Vasari’s Lives of the Artists (1550) marked a significant change. He looked for the origins of perspective in painting practice of the thirteenth century. In his view, perspective arose as part of a general quest for naturalistic representation in art: "They sought to reproduce what they saw in Nature and no more, and thus they came to consider more closely and understand more fully. This encouraged them to make rules for perspective and get their foreshortening in the exact form of natural relief."

    Vasari noted the contributions of Giotto (1266-1377) with respect to foreshortening, while Giotto’s pupil, Stefano (1301-1350), "drew an edifice in perspective perfectly, in a style then little known, displaying improved form and more science." Vasari cited the work of Domenico Bartoli and Jacopo della Quercia. He claimed that Paolo Uccello’s Annunciation was the first painting to use perspective, rather than Masaccio’s Trinity as is often claimed in the twentieth century. Vasari explicitly suggested links between the use of ground-plans and elevations in architecture and early methods of perspective developed by both Uccello and Brunelleschi. In addition, he noted connections with the measurement of ancient ruins, as well as with marquetry, scenography and implicitly with goldsmithing. A complete survey of Vasari’s comments on the early history of perspective is found in Appendix 5.

    In the latter half of the fifteenth century, the origins of perspective became increasingly linked with mathematics. Piero della Francesca, in his Perspective of Painting, cited Euclid’s Elements and in his other two treatises, On the Five Regular Solids and Book of the Abacus, focussed on the construction of the regular solids, thus linking one of the major themes of the western mathematical tradition with perspective. His townsman (from Sansepolcro) and colleague, Luca Pacioli, developed this trend publishing the first treatise on perspective in his Summa of Arithmetic, Geometry, Proportion and Proportionality (1494) and by linking perspective explicitly with mathematical proportion in his Divine Proportion (1509). Dürer’s treatment of perspective in his Instruction in Measurement (1525) also took for granted this mathematical context.

    In the second half of the sixteenth century, a small circle of scholars at Urbino explored the mathematical principles of perspective in greater detail. For instance, Commandino (1559), linked perspective with Euclidean geometry and related it directly to Ptolemy’s work on the planisphere in the context of astronomy. His student, Guidobaldo del Monte (1600) pursued this approach. In the Netherlands, Stevin (1604), reported how the Prince of Orange was dissatisfied by the haphazard ways in which painters arrived at their foreshortenings and wished instead "to design exactly the perspective of any given figure, with knowledge of the causes and its mathematical proof." Paris and later London became the centres for this mathematical approach.

    Meanwhile, authors of perspective treatises were becoming interested in the question. Although, Serlio (c.1540) specifically stated that he chose not to discuss the origins of perspective since Euclid had done so, he emphasized the reciprocal importance of perspective for architecture since: "no perspective workman can make any work without architecture, nor architecture without perspective." Serlio also claimed that perspective was synonmous with what Vitruvius called scenography, "that is the upright part and sides of any building or of any superficies or bodies". Barbaro (1568) began his introduction noting that scenography was an important part of perspective; that Agatharchus had produced a tragic scene and written a first commentary on the topic; that perspective had been important among Roman scene painters and had become so again in the early Renaissance.

    A combination of these artistic and mathematical traditions was carried out by Danti (1583) in his commentary on Vignola. Like Barbaro, Danti also referred to the ancient tradition of scene painting as a source of perspective, but added a more compelling incentive for its origins: "if the marvellous operations of nature and art drew men so much to admiration that they began to philosophize and investigate the causes thereof, they rightly exerted themselves greatly in searching the reasons for the effects which happen at the eye through the variety of the visual rays."

    Hence, claimed Danti, artificers had sought to find rules and instruments with which they could imitate visual effects and appearances and he was concerned: "with the most scientific who are not content in simply knowing how to operate well and knowing that a thing is thus, but in addition to know its causes. Hence I have endeavoured to demonstrate all the principal parts of this geometrically." Danti aimed at reaching a larger group of readers than his contemporaries at Urbino but nonetheless cited various ancient sources: Aristotle, Euclid’s Optics as well as his Elements (in the editions by Peletarius and Clavius), Apollonius’ Conics, Archimedes, and Ptolemy’s Almagest. As a geographer, Danti drew on Ptolemy’s Geography. In optics his chief medieaval source was Witelo’s treatise. Danti also referred to most Renaissance authors on perspective from Alberti through to Stevin.

    In a footnote to this passage, Cassirer was content to cite Panofsky as evidence that perspective in the plastic arts was another manifestation of this phenomenon. For philosophers in the neo-Kantian tradition it was the origins of different kinds of space that was of central interest. In their view perspective was merely one of the practical consequences of this theoretical breakthrough.

    Meanwhile there had been developments on the philosophical front. Although Kant did not specifically discuss perspective he had emphasized space and time as a priori concepts. Hegel, Herder and Alexander von Humboldt pursued these ideas. Building on this tradition neo-Kantians in the late nineteenth century (e.g. Cohen 1889, 1912) claimed that there were direct connections between artistic work (künstlerische Arbeit) and scientific logic (wissenschaftliche Logik) and therefore viewed artists as researchers (Künstler als Forscher), as individuals who prepared the way for science. Cohen specifically cited the case of perspective: artists intuitively understood and drew spatial concepts before they were formalized. As we have just mentioned mathematicians held a similar view. Hence art now became a prefiguration of developments in both mathematics and science.

    The art historian, Panofsky (1914), took up these themes when he began his studies of Dürer. Renaissance art theory, he claimed, involved two major problems: accuracy (Richtigkeit) and beauty. Accuracy entailed a "geometrical-perspectival and empirical-scientific knowledge". He considered the problem of accuracy in greater detail in Dürers Theory of Art (1915). Accuracy, he explained, required representing objects "as they are", which varied according to the medium. In sculpture it entailed congruence of measured size. In painting it meant representing something equivalent to what is seen and this was precisely the problem of linear perspective. At this stage in his career Panofsky believed that one’s theory of representation depended on one’s theory of vision, and hence he searched for the origins of perspective in Euclid’s Optics.

    When Panofsky entered the Warburg circle in Hamburg (1924) he also came into the neo-Kantian sphere of Ernst Cassirer. According to this view there were two fundamentally different approaches to science: one emphasizing substance (and definition) which dominated Antiquity; a second emphasizing function (and relation) which evolved during the Renaissance. In Antiquity the focus on substance was linked with concepts of sensuous space: i.e. unhomogeneous and anisotropic (see below p. 63*). In the Renaissance the concern with function entailed mathematical space: i.e. homogeneous and isotropic. Other historians of science (Cohn,1896; Duhem,1909; Olschki,1924) referred to developments from Antiquity to the Renaissance in terms of a shift from a finite to an infinite world view. Art historians such as Riegl had postulated a parallel shift from depiction of isolated objects in Antiquity to objects in relation during the Renaissance. Panofsky produced a synthesis of these views. Hence he claimed that the Ancients had a finite world view which implied a notion of aggregate space (finite, unhomogeneous and anisotropic). By contrast, the Renaissance transformed this into an infinite world view with a concept of system space (infinite, homogeneous and isotropic). Corresponding to these were different methods of representation. Aggregate space led to a method of (visual-) angle perspective (Winkelperspektive). System space led to linear perspective. Now Panofsky claimed that one’s philosophical world view determined one’s concept of space, theory of vision and method of representation.

    There were problems with this seductive explanation. For instance, Panofsky claimed that in Antiquity a type of curvilinear perspective which he termed angle perspective produced fish-bone perspective. Veltman (1986) demonstrated that this was not so; that Panofsky had misunderstood the projection system he was using. Moreover, if ancient concepts of a finite world were responsible for Euclid’s Optics and angle perspective, then Euclid’s Optics could not be the source of linear perspective as Panofsky had claimed earlier. Panofsky was aware that Renaissance authors of perspective treatises cited Euclid’s Optics; assumed that Euclid’s fundamental premises must have been revised and cited the 1557 edition by Pena as evidence thereof. Panofsky did not explain why the concept of infinity which arose in the thirteenth century, produced a change in the theory of representation by the 1420’s yet supposedly only changed the theory of vision in 1557. If changes in the abstract world of ideas governed innovations in vision and representation why was it that empirical examples of perspectival practice were in evidence a century before the advent of perspectival theory?

