Cover image for Measuring Shadows: Kepler’s Optics of Invisibility By Raz Chen-Morris

Measuring Shadows

Kepler’s Optics of Invisibility

Raz Chen-Morris


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ISBN: 978-0-271-07098-8

$37.95 | Paperback Edition
ISBN: 978-0-271-07099-5

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264 pages
6" × 9"
12 b&w illustrations

Measuring Shadows

Kepler’s Optics of Invisibility

Raz Chen-Morris

“Raz Chen-Morris masterfully argues that Kepler’s optics is a response to widely shared anxieties about vision in Renaissance culture. This book is the first to show why the Paralipomena was important for Kepler, and how it was a book of cultural significance instead of a response to a narrowly defined technical issue.”


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In Measuring Shadows, Raz Chen-Morris demonstrates that a close study of Kepler’s Optics is essential to understanding his astronomical work and his scientific epistemology. He explores Kepler’s radical break from scientific and epistemological traditions and shows how the seventeenth-century astronomer posited new ways to view scientific truth and knowledge. Chen-Morris reveals how Kepler’s ideas about the formation of images on the retina and the geometrics of the camera obscura, as well as his astronomical observations, advanced the argument that physical reality could only be described through artificially produced shadows, reflections, and refractions.

Breaking from medieval and Renaissance traditions that insisted upon direct sensory perception, Kepler advocated for instruments as mediators between the eye and physical reality, and for mathematical language to describe motion. It was only through this kind of knowledge, he argued, that observation could produce certainty about the heavens. Not only was this conception of visibility crucial to advancing the early modern understanding of vision and the retina, but it affected how people during that period approached and understood the world around them.

“Raz Chen-Morris masterfully argues that Kepler’s optics is a response to widely shared anxieties about vision in Renaissance culture. This book is the first to show why the Paralipomena was important for Kepler, and how it was a book of cultural significance instead of a response to a narrowly defined technical issue.”
“Neither the disembodied mind that charted the path toward modern mathematical physics, nor the Neoplatonic magus who dreamed of hearing the music of God's celestial spheres, Johannes Kepler, in Raz Chen-Morris's erudite and multiperspectival reading, is a fully embodied early modern intellectual striving to resolve deep questions at the heart of early modern thought. Measuring Shadows is not just a new history of Kepler’s optics; it is a book about the early modern European life and preoccupations that led Kepler to his world-changing scientific achievements. As such, it is a brilliantly insightful contribution to the cultural history of early modern science.”
“Students of the history of astronomy, science historians, and graduate-level students who are involved in the study of optics and how Kepler derived his planetary laws of motion will benefit from this work. It is also a valuable acquisition for university and college libraries and major public libraries.”
“The picture Chen-Morris paints is important because it fills out the world within which the later Scientific Revolution could emerge, and presents new questions to ask about later developments in optics and natural philosophy.”
“Like Kepler in the Somnium finding a way past earlier models of sense perception to visit extraterrestrial reality, Chen-Morris abandons older interpretations to present a fresh take on a familiar topic.”
“It will be difficult to find as helpful an introduction to Kepler’s optics as the book Chen-Morris has produced.”
“Presents a well-researched yet original interpretation of the relationship between science, philosophy, and the arts during several significant periods of extreme transition in an impressively aesthetic manner. It is recommended to readers particularly in the humanities, who may appreciate the author’s conceptual expression of scientific ideas, which will nevertheless not be lost on readers of a scientific background. Raz Chen-Morris’s work is both clear and, if I may say, imaginative, true to the transiting ethos of Kepler’s time.”

Raz Chen-Morris is Senior Lecturer in History at the Hebrew University of Jerusalem.


