SUMS

Dr. Kim H. Veltman

Conclusions


    A survey of the literature shows that previous scholars have concentrated on details of Leonardo da Vinci's optical researches, and have taken into account little more than five percent of the extant diagrams. The present study, with 2,150 diagrams, is the first comprehensive treatment of the subject. By way of introduction the chief themes of classical and mediaeval optics are outlined. A gradual shift towards optics as a problem of physics is identified. Leonardo's role in this shift is suggested. In the Epilogue to Volume One attention was drawn to Leonardo's visual literalism in general. In Volume Two, which is a case study of how he approaches a specific branch of science, it is shown that this mentality underlies his physics of light and shade.

    Writers in Antiquity such as Aristotle, Seneca and Vitruvius, had used verbal metaphors and analogies in their claims concerning the natural world. For instance they compared both sight and sound to the blow of a hammer or a bell, and compared the propagation of light and sound to circular waves produced by a pebble when thrown into water. Leonardo uses the same similes but with an important twist. He explores the similes literally (a heightened nominalism?) and records them visually. Hence traditional verbal comparisons between percussion, light, sight and sound become translated into diagrams.

    This visualisation of verbal concepts is part of Leonardo's quest to analyse Nature in terms of mechanical principles. As he explains on K/P153r (W19060r), he has drawn up the rules of the four powers of Nature in order to account for movement in animals in mechanical terms. This is also why he plans that his "book of elements of mechanics" should precede "the demonstration and the force of man and of other animals." Leonardo thus points to a strictly mechanical model of Nature as later codified by Huygens and Newton.

    Nonetheless, a careful analysis of Leonardo's definitions of basic concepts such as point and line confirms that he has neither Huygens' purely atomistic corpuscular theory nor Newton's wave theory. Using Euclid's Elements as his starting point, Leonardo attempts to make a non-material point the basis of his physics of light and shade. From this analysis it becomes clear that Leonardo must have been familiar with a number of traditional sources, hardly surprising for a man who studied with the humanist Latin scholar, Nicolo Perotti,1 and who, by 1504, had a library of 119 books.

    Nonetheless, the question of how Leonardo used his sources, permits no simple answer. On occasion, as in the case of Pecham or Alberti he copies out or translates passages of earlier authors. When he reads Francesco di Giorgio Martini he adds his comments in the margin. We have no evidence, however, that he made a systematic study or commentary of the optical writings of Euclid, Alhazen, Witelo or Pecham.

    Detailed study of his work on light and shade confirms that although his notes are scattered and repetitious, they contain the outlines of coherent treatises which, in a number of instances, involves a systematic experimental approach now associated with modern science. He isolates key variables in a problem, keeps all but one of these constant and examines the consequences of changing one variable, step by step.

    He applies this experimental approach to his study of one to four light sources, to interposed objects of different shapes such as a pole and cross, and to his studies of the camera obscura, which he examines the effects of light passing through triangular, square, slit-form, cruciform, octagonal and other apertures. In contrast to his predecessors who had examined isolated aspects of these problems, Leonardo considers a series of situations. He frequently offers concrete and abstract solutions to a given problem. He does not, however, arrive at general laws. Algebra as a means of expressing formulae remains foreign to him.

    He devotes over 270 diagrams to the camera obscura alone. This is because the instrument serves to demonstrate a number of basic optical phenomena - such as inversion and non-interference of images or their property of being "all in all and all in every part." Because the camera obscura simulates basic aspects of the opticsl process, his well-known comparison of camera obscura and eye takes on new meaning. Far from being a passing simile, it is a bold claim based on a series of empirical studies. For instance, he studies slit-form apertures in camera obscuras becasue he wishes to understand the properties of cats' eyes which are slit-formed.

    He also makes glass models of the eye in order to simulate aspects of the visual process. These models are not entirely accurate and even lead him to wrong conclusions, such as the conviction that a double inversion of images occurs in the eye. The real importance of these models lies, however, not in the conclusions which they prompt, but rather in the approach which they assume, namely, a redefinition of vision strictly as a problem of physics.

    Leonardo's treatment of various parts of the eye varies considerably, ranging from passing comments in the case of the optic chiasma to very detailed discussions concerning the nature and function of the pupil. Although he plans a thorough anatomical study of the eye and other parts of the visual process, his extant notes suggest that he did not carry out his intent in full. As early as 1489-1490 he studies the sockets of the eye and optic foramen. In the period 1506-1508 he makes experiments using wax injections to determine the shape of the ventricles in the brain and also makes careful studies of the optic nerves and eyeball. There is no conclusive evidence, however, that he ever made an actual dissection of the eyeball.

    With respect to the visual process he considers various arguments in favour of an extromission theory of vision, but then rejects these and later unequivocably supports an intromission theory of vision. In his early writings images are discussed in purely theoretical terms. By 1508, the question of image formation has become a physical problem.

    Both the Greek and Latin terms for images (Eidolon, imago, simulacrum) had referred indiscriminately to (a) literary images (b) mental visual images such as dreams and hallucinations and (c) visual images. Leonardo's model-making as well as his visual testing of verbal images cuts through this polyvalence of meaning and prepares the way for Kepler's subsequent distinction between imagines rerum (subjective images) and picturae rerum (objective images on walls, etc.).

    His theories of the visual process change with time. At first he accepts that images coverge towards a single point. By 1492 he is exploring the possibility that images intersect and subsequently diverge again. Experiments with small objects inf ront of the eye and with objects seen beyond a pinhole aperture convince him that the visual power is spread throughout the eye. These experiments, along with his models of the eye, lead him to conclude that a double inversion of images occurs in the visual process.