    There were other difficulties. Panofsky implied that one world view caused one corresponding theory of vision and one theory of representation. The artistic evidence suggests that there were at least four methods of representation in Antiquity which supposedly emerged from their one world view and one theory of vision: 1) optical adjustments methods which represented things higher up as larger in order that they would appear the same size; 2) so-called fish-bone or axial perspective; 3) inverted perspective and 4) those Pompeian examples which approximate effects of and some have associated with linear perspective. In the case of the Renaissance this proliferation of methods was even more dramatic. For, rather than being replaced, the methods used in Antiquity were continued and in addition there emerged new methods of linear, cylindrical, spherical, conical and pyramidal perspective. The proponents of linear perspective so often projected images onto curved vaults and ceilings that it even becomes difficult to claim that linear perspective was the dominant mode during this period.

    Subsequent champions of Panofsky’s ideas did not remove these difficulties. For example, White (1949-1951, 1957) claimed that he accepted Panofsky, yet insisted that Pompeii showed evidence of linear perspective. If a given world view governs a particular method of representation then why should both a finite world view in Antiquity and an infinite world view in the Renaissance have produced linear perspective? White also claimed that the implications of Euclid’s Optics of Antiquity were the basis for Leonardo’s "synthetic perspective" during the Renaissance. Yet since this synthetic perspective was closely related to Panofsky’s angle perspective, why should a method associated with a finite world view in Antiquity have been developed in the context of an infinite world view during the Renaissance?

    There were further problems with this approach to the origins of perspective. Panofsky relied on Cassirer’s framework which assumed a basic dichotomy between finite and infinite and provided an elegant contrast between Antiquity and Renaissance. The dichotomy was questionable to begin with, for it could be argued that notions of vision and representation in Antiquity were too nebulous to identify a single theory, whereas in the Renaissance there were clearly alternative methods of representation, namely linear, cylindrical and spherical perspective and anamorphosis, such that one could not claim that one world view evoked one theory of vision and representation. Was one to assume, moreover, that there had been no developments since the fifteenth century? If this still seemed feasible in the 1920’s, it was no longer possible in the 1990’s with advanced quantum physics, fractals and catastrophe theory.

    Panofsky’s attempt to find the origins of perspective in philosophy and metaphysics may excite more general attention than precise reflection, but it has helped more than any other text to make questions of origins of perspective important in the twentieth century. The answers offered have ranged from incidental remarks to complex theses. Since many are repetitive it will suffice to mention only some of the key examples. Kallab (1900) argued that Christian symbols as they developed in the later mediaeval period required perspective to a certain amount. This idea was taken up by Kern (1912) who searched for the origins of perspective prior to Brunelleschi in the painting practice of Lorenzetti and suggested links with Ptolemy’s Geography. Later Kern (1938) also suggested that the origins of perspective lay in mathematics and optics, both classical (Euclid) and mediaeval (Witelo). Malle (1960) suggested literary, philosophical and mathematical roots.

    Argan (193), in an influential article, explored the idea that perspective had its origins in a new concept of space in architecture with Brunelleschi. Francastel (1951) used this as a starting point for one of the most eloquent interpretations of Renaissance perspective. He claimed that Brunelleschi introduced a "new aesthetic conception of space....space ceased to be the cube of air that a vault covers; it possesses an homogenous quality and is found everywhere. it is at once container and contained; it envelops and is enveloped." Francastel insisted that Renaissance perspective had enormous consequences after noting that it was a:

fundamental discovery, which concerns the particular qualities of light - an invisible substance, but susceptible to let itself be measured and manipulated by the artist, inspired not only the idea of a new architectonic functionalism but also a new system of pictorial space to be elaborated. Brunelleschi is the man who substituted the plastic evidenc eof the Middle Ages founded in stereotomy, the size and assemblege of blocks and the manipulation of enclosed light, the necessity of another compartmentalization of space, in a system which reproduces a sort of imaginary model but which allows all the regions of space to communicate amongst themselves....

It is not only a new architecture and a new [style of] painting that resulted, but a new society and almost, materially speaking, a new world. The integration of concrete and subtle parts of the physical universe, the faith in the magic of number, prepared the discovery of America, and the new jurisprudence founded on the equilibrium of the States.

    Exactly how all this followed was not explained. Instead, Francastel offered his own provocative survey of the history of perspective from the fourteenth to the twentieth centuries (see below p. 52*). In his concluding section he cited the ideas of Levi-Strauss and insisted that "Scientifically there is no doubt that the art of an epoque is greater than the literary expression of a society: it is founded on the most profound mental and physiological structures of man. It is not asuperstructure, but a language". Francastel developed this analogy of language and art in his Figure and place. (1967) and suggested that seeing was deciphering.

    Boskovits (1962), claimed that the origins of perspective lay neither in vision nor in geometry, but rather in the auxiliary sciences of mediaeval architecture, in workshop traditions; in problems concerning the correct representation of architectural proportions; that perspective involved the geometrical representation of proportions which link one object with another. Hence Ghiberti had insisted that measures were inherent in nature and hence symmetry, proportion, proportionality and commensuration were all linked with the early development of perspective in the Renaissance.

    Garin (1954), turned to the scientific and cultural atmosphere in his search for origins and argued that Leonardo’s interests in optics were more important than his interests in geometry. In the next decade it became the fashion to see optics as a key to the origins of perspective. Parronchi (1964), focussed attention on mediaeval authors, notably Alhazen, Witelo, Bacon, Peckham and Blasius of Parma. Edgerton (1967), also claimed that mediaeval optics was the main source for Renaissance perspective. Dalai (1968), cited both Sanpaolesi’s attention to physiological optics and Parronchi’s twin focus on mediaeval optics and mathematics (e.g. Leonardo Pisano). Dalai also suggested that there were two lines of development: one which had come via Brunelleschi, was based on concerns with reflection and which, though it involved architectural practice and Ptolemaic geography, was concerned primarily with laws of mirrors. A second line of development, based largely on mediaeval sources advanced via Ghiberti and Uccello. Battisti (1971), stressed that Florence was not the only centre to be considered; the Flemish school of Van Eyck had played an important early role, as had other Italian cities including Milan, Padua and Rome. Edgerton (1978), offered an important summary of alternative explanations for origins, suggesting that there were no less than four traditions to be considered: optics, geometry, geography and metaphysical theology. Veltman (1980) noted that in terms of perspective, Ptolemy’s work in astronomy, namely his treatise on the Planisphere, was probably more important than his work on geography, an idea which has been pursued by Aiken (1986) and Sinisgalli (1993).

    Fernande Saint-Martin, in The Topological Foundations of Painting (1980), devoted a chapter to Euclidean space. She claimed that perspective was very much an occidental phenomenon which had (119): "established an essential break in human sensibility such as it was expressed in the pre-history of nearly all other cultures". She acknowledged that many saw it as the ultimate product of sensibility and rationality and that it was an attempt to deal with problems of depth, of foreground and background. She cited the ideas of Gleizes and Metzinger that the space of painters would preferably be Riemannian rather than Euclidean and called for a wider definition of the term (124): "By the term perspective, rather, one should understand every global system which defines the modes of interrelations among the collections of elements, in accordance with certain a-priori co-ordinates." The term Euclidean perspective, claimed Saint Martin, was misleading because it was not based directly on Euclid. Rather, perspective as it developed in the Renaissance, had only been possible as (127): "a result of a sort of transubstantiation of the sensible intuitions subjected to the elements furnished by Euclid, stripping them of their finite and concrete character to permit them to integrate themselves in much more abstract systems of interrelations."

    Saint-Martin cited Doesschate (1964) to note that there was no clear evidence that Alberti or Piero were familiar with Euclid's geometry and followed Edgerton's (1975) claim that it was spatial co-ordinates of Ptolemy's cartography that provided (128) " the fundamental elements in the spatial infra-structure of the Renaissance". The resulting space corresponded neither to the experience of the senses nor to the findings of science concerning the nature of reality. Hence (129) "homogeneous space is never a given; it is a space engendered by a construction". According to Saint-Martin (132), it was Alberti who introduced the vanishing point although, she claimed, it was not until Leonardo that a majority of fifteenth century artists began adopting perspective. In contrast to some historians who have seen the rise of perspective mainly in positive terms, Saint-Martin was convinced that perspective imposed new limitations on western culture (134):

Euclidean perspective imposes a particular hierarchy of emotive experience where the projection of the me in the foreground, the mass, the vivid colouring is at once negated by its insertion into an abstract system where the distant imposes itself as the limit, the end, the point where the co-ordinates of particular experiences join. This forced equilibration always remains an artificial model of the experience of the me and the non-me, because it tends to deny the expressive validity of the near which will inevitably only constitute a stage in a passage towards the far. It also denies the distant itself, by the impossiblity of affirming it by pictorial means themselves, which shrink it to render it nearly imperceptible, which hide it in zones of shade or confused atmospheric pockets, or alternatively bathe it in a diffuse luminosity. Inside this fixed schema, with irremovable boundaries our civilization would like to confine the representations that a person can give of their experience -of me -in the world. It is certain that the survival of artistic activity is linked since the last century with a continuous battle more or less overt but definitive nonetheless, not just against the primacy of the figurative image but in a more essential way in favour of a resourcing, a peremptory reaffirmation of pre-Euclidean spatial experiences at the level of primary forms and topological relations.

