Extract from Art and Science: A Parallel History [forthcoming]

Section I – The origin of the natural sciences in music and painting

Western achievements in the arts and sciences began with the Greeks. During the great age of Classical civilization, that of the glory of Greece and the grandeur of Rome, the basis was laid for all the later achievements in the development of the arts and sciences in the West. In the arts, the Classical tradition has not only been paramount in the West ever since, but to a much more limited extent it had been diffused throughout the Old World from the Atlantic to the Pacific. Thus, for example, Classical sculptural forms are to be found in Buddhist art, the results of Alexander’s conquests and the foundation of the Greek kingdom of Bactria in Central Asia, from which derives the famous Ghandara style. In a more attenuated version this sculpture was carried by Buddhism to both China and Japan. Something similar holds for the realistic Indian painting of the Gupta dynasty and later periods, found in the Ajanta caves. Sanskrit drama very likely had Greek origins; and possibly Roman ones as well due to the extensive sea-trade with Roman Egypt. However, these classical influences in the East did not last, as the rational realism of this art went against the other-worldly spirituality of Eastern religions.

For a time, something similar happened in the West as well, as the pagan art of Classicism fell under the Christian ban on heathen gods. Christianity favoured a more symbolic narrative art, but many Classical stylistic features were retained. The literary classics from Homer onwards also continued to be read in Byzantium, though no longer in the Latin West where Greek had been forgotten. However, Virgil was still current. All that was left of the Classical tradition was, of course, revived during the Renaissance and has been present ever since. One by one the major epochs of Classical civilization have been revived, going historically backwards: Roman influences came first, then Hellenistic ones followed later by Hellenic, and eventually it was the Classical Archaic period that came to the fore early in the twentieth century. Thus, Classicism remained a living presence in the West at all times till now. Picasso is as much a Classical as a Cubist painter.

A very similar story might be told for the sciences as well. The Greeks initiated most of the sciences and these were at least partially retained in the West during most of its history. The Arabs inherited some of these sciences and they have exercised a more fitful influence in the rest of Asia, starting with India. The early Greek philosophers introduced the idea of theory and rational proof, which was not available in the mere information gathering forms of knowledge of the older civilizations. In this sense, the Greeks initiated science or episteme in the proper sense of the term. There is nothing like Euclidean geometry outside the West, or Greek dominated Islamic science. There were schools of logic in India approximating to Aristotelian logic, but it is likely that, as in art, there were Greek influences at work.

In the natural sciences, too, the Greeks made the initial start towards systematic research. Much of this research was summed up in the Aristotelian corpus of works. There is nothing like it in either India or China. The Aristotelian system of classification according to species and genera provided a model of systematic definition for all kinds of other types of natural phenomena. Organized scientific research was first practiced in Aristotle’s Lyceum and from there was transferred to the Museum at Alexandria, most probably through the agency of Strato, the second head of the Lyceum after Theophrastus, Aristotle’s successor. The Museum was the nearest that science had ever come to a contemporary research institute. Science developed at a remarkable rate in the Hellenistic world.

Perhaps the very first fully established scientific fact was Eratosthenes’ calculation of the circumference of the earth to within between 50 and 500 kilometres of the correct figure (depending on the length of the stade, the unit of distance used). His deduction involved all three of the crucial aspects of a scientific representation: measurement, mathematics, and a model that is as realistic as possible. What makes for a realistic model is a contentious issue, but clearly the Ptolemaic model of the heavens based on the metaphysical assumption of circular motion at the same velocity around the earth is not realistic. Despite the heliocentric hypothesis suggested by Aristarchus, it prevailed till Copernicus overthrew it during the next crucial period in the development of science – the Renaissance.

Summing up the whole history of modern science, Weber arrives at a dual origin: what he calls the Concept, theorized by the Greeks, and the Experiment which was devised during the Renaissance. What he means by the Concept is the rational definition of terms, which he ascribes to Socrates, but is actually owing to Plato; and in science this entails the elaboration of a theory which reached its culmination in Aristotle. What he means by the Experiment is a methodical testing procedure, usually involving a constructed apparatus. This, he argues originated in art during the Renaissance, developed by experimentalist musicians, such as Vincenzo Galilei, and artist-engineer painters among whom Leonardo remains the cynosure. Both Concept and Experiment come together in the work of the early modern natural philosophers, or scientists as we would now call them, Galileo Galilei, Kepler and Descartes.

