22 - The mathematical realm of nature

Summary

MATHEMATICS, MECHANICS, AND METAPHYSICS

At the beginning of what we now call the scientific revolution, Nicholas Copernicus (1473-1543) displayed on the title page of De revolutionibus (1543) Plato's ban against the mathematically incompetent: ‘Let no one enter who is ignorant of geometry’. He repeated the notice in the preface, cautioning that ‘mathematics is written for mathematicians’. Although Isaac Newton posted no such warning at the front of the Principia a century and a half later, he did insist repeatedly that the first two books of the work treated motion in purely mathematical terms, without physical, metaphysical, or ontological commitment. Only in the third book did he expressly draw the links between the mathematical and physical realms. There he posited a universal force of gravity for which he could offer no physical explanation but which, as a mathematical construct, was the linchpin of his system of the world. ‘It is enough’, he insisted in the General Scholium added in 1710, ‘that [gravity] in fact exists.’ No less than the De revolutionibus, the Principia was written by a mathematician for mathematicians.

Behind that common feature of the two works lies perhaps the foremost change wrought on natural philosophy by the scientific revolution. For although astronomy had always been deemed a mathematical science, few in the early sixteenth century would have envisioned a reduction of physics – that is, of nature as motion and change – to mathematics. Fewer still would have imagined the analysis of machines as the medium of reduction, and perhaps none would have accorded ontological force to mathematical structure.