    Johannsen and Marcussen (1981), in an important article, explored the role of several disciplines in explaining the origins of perspective: optics, measuring (including surveying) and statics, geography and astronomy as well as the cultural background of early fifteenth century Florence. Five conditions necessary for the construction of perspective were identified: 1) use of a visual pyramid as a geometrical model of the visual process; 2) a plane corresponding to the picture plane; 3) proportionality between the size of an object and its dimensions on the picture plane; 4) a graphic representation; 5) projection methods. Veltman (1986) focussed on the third of these problems, the question of plane thinking, and suggested at least five traditions which helped in this development: geometry, astronomy, architecture, surveying and optics and has since claimed (1992) that all of the above mentioned traditions played some role. Meanwhile Andrews (1988) and Veltman (1992) have emphasized the importance of narrative for the development of pictorial perspective.

    Simon (French, 1988; German, 1991), in a book that focussed on the optical theories of Euclid and Ptolemy, examined the possible consequences thereof for representation. Following the view of Panofsky, Simon (1991, 79) suggested that the fourth postulate of Euclid’s Optics entailed curvilinear rather than linear perspective. Consequently, he claimed, Renaissance theoreticians were torn between two conceptions of perspective, an artificial (künstlichen), plane one for painterly representation and a natural, angle based one for optics. He went on to suggest that (79-80): "the still limited character of their trigonometry" might help account for "the lack of rigour in the perspectival drawing of the Ancients." According to Simon (84): "The analysis of visual perception was doubtless not yet sufficiently advanced in order to be able to distinguish clearly between the description of natural vision and the experiences of perspectival representation."

    Salvemini (1990) offered new criticisms of Panofsky, claiming (60) that his method was a transposition of ideas of pure visibility of the late nineteenth and early twentieth centuries to the past, that was not supported by historical evidence. His method of iconographical analysis was wrong because it (62): "constantly reduces to a schema all that which is not demonstrable extensively through the lack of concrete sources." Salvemini claimed that the inverse size/distance rule was known to Levi ben Gerson,and used this as a starting point for another attack on Panofsky's method (73):

Propositions are demonstrative, they assume the form of a question (quaestio), which is the literary form of the mathematical theorem in which the concepts are not logistic as in contemporary theories of physics....This measure of distance will therefore be neither fixed, nor arbitrary, nor casual nor objective, nor subjective but rather an independent variable.To recognize this general rule in itself does not mathematicize empirical space any more than the perpendicularity of the optical axis geometricizes the visual image.

    Elsewhere Salvemini lamented (97) "the material impossibility of establishing a typological model for perspective studies."

    Kemp (1990), offered three principal reasons for the origins of perspective: a) that the systematic recording of visual phenomena should be seen as a worthwhile goal; b) that the invention should be attainable in terms of the necessary levels of understanding and skill and c) historical factors ranging from the most general aspects of what may be called the world view to the specific circumstances (intellectual and social) of the individual or individuals involved. Kemp noted his intuition (335):

to emphasise the striving for ‘domestic’ naturalism in religious art in response to new kinds of devotion as a necessary background condition for the notion that an illusion of how things appear was desireable. A key stimulus in determining that a precisely proportional system was used, rather than the highly effective but essentially non-mathematical method of Jan van Eyck in the Netherlands, was the annexing of classical aesthetic values, particularly the proportional system of architectural design and town planning. By contrast, mediaeval surveying and optics can be seen to provide available resources, but these resources only became relevant to the painter within a framework of new assumptions about the functions of what we call art.

    Edgerton (1991), returned to these questions of the origins of perspective in The heritage of Giotto’s geometry. Edgerton drew attention to a series of unpublished lectures by F. Cranz (1984) in which he had characterized the re-orientation of the twelfth century as a shift from conjunctive to disjunctive thought: i.e. from an assumption that one was a part of everything that one considered to an awareness that what one sees in one’s mind differs from things in the external world. According to Cranz, Anselm and Abelard had played an important role in leading philosophers to understand themselves (40): "as detached from nature, as outside observers limited by the inadequacy of their mental formae and describing phenomena only metaphorically". Edgerton suggested that the recovery of ancient texts of geometry would have (41) "complemented this increasing twelfth century predilection for disjoining the forms in the mind from the forms in the external world". Edgerton focussed on the importance of Bacon’s views citing in particular a passage from his Optics that stressed the importance of visualization using figures (88):

For without doubt the whole truth of things in the world lies in the literal sense, and especially of things relating to geometry, because we can understand nothing fully unless it is presented before our eyes in figures, and therefore in the scripture of God the whole knowledge of things to be made more certain by geometric figuring is contained and far better than mere philosophy could understand it.

    In his book Edgerton outlined the geometrization of pictorial space, supernatural space, terrestial space, heavenly and astronomical space, emphasizing the importance of sixteenth century printed books in the spread of these principles. With respect to the actual origins Edgerton claimed that there were two serious interpretations, one claiming (89):

that Brunelleschi’s two lost pictures were but the latest examples in the gradual evolution of Western art toward realism, incremented by some sort of application of traditional architectural or surveyor’s projection....The second opinion - more revolutionary in the sense of a classical revival- holds that Brunelleschi was inspired less by architectural and surveying technique than by the ancient science of optics....Brunelleschi seems to have exploited an optical theory never applied to painting before, that the implied eye level of the artist/observer must determine the centric point on the picture surface and therefore the horizon within its fictive depth.

    Edgerton did not discuss the possibility that Renaissance optics had in fact integrated essential aspects of the surveying tradition (cf. Sources, p. 142-154*). He returned to his earlier (1975) claims that a third method of cartographical projection attributed to Ptolemy had also played an important role in what he claimed to be the re-discovery of perspective. Notwithstanding, these points on which we disagree, Edgerton’s book is an important attack on fashions in critical theory and methodology that reduced perspective and chiaroscuro as (4):

artificial systems within a linguistic-like sign system expressing the peculiar values of western civilization. Radical supporters of this latest relativism ("multiculturalists" as they like to call themselves) argue that during the Renaissance, upper-class patrons championed linear perspective because it affirmed their exclusive politicial power. Single viewpoint perspective after all, encourages the "male gaze", thus voyeurism and the denigration of women, police-state surveillance and imperialist "marginalizing of the other".

    Piaget had identified five stages in the development of a child (see below fig. 57 and p. 139*). Gablik was able to reduce these to three essential stages. First, there was a pre-operational stage (eighteen months to four years in the child), involving topological relations of space, an enactive mode of painting, and corresponding to ancient and mediaeval art in terms of cultural development. Second, there was a concrete-operational stage (six to fourteen years in the child), involving projective and Euclidean relations of space, and an iconic mode of painting, corresponding to the Renaissance in terms of cultural development. In this model, linear perspective was characterized by the static viewpoint of a single observer and separation of observer and the world. Third and finally, there was a formal-operational stage (above fourteen years in a child) involving indeterminate, atmospheric space, a symbolic mode of painting, and corresponding to modern art in terms of cultural development. In Gablik’s view (12,31):

These stages in the development of art correspond to learning processes and to transformations in concepts of self and society (fundamental transformations, that is from one picture of the world to another)....I wish to assert that it is the transformational element in thinking that is actually the source of art’s development. It has led pictorial imagery on the one hand toward greater mobility; on the other, it has brought about a complete independence from figurative or representational elements.

