Dr. Kim H. Veltman

IX    Epilogue

1. Introduction
2. Vision, Representation and Culture
3. Ambiguities
4. Price of Vision
5. Scale
6. Fractals and Scale
7. Passive Recording and Active Intervention
8. Objectivity and Subjectivity Reconsidered
9. Scales and Samples

1. Introduction

    The discovery of perspective has been ranked with the discovery of the new world as one of the great events of western culture.  Its advent has been described as a day the world chaged.  Inded some popular accounts could lead us to believe that Brunelleschi woke up one morning and decided that he would change the western concept of space.  We have shown that there was no sudden revolution.  A gradual evolution n spatial representation was part of a larger phenomenon involving changes in the construction and reconstrucion of space.

    Awareness of these changes came more slowly.  A generation passed before Manetti and Filarete even mentioned Brunelleschi's demonstration.   Another generation passed before Pacioli (1494) mentioned by name some of ther early Italian practioners and theorists.  Vasari (1560) widened the scope considerably mentioning a number of individuals, some specific paintings and several treatises but usually without specific titles or dates.  Lomazzo (1590) alluded to at least seven treatises which can be identified.  Thirty four subsequent bibliographies have increased the number of sources to 1284 (Index at V.1).  The present bibliography contains 7,900 sources. With respect to perspective in a strict sense we have attempted to be more comprehensive. But under more general headings such as geometry there is more to be found and with respect to related topics such as sundial projection or cartography there is a vast amount of material that has yet to be examined. Hence although 450 years have passed since the advent of perspective, awareness of even the basic sources remains incomplete. Of these only a tiny sample has, in turn, been used in considering the history of perspective in particular and projection methods in general. Poudra's (1864) standard history cites 167 sources. Panofsky (1927), the most famous single study in the field, cites 24 sources. It is not surprising, therefore, that the claims made by these authors need revision. We shall begin with changing relations of vision, representation and culture. We shall then show that vision, as used in the West since the Renaissance, is complex and comes at a considerable price but nonetheless brings enormous advantages largely through concepts of scale. Recent developments with fractals challenge us to reconsider basic assumptions of perspective in terms of scale, whether the process is passive or active, objective or subjective, and indeed, the very foundations of scientific method. We shall suggest that this offers new ways of understanding the unique characteristics of western culture.

2. Vision, Representation, and Culture

    Panofsky's most famous claim was that perspective is not something absolute, that is can be seen as a symbolic form in Cassirer's sense, that each culture has its own world view, particular theory of vision and corresponding theory of representation. According to Panofsky a finite world view of the Greeks led to a spherical theory of vision and perspective, while the emergence of an infinite world view in the late middle ages led to linear perspective and a corresponding adjustment in Euclidean optics. As we have shown (p.202), this model is too simple.

    We have shown that these changing relationships of vision, representation and world view are better understood if we see them in the context of texts and literacy. In pre-literate societies, for instance, individual artists might reflect on these questions but, because they did not write them down, no fixed theory could be identified with their particular culture. The absence of texts meant absence of a defined standard. This allowed freedom with respect to loosely defined boundaries of a given style, yet imposed constraints in that such societies were usually limited to one style with which to identify themselves. The advent of manuscripts was a necessary but not sufficient condition for texts on vision and representation. India developed a complex culture without texts on optics or representation. China produced texts on representation without reference to theories of vision. Islam produced texts on optics without reference to representation. Greece, which produced texts on both vision and representation was an exception. These texts were more ambiguous than Panofsky assumed. Euclid's theory of vision could be taken to imply spherical, cylindrical or even flat projection planes. Hence Greece did not establish a given projection method for optics and art. Its contribution lay, rather, in using geometry for vision and representation, but geometry without reference to measured size and distance, i.e. without a defined scale.

    During the Renaissance, which saw the advent of printing, written theories of vision and representation became more widespread. Geometry was applied increasingly in conjunction with measured size and distance. But it was again the case that no single projection method was used exclusively for vision and art. Explorations of planar projection methods in linear perspective went hand in hand with study of angular, pyramidal, conic, cylindrical and spherical projection methods. Hence the important characteristic of the period 1400-1600 was not simply the use of linear perspective but rather a recognition that, depending on the surface used, representation involved a number of projection methods governed by mathematical laws: i.e. that projection depended on geometry rather than optics. This raised further questions which came into focus in the period 1600-1800: whether there might be different projection methods in everyday vision and representation and whether there could be conflicts between these methods. One reaction was to concentrate on representation. Another was to consider only cases where there was no conflict. Since 1800 there has been increasing interest in what the precise nature of these conflicts might be and has led, more recently, to renewed study of cylindrical, spherical, hyperbolic and other complex planes which frequently reflect personal theories of vision rather than claiming to embody universal optical laws.