Weber states his case in a condensed form in his late speech “Science as Vocation” and also elsewhere scattered throughout his voluminous writings. Concerning the Concept, he puts it as follows:

Plato’s passionate enthusiasm in The Republic must, in the last analysis, be explained by the fact that for the first time the Concept, one of the great tools of scientific knowledge, had been consciously discovered. Socrates had discovered it in its bearing. He was the only man in the world to discover it. In India one finds the beginnings of a logic that is quite similar to that of Aristotle. But nowhere else do we find this realization of the significance of the Concept .

Weber, 1958a, p. 141

The Experiment he maintains “made its appearance at the side of this discovery of the Hellenic spirit during the Renaissance period.” In a remarkable passage that sociologists and historians of science have only rarely referred to, he goes on as follows:

They were the great innovators of art, who were the pioneers of the experiment. Leonardo and his like, above all, the sixteenth century experimenters in music with their experimental pianos were characteristic. From these circles the experiment entered science, especially through Galileo, and it entered theory through Bacon, and then it was taken over by the various exact disciplines of the continental universities, first of all those of Italy and then those of the Netherlands.

Weber, 1958a, pp. 141–2

The term that the translators render as “pianos” is, of course, anachronistic for what Weber has in mind, most probably the clavichord. And he does not explicitly mention either Nicola Vicentino or Vincenzo Galilei, the father of the more famous son, both great musical experimentalists. As we shall see, Vincenzo’s contribution to the experimental method was taken up half a century after Weber by Stillman Drake, but without any acknowledgement or awareness of Weber’s precedence in this matter.

But before we can discuss the experiment and music we must deal with a potential objection, first raised by Benjamin Farrington. Farrington took umbrage at the criticism of a reviewer who stated that “experimentalism as a systematic theory was unknown in antiquity: it is a product of the Renaissance” (Farrington, 1943, p. 177). Farrington is determined to prove this wrong and argues at great length against it, largely by reference to a work attributed to Hero of Alexandria, Pneumatics, but which Farrington believes originally came from Strato. He concludes that “these examples are enough to show that Strato had fully established the experimental method and that he had given it a wonderfully wide application” (Farrington, 1943, p. 181). He grants that there is much lacking in Strato’s supposedly experimental procedure: “There are innumerable weaknesses in these demonstrations, but everywhere we are in the presence of a man who, where physical facts are in question, prefers a demonstration to an argument” (Farrington, 1943, p. 181). There is no doubt that Strato, like many others after him, employed ingenious demonstrations to support his hypotheses, but the real issue is whether such ad hoc tests amount to experiments in the scientific sense of that term. As we shall show, experiments require controlled conditions that can be systematically varied through specially constructed apparatuses, and these are lacking in demonstrations.

Weber had already touched on this issue and come to a similar conclusion. He grants that the testing of hypotheses was known throughout the ages in the West and also in the East:

… for instance, in India physiological experiments were made in the service of ascetic yoga techniques, in Hellenic antiquity, mathematical experiments were made for purposes of war technology; and in the Middle Ages for purposes of mining.

Weber, 1958a, p. 141

Much could be written about such testing procedures, which Weber’s translators render with the word “experiment”. But Weber is quite clear that they do not amount to experimental method in the scientific sense, for as he states: “to raise the experiment to a principle of research was the achievement of the Renaissance” (Weber, 1958a, p. 141). As we shall see, Drake comes to the same conclusion by arguing against Bacon’s much looser sense of what experimentation amounts to, in accord with his method of induction.

Weber arrives at his view of the derivation of experimentation from music in the context of his whole account of the rational nature of Western music, which distinguishes it from all other kinds of music, as he puts it:

But rational harmonious music, both counterpoint and harmony, formation of tone material on the basis of three note triads with the harmonic third; our chromatics and enharmonics, not interpreted in terms of space, but, since the Renaissance, of harmony… all these things are known only in the Occident…

Weber, 1967, pp. 14–15

There are many things Weber refers to in music that are peculiarly Western, but the ones above to do with tones are the most relevant to our investigation (Weber, 1967, p. 14).