List of Illustrations



1 The New Optical Narrative: Light, Camera Obscura, and the Astronomer’s Wings

2 “Seeing with My Own Eyes”: Introducing the New Foundations of Scientific Knowledge

3 The Content of Kepler’s Visual Language: Abstraction, Representation, and Recognition

4 “Non tanquam Pictor, sed tanquam Mathematicus”: Kepler’s Pictures and the Art of Painting

5 Reading the Book of Nature: Allegories, Emblems, and Geometrical Diagrams

6 Nothing and the Ends of Renaissance Science






<1>Towards Copernican Optics

In January 1604 Johannes Kepler, the young imperial mathematician at the court of Rudolf II, dedicated a treatise on optics to the emperor. The treatise presents some novel ideas on the formation of images on the retina, and an elegant geometrical explanation of the operation of the camera obscura, together with a manual of measurements of astronomical observations. Throughout these topics a startling notion is threaded: that in order to account for real physical motions, one has to investigate artificially produced shadows and reflections. This book sets out to explore this paradoxical notion, its epistemological function in shaping early modern practices of observation, and especially the role it played in Kepler’s own scientific endeavor. Recent accounts of Copernicus and of Copernican astronomy have concentrated on the way astronomy changed its disciplinary character and its social role following the publication of De revolutionibus orbium coelestium in 1543 or on Copernicus’s philosophical underpinnings and indebtedness to Aristotelian logic and principles of natural philosophy. These accounts, while widening the scope of scholarly understanding of the evolvement of Copernicanism, fail to pay due attention to the changing notions of visibility crucial to the new astronomy. One of the core aspects of Copernican astronomy is the replacement of daily sense-experience with the invisible motion of the earth, thus rejecting perception as the basis of human knowledge. This book concentrates on the way in which Kepler tackled this question of visibility, setting his paradoxical optics as the cornerstone to his radical Copernican astronomy. The new optics enables him to get “beyond the threshold of perception,” thus merging physical considerations with the vast invisible space of his new astronomy.

It was less than three years after Kepler arrived in Prague to assist the great exiled Danish astronomer Tycho Brahe, then an imperial mathematician. Both Kepler, the young provincial mathematics teacher, and Tycho, prince of astronomers, were refugees from the crises of late sixteenth-century European culture and politics: the first a victim of the Counter-Reformation and the growing religious hostilities in the lands of the Holy Roman Empire; the other exiled due to courtly intrigues symptomatic of the burgeoning early modern centralized state. The two advocated divergent solutions to the problems that haunted Renaissance astronomy in establishing its practices and theories on firmer philosophical foundations, motivated by a desire for complete and pure transparency. Overcoming the opacity of the celestial realm, which hid its secret causes from the frustrated gaze of human observers, Tycho devoted his efforts to improving astronomical instruments, practices of observation, and methods of calculating the results, aspiring to present his European audience with the most exact astronomical data possible. Kepler, on the other hand, set out early in his intellectual career to construe, using mathematical speculations, an extraterrestrial point of view from which the celestial mechanism could be revealed. Their meeting in Prague, the glorious capital of Mannerist culture under the irenic rule of Emperor Rudolf II, could not have been more emblematic. Prague was the nerve center of various strands of late Renaissance philosophy and a lodestone attracting philosophers, spiritualists, alchemists, and mathematicians, most notably (besides Kepler and Tycho) John Dee and Giordano Bruno. Prague was also the appropriate geographical and cultural location for an intellectual shift from Brahe’s Renaissance-style astronomy to Kepler’s new mathematical mode of practicing a philosophical inquiry into the celestial realm.

Kepler’s assignment was to assist Brahe and his few assistants in completing his astronomical tables. The idea was to supply Europe with the most complete astronomical data ever, which would replace older tables and compendiums of observations. Under Tycho, Kepler worked on a theory for the planet Mars, a task that had eluded Tycho’s other assistants. For Kepler, it was also an exceptional opportunity to use Tycho’s most accurate astronomical data to corroborate his own speculation on the structure of the heavens, which he published in 1596 as Mysterium cosmographicum. In this treatise Kepler claimed that the gaps between the planets exactly fit a structure composed of the five Platonic solids nested one within the other. This was intended to prove Copernicus’s heliocentric theory not only astronomically but also physically. Some discrepancies, however, existed between Kepler’s speculations and his numerical data. For this reason, Tycho’s treasure of observations was attractive to him, and he hoped to find the data needed to establish that God’s harmonic plan of the universe is Copernican.

