Baroque Science

Ofer Gal, Raz Chen-Morris

• Publisher: University of Chicago Press
• Year: 2013
• ISBN:
  9780226923994
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

In Baroque Science, Ofer Gal and Raz Chen-Morris present a radically new perspective on the scientific revolution of the seventeenth century. Instead of celebrating the triumph of reason and rationality, they study the paradoxes and anxieties that stemmed from the New Science and the intellectual compromises that shaped it and enabled its spectacular success.Gal and Chen-Morris show how the protagonists of the new mathematical natural philosophy grasped at the very far and very small by entrusting observation to the mediation of artificial instruments, and how they justified this mediation by naturalizing and denigrating the human senses. They show how the physical-mathematical ordering of heavens and earth demanded obscure and spurious mathematical procedures, replacing the divine harmonies of the late Renaissance with an assemblage of isolated, contingent laws and approximated constants. Finally, they show how the new savants, forced to contend that reason is hopelessly estranged from its surrounding world and that nature is irreducibly complex, turned to the passions to provide an alternative, naturalized foundation for their epistemology and ethics.Enforcing order in the face of threatening chaos, blurring the boundaries of the natural and the artificial, and mobilizing the passions in the service of objective knowledge, the New Science, Gal and Chen-Morris reveal, is a Baroque phenomenon: deeply entrenched in and crucially formative of the culture of its time.

PART II

Mathematization

CHAPTER FOUR

Nature’s Drawing

Problems and Resolutions in the Mathematization of Motion

INTRODUCTION

For Galileo, mathematics was a justification for the new practices of instrumental observation. For Kepler, it was a justification for causal arguments about the heavens. Their mathematics was to be descriptive and explanatory. Nature, as it presented itself through the new instruments, had to comply. The dramatic challenges and marvelous accomplishments of the new empirical and mathematical practices determined the theoretical and metaphysical aspects of the “mathematization of nature.”

One might have expected the application of mathematics to theory to have been a much more straightforward process. The motivations for the mathematization of natural philosophy seem clear: enjoying the clarity and certainty of mathematics; the resources can be easily identified: the mathematical “middle sciences” of the schools and the revival of Archimedean mathematics; and the rivals and challengers long recognized: the Aristotelian dismissal of the explanatory power of mathematics. Still, the mathematization of nature was not a progressive process of successful submission of the varied phenomena to a handful of simple, universal mathematical laws. What was hoped that mathematics would achieve; what had been perceived as the main obstacles and their solutions; and the ways in which the new mathematical natural philosophy was justified—all changed dramatically through the seventeenth century.

TRACES

And I have not satisfied my soul with speculations of abstract Geometry, namely with pictures, “of what there is and what is not” to which the most famous geometers of today devote almost their entire time. Instead, following the traces [vestigia] of the Creator with sweat and heavy breath, I have investigated geometry through the actual [expressa] bodies of the world themselves.¹

These are the words with which Kepler expresses his ideal of mathematical investigation of nature. Below are the words with which Galileo introduces his great achievement in the mathematical “new science,” the analysis of accelerated motion:

And first of all it seems desirable to find and explain a definition best fitting natural phenomena. For anyone may invent an arbitrary type of motion and discuss its properties; thus, for instance some have imagined helices and conchoids as described by certain motions which are not met with in nature, and have very commendably established the properties which these curves possess in virtue of their definitions; but we have decided to consider the phenomena of bodies falling with an acceleration such as actually occurs in nature and to make this definition of accelerated motion exhibit the essential features of observed accelerated motions.²

The similarity of their phrasing is telling. Both Galileo and Kepler had their mathematical skills and repertoires well rooted in the mixed sciences—Galileo’s in mechanics, Kepler’s in astronomy and optics (sharing an interest in music).³ Yet it is commonly alleged that their trust in the extension of mathematics to natural philosophy originated from different sources: Kepler’s from Neo-Platonism, and Galileo’s from the success of its practical applications. Here, however, they apply the same contrast and aver the same choice. Between “abstract geometry” produced by “motions which are not met with in nature” on the one hand, and geometry that “exhibits . . . observed . . . motions” or “expresses the body of the world” on the other, both choose to follow real “traces.”⁴ Galileo and Kepler, we saw, shared an idea of mathematics as a guarantor of the new ways of seeing. Here they seem to share the demand that mathematics itself be seen.

The obscure concepts of geometrical “traces” and of a mathematical definition “fitting natural phenomena” suggest that it is not epistemology that worries the two court mathematicians here, but ontology. Neither of them questions the power of mathematics to provide the knowledge they seek; it is the objects that mathematics can be true about that they both feel forced to establish. Mathematics is not easily applied to “natural phenomena”; it coheres much more easily with “an arbitrary type of motion.” What, therefore, does real motion need to be if it is to be captured by mathematics, and what can be the mathematical entities that apply to real “observed . . . motions”?

These ontological dilemmas and the ways in which they were confronted were not free-wheeling philosophical musings. The traditions from which Galileo and Kepler borrowed their mathematical tools determined their proper use with a set of metaphysical presuppositions: the understanding of what mathematics is, and what the objects to which it is applicable are, established the proper questions, the permissible answers, and the distribution of intellectual labor between practices and practitioners of mathematical knowledge. Kepler and Galileo’s metaphysical toil embed their efforts to accommodate and modify these tools so they could serve their own mathematical project, which was far more ambitious than tradition allowed. Freed from the difficulties Kepler and Galileo perceived themselves as confronting, their successors found their solutions of little use as they further reshaped the mathematical means and ends of Baroque natural philosophy.