The rationality of Western music is manifest in the twelve-tone scale system, made up of the twelve black and white keys of the piano tuned to equal temperament. It was in order to arrive at that tonal-harmonic system that many of the experiments on the so-called “pianos” – actually, earlier keyboard and fretted instruments such as the archicembalo – were carried out. Weber devoted a little book (1958b) written in 1910 to the subject. Anyone interested in the subtle tonal technicalities and mathematics of the matter can still refer to it. What makes these investigations experimental in the scientific sense is that mathematics and controlled manipulation – usually on the length and tension of strings or columns of air – is related to empirical observation of the harmonious (or otherwise) qualities of sounds, as judged by a trained and discerning musical ear. It is this conjunction that makes for experimental science.

It is with this insight that Drake begins his account in relating Galileo Galilei’s experiments on motion to Vincenzo Galilei’s experiments in tuning. As he puts it with somewhat hyperbolic exaggeration, “the sixteenth century controversy over musical tuning created modern music, with experimental physics as a by-product” (Drake, 1970, p. 492). And he goes to the nub of that controversy: the battle between the old music whose main exponent was the theorist Gioseffo Zarlino and the new music whose main theoretical advocate was Vincenzo Galilei:

In one corner stood the mathematical theory of antiquity which took sonorous number as the cause of concord and asserted that number must govern string-length or the placement of wind-holes or the like. In the other was the human ear, with that curious taste for pleasant sounds that goes along with – or at least once went along with – the composition and performance of music.

Drake, 1970, p. 492

In overthrowing the old musical theory, first into the breach went G.B. Benedetti even before Vincenzo made his move, as Drake explains:

G.B. Benedetti has long been recognized among historians of science as the most important by far of the Italian precursors of Galileo, but only recently Professor Palisca has called attention to his achievements in the physics of sound.

Drake, 1970, p. 493

Drake sets out Benedetti’s revolutionary ideas on the acoustics of sound generation and goes on to conclude that “in framing these ideas, Benedetti had had recourse to experiment; that is the deliberate manipulation of physical equipment in order to test a pre-existing mathematical theory” (Drake, 1970, p. 494).

But Vincenzo Galilei went further than Benedetti, about whose unpublished work he might have heard, in developing the experimental method. He experimented not only with strings of different lengths but also ones made of different materials and subject to various degrees of tension, for which purpose he suspended various weights to them. Thus he “remarked in his final diatribe against Zarlino [who had once been his teacher], that the same ratios did not hold at all for the weights that must be used to stretch a given string to the equivalent pitches…” (Drake, 1970, p. 498). Hence, according to Drake, “it is in Galilei’s final refutation of Zarlino that we find for the first time the specific experimental rejection of sonorous number as the cause of consonance” (Drake, 1970, p. 496). Drake goes on to conclude his argument as to the provenance of experiment:

The experiments of Vincenzo Galilei, like those of Benedetti, were true scientific experiments in the sense we have defined that term: the manipulation of physical objects for the purpose of verifying a mathematical rule preconceived as applicable to their behaviour, or for the purpose of discovering a rule involved in that behaviour.

Drake, 1970, p. 499

But what have these experiments on sound to do with Galileo’s experiments on motion? Galileo was the faithful son of his father, he was musically educated, and Drake surmises that “Galileo was himself involved in his father’s experiments, some of which he appropriated and published many years later in his Two New Sciences” (Drake, 1970, p. 497). Hence, it is highly probable that “the conception of experimental verification of mathematical laws in physics, which is often illustrated in Galileo’s books, may have been inspired by his father’s work” (Drake, 1970, p. 498). Drake surmises that Galileo’s observations on the oscillations of the pendulum came from the experimental arrangement of Vincenzo’s work in measuring the tautness of strings by suspending differential weights to them; if these were set swinging it “would invite attention to the lengths of periods of oscillation” (Drake, 1970, p. 498). Apparently, Galileo’s early unpublished works are based on many such experimental set-ups including motion down an inclined plane. Thus, Drake comes to the following final conclusion as to the origin of experiment from music:

The first conscious experiments to test a pre-existing mathematical theory were probably the musical experiments of Benedetti and Vincenzo Galilei. They were extended into mechanics by Galileo, whose pupils Castelli and Torricelli carried them over into hydraulics and phenomena of air pressure. Boyle’s law is said to have been the first scientific law to be experimentally discovered.

Drake, 1970, p. 499

In his final comment Drake notes that the transition from music to physics is prevalent throughout the new sciences. Thus, for example, Mersenne wrote an extensive treatise on music as did Descartes. Hence, Drake refers to this as further evidence for his case: “The intimate linkage of music, mathematics and experiment that is made in Mersenne’s work tends to increase the probability of my general thesis concerning the origin of experimental physics” (Drake, 1970, p. 500).

