)It is sensible to begin any discussion of the scientific revolution with Galileo. The above quotation,
which has been used to excess as a description of his position, at any rate serves to link Galileo’s
physics with the history of mathematics. It also illustrates the role which mathematics often plays
in accounts of the scientific revolution—as a language whose use transforms science, not as an
object of study in itself. As a result, those mathematicians for whom physics was not an obvious
interest, like Cardano and Viète—whom we will discuss later—or who were better mathematicians
than they were physicists, like Descartes, receive little or no attention in the history. Our version will
necessarily have to be skewed in a different direction—to the development of mathematics itself,
and to its interaction with physics; questions of the role of experiment and observation, which are
central to the usual history, are not really important. There were exceptional changes in the way
mathematics was done between, say, 1550 and 1700, some of which are discussed in this chapter.
The most notable, the calculus, is the subject of the next chapter, but it is generally agreed that by
the time Descartes’sGéométriewas published (in 1637), a ‘new mathematics’ had come into being;
and that the works of Viète, Stevin, Descartes, and others radically changed the way in which even
ordinary practitioners worked. Much of this had some relation to the wider scientific revolution,
but both the question of what was new and the question of origins need to be considered with due
reference to the particularity of mathematics. So let us begin by posting, as major concerns for this
chapter, some questions:
- Was there a specific ‘mathematical revolution’ of the fifteenth to seventeenth centuries (say)?
If so, what was its nature? - How far can developments in physics and mathematics in the period be ‘disentangled’, that is,
to what extent do changes in one depend on the other? - To what external factors (if any) should we attribute any changes in mathematics which take
place?
To ask our usual naive question: what is so important about the scientific revolution? Briefly,
however it is defined it is central to the narrative of Western culture and how, for better or worse,
it is viewed. And Galileo was only the most gifted among many contemporaries who, under the