Kepler’s turbulent years from 1598–1601 and his pugnacious relationship with Tycho Brahe are well documented, yet Kepler did not sway from his aim of establishing astronomy on physical grounds. He stayed with Tycho, investing his time in complicated calculations of Mars’s orbit. In 1601 Tycho died suddenly, and Kepler found himself the new imperial mathematician. His job included responsibility for Tycho’s unfinished publications, in particular completion of astronomical tables now officially dedicated to the emperor and proclaiming his name. Kepler had to tackle some of the basic problems of early modern astronomy, and at the beginning of 1604 was on the verge of major discoveries that would radically change the nature of astronomical knowledge. Yet, instead of rapidly declaring his achievements and showing his patron his progress in accomplishing a theoretical basis for the new astronomical tables, Kepler preferred to dedicate to Rudolf II a book on optics as his first major treatise. This was a strategic move on his part. In a letter to Herwart von Hohenburg on November 12, 1602, Kepler outlined his plan of forthcoming publications: first Optics, and only then his “Commentaries on the Theory of Mars . . . or the Key to Universal Astronomy.”

Kepler, then, kept at bay his difficult research into a comprehensive theory of the planetary orbits, supposed to supply Europe with a “key to universal astronomy.” Instead he embarked on a time-consuming work, according special urgency to the publication of his optical treatise. While some historians of science assume that Kepler’s scientific curiosity is sufficient to explain such a diversion in his work, most of the historiography of early modern optics concentrates on whether Kepler’s optical investigations truly constituted a revolutionary break with the medieval tradition. However, only the short second chapter of the work is dedicated to this problem. The reader may ask why a whole treatise was written around what seems to occupy only a small part of his optical theory. Furthermore, is the understanding of the camera obscura’s operation on par with the first two laws of planetary motion?

The title of the optical treatise increases the reader’s puzzlement—Ad Vitellionem paralipomena: Quibus astronomiae pars optica traditur (Paralipomena to Witelo: which is the optical part of astronomy). It states at the outset the question of tradition and innovation, and Kepler’s relationship to his medieval perspectivist precursors. The name of Witelo, a medieval mathematician, appears here as a metonym of an entire discipline, and as that of the writer whose work embodies the great synthesis of medieval perspective. Witelo’s treatise on perspective from 1270 was a thorough interpretation and adaptation of the work by the great eleventh-century Arab mathematician Ibn al-Haytham (Alhacen). The two works were published together in 1570 by a follower of Petrus Ramus, the mathematician Fredericus Risner. Kepler rightly took them as representatives of the apogee of medieval geometrical optics, and acknowledges his debt to this tradition. This indebtedness is turned awry by the adjunct tag paralipomena. Kepler does not proclaim it to be a “new optics,” since Witelo’s name appears as the framework for his own ideas. Paralipomena, however, is no mere supplement, as it is so often translated, but stresses the act of omission, dealing with those things that Witelo disregarded, left unnoticed to the side. From the outset, Kepler portrays the perspectivist tradition as defective, incomplete, and in need of a thorough reform, insinuating that those things neglected and refused by the perspectivist tradition should become the cornerstone of the new mode of artificial observation.