    Panofsky claimed that each society develops a specific theory of vision and corresponding theory of representation. Our claim is that articulate theories of vision and representation do not emerge in pre-literate societies; that such theories require manuscripts and only begin to thrive when there are printed texts and that, paradoxically, the advent of print culture, instead of establishing one specific method to the exclusion of others, proliferates the number of methods. Advances within such cultures cannot therefore be seen as a simple choice of a new method and are better understood in terms of increasing distinctions between vision and representation and attention to personal solutions for bridging these distinctions. So it is not really a question of which kind of perspective is used in a society, but rather a more basic problem of the ways in which mathematics, and particularly geometry are used in explaining vision and representation. If Panofsky were writing today he might have discussed mathematics in optics and representation as a symbolic form.

3. Ambiguities of Vision

    It is so difficult to discuss these changing relationships largely because vision, which is often assumed to be constant, varies culturally and historically. A paleolithic tribesman, an Athenian Greek, a Renaissance Florentine, an eighteenth century Parisian and a modern New Yorker all have two eyes. Yet what each of them could see varies tremendously. A contemporary native of the Amazon rain forests sees all kinds of dangers which we as casual tourists would never notice: dangerous animals, deadly snakes, poisonous plants, and at the same time is only aware of a small percentage of the 1700 species of birds which fly around him. An ornithologist will see the species, but may not see the trees for the birds. Someone who grows up driving automobiles at 200 kilometers per hour on German highways sees very different things. Every occupation and profession focuses on certain visual skills at the expense of others: a hunter, a goldsmith, tool and die maker, geologist, detective, botanist and an artist each see different dimensions of what is theoretically one world. Most? cultural history is frequently approached in terms of isolated representations of artists which are then taken as typical of the way in which a culture "saw." Sir Ernst Gombrich has explored other reasons why one might wish to avoid speaking of what persons "saw" altogether. Strictly speaking we can, at best, only attempt a history of what persons recorded in the form of words and pictures as having seen: a second-hand history of sight, as it were. Even in this we have scarcely begun. Histories of graphic methods such as Dubery and Willats are strikingly summary. A comprehensive history of projection methods has yet to be written. A history of how different trades and professions changed the boundaries of the visible has yet to be attempted.

    There are also more subtle problems. We have shown that perspective owed much to a late mediaeval commitment to transform storytelling into painting, and we have emphasized the positive dimensions of this process. It exploded the boundaries of representation. It introduced spatio-temporal dimensions. But all this also came at a price. For it reduced the dynamic act of storytelling to static moments. It took away the performance aspect, the spontaneity, the uniqueness of the process, replacing this with something fixed, motionless, but capable of being reproduced almost exactly. Cultures such as China, India and Africa chose another path. They frequently avoided pictures and even words altogether, preferring to translate their stories into dance. In this form each version of a story was unique, spontaneous, full of motion and life, yet incapable of being repeated exactly. The west wanted repeatability and gradually found it, but again at a price. Each step closer to repeatability meant more mechanical aids, first compasses, then pantographs, gradually cameras, photo copy machines and CAD graphics packages. Every step closer to a perfect copy, threatened to become more impersonal. Fortunately there were also enormous advantages which made this price bearable: these involved systematic control of representation which came through mastery of scale, size and distance.

    In pre-literate societies, where there were no fixed rules of vision and representation, there were no concepts of scale, size and distance. A voodoo witch could use a tiny doll to affect a large man whether he were near or far away. The size of the doll, the size of the victim, the distance between the two, were meaningless factors in a magical context. Greek theories of vision and representation included some ideas of lines, angles and proportion. This brought a concept of scale to individual objects rather than contexts, as becomes clear if we return to our earlier example of the planisphere (fig. 64a). When the tropic of cancer was projected onto the equator its scale was reduced. Whether the drawing involved was small as it is here or as large as the actual size of the earth made no difference. Hence although scale within a drawing was important, the scale of the drawing itself was irrelevant. This applied to all representations (sculptures, paintings and drawings) where proportions were constant (fig. 64.b-c). Hence tiny statuettes and monumental statues had the same effect, and there was no incentive to change scale in order to bring objects into focus and study them more closely. Only changes in angle and proportion were significant (fig. 64. d-e).