    Gablik served as a point of departure for a more serious treatment of these problems by Blatt and Blatt (1984). According to their view the tradition of Kant and neo-Kantians such as Cassirer had led to structuralism which attempts to (39): "define principles and cognitive structures that underly all human intellectual endeavors....This search for the underlying, unverbalized (unconscious) order in cognitive endeavors is a quest for the identification of the basic constructs through which individuals understand and organize their universe". The Blatts cited evidence from a whole range of disciplines, to claim that such cognitive schemata had been used to understand neurological processes, memory, perception, information processing, linguistics, social order, structural anthropology, psychoanalysis and the development of children. They related this quest for structure to the search in art history for a (39) "vocabulary of form", "a matrix or scale of structured relationships" and a larger quest to discover (40) "basic relationships of form and their processes of transformation", which they termed mental constructions, "cognitive schemata, patterns or gestalts". They claimed that these conceptual explanations had replaced traditional perceptual explanations.

    Gablik had specifically challenged the perceptual views of Arnheim and the Gestalt school. By contrast, the Blatts accepted the Gestalt school as yet another example of a quest for structure which had been making serious strides since the time of Kant. Historically, Kant himself had been very much concerned with the ways in which knowledge acquired through our senses affected our ideas. The Blatts did not mention this. Historically, there had been notable differences in the approaches of Kant and Hegel in this regard. Hegel was not mentioned in the Blatts’ account. Historically, there had been major differences in approaches to knowledge which psychologists have classed as a struggle between nativism and empiricism (see below pp. 60-61* and fig. 10). The Blatts’ account gave the impression that nativism was the only valid school.

Fig. 1. Parallels between concepts of space, object, and scale, periods in art history and cosmological world view from the time of the Greeks to Impressionism according to Blatt and Blatt (1984).

    In terms of art history, the Blatts used Piaget as a starting point. Piaget’s sensorimotor and pre-operational levels were used to cover paleolithic and Egyptian art. Piaget’s intuitive level was renamed an intuitive (perceptual) level, linked with projective-Euclidean concepts of space and used to explain the time span from Greco-Roman art through to the early Renaissance. Piaget’s concrete operational level was linked with further developments in projective-Euclidean concepts of space, with the period from the late Renaissance to Impressionism, with the Copernican and Newtonian world views and with Stevens’ concept of interval scale. Various steps of each stage were carefully identified (e.g. fig. 1).

    Such schemata which appear to explain the key developments of man’s intellectual and cultural development since the beginning of time in four pages of charts are very seductive. Unfortunately they explain less than they seem. If art from the Greco-Roman period, the Middle Ages and the Early Renaissance belong to the same stage of development how does one account for the rather remarkable differences in style between these periods? Are nearly one thousand years of mediaeval art simply to be explained away as equivalent to a slight regression or progression in the growth of a child? If we accept parallels between cultural growth and child development as true, we are accepting that the greatest achievements of Antiquity correspond to the activities of children between the ages of six and nine and similarly that the heights reached by Leonardo, Raphael and Michelangelo in Renaissance art correspond to the development of persons under the age of twelve. Indeed this view reduces the whole of human culture rather dramatically to various stages of puerile (or puellile) activity.

    There are further problems. Piaget’s claims were based on experiments with Swiss children in the 1940’s, and as subsequent critics have pointed out, these were mainly male children. An obvious question arises: would the spatial abilities of Swiss girls at the time have been the same? More fundamental for our purposes is to ask why this particular sample in a particular place and time should be a model for the whole of history? A child living in Egypt in the eighteenth century B.C. before the discovery of perspective would obviously have reached neither projective-Euclidean concepts of space nor a concrete operational level of objects by the age of eleven nor at any point in their lives. Nor would Renaissance children have mastered Riemannian space at the age of twelve or during their lifetimes.

    While some scholars have gone to considerable pains to distinguish clearly between the rules of grammar applicable to verbal language and other rules in visual language (cf. Saint-Martin, Sonesson), there has been a trend in Russian authors to conflate analogies between language and painting (e.g. Uspensky, see below pp. 51-52*). Damisch followed this Russian structuralist tradition, drawing on analogies of Jakobson (386) "between the role of grammar in poetry and the rules of composition founded in the art of painting on a geometrical order either latent or manifest." Damisch discussed painting in terms of reading, not just a process of describing in the sense of Alpers, but rather as something demonstrative which creates a system. Like the neo-Kantians, he suggested that this system did not derive from geometry but rather prefigured its later developments. Like Husserl, he was interested in the metaphysical or at least the meta-logical implications of these spatial developments. Like the structuralists he continually referred to grammar, but ultimately assumed a combination of geometry and language (406):

In the historical context where we are placed, artificial perspective furnished painting with a formal apparatus such as that of enunciation can be, with which it presents numerous common traits. To begin with the distribution which it organizes of points of view, vanishing points and distance points, and (the corollary thereof), that of the here, the there and the over-there, which allows one to speak, not yet in a metaphorical sense, of a geometry of enunciation which would have its analogue in the figurative register....The enunciation cannot be assigned simply to the network of pronouns and indices of position in time and space. The formal apparatus which puts in place the perspectival paradigm is the equivalent to that of enunciation to the extent that it confers a sense to its direction at the same time that it opens the possibility of something like an enunciation in painting. As Wittgenstein writes, the word is nothing other than a point, the proposition is a vector endowed with a sense, that is too say with a direction.

    In itself this phrase is not particularly dramatic, but it is symptomatic of a branch of Marxist rhetoric which uses a scientific phenomenon as its starting point, interprets it metaphorically, usually socially, such that it completely loses its scientific truth, yet by association with the scientific principle from which it departed takes on an air that is more serious than it deserves. In the hands of enthusiastic commentators this particular sentence has become seen as serious evidence for undermining a one-to-one correspondence between original objects and their images, and has come to play a role in a trend towards anti-ocularism (cf. below p. 215*). A physical phenomenon treated metaphorically has become a starting point for claims about social realities. Debord (1967) extended this approach from a particular image to the concept of spectacle, now denying the physical to emphasize the social: "The spectacle ‘is not a collection of images but a social relation among people, mediated by images. It is the material objectification of alienated socioeconomic relations, the "true reflection of the production of things and the false objectification of the producers.’

    Abels (1982), drawing on ideas of Marx and Holzkamp (1976), considered a developmental approach in which perception and representation became functions of class levels and other societal structures. Goldstein (1988) presented a thorough Marxist analysis which offered the most daring explanation thus far for the origins of perspective. Goldstein began with a critique of Panofsky, Cassirer and Edgerton before arguing (25):

that the relationship between linear perspective and the new cosmology of the renaissance is one of parallelity since both are different representations of an emerging social structure, namely, modern capitalism. Further, the various cultural activities, such as music, drama, prosody and the like are representations of the new production relations; they are parallel precisely because they are representations of one and the same social base.

    Goldstein was concerned with three aspects of linear perspective: first, that space is quantifiable and homogeneous. In his view this was a result of divided labour production because it transformed traditional artisan labor (63):

into unskilled, undifferentiated, homogenized labor. When labor becomes homogenized in fact, it becomes homogenized in concept: it becomes labor as such. The cost of such labor can now be calculated and expressed in terms of expenditure of energy and duration of time....Labor thus becomes quantified....The attitude of calculation spreads as an indispensable part of the new mode of production to all areas of culture, science included.

    This was restated more forcefully when he claimed that the source of quantification lay (73): "in the experience of divided-labor production whereby unskilled labor can and indeed must be regarded as labor as such, homogenized and then divided into time units which can then be multiplied by the rate of reproduction of the worker which is set at subsistence level, which is itself a mathematical calculation".

    One problem with this explanation as he himself admitted (73) "is that it places divided-labor production earlier than any empirical evidence would appear to justify". This question of periodization became the more acute when he turned to what are supposedly corresponding developments in other branches of culture, notably (109) polyphony in music (c.900-1050) and in prosody (110) "the development from alliterative form to accentual-syllabic in the period between the ninth and the thirteenth centuries." If there is a unity of cultural expressions as he claimed then why did perspective not emerge in Carolingian times rather than the Renaissance? And what evidence is there of divided-labor production at the time of Charlemagne? None.

    There were further problems. Goldstein assumed that this new phase entailed a loss of artisinal skills and the rise of unskilled labor. Why then was it precisely in the Renaissance that there was a dramatic development of books on specific trades of which the Book of Trades (Ständebuch) of Jost Amman was the most famous? Or why should Vasari, who was the first to document the rise of perspective, take such pains to emphasize the particular professions and trades of those responsible, be they painters, sculptors, architects, or goldmiths? Indeed was there not serious evidence that the Renaissance saw a new self-consciousness in this tradition of skilled artisans and was it not they, rather than their anonymous unskilled counterparts, who were responsible for the great achievements of pictorial and architectonic space? How else are we to explain that so many Renaissance masterpieces were produced by well known, well trained artisans? What happened to the supposedly revolutionary achievements of the anonymous unskilled?