<1>A Historiographical Remark

The prevailing historiographical attitude towards Kepler’s optical investigations defines their import by placing them in a progressive historical narrative. In an endeavor to define Kepler’s positive achievement, historians seek to determine whether his optics is a revolutionary gambit leading to the great scientific triumphs of Descartes, Newton, and Huygens, or whether his optical theories are the culmination of medieval perspectiva tradition. This attitude concentrates on immediate problem solving, such as Kepler’s analysis of the process of image formation through a pinhole, and thus on the physical aspects of optics. On one side of this historiographical debate one finds Alistair Crombie and Richard Straker, who underline how Kepler, in following Renaissance “rational artists,” formulated a new model of the eye as a camera obscura and thus initiated the mechanization of sight. On the other side, David C. Lindberg points out the continuity of the geometrical procedures Kepler applied with the medieval traditions of perspectiva communis, and the marginal role the identification of the eye with the camera obscura played in Kepler’s general scheme. Lindberg further stresses that portraying Kepler as a problem solver overlooks the great mathematician’s indebtedness to Neoplatonic speculations on the metaphysics of light and that this consideration is of foremost importance to an understanding of his optics. In suggesting a Neoplatonic frame for Kepler’s optics, Lindberg reveals the problems involved in philosophically characterizing Kepler’s work in general. Lindberg is in accord with the prevailing view, which stresses Kepler’s Neoplatonic and somewhat mystical disposition. J. V. Field, however, rejects this interpretation, claiming instead that Kepler was a “radical Platonist” who renounced Renaissance mathematical mysticism as irrelevant to his scientific endeavor. Contrariwise, William Donahue, amongst others, emphasizes Kepler’s indebtedness to the Aristotelian tradition in establishing the logical and philosophical foundations of both his optics and his astronomy. As noted above, others see Kepler as a forerunner of the mechanistic worldview of the seventeenth century. This interpretation is poignantly criticized by Patrick Boner, who stresses instead Kepler’s conception of the universe as an organic living body and not a world operating like clockwork. For my part, I embrace Sheila Rabin’s observation that in employing a variety of philosophical views and concepts in his investigations, Kepler tends to turn them on their head (a most suitable idiom for Kepler’s inverted retinal pictures). In order to understand Kepler’s project, one has to follow the way he mobilizes certain intellectual resources, thus seeking novel modes of knowing that, while providing groundbreaking solutions, reframe the old questions he pursues in a manner irreducible to any preconceived philosophical system or worldview.

This approach is in accord with developments in the historiography of medieval optics that embed the scholastic discourse of optics within a more general theory of human cognition relating to certain epistemological problems that vexed theologians and philosophers through the thirteenth and fourteenth centuries. While in medieval studies this attitude embedded the geometrical discussions of optics in a rich tapestry of theological and philosophical debates, the discussion of Kepler’s optics remained chiefly concerned with its historical significance in the emergence of the New Science of the seventeenth century. Mark Smith synthesizes Lindberg’s magisterial account of the development of medieval theories of vision with insights taken from Alistair Crombie’s comparative analysis of Alhacen and Kepler’s models of sight, and thus suggests that the import of Kepler’s optics was in severing the bond assumed by medieval perspectiva between “the perceiving subject and perceived object.” Kepler thus followed the medieval tradition in his application of geometry to solve and explain optical problems and issues, but his conclusions diverged from the medieval path to open a new understanding of visual experience.

Accepting this assertion raises a crucial difficulty: if the geometrical techniques at Kepler’s disposal were not different than those of his predecessors, and if his metaphysical convictions descended from medieval light metaphysics, then what motivated Kepler to initiate such a bold move that turned medieval perspectiva upside-down? In tackling such a historiographical difficulty, this book places Kepler in a wider context, examining it both in relation to his own intellectual endeavor to establish astronomy on a more secure epistemological foundation and in relation to general cultural concerns at the turn of the seventeenth century. It thus provides an additional comment on the place of sight in early modern culture.

One should mention in this context a few historians who have disputed the role vision played in early modern culture. In The Art of Describing, Svetlana Alpers locates a common ground for Keplerian analysis of the formation of pictures over the retinal screen with a northern European (or Netherlandish) mode of pictorial representation as an art of describing. According to her view, Kepler’s theory of optics takes its cue from the concerns of northern European artists, thus giving Dutch aesthetic sensibilities scientific form:


[I]t was established concerns of artists in the north that were in effect taken up by Kepler. He turned his attention not only to the camera obscura, but also to lenses, mirrors, and even to glass urinary bottles filled with clear liquid, all of which served him as models of refracted light. Contemplating these models, we cannot help but be struck that these are the phenomena that had traditionally fascinated northern artists. . . . We have a case of traditional crafts and skills sustaining or keeping alive certain interests that eventually become the subject of natural knowledge. Northern art came of age, came into a new age, by staying close to its roots. In Kepler’s study of the eye, natural knowledge caught up with the art.