Fig. 64 Greek projection methods concentrated on scale within an object rather than scale between objects. Whether a diagram was small or large did not matter.     Only changes in angle were important.

    The advent of perspective in the Renaissance integrated Greek geometrical ideas of line, angle and proportion with measured size and distance. A small picture might represent small objects which were nearby or large objects at a distance. Size now became a relation between apparent and measured size which varied with distance. It was not distance between isolated objects, but distance between planes that counted. If distances were too great and objects too small, this could be solved by changing their scale. Perspective thus brought incentives for the development of telescopes and later of microscopes. All this shifted attention from scale within an object to scale between objects in a given plane and scale between objects and contexts: persons and buildings to townscapes and landscapes, and these in turn to surveyors' charts, topographical views and maps. An inverse size/distance law governed these relations and all one needed to do was to decide which scale was appropriate for which purpose. This had enormous consequences for representation: scenes, townscapes, landscapes, views and maps could all be coordinated systematically. A sense of mastery and domination of nature emerged, a sense that everything could be measured, but a key to objective control had been found. Objectivity was simply a question of changing scale in order to get things into focus.

    Renaissance perspective was based on the assumption that every object has a fixed measured size, that size and shape within a given plane are constant and that size varies only with distance. The advent of microscopes called these assumptions into question. Within a certain range of magnification objects simply appeared larger, i.e. scale affected only size. Magnification beyond this range affected both the size and shape of objects. This was known in the seventeenth century and it became obvious in the eighteenth century when instrument makers such as Brander and Martin began using telescopes and microscopes in connection with perspective. Electron microscopes introduced more vivid examples. Yet, curiously enough, the philosophical implications of the discrepancy remained unnoticed and it took the development of fractals to recognize that this principle involved something far more basic than special conditions in microscopes and telescopes.

    James Gleick used a map of England as an example. If one uses a ruler one kilometer in length then the coast has a certain number of corners and a given length. If one uses a ruler one meter in length than the same coast has a thousand more corners. If one uses a ruler one centimeter in length the same coast may have 100,000 more corners then the same coast measured in terms of kilometers. The coast measured in centimeters will also have a far greater circumference than the coast measured in kilometers. Perspective assumed that scale affects only size. Fractals confirm that scale affects shape as well as size.

    The consequences of this corollary run deep. As long as scale affected only size, it could be claimed that perspective, which recorded the world in different scales, was a passive recording technique which did not interfere with the essential characteristics of that which it examined. Perspective was therefore a model for the scientific method of passive, objective observation and recording without active subjective intervention. If, however, scale affected the basic shape of what was studied, then perspective, which played with scale, was tampering with the evidence that it claimed to be recording and was subjective in a way that Panofsky and his followers had not suspected.

    The problem is partly conceptual. The subject-object distinction as formulated by Cassirer, was mainly in terms of a Cartesian duality, as if subjective and objective were in opposition to one another like mind and matter or quality and quantity; the subjective actively imposing itself onto the world, the objective passively recording the world. This model was too simplistic. Perspective might aim to record the outside world passively but to do so required reducing nature's incredible complexity to simple forms and patterns which could easily be traced on the picture plane. Hence it was no coincidence that regular polygons and regular architectural forms such as arches and cupolas played so prominent a role in early perspectival treatises. In the case of fields and landscapes the problem was resolved by reducing their complex irregular surfaces to a small number of station points which could then be joined to produce simple polygonal forms. Passive recording of a landscape required an active imposition on its surface of geometrical shapes amenable to being recorded.

    Heisenberg's indeterminacy principle introduced the idea that one could not study problems in quantum physics without disturbing the evidence. Perhaps we need to see the whole of early modern science in these terms: that universal measurement in the Renaissance needed more than a conviction that the language of nature was written in the alphabet of geometry. It required an active imposition of Euclidean geometry on nature, and this particular kind of active, subjective interference with nature was paradoxically inseparable from the passive objective recording to which it is frequently described as being opposed. And like the size of the mesh in a fish net which determines the size of fish which can be caught, the geometrical grid of Euclidean geometry determined the scale of reality which could be recorded. Accordingly geometrical figures with straight lines and circles replaced the complex curves of botany and biology in early scientific textbooks. Nor did this change dramatically in the nineteenth century with the non-Euclidean geometries of Lobachewsky, Bolyai and Riemann which projected these simple geometrical forms onto spherical and hyperbolic surfaces. Mandelbrot's fractal geometry was the first to offer new possibilities in recording nature's complexity.