The relationship between the two Galilei, Vincenzo and Galileo, goes beyond the collaboration in experimental science to which both Weber and Drake refer. It points to a fundamental epochal transition in Western civilization, embracing art and science at once. It inaugurated a new symbolic system for culture as a whole that we called representationalism in an earlier work, A New Science of Representation (1994). Then we noted that there is much more than a mere verbal similarity between Vincenzo’s major work on music Dialogo della musica antica and della modern and Galileo’s book Dialogues Concerning Two New Sciences. which got him into such difficulties with the Inquisition. Both father and son were intent on overthrowing an old conception of their respective worlds and introducing in its place a new conception, both with far-reaching consequences.

Vincenzo was arguing against Zarlino, the theoretical upholder of the old music theory going back to Pythagoras that expounded the view that harmony lay in number and that it underlay the order of the world. Ironically, as Drake points out, it was already an old-fashioned view, but one that Kepler still accepted as the music of the spheres in his Harmonia Mundi of 1619 in relating the heavenly bodies to each other; even while he arrived at laws of planetary motion that served to overthrow it. However, like his father in music, Galileo openly argued against Pythagoreanism as well as against the Aristotelian-Ptolemaic system that had held at least till Copernicus. Galileo added to the Copernican hypothesis by refuting Aristotle’s explanation of falling bodies and motion in general and substituting them with his own experimentally established laws. The work of Kepler on motion in the heavenly sphere and Galileo on motion in the sublunary realm was then combined by Newton with the law of gravity within the one abstract universal space. As we shall see, Descartes also played a key role in this conception.

At the same time as Galileo’s work triumphed in physics, Vincenzo’s work triumphed in music and aesthetics in general. The new physics and new music continued to be culturally linked to each other through their common representationalist semiotic paradigm. Vincenzo’s work had not only theoretical consequences but practical ones as well; as we expounded in A New Science of Representation, he was the originator of a new musical style called stile rappresentativo, the representationalist style. To do so, he had to overthrow the old polyphonic style, one of whose staunch upholders was Zarlino. This is the music that originated in the early fifteenth century in the Netherlands and reached its culminating perfection among the Flemish composers working in Italy, especially those at St Mark’s cathedral in Venice, such as Adrian Willaert and his pupil Cipriano de Rore, with whom Zarlino corresponded.

In direct opposition to this polyphonic music, Vincenzo devised both the theory and practice of monody, which became the basis of opera. The early operas were composed by his friends and collaborators in the Camerata Fiorentina, Peri and Caccini, but it was not till Claudio Monteverdi that opera took off and became the foremost instance of what is now called Baroque music. This new representationalist aesthetic is also to be found in the literature and painting of this period, as explained in A New Science of Representation. This style of painting in Italy is pre-eminently associated with Michelangelo da Caravaggio and his school of tenebrists who were prominent throughout Europe in the first half of the seventeenth century. It is very likely, as we argued in the previous work, that Caravaggio was influenced by the new science of optics and the devices, such as the camera obscura, on which it was based.

With painting we turn to another side of the origin of experimental science, also referred to by Weber when he speaks of the “great innovators in art who were the pioneers of experiment” (Weber, 1958a, p. 141). He explicitly mentions Leonardo, but that is far too late for what he has in mind. Elsewhere he clearly reveals who he means to refer to when in his discussion of the difference between Occidental and Oriental art he gives the following as two key examples: “But the Orient lacked that solution of the problem of the dome and that kind of rationalization of all art – in painting by the rational utilization of lines and special perspective – which the Renaissance created for us” (Weber, 1967, p. 15). There is but one man to whom the solution of both these “problems” can be ascribed – Filippo Brunelleschi.

Brunelleschi solved the problem of building a dome across the huge span opening of the Florentine cathedral Santa Maria del Fiore. It was certainly a remarkable engineering feat and how he did it has to this day not been fully explained, though a number of proposals and scaled down models have been built in line with these. It has in this sense remained a secret and as such contributed little to either engineering or science. What Weber meant by the expression “the Orient lacked the solution to the problem of the dome”, which apparently was solved during the Renaissance, is also not clear. Even before the Renaissance, Roman domes were built, such as the Pantheon in Rome, still standing, and the Hagia Sophia in Constantinople. There were numerous Islamic domes throughout the Middle East and Central Asia. Perhaps by the Orient Weber means China and Japan, but there the dome did not figure in architecture and so could not have been a problem to be solved.