KEPLER

Physica

It may seem surprising that Kepler found it necessary to justify his use of geometry with such an ornate idea as “traces.” As discussed in the previous chapters,⁵ his trust in mathematics as a key to unlocking the mysteries of the cosmos was anchored in Neo-Platonic religiosity, which should have demanded little else:

geometry . . . is coeternal with God, and by shining forth in the Divine Mind supplied patterns to God . . . for the furnishing of the world, so that it should become best and most beautiful and above all most like to the Creator. Indeed all spirits, souls, and minds are images of God the Creator. . . . Then since they have embraced a certain pattern of creation in their functions, they also observe the same laws along with the Creator in their operations, having derived them from geometry.⁶

Yet from very early on Kepler is clear that he wants more from the mathematical study of nature than could be provided by either the Neo-Platonism of his time or the long mathematical traditions of the mixed sciences. The physicalization of optics, with its dramatic effects that we expounded in the first chapter, was a means rather than the primary end of this endeavor. The speculations he was sending to his erstwhile teacher Michael Maestlin even before his Mysterium Cosmographicum of 1596 (and which the latter was finding of minimal value) were already aiming at a full-blown, causal science of the heavens:

The moving soul [is] . . . in the sun . . . But what makes the remote [planets] slower is due to another cause. We comprehend this from our experience with light. For light and motion are connected by origin [i.e., the sun] as well as by action and probably light itself is the vehicle of motion. Therefore, in a small orb, and so also in a small circle [of light] near the sun, there is as great [a quantity of moving force or light] as in the greater and more distant [orbit]. The light in the larger [orbit] is certainly more rarefied, whereas in the narrower it is denser and stronger. And this power again is in a proportion of circles, or of distances.⁷

This is the dream of physica coelestis, which Kepler believed he realized in his Astronomia Nova of 1609. It was novel, he later bragged (in the 1621 second edition of the Mysterium), and indeed superior to his first attempt in the Mysterium, in managing to find mathematical relations that are maintained purely physically:

Proportions between the motions have been preserved . . . not by some understanding created jointly with the Mover, but by . . . the completely uniform perennial rotation of the sun [and] the weights and magnetic directing of the forces of the moving bodies themselves, which are immutable and perennial properties.⁸

Order in Motion

Kepler’s challenge is capturing motion mathematically. It is not the ancient task of reducing “anomalies” to uniformities that should be as close to rest as possible. Rather, “rotation” and “weights”—physical causes and motions—were to cause mathematical “proportions.” This is the insight that makes music and astronomy share not only their mathematical method but also their physical underpinning:

In general in everything in which quantity, and harmonies in accordance with it, can be sought, their presence is most evident in motion rather than without motion. For although in any given straight line there are its half, third, quarter, fifth, sixth, and their multiples yet they are lurking among other parts which are incommensurable with the whole.⁹

Static lines comprise only the possibility of significant mathematical proportions; they contain all relations, and most of those are “incommensurable.” Kepler adjoins this metaphysical reasoning on the primacy of motion with an epistemological corollary:

The mind, without imagining certain motion, does not discern harmonic proportions from the confused infinite [proportions] surrounding them within a given quantity.¹⁰

The divine origin of the mathematical order of nature and the warranty it provides for geometrical knowledge do not entail that the mathematical “pattern” be at rest. Quite the contrary: without motion there are no “harmonic proportions” at all, hence nothing to know. Moreover, geometrical lines themselves should be understood as motions:

A chord is understood here not, like in Geometry, as subtending an arc of a circle, but as any length capable of emitting a sound; and because sound is produced by motion, in abstract a chord should be understood as a length of some motion, and so should every length conceived by the mind.¹¹

Mathematics—order—is in motion. This is what makes Kepler’s new astronomy, as was his optics, a real mathematical physica, distinguished from the scientia media in which he was educated: motion, forces and actions of nature, are not only reduced to static mathematical structures; they are expected to produce mathematical curves, “traces” for the mathematician to follow.

Light and Pure Motion

Of course, not all moving bodies trace perfect geometrical curves—Kepler was very alert to the imperfections of the material world. However, he also had a model of pure motion, thoroughly mathematizable: light. Light, as we discussed in chapter 1 and will return to in chapter 6, is essentially mathematical: “Light falls under geometrical laws . . . as a geometrical body” is Proposition 1 of the Optics.¹² It can be thoroughly mathematical because it is incorporeal: “Light has no matter, weight or resistance” (Prop. 3) and “To light there belong only two dimensions” (Prop. 10). Embedded in the material world, a physical and causal agent, it is still a proper object of physica. As Kepler put it in the letter to Maestlin, light is a “vehicle of motion.” This combination of properties enabled Kepler to apply the mathematical techniques of traditional optics to light and turn it into the model of mathematical science that Descartes was to adopt. The letter to Maestlin suggests that from early on he intended it to serve a similar role in turning traditional mathematical astronomy into the physica coelestis of the Astronomia Nova.

It is a complex meditating role that light fulfills for Kepler in the establishment of a mathematical philosophy of nature. Intellectually, light mediates mathematics and motion: it suggests that notions from mathematical optics could be applied to physics. Physically, it mediates between the sun and the planets, as the hypothetical virtus motrix by which the sun moves the planets about itself, or at least the carrier of this force. Ontologically, light mediates between the ideal and the corporeal: as the mathema...

Table of contents

• Cover
• Copyright
• Title Page
• Dedication
• Contents
• List of Figures
• Acknowledgments
• Introduction
• I. Observation
• II. Mathematization
• III. Passions
• Abbreviations
• Notes
• Bibliography
• Index