<end ext>

Jonathan Crary, instead of focusing on the convergence of optics and painterly style, suggests analyzing the role of camera obscura as an organizing metaphor for early modern visual experience. Both of these suggestive interpretations, however, assume the camera obscura was simply given and not a matter of epistemological contentions and concerns, thus neglecting a certain cultural dynamic that guaranteed the camera obscura its significant role in shaping early modern modes of perception. More recently, Stuart Clark, in his authoritative Vanity of the Eyes, criticizes the prevailing assumption that visual experience, and especially visual metaphors of knowledge, hold hegemonic position in Western culture, and that their assent to this position began in the seventeenth century. Instead Clark presents the early modern field of vision as haunted by epistemological anxieties and doubts. His portrayal of the early modern apprehension of sight is static, however, as if a component of an early modern mentalité. Furthermore, while he uses and analyzes a variety of theological, literary, and medical sources in his vast historical synthesis, he relegates geometrical optics to the background, taking for granted the explanation of vision prevalent at that period.

In concentrating on Kepler’s optical investigations, this book suggests a more dynamic approach where various practices and theories are formulated in order to secure the epistemological foundation of observation and knowledge through rethinking the relationship between mathematical procedures, instruments of observation, and the human mind. In following Kepler’s struggle with the insecurity of visual knowledge, one can come to understand the role of optics in his philosophical and astronomical endeavor, and its bearing on the early phases of the New Science of the seventeenth century.

<1>Kepler and the Question of Reading the Optical Tradition

Stepping beyond this old and deficient science and adjusting it to a new physics of the heavens, Kepler breaks away from the medieval and Renaissance modes of reading the ancient authorities. Embracing a critical stand towards his traditional sources situated Kepler in the midst of an emerging new conception of reading that treated the text not “as a universal and permanent memory,” but as “a heuristic exercise, proffering topoi that the reader may appropriate and reorganize in relation to an unforeseen mental horizon.”

What effects did these changes in the modes of reading, in the status of the auctoritas and the figure of the author, have on scientific discourse? To the medieval practices of commentary and interpretation Renaissance humanists added the critical editing, emending, and reconstructing of ancient scientific texts. In accordance with Ciceronian ideals, Renaissance humanists hailed the imitation of ancient texts, ascribing intellectual and stylistic authority to these ancient textual patterns and models. Kepler’s position in regard to the Hellenistic and medieval traditions was different. The classical sources were no longer the origins to be restored into their correct form, nor were they the authoritative suppliers of textual patterns. They were to be historicized as steps in a long tradition, but with no exceptional claim to truth. Kepler had to introduce, instead, new grounds for his own claims to truth. This was why he had to formulate anew the principles of optics as the obvious foundation of astronomy. The classical texts thus become mere triggers, offering Kepler an opportunity to initiate his own analysis. As the new discourse on optics unfolds, it leaves the classical authorities behind, presenting a new mode of observation with new entities to see and a new language to assess them. How, then, did Kepler reread his precursors? Which new entities were neglected by the medieval perspectivist tradition that Kepler now suggested positing as the foundation of his new edifice of scientific observation?

Placing Witelo in the title of his treatise shows Kepler’s historical awareness, and his appreciation of the great advancement made in optics during the Middle Ages. It also points, however, to the stability of this tradition. The thirteenth-century synthesis was still at the core of the late Renaissance understanding of vision and other optical phenomena. This synthesis consisted of a geometric analysis of visual phenomena together with a physical explanation of sight. Medieval optics thus supplied a coherent and attractive theory of human visual experience. In the words of John Pecham, one of its foremost exponents, “[A]mong the investigations of physics, light is most pleasing to students of the subject. Among the glories of mathematics it is the certitude of demonstration that most highly exalts the investigators. Therefore, perspective, in which demonstrations are devised through the use of radiant lines and in which glory is found physically as well as mathematically so that perspective is adorned by the flowers of both, is properly preferred to [all the traditional] teachings of mankind.”