However, Brunelleschi began the solution to another problem in painting which did prove crucial to the experimental method in science – that of perspective. At some time, most probably the early 1420s, while he was building the dome, Brunelleschi painted two small panels; unfortunately, both have been lost. However, we do have an account of what they contained from his biographer Antonio Manetti, written more than half a century later. Apparently, one was a depiction of the baptistery of San Giovanni as seen from the door of the cathedral; the other was a view of the Piazza del Duomo. As Manetti writes: “Thus in those days he himself proposed and practiced what painters today call perspective; for it is part of that science, which is in effect to put down well and with reason the diminutions and enlargements which appear to the eyes of men from things far away or close at hand…” (Antonio Manetti, Vita di Brunelleschi, cited in White, 1967, p. 113). We do not know how Brunelleschi discovered perspective – or actually rediscovered it since the ancient painters were fully aware of it – or whether it was a theoretically informed demonstration or simply a practical painting technique. But the fact that Brunelleschi is said to have studied geometry with Toscanneli, the renowned Florentine cartographer suggests that it was more the former than the latter. Whichever it was, it was truly revolutionary in its consequences both for art and for science, as Michael Janover reports:

But though he worked as a pragmatic artisan-engineer, he did not proceed solely by trial and error. He put a rule to the production of visual scenes he depicted and proceeded to check the results, produced in applying the rule, by constructing his perspectives and then comparing them, testing them, against the actual scenes. What is truly “revolutionary” in the novelty of the procedure – whatever argument is accepted as to precisely how Brunelleschi drew up the perspective construction – is the fusion of experimental attitude and a geometric plan or rule of procedure. This fusion of experiment and mathematics, no matter how attenuated we find Brunelleschi’s geometric theory or how limited his sense of experiment, is one of the very first announcements of the fully-fledged union of those two modes of knowledge which comprises modern science.[1]

Janover, 1989

Thus, almost a century and a half before Vincenzo and Galileo Galilei we already find the rudiments of the experimental approach among the Florentine painters.

Perspective – one of the key features that Weber ascribes to the rationality of the West, for it is not to be found in any other art – has had a long history of two and a half millennia from the ancient Greeks down to our time. It is this history which is the subject of Janover’s remarkable dissertation. His main subject is the opposition between the role perspective played in the philosophies of the ancients, especially in Plato and the Sceptics, and its role in the work of the painters and scientists of the modern period. In the former it served as a key argument against empirical scientific knowledge: for either knowledge was to be located in geometry and metaphysics, as in Plato, or it was not to be found at all, as in Pyrrho and the later Sceptics who inherited Plato’s Academy. It was only among the modern Sceptics of the late sixteenth century, starting with Montaigne, that knowledge was to be found within empirical experience, provided that it was sought by means of mathematics and experiment. Descartes took up this attitude and began with the scepticism of methodical doubt before proceeding to lay the foundation of his science, which he defined as that of certain knowledge.

Janover recounts these opposed attitudes to knowledge and Scepticism and explains why such a fundamental opposition between them should have arisen. He begins by noting that in the ancient world perspective arose as a set of practical techniques to be used for conveying space by painters and scenographers who painted the backdrops to scenes in plays. Hence, “the classical world… developed perspective as a technique but not as a theory. It was never developed abstractly, but as a set of unsystematic experiments in the representation of visual appearance” (Janover, 1989). As such, perspective stood for techne in opposition to theoria, one of the fundamental contrasts of Greek philosophy to be found as early as Heraclitus’ opposition of metis or polypragmata to logos (See Redner, 1986, chap. 6). This was one of a number of such binary divides that precluded the search for knowledge in experience and separated philosophy from any practical or technical activity. Even Aristotle, who was so given to the rational definition and systematic orderly elaboration of things, was nevertheless the upholder of such fundamental dichotomies, as between theoria and praxis, praxis and poiesis, episteme and aesthesis, nous and psyche and many more such. This whole intellectual scheme of philosophy worked against any lessons to be drawn from the practical activities of craftsmen and technicians, such as Bacon much later advocated as the necessary basis of science or natural philosophy as it was then known.

