[Excerpt Be and Become, ProCreative, Sydney 2000]
Historically, the mathematicians’ use of unreal, immeasurable numbers to explain real phenomena was initially developed by Aristotle to resolve Zeno’s troubling paradoxes.
Scientists, in the intervening 2,300 years, have further refied the use of such unknowable numbers. Of particular note were Newton and Leibniz who developed (independently of each other) differential calculus in the latter half of the 17thcentury. Differential calculus greatly refined the use of these unknowable infinitesimals to such an extent that it became the mathematical foundation of the industrial revolution.
As physicist and science writer Richard Morris noted:
As a result, calculus is not only used to resounding effect by the physical sciences, but also by the biological and social sciences.
Differential and integral calculusii has become an indispensable tool in our modern technological society. In fact, physicist Richard Morris claimed that
The tremendous success of calculus (and the use of infinitesimals
in general) exacerbated the contrast between the practical real world and the theoretical use of unreal measures. So it is not surprising that with the advent of calculus came those who were at odds with the idea of using unreal measures in order to explain real phenomena.
Richard Morris, in his book “Achilles in the Quantum Universe,” cites one such example.
In 1734, British philosopher Bishop George Berkeley published a book in which he argued that
- 1. Richard Morris, Achilles in the quantum universe: the definitive history of infinity, Souvenir Press, London 1998, page 63
- 2. “Calculus,” The Funk & Wagnalls New Encyclopedia, (Electronic Edition), Funk & Wagnalls Corporation, 1994.
- 3. Morris, page 63.
- 4. Morris, page 65 (citing Bishop George Berkeley, The Analyst Or a Discourse Addressed to an Infidel Mathematician....)