    The second aspect which interested Goldstein was that physical space is continuous, isotropic, material, three-dimensional and infinite. Here he drew on Marx’s concepts of alienation (Entäusserung) and estrangement (Entfremdung) to claim that (35-36):

the objectification of nature takes place not because labor is alienated in the product, but because under conditions of private property the product is estranged from the producer: the product becomes a commodity....Under conditions of estrangement as it occurs in commodity production, the human being regards nature as an object, distanced and opposed to him, so that space is conceived not as a closed system of which nature is a part, such as we find it in organic conceptions of nature, but as a void within which objects move and which extends in all directions without end. It is a three dimensional infinite world; it is at the same time a mechanistic world.

    In developing these ideas Goldstein also drew on the views of Ruben (74):

The concept of infinity develops as part of a process in which the organic community dissolves and the emphasis is placed on the individual. What is lost in this process is the well defined place of the individual in feudal society as against the indefinite place of the active property owner. It is the transition from immovable property in land to the moveable property (i.e. money itself, tools, commodities, etc.) that generates the new conceptions of time and space. With respect to space, since the individual as property owner has greater potential for movement, his sense of his own movement changes. He conceptualizes his activity as the free movement of a body in absolute space (and time).

    Goldstein reformulated this idea in his own terms (147):

Divided labor is labor coordinated around a machine, so that interdependence in the production of goods is visualized as spatiality. The living experience of co-ordinated undifferentiated labor centered around a machine is visualized as geometrized space in the form of a three-dimensional drawing or a new cosmology, geometrized physical space within which bodies move subject to constant universal natural forces, so that their motions and relationships can be expressed mathematically in equations. In perspective drawing objects diminish in size in proportion to their distance from the viewer: the view is that of a quantifying, geometrizing, mechanizing mentality which is specific to capitalism.

    Here again there were problems. Goldstein claimed that the separation or estrangement of worker from the products of his work caused the distance necessary for a new concept of space. Yet the painters who produced the early works of perspective were precisely those who were not estranged from their work. Artists such as Brunelleschi, Ghiberti and Uccello received commissions and were rewarded for their efforts. Ruben’s assumption that community needed to dissolve for individuals to emerge, was equally misleading. Were not many of the key artists in the Renaissance members of guilds and very much members of their local communities? The notion that mobility generated a concept of space is intriguing. It is true that Brunelleschi went from Florence to Rome and that the author of the first printed French book, Jean Pélerin, was called the pilgrim (le Viateur). But why then were the earliest spatial paintings not done by ancient soldiers or mediaeval pilgrims? Money is spoken of as one of the universalizing elements. This is only partly true since each major town in the Renaissance usually had its own currency as well as its own measures. Whence equivalences through money were by no means as universal then as they are today in a world where credit cards offer a standard.

    A third aspect which interested Goldstein was that perspectival pictures depend on vision of a single pair of eyes viewed from a fixed position. Here he claimed that the rise of individualism, particularly the individual entrepreneur of capitalism, was the source of one-point linear perspective. As he put it (83):

The painting rendered in terms of linear perspective is no less an expression of the bourgeois individual. In such a picture the view presented is, as we have seen, that of a particular pair of eyes, in a particular position, and at a particular time, so that nothing is seen but what the viewer can rationally see. It is the high valuation set on the here and the now that finds expression, the practical realism of the bourgeois-rational, ahistorical and hence, static.

    In itself Goldstein’s association of the capitalist’s viewpoint and one-point perspective is attractive, but becomes confusing in the context of his other arguments. For he also claimed that the concept of homogeneous space necessary for perspective was created by the estrangement of unskilled workers. If the victims of capitalism had this new insight why was it not they who produced the consequences rather than their exploiting entrepreneurial capitalist employers? If the employers could get these insights without their employees, why then should one emphasize a move towards unskilled production? Indeed if unskilled production was so important in this context, why then was the development of perspective linked with the rise of artists’ guilds, academies and eventually schools of drawing? Suppose we accept that both sides of Goldstein’s arguments are important, namely, employers and employees. Why then do Brunelleschi’s first two examples reflect neither a capitalist viewpoint nor unskilled workmanship? Moreover, why are most of the early examples of perspective in an ecclesiastical context and linked with sacred narrative rather than reflecting the new modes of production which were presumably the source of their inspiration?

    Notwithstanding the logical and other contradictions in Goldstein’s approach, subsequent commentators such as Jay (1994) have cited his work as if it were authoritative. Jay, whose work is discussed at length below (p. 215*), related these claims (59) to Williams’ (1973) contention that "only the exaggerated capitalist separation of the spaces of production and consumption permitted a radical disjunction between the working the land and merely viewing it from afar as an aesthetically ‘pleasing prospect’, which was the real estate form of perspectival art." The problem with this reasoning is that a separation of landowner and worker was well established in Egyptian times and continued trhoughout the Middle Ages. Witness, for instance, the Duc de Berry and his Very rich hours (Très riches heures), who must have been very conscious of this distinction in the fourteenth century, even before linear perspective in its technical sense had been discovered. Jay went on to surmise that (59): "The placement of objects in a relational visual field, objects with no intrinsic value of their own outside those relations, may be said to have paralleled the fungibility of exchange value under capitalism", without offering any serious evidence by way of proof.

    Ivins served as a starting point for Marshall McLuhan’s more dramatic claims in the Gutenberg Galaxy (1962, 56): "primitive drawing is two dimensional, whereas the drawing and painting of literate man tends towards perspective". McLuhan remained unclear concerning the precise relationship between perspective and printing. On the one hand, he argued that (138): "the sheer increase in the quantity of information movement favoured the visual organization of knowledge and the rise of perspective even before typography". On the other hand, he suggested that typography was actually a prerequisite for perspective (138): "As the literal or the letter became identified with light on rather than light through the text there was also the equivalent stress on point of view on the fixed position of the reader: "from where I am sitting"....This uniformity and repeatability of typography...is the necessary preliminary to unified or pictorial space perspective ".

    These connections became part of a larger set of basic oppositions that guided his work. There was, he claimed, a basic distinction between the tactile and the visual; between acoustic space and visual space; or between the audile/tactile and the visual. Acoustic space was linked with the two dimensional: visual space was linked with the three dimensional. Visual space was linked with the linear, sequential, print oriented space of continuous vistas and perspective. Whereas acoustic space was analogical, visual space was logical. McLuhan related this to changing emphases on parts of the trivium. Acoustic space thus became linked with rhetoric, visual space with dialectic (i.e.logic). By 1976, McLuhan was relating these oppositions to his claims about the right and left hemisphere of the brain. The right side of the brain was acoustic: the left side of the brain was visual. The right side was simultaneous, qualitative and intuitive. The left side was linear, quantitative and logical. These oppositions he subsequently related to his distinction between figure and ground. Figure, he claimed is visual, conceptual and deals with ascribed cause: ground is acoustic, perceptual and deals with perceived effect.

    From these oppositions emerged a particular view of history. McLuhan saw the advent of the phonetic alphabet in Greece as having set the Western mind off on a detour in the direction of the visual and the logical. The rise of printing and perspective had given undue emphasis to this visual, logical bias and were thus negative. Accordingly the left hemisphere became described as the villain. On the other hand, electronic media, which offered a return to the acoustic, intuitive, analogical processes of the right brain emerged as the heroes of his saga of oppositional anatomical sides.

    There were problems with McLuhan's approach. He claimed that electronic media were primarily acoustic. The rise of multi-media computers has expanded the scope of electronic media to include vision as much as sound: witness the enormous rise of Computer Aided Design (CAD) packages, which rely very heavily on both vision and perspective.