The Renaissance painters who developed perspective and who practised all the other arts and crafts of the time were so-to-speak philosophically illiterate, they had no university education and were ignorant of the Aristotelian scholasticism that there prevailed. They were purely practical men or ingenui as the best among them were then known, as Janover describes them:

These were men who dealt with concrete artistic and technical problems, and who joined rigorous calculation of all kinds of quantities to the technical construction of devices for controlling natural forms. They formed, as it were, a third intellectual current alongside the scholastic (and later, neo-Platonic) philosophers and the Humanist men of letters. And these artist-scientist engineers of the Renaissance were centrally interested in the nature and workings of perspective vision in which they came to solve technical problems of representation and design, but also more generally, to treat nature as a whole as quantifiable space open to human art and knowledge.

Janover, 1989, p. 26

To achieve their practical aims they were intent on calculation, and that meant that they were interested in geometry and mathematics. Hence the role that from the very start Toscanelli played in the development of the science of perspective. As Janover points out:

His influence on Brunelleschi, who studies geometry with Toscanelli, and on Alberti (who dedicated his “snacks”, the Intercaenale to Toscanelli) is evident and his close association with Nicholas Cusanus (they were students at Padua and pursued a life-long friendship) suggests a general and pervasive concern with issues of geometrical order, astronomy, cartography, and architecture in Quattrocento Europe.

Janover, 1989, p. 239

It was precisely such interests that are evident in the next century among the mathematicians, technicians and engineers leading up to Galileo Galilei and Simon Stevin.

This gave rise to modern science in a developing tradition starting with Brunelleschi early in the fifteenth century. As Janover concludes:

Despite important differences that separate the social institutionalization and methodological self-consciousness of modern science from the virtuoso style and dilettantism of Renaissance art-science, the crucial continuities between them cannot be overlooked. These continuities centre upon the rationalization of sight through rigorous measurement and controlled observation and the rationalization of space through the mathematical assumption of its infinite and homogenous nature.

Janover, 1989, p. 23

It is this later assumption that gave rise not merely to modern science or natural philosophy but to modern philosophy as one fundamentally opposed to the basic premises of ancient philosophy. Thus, the difference between sub-lunary and celestial space, as well as the basic opposition between theoria and techne, episteme and aesthesis, and all the other dichotomies in Plato and Aristotle, were overthrown. Hence the fury and rage with which the guardians of the old intellectual traditions, especially the Church and the universities, confronted the “new philosophy”, which as John Donne declared, “puts all in doubt.”

The continuity between the mathematics of perspective and that of space in general is most evident in the work of two mathematician philosophers with similar names, Desargues and Descartes. Girard Desargues, the teacher of Blaise Pascal, is now little known except among mathematicians and aeronautic engineers, but his work on projective geometry, which emerged directly out of perspective, was a precursor in “the development of nonmetrical geometry as the most generalized science of order… [which] has played an inestimable role in the aerodynamic designs of the contemporary space-age” (Janover, 1989, p. 199). Scholars lost sight of it for centuries as it was overshadowed by the almost simultaneous publication of the much more momentous algebraic geometry of Descartes, now called Cartesian geometry.

In both these geometries, the mathematization of visual space in two dimensions, as in perspective, is extended to the mathematization of three-dimensional space in general. Cartesian geometry accomplished this through the translation of geometrical figures into mathematical equations. Thereby space as res extensa assumed a purely autonomous form and lost all relation which it previously had with location, as in beneath or beyond the moon. It became the very stuff of the universe, as Descartes declared, echoing Archimedes, “give me extension and motion and I will construct the universe.” As Janover comments, “Descartes’ mathematical conception of space as pure res extensa preserves the geometric insights of the Renaissance artist-scientists, but annuls the artistic technical form of those insights, and hence ushers in a wholly new conception of purely quantitative and abstract science” (Janover, 1989, p. 313).

Science, of course, did not derive from any one single source, not even from any one artistic origin. Thus far we have shown how Renaissance music led to Galileo on motion and how Renaissance painting at a greater remove led to Descartes on space. Next, we shall proceed to show how another painterly tradition inspired Kepler on light and optics. This was the northern art that was not so much concerned with space as with the depiction of light and its reflections.