The main physical principle of medieval optics was that there is no action at a distance; for an object to be seen, it somehow has to come in contact with the eye. For that to take place, a stream of immaterial species must flow from every point in the visual field into the eye. These species communicate the essence as well as the accidents of the visible object and imprint them on the crystalline humor. This physical description was corroborated by a geometric analysis. The species flow from each point to the eye in straight lines analogous to rays of light. Only those rays that hit the eye at a straight angle participate in the act of sight. All the other rays are either reflected or refracted. They are further weakened and cannot communicate their information to the eye. Preference was thus given to what was directly evident to the eyes. Only those objects that were clear and present in front of the eyes could testify to their visual truth. Whatever was perceived obliquely, indirectly through whatever mediation, or things that were too far away for the sense of sight to discern clearly were degraded, given secondary epistemological value. Such perception could not serve as a basis for a sound philosophical account of the natural world.

The emphasis on direct visual perception was in accord with the place assumed by the eye in the Aristotelian tradition. The eye, according to Aristotle’s De anima, is precisely suited to perform its task of visual discernment, and whatever falls out of its field of sight cannot be perceived in its reality. This state of affairs did not change through the fifteenth and sixteenth centuries, although some scientific and philosophical problems continued to haunt the optical tradition (the formation of images through a pinhole, the ontological status of the visual rays, and whether the eye is an active or a passive organ of perception). In contrast to astronomy, optics seemed to have a solid and coherent theoretical exposition of the act of sight. Rather than an abundance of competing hypothetical, fictitious constructions, there was an accepted geometrical description of the motion of visual rays with successes such as the law of reflection, the manipulation of burning mirrors, and an ability to explain away errors of vision and illusionary images. Treatises on optics (in contrast to artificial perspective) all through the fifteenth and sixteenth centuries did not win much public attention. Problems such as the formation of pinhole images were not considered disturbing, as they may appear to a modern reader of histories of optics. Maurolyco’s solution to the problem, though written in the 1520s, remained unpublished until after Galileo emerged with his telescope in 1610, when Clavius understand its importance and saw to its publication.

Kepler, however, thought that the optical tradition urgently needed a supplement. He even neglected his work on astronomy and diverted his efforts to rewriting medieval perspective, an established, and relatively stable, scientific system. A closer examination of the nature of the supplement to Witelo suggested by Kepler will disclose that its aim was not the fortification of traditional optical theories, but a radical inversion of the perspectivist system.

<1>Supplementing Witelo

The second part of the title—astronomiae pars optica—declares that the supplement to Witelo and the medieval tradition of perspective is the optical part of astronomy. This immediately raises a question: adding optics to astronomy is a supplement to the great arch-astronomers, such as Ptolemy or Copernicus, not to Witelo. Why did Kepler think that the optical part of astronomy signifies a change in optics?

Further examination of this phrase against the backdrop of classical and medieval philosophy detects a surprising oxymoron: can there be optics, that is, an account of visual experience, of the heavens? Since classical theories of visual perception emphasized direct contact with the perceived object, the remoteness of the stars leaves the observer with only indirect and uncertain appearances. Furthermore, one of the basic propositions of classical optics asserted that the distance at which an object is seen is inversely proportionate to the size of the angle of vision, and that beyond a given distance it is no longer visible on account of the decrease in the size of the angle. The heavenly visual signs are only hints of a reality one cannot perceive directly. The observer has to go beyond appearances and cannot trust the eyes as to the actual meaning of the given visual experience. Plato asserted such a separation most clearly. The heavenly phenomena are not given to human vision. Gazing at the stars does not produce knowledge but only void sense perception. True knowledge “deals with being and the invisible,” and thus the senses cannot provide true knowledge. Heavenly phenomena serve only as hints for the philosopher to contemplate the essence of motion according to number. The Platonic astronomical research program was thus a priori speculation based on geometry but without the need for empirical support. The aim of Platonic speculation was to go beyond visual appearances, and, by formulating a probable tale, to elevate the soul to contemplate the moral significance of the world. Denouncing visual experience altogether in favor of a supreme hidden truth meant that there was no need for optics to account for such experiences.