    At a more fundamental level, McLuhan assumed that perspective was necessarily connected with literacy. This was misleading. The Chinese were literate, had a knowledge of printing, yet developed no serious interest in perspective until the Jesuits persuaded them to do so in the seventeenth century. Islam, which produced a great literature tends, even today, to be opposed to perspectival representation of space. Nonetheless, it was in the context of literacy that western art made its gradual progress towards mastery of perspectival space. As we have shown (see Sources, pp. 155-169*, cf. below pp. 20-24*), this mastery occurred at the level of painting practice. At an intuitive level this began seriously with Giotto around 1300. Technically, if we accept Brunelleschi's panels (c.1415-1425) as the earliest known and Masaccio's Trinità (c.1425) as the first extant example of linear perspective, it began some 30 years before the advent of printing in the West. Early treatises consolidated this practical knowledge in mathematical terms before the advent of printing. Even during the half century after Gutenberg, printing had effectively no impact on perspectival treatises. McLuhan's assumption that printing and perspective were necessarily linked was, therefore, untenable.

    McLuhan's suggestion of connections between the development of a particular point of view in literature and a specific viewpoint in art was also misleading because it tended to conflate as if they were two, four separate factors: 1) point of view of the narrator in a text; 2) point of view of the reader of the text; 3) viewpoint established by the artist in a painting and; 4) viewpoint of a person observing the painting. Although 1) has become a popular subject of study for historians of literature (cf below pp. 116-128*) and although 2) and 4) presumably fall under the aegis of reception theory, too little work has been done, to permit a clear decision on so large a topic. As for factor 3) our brief analysis has shown that the development of perspective was not simply the fixing of a single viewpoint. Almost from the outset it involved a conscious playing with fixed viewpoints. Giedion (1941), who is said to have been a starting point for McLuhan was, therefore, also misleading in claiming that in perspective (1977, 31): "The whole picture or design is calculated to be valid for one station or observation point only. To the fifteenth century the principle of perspective came as a complete revolution, involving an extreme and violent break with the mediaeval conception of space".

    As we shall show there was no such sudden break: rather, a gradual evolution. The trend towards perspective was well underway in the fourteenth century and continued after Brunelleschi’s demonstration, Alberti’s treatise, and Gutenberg’s press. A generation later Piero della Francesca wrote the first mathematical treatise on perspective. About 1492 Leonardo made the first recorded systematic quantitative experiments concerning perspective. Seventy years passed before Commandino recognized further links between mathematical projections and perspective and another seventy years passed before Desargues expressed these principles in universal mathematical terms.

    McLuhan was not well understood. Eisenstein, in The Printing Press as an Agent of Change (1979,176), saw McLuhan’s claims as an incautious version of Erwin Panofsky’s analogy between the development of perspective in art and the way in which Renaissance thinkers began to look at the past from a fixed distance. Eisenstein challenged the analogy arguing that (186): "the capacity to see the past in this way could not be obtained by new optical effects devised by Renaissance artists. It required a rearrangement of documents and artifacts rather than a rearrangement of pictorial space". According to Panofsky the development of perspective went hand in hand with the rise of modern science. This Eisenstein challenged also (269):"it is an exaggeration to launch modern science with the advent of perspective renderings and to regard pictorial statements as sufficient in themselves. A method of preserving observations as graphics records and a chance to check them against others should not be presumed to lie in an artist’s sketchpad". Aside from these criticisms, passing comments on treatises by Alberti, Piero della Francesca, Dürer, Jamnitzer and a few general references, Eisenstein did not explore connections between perspective and printing.

    Had Eisenstein understood the larger context, she could not have claimed that printing caused so sudden a revolution, or that it offered a key to problems of periodization. She would almost certainly not have insisted that it is "an exaggeration to launch modern science with the advent of perspective". She would probably not have dismissed perspective as a lay innovation. After all most of the major examples were in the context of the church and a surprising number of them linked with a few orders (Franciscans, Dominicans, Augustinians and Carmelites). Eisenstein might well have explored the extent to which perspective offers insights into the vexed questions of continuity between middle ages and renaissance, using a periodization such as that outlined below.

    As will be suggested (see below pp. 42*), this story could readily be expanded to include links between perspective and instruments: Piero’s first mathematical treatise of perspective also contained the first description of a perspectival instrument (1434). Leonardo’s notebooks which first described the inverse size distance law also contained a first illustration of a perspectival instrument (c. 1490). The period 1500-1525 brought the first printed treatises in France and Germany and a first printed illustration of a perspectival window. The period 1525-1600 saw the spread of printed treatises to the Netherlands, England, Spain, Austria and Poland. With respect to instruments it saw early attempts at a universal measuring device. The period 1600-1800 brought treatises at different levels some concerned with high mathematics (e.g., Desargues, Brook Taylor, Lambert); some with high practice (e.g., Accolti, Troili); while others were encyclopaedic (e.g., Leupold, Kästner) or simply popularizing (e.g., Dubreuil). This period also saw the development of the Galileian sector and Bürgi type proportional compass which were successful universal measuring devices. The new confidence and universality this brought to the realms of science, was reflected in the confidence with which perspective was gradually applied to the entire environment and reflected in turn in the new confidence of politicians making absolutist claims for power.

    Meanwhile, other connections between perspective, texts and printing culture were suggested. Sir Ernst Gombrich, in Art and Illusion (1960, 129), emphasized the connection between narrative and the development of perspectival representation (mimesis, illusionism). In Means and Ends (1976, 32) he drew attention to: "the increasing demand for what I have called dramatic evocation, the return to the desire not to be told only what happened according to the Scriptures but how it happened, what events must have looked like to an eyewitness". Gombrich also acknowledged that (35): "the conquest of perspective and of anatomy play their part in this story". By implication there was a direct relationship between the re-interpretation of biblical texts and the development of perspective.

    De Kerckhove (1995, 31), made the extra-ordinary claim that: "By showing the proportionate reduction of size and distance on paper as a decreasing vista from the viewpoint, the draughtsman is putting time into space." Pictures in perspective are not per se linked with time. Often they are of timeless scenes. In the Renaissance, as will be noted presently (p. 26*), perspective introduced unexpected tensions in both temporal and spatial frames.

    He also argued that "People only developed a taste for perspective during times of great pushes of alphabetization, that is, when they first learned to read the alphabet during the Golden Age of Ancient Greece and then again around the time when print was invented by Johannes Gutenberg." According to de Kerckhove perspective (32): "could be one of the best examples of how the alphabet re-framed the mind". This unfortunately raised more questions than it answered. Why, for instance, did writing in Greece at the time of Homer begin a few centuries before pseudo-perspective at the time of Aeschylus? Why did perspective in the Renaissance begin prior to Gutenberg, and in Italy rather than Germany? How are we to explain that the Greeks produced pseudo-perspective, whereas the Renaissance produced perspective? Why did all the other cultures that developed alphabets, not develop perspective?

    Giesecke (1991), in a fundamental study concerning the complexities of fifteenth century printing, explained the origins of perspective in terms of the surveying tradition and the optical interests of mediaeval artists. His work provided the most penetrating study to date of the implications of print culture, arguing that the development of linear perspective provided a new model for describing the world systematically which led to a new concept of truth. Giesecke was particularly concerned with the ways in which the advent of printing introduced new knowledge and a redefinition of what constitutes knowledge. In earlier cultures, (both oral and manuscript), technical knowledge had been exchanged primarily through face-to-face situations. The advent of printing introduced a quest to convey knowledge directly in book form without the intermediary of an expert, master or teacher. This posed problems because the objects to be described were no longer present as in a face-to-face situation and thus required the development of a new type of artificial sight (künstliches Sehen) that became basic to scientific description.

    The early texts in the field of technical literature (Fachprosa) had a new emphasis on true (wahren) and correct (rechten) description. This, claimed Giesecke, was no co-incidence. Printing introduced a new distinction betwen inner and outer vision, focussed attention on objects seen by the outer eye, (dismissing everything else as invisible), and systematized new methods that came through the discovery of linear perspective. Others had made general claims about the links between printing and perspective usually with respect to the appearance of perspectival illustrations in printed books (McLuhan, Edgerton). Giesecke was concerned, rather, with the way in which perspective made persons aware that they were viewing an object from a given point of view and that complex objects needed to be viewed and represented from a series of viewpoints to be seen accurately. This led to the creation of multi-dimensional models which were then linked with geometry through Dürer's publications and in turn inspired a new type of verbalisation based on pictures which correlated a series of views. Hence perspective did much more than add a sense of space to illustrations: it introduced a systematic methodology for describing verbally the visual world which Renaissance scientists identified as true description because of its reversibility. While Leonardo da Vinci was the first to articulate this methodology, Giesecke claims that it required the standardizing effects of printing to become established. In this way printing introduced a theory of knowledge (Erkenntnistheorie) that has dominated the West since the Renaissance. Giesecke explored the consequences of these developments for a shift in emphasis within the trivium away from logic and rhetoric in favour of dialectic (630-635). In the final part of section six, Giesecke explored how this inspired trends towards accumulation of information; new emphasis on comparison and contrast; new knowledge and even a realistic extension of fiction.