The science of light was, of course, optics, an already long-established science which went back to the Greek philosophers at least as far back as Euclid. In the form of its later summary by Ptolemy, it was inherited by the Arabs and commented on and added to in Ibn Al-Haytham’s (Alhazen’s) masterly compendium Book of Optics in 1021. Translated into Latin in the thirteenth century under the heading of perspective naturalis (from which derives the term perspective) it was in turn taken up by a number of medieval schoolmen, among them John Peacham, Roger Bacon, Robert Grosseteste and finally Witelo. It was Witelo’s work that Kepler commented on in his Ad Vitellionem; and Descartes largely cribbed from Kepler in his Dioptrics, a fragment from his larger book Traite du monde et de la lumière which he dared not publish when he wrote it in the early 1630s due to Galileo’s condemnation, but which appeared posthumously in 1677.

It is Kepler’s work on optics that is of greatest interest to us in this context for from it derives the representative theory of perception usually ascribed to Descartes, since he made it the foundation of his epistemology and thereby the basis for all subsequent accounts of empirical knowledge. However, it is evident, as we made clear in A New Science of Representation, that it is already to be found in Kepler, who is credited with the discovery of the formation of an inverted image on the retina in vision (Redner, 1994, p. 222). Beyond that point in the eyes Kepler does not go, but he does express metaphorically the idea that some kind of representation ensues. It was Descartes who then spelled this out and gave it its full philosophical import. The importance of this not only for philosophy and science but also for culture in general we have already referred to in our discussion of the new stile rappresentativo in music and in the other arts.

All this takes its origin from Kepler’s little “picture” at the back of the retina, for that is what he calls it. Kepler’s rather naïve wording is taken up by Svetlana Alpers in her book on northern art: “Thus vision is brought about by a picture of the thing seen being formed on the concave surface of the retina” (Alpers, 1983, p. 36). She comments on this as follows:

Despite differences of opinion about what part of his analysis of the eye is based on the analogy of the camera obscura, or as to whether his research is a perfection of or a break with medieval views, all modern commentators agree on one clear innovation: Kepler was the first person ever to employ the term pictura in discussing the retinal image. As a recent study put it: “This is the first genuine instance in the history of visual theory of a real optical image within the eye – a picture, having an existence independent of the observer, formed by the focusing of all available rays on a surface.

Alpers, 1983, p. 36

Alpers’ quotation is from David Lindberg, an authority on this subject (Lindberg, 1976, p. 202). She goes on to specify what kind of picture it is and how it is made:

Kepler goes on in the Dioptrice of 1611 to refer to the retina as painted with the colored rays of visible things. The word that he chooses for what does the painting is pencilli – or little brushes – the very little brushes that Huygens called on De Gheyn to use in replicating the view in the microscopic lens. Artists’ brushes paint a picture of the world outside the eye on the opaque screen in the retina at the back of the eye.

Alpers, 1983, p. 38

Thus, the way that light paints the picture in the eye is not unlike the way in which artists paint a picture on a flat or curved surface: “In its formation the picture evokes that peculiar absorption into each other of drawing and painting that is characteristic of Netherlandish artists” (Alpers, 1983, p. 38).

The Netherlandish artists she has in mind were precisely those intent on painting the qualities of light with little brushes and coloured oil paint, a technical innovation introduced by the Flemings among whom Jan van Eyck was the supreme master. At the very same time as Brunelleschi was inventing perspective, Jan van Eyck was perfecting the rendering of light reflected from shiny surfaces and falling on textured materials such as cloths and furs. What he and his followers achieved is extremely life-like and approaches closely in its simulated verisimilitude to optical images produced by means of mirrors and lenses or the camera obscura, already long known from Al-Haytham’s book on optics. But there is no evidence that any of the Flemish painters consulted such books or knew anything about theoretical optics.

So how did they manage to achieve such extraordinary detailed effects that Panofsky speaks as if “Jan van Eyck’s eye operates as a microscope and as a telescope at the same time…” (quoted in Alpers, 1983, p. xxi). There was certainly no microscope or telescope available at that time, but there were lenses and glasses which were the precursors to them, and also a wide array of mirrors of different shapes. Hence, the thesis has been mooted for some considerable time that these early Flemish artists must have used some such optical instruments to help them render the optical features of their painterly representations. Most recently the dispute has erupted around a book published by the painter David Hockney who makes this claim very forcefully and points to considerable evidence to support it. Most markedly there is the depiction of a concave mirror at the back of the standing couple in Jan van Eyck’s Arnolfini marriage portrait. The evidence is even stronger for later painters, even Italian ones during the late Renaissance, such as Lorenzo Lotto and Michelangelo Merisi da Caravaggio, and it is almost certain that Vermeer availed himself of a camera obscura for there is no other way of accounting for some of the peculiar optical oddities in his paintings.