This emphasis on an epistemological barrier between what is immediately given and can be fully known and what is distant and beyond human perception is succinctly formulated in Aristotle’s De partibus animalium. Aristotle sets the power of human vision as the limits of human knowledge. Certain things, he says, are too distant and alien for humans to know. “Of things constituted by nature some are ungenerated, imperishable, and eternal, while others are subject to generation and decay. The former are excellent beyond compare and divine, but less accessible to knowledge. The evidence that might throw light on them, and on the problems which we long to solve respecting them, is furnished but scantily by sensation.” This is in contrast to animals and plants, “living as we do in their midst,” and of which ample data are available. An example of such distant and eternal entities is celestial bodies. Of these, although they give so much pleasure in their excellence, one has only “scanty conceptions.” Still, humans are excited and curious about them, “just as a half glimpse of persons that we love is more delightful than a leisurely view of other things, whatever their number and dimensions.” Terrestrial things, because of their affinity and nearness, are known with certitude and “in their completeness.” Human knowledge of celestial things is lofty; they are beyond one’s grasp and are known only as far as “our conjectures [can] reach.”

The outcome of this classical epistemological position is a divorce between observation and the actuality of the heavens. Yet Aristotle’s critique of observation focuses on those a priori geometrical elements that Plato and the mathematicians cherished so much. Aristotle asserts that “[t]he minute accuracy of mathematics is not to be demanded in all cases, but only in the case of things which have no matter. Therefore its method is not that of natural science; for presumably all nature has matter.” Aristotle further claims that this assertion concerning the limits on the applicability of mathematics concerns not only “what nature is,” but the way humans experience and perceive natural events. The end result of these Aristotelian notions was an utter rejection of the aspiration to mathematically based observation:


And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished, when they perished. And astronomy also cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the geometer speaks of (for no perceptible thing is straight or curved in this way . . . ), nor are the movements and complex orbits in the heavens like those which astronomy treats, nor have geometrical points the same nature as the actual stars.

<end ext>

This Aristotelian dichotomy between mathematics as the realm of pure intelligibility and perception pulled the rug out from under the epistemological claims of astronomy. As a discipline based on a combined contribution of observers of heavenly phenomena and mathematicians’ explanations of such occurrences, astronomy could not come to terms with these Aristotelian assertions. In practice this meant a separation between observation with a dubious status, mathematical descriptions as fictive constructions, and physical explanations based on metaphysical principles with very little attention to empirical verification. Scant empirical data (for instance, the apparent circular motions of the planets) was used as mere starting point for such speculations; the mathematical construction was only a theoretical tool for predictions of planetary positions. Yet none of them was expected to support a physical worldview of the heavens, nor was the physical speculation expected to support the mathematical theory.

<1>Curiosity and the Threshold of Perception

The epistemological reservations concerning the possibility and value of formulating a physical theory of the heavens founded on observation and mathematical calculation had an intellectual affinity with religious prohibitions and warnings. In the Jewish tradition, Ecclesiastes celebrates direct experience at the expense of inquiring into and speculating on the nature of things not given to human perception. The author of Ecclesiastes emphatically declares, “Better [is] the sight of the eyes than the going of the soul” (Eccl. 6:9). The biblical author denies the human soul’s desires for what is not directly given. This point was emphasized in ancient Christian commentaries; Saint John Chrysostom, for instance, wrote, “Better to enjoy with the eyes . . . than things that are stored away which the eye does not see.” The moral dimension, then, aiming to quiet desires and passions, has immediate epistemological implications. One should embrace appearances that are immediately present before one’s eyes and not inquire into and speculate about hidden meanings and causes. Later generations emphasized this epistemological warning against human desire for knowledge and vain curiosity. In the apocryphal book of Sirach, one is warned,


Seek not (to understand) what is too wonderful for thee,

And search not out that which is hid from thee.

Meditate upon that which thou must grasp,

And be not occupied with that which is hid.

Have naught to do with that which is beyond thee,

For many are the conceits of the sons of men,

And evil imaginations lead astray.

<end L/L>

A succinct formulation of this prohibition on inquiring what is beyond human direct perception is found in the Mishnah in a passage dealing with mystical experience and esoteric knowledge: “Whosoever gives his mind to four things it were better for him if he had not come into the world—What is above? What is beneath? What was before time? and what will be hereafter?”