    With respect to visual appearances and illusions there are may parallels between propositions in Euclid's Optics and claims made by Leonardo in his notes. Even so, there are a number of Euclid's propositions which Leonardo does not consider. Euclid's Optics was devoted primarily to the perception of isolated objects. Leonardo, by contrast, studies the perception of objects in context, including effects of background on apparent size and brightness. Some of his examples have their roots in mediaeval procedents. Other experiments appear to be his own and are again characterized by a step by step method.

    These trends are also evident in his study of optimal and minimal conditions of vision. His treatment of problems such as the central ray, the limits of the visual field, perception of objects smaller than the eye and diplopia also buids on the mediaeval optical tradition. But here again his use of diagrams, models and experiments sets him apart from his predecessors.

    In part four it is shown that manuscripts D and F are advanced drafts in which a series of ideas are restated, often more than once. It is found that the sequence of his arguments does not follow a straightforward page sequence. This is important because it establishes that the inherent order of Leonardo's ideas cannot be achieved by a simple reshuffling of pages and is only possible through a thematic treatment such as in this study.

    An analysis of Manuscripts D and F confirms that Leonardo's optic studies have a practical goal of understanding illusions in astronomy. This leads to an outline of his treatise On the Earth and its Waters in which he uses everyday experiences of the sun's image reflecting in water on earth as a basis for his claims that the sun's image is equally reflected by the oceans of the moon and that the planets are therefore, ultimately equivalent in their functions. He concludes that from a great distance, the earth is effectively a star.

    In the Appendices Leonardo's writings on optical instruments are analysed. In the case of spectacles, it is shown that he considered both bi-convex and bi-concave lenses. His notes concerning early forms of telescopes are assessed and his various lens grinding devices are described. Leonardo gives relatively little attention to plane mirrors. By contrast, he makes detailed studies of convex and concave mirrors in order to determine the location of the angle of incidence. For this difficult task, today remembered as Alhazen's problem, he appears to have relied very little on Alhazen and focussed instead on his own experimental evidence. He does not, however, achieve his own stated aim to discover a general rule.Leonardo's notes on refraction, the rainbow, and other meteoreological effects do not incorporate the findings of his late mediaeval predecessors.

    A complex picture of Leonardo's position within the optical tradition thus emerges. In some cases he did not know of, or ignored the work of his predecessors. In many cases he used their examples as a starting point for more systematic studies. This systematic aspect of his work helps explain the great increase in visual expressions - sketches, diagrams, drawings and paintings - at the end of the 15th Century. With the development of methods for rendering individual organs and objects came a challenge of drawing from four, six or eight viewpoints and in as many as eight or ten layers. Hence there evolved also a commitment to consider a problem in as many situations as possible. Instead of mentioning camera obscuras in passing, Leonardo draws over 270 examples. Instead of copying a traditional model of the eye, he draws at least 30 variants. A systematic play with variables thus generates an unprecedented number of images both in science and in art.

    The explosion in artistic activity, now associated with the Renaissance, is thus, in large part, an active process on the part of a handful of exceptionally conscious individuals. This bears emphasis in order to balance a fashion which explains this increase in the scope of art as a passive response to economic and social factors, one argument being: newly affluent bankers and capitalists wanted novel means of displaying their wealth and thus created a demand for more art.

    In Leonardo's case the situation is more complex. Some of the commissions for which he is specifically paid he never completes. The practical tasks for which he is paid, as engineer, architect and military advisor, he does well, but these do not explain his universal fame. His patrons, the Medici, the Sforza and ultimately Francis I have the wisdom to leave him alone sufficiently to enable his exploring many "useless" pursuits: anatomical drawing, perspective, movement of water, flight of birds, principles of mechanical motion, geometrical transformations and a theory of four powers of Nature. Paradoxically it is precisely these activities which his contemporaries would have dismissed as useless and a waste of time that later become cornerstones of early modern science and art.

    Optics was among these useless activities. There was no profit to be gained from studying the physics of light and shade, drawing models of the eye or examining illusions of sight. Yet such studies are a central dimension both of his own development and that of the Renaissance. The Sforza court where Leonardo works for more than fifteen years is an experiment in creating a context where individuals pursue study for its own sake, and results in studies which, in the long run, prove more useful than the most practical machine or financially attractive investment.

    On the other hand it is mistaken to imagine that Leonardo is centuries ahead of his time. In the case of optics his insights and experiments may often presage the later work of Kepler, Huygens or Newton, but he lacks their mathematical formulation of optical principles. He lays the cornerstones for a new study of optics strictly as a problem of physics, independent of philosophy and theology. But it remains for others to complete the construction that he begins.

    The full story of how that edifice is built requires much further study. This contribution has analysed only writings unquestionably linked with Leonardo. Other scholars, will need to correlate these with the Zaccolini manuscripts to which Pedretti drew attention, and which Clearfield Bell has examined in part. It will then be necessary to reassess Leonardo's influence on Jerome Cardan, Fracastoro, Maurolyco, G - B della Porta and other sources that lead to Kepler, Snell, Grimaldi, Huygens, Hooke and Newton in the seventeeenth century.

    Many of us imagine that a genius is one who is ahead of his time, an individual who warrants study because he has quick ways of reaching answers, possesses an easy way to truth. Perhaps, however, a genius is precisely he who knows that restatement, repitition and even blind alleys are essential aspects of profound searching. If so a genius confronts us not with the simplicity of intellectual pregress, but with its complexity, prompts us to reflect upon the cumulative nature of knowledge and the continuity underlying innovation. He knows that there are ultimately no short cuts and, like Leonardo, rejects abbreviators.


kim_veltman@hotmail.com

Last Update: July 11, 1999