Thus, it seems highly probably that these painters, starting with the Flemings, were making use of the very instruments that featured in theories of optics and whose eventual technical perfection into telescopes and microscopes was indispensable for the development of the modern sciences of astronomy on the one hand, and biology and medicine, on the other. Galileo turned his eye to the heavens with the aid of a telescope, a then crude invention of the Dutchman Hans Lipperhey; and Antonie van Leeuwenhoek looked into a drop of water through a microscope invented by Cornelis Drebbel. But apart from this fact, that both the artists and the early scientists used optical instruments, there is no direct relation between them. The artists knew no science and the scientists do not refer to art, except for the curious reference that Kepler makes to the picture in the eye painted by rays of coloured light.

And yet, there is a kind of Weberian elective affinity between art and science in northern Europe. Alpers draws this conclusion in rhetorical terms:

The fact that the country that first used microscopes and telescopes had Van Eyck and other works like his in its past is not just an amusing coincidence, as Panofsky once claimed. Didn’t northern viewers find it easier to trust what was presented to their eyes in the lens, because they were accustomed to pictures being a detailed record of the world seen?

Alpers, 1983, p. 25

Hence, despite the absence of any direct sources of influence, Alpers nevertheless concludes that “there is a two-way street here between art and natural knowledge”.

We have traced such two-way streets between art and science in music, Renaissance perspective and Flemish-Dutch illusionism leading to the science of Galileo, Descartes and Kepler, the main initiators of the Scientific Revolution. But once that science was under way, this two-way street petered out. It is the above beneficiaries of the arts who were themselves most intent on breaking any connection with the arts. Descartes revives the argument from illusion, using perspectival phenomena as his key examples, in the same way that Plato and the Skeptics did in antiquity, to argue that the senses cannot be relied on to give rise to certain knowledge. Galileo showed that the sensory qualities conveyed through the senses are purely subjective and have no external reality. Kepler demonstrated that there are distortions built into the eyes that affect what we see. In short, the arts which rely on sensory perception are not to be trusted in science.

This went further once the scientists or natural philosophers organized themselves into societies with strict methodological procedures for arriving at knowledge, recording it in written form, and communicating it to all others. For then language itself and all the arts of discourse were called into question. Only the barest and simplest reporting of observations of facts, preferably in quantified mathematical terms, and the logical deduction of conclusion to be drawn from these were allowed. Anything that smacked of the literary arts was eliminated, language had to be plain and to the point with no fancy figures of speech. Hearsay was banned, and consequently the whole of history was dismissed as useless to knowledge. Thus, was born the protocol governing the discourse of the modern scientific paper.

But history and literature were precisely the arts that stood at the origin of another kind of science, that which we now call social science. Just how the social sciences relate to both the literary and historical arts, on the one hand and to the natural sciences on the other has been a contentious issue ever since. But that is another story of origins to which we go next.

Notes

[1] It is sad that this brilliant work remains unpublished to this day.

References

Alpers, S. (1983) The Art of describing Dutch art in the seventeenth century. Chicago: University of Chicago Press.

Drake, S. (1970) ‘Renaissance Music and Experimental Science’, Journal of the History of Ideas, 31(4), p. 483.

Farrington, B. (1943) Greek Science, Its Meaning For Us. London: Penguin Books.

Janover, M.M. (1989) Seeing and knowing: the figure of perspective from Plato to Nietzsche. Clayton, Victoria: Monash University.

Lindberg, D.C. (1976) Theories of vision from al-Kindi to Kepler. Chicago: University of Chicago Press (University of Chicago history of science and medicine).

Redner, H. (1986) The ends of philosophy: an essay in the sociology of philosophy and rationality. London: Croom Helm.

Redner, H. (1994) A new science of representation: towards an integrated theory of representation in science, politics, and art. Boulder: Westview Press.

Weber, M. (1958a) ‘Science as a Vocation’, in H. Gerth and C. Mills (eds) From Max Weber: Essays in Sociology. New York: Oxford University Press.

Weber, M. (1958b) The rational and social foundations of music. Translated by D. Martindale, G. Neuwirth, and J. Riedel. Carbondale: Southern Illinois University Press.

Weber, M. (1967) The protestant Ethic and the Spirit of Capitalism. Translated by T. Parsons. London: Unwin University Books.

White, J. (1967) The birth and rebirth of pictorial space. London: Faber and Faber.