A similar and parallel negative attitude concerning curiosity is found in Hellenistic literature at the beginning of the Christian era, from Plutarch to Apuleius. Lucian, for instance, in several treatises mocks the intellectual vanity of philosophers, historians, and scientists. His main target is what he takes to be their ludicrous claim to know. In his treatise on Icaromenippus, Lucian expresses his disappointment with the different astronomical schools and their vain claims about the structure and nature of heavens. The main target of his satirical arrows is their boastful theories about things they cannot assess directly with their eyes:


You will laugh, my friend, when I shall tell you of their pride and impudence in the relation of extraordinary events; to think that men, who creep upon this earth, and are not a whit wiser, or can see farther than ourselves, some of them old, blind, and lazy, should pretend to know the limits and extent of heaven, measure the sun’s circuit, and walk above the moon; that they should tell us the size and form of the stars, as if they were just come down from them; that those who scarcely know how many furlongs it is from Athens to Megara, should inform you exactly how many cubits distance the sun is from the moon, should mark out the height of the air, and the depth of the sea, describe circles, from squares upon triangles, make spheres, and determine the length and breadth of heaven itself: is it not to the last degree impudent and audacious?

<end ext>

Lucian criticizes any sort of astronomical knowledge, be it mathematical calculations and measurements, or speculations concerning the physics of the heavens. “When they talk of things thus obscure and unintelligible, not merely to offer their opinions as conjectures, but boldly to urge and insist upon them: to do everything but swear, that the sun is a mass of liquid fire, that the moon is inhabited, that the stars drink water, and that the sun draws up the moisture from the sea, as with a well-rope, and distributes his draught over the whole creation?”

The insistence on direct perception as the only solid foundation of knowledge persisted throughout the Middle Ages. The dichotomy between direct “facie ad faciem” perception and mediated perception “per speculum” was an organizing principle in theological writings, in mystical experiences, and in philosophical treatises. Such direct experience, however, was beyond the reach of human senses as well as beyond human reason. The fourteenth-century Scholastic philosopher and mathematician Nicole Oresme asserts that exact knowledge of the heavens is impossible for a human observer, as the motions of the heavens are “innumerable for men” and “because of defects of the senses.” Oresme concludes that “all things lie hidden behind him who numbers the multitude of the stars, and who governs the world by reason everlasting. No one, therefore, should presume to judge so facilely about the cause of uncertain things.” One is urged to pursue the study of astronomy so to “repudiate errors scientifically by solid demonstrations and not by empty babbling as do those who are ignorant.” Furthermore, through the observation of “visible things the perfect works of God might magnify the invisible creator.” Oresme ends his treatise with a clear specification of the role of the “good astronomer” and the kind of knowledge such an astronomer may legitimately aspire to: “Thus it is sufficient for a good astronomer to judge motions and aspects near a point, and that his senses do not observe and judge the opposite.” Whatever is beyond these limited and approximated mathematical measurements, Oresme admonishes, is vain “and impairs the spirit and is foolishly presumptuous. . . . Except in a very general and doubtful way, no one ought to speak but rather restrain the tongue about things which are in the hands of God, for only he knows,” to whose eyes “all things are naked and open.”

Renaissance humanism revived classical satirical sentiments. Erasmus echoes Lucian’s sarcasm and mocks the epistemological presumptions of the astronomers:


Theirs is certainly a pleasant form of madness, which sets them building countless universes and measuring the sun the moon, stars and planets by rule of a thumb or a bit of string, and producing reasons for thunderbolts, winds, eclipses and other inexplicable phenomena. They never pause for a moment, as if they’d access to the secrets of Nature, architect of the universe, or had come to us straight from the council of gods. Meanwhile Nature has a fine laugh at them and their conjectures, for their total lack of certainty is obvious enough from the endless contention amongst themselves on every single point.

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Erasmus’s epistemological mocking of astronomical presumptions resonated well with sixteenth-century understanding of Ecclesiastes and its confinement of human curiosity. In Luther’s commentary on this book of the Old Testament, the point is emphasized over and over again. Fallen humanity can know and handle only those things that are sub sole. Humanity must be satisfied with the ability to exercise its power over those things placed