    Hence the distinction between inner subjective and outer objective forms remains valid, as do the quest for quantitative measurement traditionally associated with objectivity and perspectival projection principles which apply equally whether one records a simple square or a fractal form. But more is involved than a passive recording of an object in one scale onto a picture plane in a second scale (fig. 65).

Fig. 65 The recording principles of perspective apply whether the object recorded be a Euclidean square or a fractal form. Yet the scale of the original object affects the shape as well as the size of the object to be recorded.

    An active choice is required to decide the initial scale of the first object for this determines the shape as well as the size of the object to be recorded. In other words, besides actual measurement of an external physical object, objectivity involves a subjective decision about the scale of measurement which provides parameters and tolerances of what is to be measured.

    Simple as these distinctions may seem, they have basic consequences for concepts of knowledge and are very much bound up with western culture. In cultures where there was no distinction between subjective (inner, mental) and objective (outer, physical) images, knowledge was internal, psychological and lay in a person's conception of an image with no need to study further examples and no incentive to communicate this conception. In this extreme case knowledge could stop with a sample of one. Already in Greece, the west embarked on a different course. Plato combined this approach with a belief in ideal images which theoretically required only introspection but in practice assumed the external stimulus of dialogue. His student Aristotle argued that knowledge was something to be collected rather than meditated, appropriated from outside rather than sought inside, an approach inherited by Islam and in turn by the Christian West, where it was reinforced by a belief in Creatural realism, particularly through the Franciscans and Dominicans. The development of perspective brought into focus a distinction between outer images which could be seen, recorded and measured and inner images which could not. Perspective introduced systematic rules for recording external objects. Instruments such as the perspectival window or compass and ruler, and later the proportional compass and pantograph were intended to simplify this process. They also revealed that the process was much more complex in practice than in theory and that the catalogue was potentially much larger than suspected.

    While visionaries such as Francis Bacon made pleas for a catalogue of all possible examples, two decisive factors stood in the way. First, the neo-Platonic heritage fostered deep-seated assumptions about the regularity of knowledge which limited attention to ideal examples. Secondly, as we have noted, the recording process itself used the idealizing filter of Euclidean geometry. This meant that knowledge was limited to an empirical example of regular cases. Nonetheless, the development of ever more precise instruments assumed that the recording and collecting process continued to be cumulative. For instance, the camera revealed many new complexities in the process of recording and greatly expanded the size of the potential catalogue. The computer is doing the same. A recent study at the Bell Laboratories compared vocabularly used in the New York Times over a six month period with that of standard dictionaries and found that over 30% of the words in the newspaper were not in standard dictionaries. International projects of Greek vases, coins, statues or bibliographies such as the present one all point in the same direction: earlier claims were all made on the basis of surprisingly small samples which were frequently kept deliberately small.

    An interesting pattern thus emerges. Societies where no distinction was made between inner and outer tended to be closed, and focussed attention on their own culture, rather than looking futher. Societies with some awareness of inner and outer began to appropriate knowledge from other cultures. As the distinction became more clearly defined, this process of appropriation became more visible. The emergence of perspective in early fifteenth century Florence thus went hand in hand with an unprecedented interest in other cultures through the collection of Hebraic, Arabic, Chaldaian, Babylonian and other sources, leading gradually to the disciplines of anthropology, archaeology, ethnography and comparative religion which have developed in the west as nowhere else, although ideologies such as fascism and other-isms have tried to limit this looking outwards and control ideas even more systematically than in earlier closed societies.

    Perspective, as described by Panofsky and most subsequent authors, was a phenomenon linked specifically with the Renaissance. Its impact, as they described it, was mainly in the domain of painting, the creation of a particualr approach to space. We have shown that it had fundamental consequences for both science, art and literature; that it changed the way western man constructed his environment, and we are suggesting that it transformed the ways in which he acquired knowledge, that the distinctions between inner and outer which it set in motion, led to an increasing externalization and objectivization of the world, which focussed attention away from verbal universals to visual particulars and thereby challenged him to use ever larger samples in making claims concerning knowledge. Meanwhile, the concepts of scale which perspective introduced had long term implications for both the recording and organization of knowledge. For these reasons perspective needs to be seen as more than a cultural expression specific to the Renaissance, and recognized as one of the pivotal concepts of European culture, the implications of which are still being explored. For what began as a looking into, a seeing through, has led from a literal fixing of the horizon to a metaphorical looking beyond one's horizons and a study of other cultures. What began as a symbol for a fixed approach to space has become an emblem of spatial play, of imagination and freedom.

finnigan@idirect.com

Last Update: August 4, 1998