Unrolling Time: Christiaan Huygens and the Mathematization of Nature [Hardcover]

Joella G. Yoder (Author)

Book Description

Publication Date: February 24, 1989 | ISBN-10: 052134140X | ISBN-13: 978-0521341400

This case study examines the interrelationship between mathematics and physics in the work of one of the major figures of the Scientific Revolution, the Dutch mathematician, physicist, and astronomer, Christiaan Huygens (1629-1695). Professor Yoder offers a detailed account of the discoveries that Huygens made at the end of 1659, including the invention of a pendulum clock that theoretically kept absolutely uniform time, and the creation of a mathematical theory of evolutes. She also describes the way that each of these important discoveries arose from the interaction of Huygens' mathematics and physics. A discussion of Huygens' relationship with other scientists and the priority disputes that sometimes motivated his research help place his work in the context of the period. The reception of Huygens' masterpiece, the Horologium Oscillatorium of 1673 and the place of evolutes in the history of mathematics are also analyzed. Finally, the role of Huygens in the rise of applied mathematics is addressed.

Editorial Reviews

Review

"In her account of Huygen's mathematical reasonings, Yoder achieves an admirable combination of clarity and concision with faithfulness to the original. Her book casts a new and clear light on a mid-seventeenth-century phase of the scientific revolution." The Eighteenth Century

"...a significant contribution to scholarship on Huygens and to our understanding of scientific thinking in his time." Choice

"...an enlightening, sometimes surprising account fo the 'beautiful, intricate display of creativity.'" Perceptual and Motor Skills

"...Yoder has written a little gem of modern history of science at its scholarly best...it deserves to be read outside the confines of that discipline." Contemporary Physics

Book Description

This case study examines the interrelationship between mathematics and physics in the work of one of the major figures of the Scientific Revolution: the Dutch mathematician, physicist, and astronomer, Christian Huygens (1629-1695).

Product Details

• Hardcover: 256 pages
• Publisher: Cambridge University Press (February 24, 1989)
• Language: English
• ISBN-10: 052134140X
• ISBN-13: 978-0521341400
• Product Dimensions: 9.1 x 5.7 x 0.8 inches
• Shipping Weight: 15.2 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #4,719,540 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

5.0 out of 5 stars "Huygens's stile and manner" (p. 145), May 25, 2011

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: Unrolling Time: Christiaan Huygens and the Mathematization of Nature (Paperback)

This well-written book is a pleasant read, albeit at times perhaps more sleek than profound.

The fundamental problem underlying Huygens's work on pendulum clocks arises very naturally from Galilean mechanics, and this in two forms (chapter 2). From a practical point of view, experimental verification of the Galilean laws of motion and their implications requires accurate timekeeping at the level of seconds, and thus one desires a pendulum clock that beats seconds. From a theoretical point of view, one desires to determine the constant of gravitational acceleration. In the context of pendulum clocks these problems are essentially equivalent since the period of a pendulum is inversely proportional to sqrt(g/L) for small amplitudes. Huygens of course eliminated the approximation and solved both problems with his discovery of the cycloidal pendulum clock.

Incidentally, one should be careful here not to confuse the fundamental importance of the elementary principles of "Galilean" mechanics with the negligible importance of Galileo himself. Indeed, already at age 17 Huygens had independently rediscovered all of Galileo's results on gravitational acceleration and projectile motion (p. 9) and even gone beyond him in proving that the catenary is not parabolic, as Galileo had thought (p. 10).

Huygens derivation of the isochronous property of the cycloid is a "mathematical labyrinth" (p. 50) very different from his published proof. Contrary to previous scholars, Yoder wants to argue that in his derivation of this result Huygens did not know or suspect in advance that the answer was a cycloid but only arrived at this result as the outcome of elaborate and explorative calculations.

Her argument has merit but it seems to me that she pushes it too far. For example she wants to argue that on the manuscript page containing Huygens's deduction (p. 54), he drew the cycloid-like figure of the pendulum path before he knew that it was a cycloid. Thus she argues:

"Indeed, the inaccuracies of the drawing seem to indicate that he did not know ABB is a cycloid when he sketched the curve; for example, the normals should cross." (p. 60)

In other words, Yoder is claiming that the normals of a cycloid cross above the axis, which is clearly nonsense. On the contrary, it is of course a fundamental fact that the evolute of a cycloid (which is the locus of meeting points of normals) lies completely below the axis (p. 76).

Huygens's work on the pendulum clock also gave rise to his theory of evolutes. A guiding theme of Yoder's account here is the tension between the traditionalist Huygens and the modernists Leibniz and Newton. For example, "Huygens's application of evolutes to rectification rather than curvature is a good example of [his] tendency to focus on geometric measure over analytic description" (pp. 142-143). Indeed, Huygens never defined evolutes in terms of radii of curvature. And although he seems to have been the first to use the term radius of curvature in print, in the context of the problem of the shape on a catenary, he defined it only at the vertex of the catenary (p. 109). Thus it seems that he though of it as a parameter of the catenary akin to the latus rectum of a parabola rather than a measure of curvature applicable at any point. The ensuing priority quarrel with Leibniz reinforces this impression (pp. 109-114).

Another aspect of Huygens's conservative attitude is expressed in this passage:

"I would never amuse myself with the different kinds of catenaries that Johann Bernoulli proposes to achieve as before or urge on further this speculation. There are certain curves that nature often presents to our view, and which it itself describes, so to speak, those I judge worthy of consideration ... But to invent from them new ones only in order to exercise his geometry, without anticipating there any other utility, it seems to me that it is difficulties dealing with trifles" (p. 174; Leibniz agrees "except if it can serve to perfect the art of discovery")

But although Yoder is happy to admit that Huygens's tastes were often conservative, she refuses to accept "the claim that Huygens was restricted by ... ancient methods" (p. 63). Thus for example she laments "the tendency of commentators to fault [Huygens] for not having developed, or at least accepted, the calculus and modern Newtonian dynamics," and dismisses this critique by quipping "What other scientist is blamed for not having discovered the inventions of a succeeding generation?" (p. 177)

It is certainly true that one should watch out for anachronistic critiques, but Yoder's rejectionism seems to me too simplistic in the opposite direction. For example, Huygens's method of rectification by evolutes published in the Horologium Oscillatorium of 1673 is arguably inferior to that of Newton in his treatise on fluxions of 1666, a discrepancy that can hardly be attributed solely to Newton being a "succeeding generation." (Yoder does not recognise the full scope of Newton's theory, admitting only that it "duplicated Huygens's results in a different context" (p. 106) when in fact it went some way towards overcoming what Yoder herself admits is a fundamental "flaw" (p. 147) in Huygens's theory.)