    Giesecke traced how these developments led to a redefinition of knowledge (Wissenschaft). In the mediaeval tradition knowledge of nature was very much linked with physical ability (cf. the Greek techne which as Panofsky pointed out explains the close connection in German between Kunst and können). This tradition, which led to artist-engineers, assumed that knowledge involved sensori-motor and muscular skill and dexterity, whence the mediaeval emphasis on experts, experience (Erfahrnis), practical wisdom (Weisheit), and a tendency towards secrecy (Geheimnis, Arcanum). By contrast, the new approach defined knowledge as: 1) won through regulated (normierte) processes of visual perception and description or representation by an external observer; 2) stored in print form and 3) spread through a free market, which secured a commitment to dissemination or even revelation (Offenbarung) as they termed it. This led (669) to a new distinction between use (Brauch) and understanding (Verstand) and a gradual supremacy of theory over practice. Giesecke shows (672-678) that these new ideals of knowledge applied even to traditional topics as in Libavius' Alchemy.

    The rise of early modern science is frequently described as a new emphasis on observation. Giesecke's analysis showed that this is too simplistic; that it was rather a question of developing a systematic method of communicating results of observation indirectly, using descriptions that reflected the objective aspects of linear perspective. Giesecke showed that this led to new links between experimenting and idealising (620-623), noting that this redefinition of (scientific) knowledge also entailed new emphasis on instruments (673). This closely argued and carefully documented work led to dramatic conclusions that "knowledge" (Wissen) in its modern sense did not exist (677) and indeed was unthinkable (655) prior to the development of print culture as it evolved in Europe. Giesecke was very sensitive to the price that was paid to achieve this (650):

Authors of technical literature (Fachprosa) and particularly their most radical representatives, "scientists" (Wissenschaftler), are forced to uniocular perception, concentration on visible characteristics (Gestaltmerkmale) and thereby to suppress more complex organs of sense and perceptions.

    This monosensual focus (653) of early modern science destroyed earlier notions of unity of the senses, and required an isolation of the sense of sight which, Giesecke suggested, needed to be transcended in light of the ecological crisis that this one-sense approach to knowledge has produced. New age concerns with body language, feelings, and new relations to nature could be seen as a contemporary expression of this quest to redefine the visual bias of our culture (653). By implication the origins of perspective and printing were intimately connected with a new approach to knowledge.

    Giesecke was very conscious that his telling of the story from a modern point of view meant emphasizing the new aspects of the process and that if one wished to compensate for this shortcoming one would ultimately need to retell the whole story using a mediaeval viewpoint (703). He repeatedly emphasized the gradual evolution of these developments and explicitly acknowledged their roots in mediaeval manuscript culture. He noted, for instance (668), the presence of striking morphological descriptions in the work of Albertus Magnus and Hildegard of Bingen. He accepted that there were numerous mediaeval examples of visual experience and even commitments to dissemination (677). In the case of Ortolf von Bayerland's medical book (Arzneibuch) he described (554-55) a fourteenth century treatise with over 100 manuscripts which explicitly set out to disseminate knowledge in clear tables. In analysing the nexus of perspective, geometry, model-making and systematic representation of knowledge, he repeatedly cited Leonardo da Vinci (e.g. 617, 624, 636, 658, 663). Giesecke did not pretend that printing started the process: he claimed, rather, that printing set in motion a technological system of communication that standardized and spread the process through Germany, made it a European, and ultimately a world-wide phenomenon.

    In terms of stages, distinctions need to be made between (proto-) perspective in a loose sense of some spatial effect as in Giotto; (proto-) perspective with an approximate central vanishing point as in Lorenzetti’s Annunciation (Siena); perspective with a technical vanishing point as in Brunelleschi’s panels or Masaccio’s Trinity (Florence, Santa Maria Novella); general mathematical demonstrations as in Piero della Francesca, or precise ones as in Guidobaldo del Monte or Desargues. Hence the question of origins changes in the course of over three centuries from c. 1300 to 1636.

    If we are concerned with the origins of Giotto’s breakthrough into a general spatial setting witnessed in his cycles at Assisi, Padua and Florence in the first quarter of the fourteenth century, then it is important to recall a new emphasis on narrative painting, inspired by a new attention to nature through the Franciscan Order, which became combined, largely through the English Franciscans (Robert Grosseteste, Roger Bacon and John Peckham), with a new metaphysical theology focussing on geometry and optics as a means of understanding God. The views of optics in this programme came via Witelo (c.1270) from the Arabic tradition of Alhazen (Ibn al-Haytham) who had focussed attention on the criteria for certification of sight and had brought problems of representation within the scope of optical studies.

Fig. 2. Key events in the history of perspective with corresponding origins.

    The tendency in Romanesque and Gothic churches to provide spatial doorways and to a lesser extent windows was common throughout Europe. Some windows, as in the Andreas Kirche (Braunschweig), were actually shaped in the form of pyramidal cones of vision. This provided a common framework for spatial interests within which there were national and regional differences that varied in accordance with different functions and media. Initially there had been a focus on key events in the life of Christ often balancing Old Testament prefigurations with New Testament happenings. Those countries such as France (e.g. Chartres) which used stained glass in their great rose windows to depict these events were severely limited in their spatial explorations.

    This is not to say that perspective was impossible in this medium. The first stained glass window to use pseudo-perspectival effects was by an artist in the workshop of Cimabue, who produced a Coronation of the Virgin in Siena Cathedral (1287-1288), which has been called the (78): "first occasion on which the laws of perspective were used in stained glass." These techniques were developed in a Life of Saint Anthony of Padua at Assisi by the workshop of Giovanni di Bonino (1320). From there the idea went North to the the Cistercian abbey at Königsfelden (1325-1330). It was used again at Stassengel near Graz (c.1350) where "the scenes are each enclosed within a three dimensional niche, like a sort of tower seen in perspective. At Evreux Cathedral (1395-1400), figures were placed on pedestals portrayed in perspective. and in the choir of Tewkesbury Abbey in Gloucestershire, the baldachins were arranged in accordance with....[pseudo-]perspective .

    In the fifteenth century a number of the early pioneers in perspective were also active in stained glass, notably, Lorenzo Ghiberti, Paolo Uccello, Andrea del Castagno and Donatello. Later examples include episodes from the Life of Saint John the Baptist such as the Meeting with Craton (1478) by Cristoforo de Mottis; from the Story of Saint Eligius such as the Investiture of the Saint as a Bishop (1480) by Niccolo da Varallo 127 or the Expulsion of the Merchant from the Temple by Guillaume de Marcillat in Arezzo Cathedral (1519-1525).

    These spatial explorations remained limited when the medium was mosaic as at Monreale. In Italy, where the medium became fresco as at Assisi, Padua or San Gimignano the spatial potentials increased considerably and even more so when the function changed from depicting key events in the life of Christ to narratives of saints’ lives. This quest occured mainly on the walls of chapels in fresco, to a lesser extent in the predellas of altars and occasionally in sculptural reliefs.

    In the Netherlands the scenes were almost always on altars painted in oil. The emphasis remained on the life of Christ and the Virgin, particularly key moments such as the Annunciation, the Adoration of the Shepherds or the Virgin and Child alone or surrounded by saints and/or donors. The spatial setting for all these scenes almost invariably involved a church. Sometimes the portal of the Church served as a window to the interior; sometimes it served more as a gate to a scene beyond; at other times the whole front facade of the church was cut away and served as a window to a scene inside the church. Occasionally the entire scene occured inside the church. In these arrangements the portal often contained painted sculptures which continued the tradition of Old Testament prefigurations and parallels to the New Testament scene. This contrast between the old and the new law in terms of painted sculpture versus painted nature meant that the Netherlandish tradition had a quite different approach to the paragone tradition which in Italy contrasted the effects of sculpture and painting. At the same time the great emphasis this gave to the portal and church interior in Netherlandish art meant an early focus on sacred interior spaces that was to culminate two centuries later in the great interiors of Neefs, De Witte and Saenredam.

