# Week 4. The mathematisation of the world, 1400-1700. Measurement.

Click here for the handout and slides for this week's lecture

'The book of nature is written in the language of mathematics.' So wrote the Italian courtier Galileo Galilei in 1623, expressing a view that was shared by many other scientists in Europe the seventeenth century. There is no doubt that the study of the natural world was transformed by mathematics in this period. New mathematical laws were articulated about light, pressure, and planetary motion, and new instruments invented to put numbers on these phenomena. As for experiment, these changes came about through the interaction between scholarly practices with artisanal ones. But the change was far from complete in 1700. Questions remained about what could be quantified, who should quantify it, and how they should do so.

**Seminar questions:**

Who measured things in early modern Europe?

How were things measured? What needed to be in place – intellectually, materially, socially – before a measurement could be made?

Why was measurement increasingly applied to the study of the natural world in this period?

###### Essential readings:

Robert Norman, *The Newe Attractive* (first published 1581) - read 'To the Reader' and pages 13-17 (including the image on p. 17). 1720 edition available at Internet Archive.

Blaise Pascal, 'Story of the Great Experiment on the Equilibrium of Fluids' (first published Paris, 1648), in Frederick Barry and Spiers, *The Physical Treatises of Blaise Pascal* (Columbia UP, 1937), pp. 97-109.

John Ellicot, A Letter Concerning the Specific Gravity of Diamonds, Philosophical Transactions of the Royal Society of London, 1744 (43), 468-472. Available online here.

**Additional readings:**

**General**

Cohen, H. F. *Quantifying Music: The Science of Music at the First Stage of the Scientific Revolution, 1580-1650*. Dordrecht, Reidel, 1984.

Cohen, Floris. 'Alexandria-plus Spreads on like Wild-Fire.' In *The Rise of Modern Science Explained*, 184-197.

Crosby, Alfred W. *The Measure of Reality: Quantification and Western Society, 1250-1600*. Cambridge: Cambridge University Press, 1997.

Darrigol, Oliver. *A History of Optics: from Greek Antiquity to the Nineteenth Century.* Oxford University Press, 2012.

Feldman, Theodore S. 'Mathematization and Quantification.' In *The Oxford Companion to the History of Modern Science*. Oxford University Press, 2003.

Lindberg, David C. *Theories of Vision from Al-Kindi to Kepler*. Chicago: University of Chicago Press, 1981.

Poovey, Mary. *A History of the Modern Fact: Problems of Knowledge in the Sciences of Wealth and Society*. Chicago: Chicago University Press, 1998.

Wootton, David. *The Invention of Science*, chapter 5 (The Mathematization of the World)

Westfall, Richard. *The Construction of Modern Science*. Cambridge UP, 1977. Good for short introductions to mathematical branches of 17th-century science, especially astronomy and mechanics (Chapter 1), and pneumatics and optics (Chapter 2).

**Scholars**

Dear, Peter. *Discipline and Experience: The Mathematical Way in the Scientific Revolution*. Chicago: University of Chicago Press, 1995.

Feingold, Mordechai. *The Mathematicians’ Apprenticeship: Science, Universities and Society in England 1560-1640*. Cambridge: Cambridge University Press, 1984.

Grant, Edward, and John E. Murdoch, eds. *Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages: Essays in Honour of Marshall Clagett*. Cambridge: Cambridge University Press, 1987.

Grant, Edward. 'The Physics of Motion.' In *Physical Science in the Middle Ages*. Cambridge: Cambridge University Press, 1978. [course extract needed since book is not in Warwick library; Dr. Michael Bycroft, module convenor, has a copy in his office that can be used for the scan]

Koyré, Alexandre. "Galileo and Plato." *Journal of the History of Ideas* 4:4 (1943), pp. 400-428.

Rose, Paul Lawrence. *The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo.* Genève: Droz, 1975.

Wallace, William. 'Galileo's Jesuit Connections and Their Influence on his Science.' In Mordechai Feingold, *Jesuit Science and the Republic of Letters*, 2003.

**Artisans**

Bennett, Jim. “The Mechanics’ Philosophy and the Mechanical Philosophy.” *History of Science* 24: 1 (1986): 1–28

Cormack, Lesley B., Steven A. Walton, and John A. Schuster, eds. *Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe*. Springer, 2017.

Drake, Stillman. "Galileo's Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts (Galileo Gleanings XXII)." *Isis* 64:3 (1973), pp. 291-305

Field, Judith Veronica. *The Invention of Infinity: Mathematics and Art in the Renaissance*. Oxford: Oxford University Press, 1997.

Henninger-Voss, Mary J. “How the ‘New Science’ of Cannons Shook up the Aristotelian Cosmos.” *Journal of the History of Ideas* 63.3 (2002): 371–397.

Johnston, Stephen. “Mathematical Practitioners and Instruments in Elizabethan England.” *Annals of Science* 48.4 (1991): 319.

Kemp, Martin. *The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat*. New Haven: Yale University Press, 1990. See especially the chapter 'Linear Perspective from Brunolleschi to Leonardi,' and 'AppendixI: Explanation of Linear Perspective,' both of which are available as course extracts [to transfer from HI296 list]

Long, Pamela. 'Artisans, Humanists, and the De architectura of Vitruvius'. In *Artisan/Practitioners and the Rise of the New Science, 1400-1600*. Oregam State University Press, 2011.

Newman, William, and Lawrence Principe. “Number, Weight, Measure, and Experiment in Chymistry: From the Medievals to Van Helmont.” In *Alchemy Tried in the Fire: Starkey, Boyle, and the Fate of Helmontian Chymistry*. Chicago, IL: University of Chicago Press, 2002.

Ofer Gal and Raz Chen-Morris. *Baroque Science*. Chicago UP, 2012. Especially chapter 1 (on optics) and chapter 5 (on maths in general). [Need to order book for Warwick library]

Peterson, Mark A. *Galileo’s Muse: Renaissance Mathematics and the Arts*. Cambridge, Mass: Harvard University Press, 2011.

Valleriani, Matteo. 'Ancient Pneumatics Transformed During the Early Modern Period.' *Nuncius*, 29, 2014, 127–174 [article needs to be ordered as course extract]

Valleriani, Matteo. *Galileo Engineer*. London: Springer, 2010.

**The limits of mathematics**

Heilbron, John. 'Quantitative Physics.' In *Elements of Early Modern Physics*. University of California Press, 1982.

Heilbron, John. 'Unfair Balance'. In *Galileo, *245-252. Oxford UP, 2010.

Kuhn, Thomas. 'Mathematical Versus Experimental Traditions in the Development of Physical Science.' *Journal of Interdisciplinary History* 7, no. 1 (1976): 1–31.

Shapin, Steven. 'Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice.' *Science in Context* 2, no. 01 (1988): 23–58.