    In Switzerland this concern with church interiors emerged with Konrad Witz in the first half of the fifteenth century. In Germany this fascination with church interiors became important in the second half of the fifteenth century with the Master of the Life of Mary (Meister des Marienlebens). In the first decades of the sixteenth century, Altdorfer and Huber developed this theme in important new ways in the context of drawings and engravings, recording actual synagogues as well as churches. In Italy, by contrast, it occured primarily in the context of intarsia work and spread to other media such as painting in the eighteenth century (e.g. Pannini). In Italy, a trend towards secular art, showing everyday events in a sacred context, emerged largely on the walls of the public palaces of the city states, their equivalents of city halls. At the Burgundian court this emphasis on secular events in a sacred context developed in the illustrations to Books of Hours.

    In both sacred and secular art the chief media used included stone, paint, paper, wood, earth and plants (fig. 3). Often these media were used together either in the production of proto-perspectival or technically perspectival spaces. For instance, Giotto used a combination of architecture and paint to produce his proto-perspectival, fictive coreto (Cappella degli Scrovegni, Padua, 1305). This continued in the later work of Bramante (Santa Maria Presso San Satiro, Milan) and Michelangelo (Sistine Chapel, Vatican). Medium specific examples evolved in tandem. For example, in the late twelfth century, a purely architectural sculpture showing a fictive doorway was constructed in the Baptistery of the Palace of Kings of Majorca (Perpignan). By the early fifteenth century, Donatello, was applying proto-perspectival techniques to sculpture in stone while his contemporary, Ghiberti, applied these techniques to sculpture in bronze on the doors of the Baptistery in Florence.

    Paint constituted one of the most complex media. In terms of fresco it was applied to panels, walls and ceilings or quadratura. Here combinations of painting and architecture were often involved. Following early exceptions such as Mantegna’s oculus (Camera degli sposi, Palazzo del Te, Mantua), these became the fashion in the 1560’s in Bologna with Laureti, emerging in the published literature in 1583 (Has, Danti) although it was over a century later that the most famous examples appeared with Pozzo, a trend that continued especially in southern Germany and Austria throughout the eighteenth century. Oil paintings were more specialized.

    Paper was one of the most important media of perspective. Sometimes these were individual sheets. In terms of manuscripts and books, in addition to those devoted to sacred themes, there were texts devoted specifically to regular and semi-regular solids. In Italy the fashion began with Piero della Francesca and Pacioli around 1489 and culminated in the years 1496-1499 when Pacioli and Leonardo worked together to produce the Divine Proportion (published 1509) which was the basis for later work in the period 1568-1596 (Barbaro, Danti, Vasari, Jr. and Sirigatti). In Germany this activity began seriously with Dürer (c.1514) and effectively ended with Halt (c.1625). Another major theme was Roman ruins which, as Vasari reported, began in Italy with Brunelleschi and Donatello (c.1401). The inclusion of a map of Rome with ruins by the Limbourg brothers in the Very rich hours of the Duke of Berry (c. 1415-1416) attests that this interest spread quickly. Even so, systematic study appears not to have occured until the time of Peruzzi (c.1520-1535) whose notes were inherited and published by Serlio from 1537 onwards. The period 1540-1560 saw a high point in this genre with the publications of Androuet Du Cerceau and Cock. Piranesi (1740) brought a revival. As we have shown elsewhere (cf. Sources, pp. 89-98*), the perspectival treatises gradually evolved a whole series of themes.

    Wood also became an important medium. From the fourteenth century onwards, there were proto-perspectival uses of inlaid wood or marquetry in a sacred context, specifically choir stalls, in Italy, with the most famous perspectival examples in the period 1470-1530. In Germany and the Netherlands, where the emphasis in marquetry was rather on secular cabinets often showing combinations of ruins with semi-regular objects, the most important period was from c.1550-1625. Wood also played an important part in stage scenery and scenography, although this typically entailed a series of media including painting and machines. From the outset pioneers in perspective such as Brunelleschi and Masaccio were also engaged in theatre decorations, although these were more by way of machines than stage scenery. Serious stage scenes emerged in the latter half of the sixteenth century (1567, 1589); did not become a regular feature until the early seventeenth century and reached their heights in the first half of the eighteenth century (e.g. 1710, 1740) with families such as the Juvarra, the Bibbiena and others.

Medium Early Examples First Published Famous Examples

Stone:

Architecture c. 1478 1521 1521-

Fictive " " c. 1478 1568 1500-1900

Sculpture c. 1400 1504 1400-1900

Paint:

Fresco c. 1425-1427 -- 1430-1510

Oil c. 1457 -- 1484

Ceilings c. 1480 1568 1500-1700

Paper (Drawings):

Roman Ruins c. 1400 c. 1550 1550-1580,1740-1760

Regular Solids c. 1489 1509 1489-1625

Manuscripts c. 1434 1540 1434-1515

Books 1494 1494 1494-

Wood:

Marquetry c. 1470 1567 1480-1625

Stage Scenery c. 1567 1568 1600-1800

Earth, Plants:

Gardens c. 1550 1600 1550-1800

Fig. 3 Examples of different media that used perspective and related dates.

    In Italy, perspective was applied to gardens from the first half of the sixteenth century onwards. As a topic it entered the literature with Vredeman de Vries and Androuet du Cerceau in the 1560’s. But it was not until the sevententh century that perspective was applied to gardens on a grand scale and not until the eighteenth century that it reached its heights. It continued to be an important theme in the nineteenth century. When we examine these combinations more closely we find that some were particularly favoured in Italy (fig. 4), whereas others were favoured in the North. For example, altars were particularly developed in the Netherlands and Germany; manuscripts, particularly books of hours and histories were favoured in Burgundy and France; while the use of perspective in printed books was favoured first in Germany and subsequently in the Netherlands and France.

Place Medium Italy Burgundy France Netherlands Germany

Walls Mosaic, Fresco *

Chapels Fresco *

Ceilings Fresco *

Choirs Inlaid Wood *

Altars Oil on Canvas * * *

Predellas Fresco, Tempura *

Paintings Oil on Canvas *

Reliefs Sculpture *

Manuscripts Painting * * * * *

Books Woodcut * * * * *

Engravings Ink on Paper * * * *

Gardens Earth, Plants * * * *

Fig 4. Some of the different media and functions of perspective favoured in Italy, Burgundy, France, Netherlands, and Germany.

    Some themes such as gardens were explored throughout Europe but with regional variations (cf. Sources, pp. 170-182). Striking also from this overview is how the uses of perspective were initially much more diverse in the Italian context, which may be one of the central clues why perspective took nearly a century to spread to the major centres of Europe (fig. 5).

Country Italy France Netherlands Germany

Date 1415-1425 c.1450 c.1457 c.1505

Fig. 5. Dates when perspective was first introduced into major European countries.

    Panofsky noted that one of the key sources for Suger's approach lay in the writings of Dionysius, the Pseudo-Areopagite, who used the study of visible things as a means of studying the invisible:

Every creature, visible or invisible, is a light brought into being by the Father of the lights...This stone or that piece of wood is a light to me....For I perceive ...that it exists according to proper rules of proportion; that it differs in kind and species from other kinds and species; that it is defined by its number....As I perceive such and similar things in this stone they become lights to me, that is to say, they enlighten me.

    Read narrowly, this passage would lead one simply to use examples from the material world as a starting point for mystical contemplation of the spiritual world. This, it could be argued, was essentially the path taken by Abbot Suger. Read more broadly, it could lead one to a scientific study of the physical world as a means of gaining understanding of the invisible world of God. This, as will be suggested below, was effectively the path taken by his colleague, Peter the Venerable, Abbot of Cluny, when he instigated a new search for basic texts on scientific knowledge in 1143, one year before Abbot Suger consecrated his new church at Saint-Denis.

    There was more to Saint-Denis than simply a place where the visible beauty of precious stones and objects were a point of departure for invisible truths of religion. In the Latin, Saint-Denis, was Sanctus Dionysius and thus etymologically linked with Dionysius, the Pseudo-Areopagite. Saint-Denis had been the royal abbey for many centuries. It housed the tombs of Charles the Bald and Hugh Capet, founder of the ruling dynasty. Its sculptures and art reflected this historical context. At the same time it brought new emphasis to contemporary figures within this sacred and secular tradition. Hence, an Annunciation scene (c. 1140-1144), in the stained glass windows of the church, showed Abbot Suger, as a donor at the Virgin's feet. Saint-Denis also housed the Chronicle of Saint-Dénis, which was begun in the early twelfth century, with a second version up to the time of Louis VIII in the thirteenth, and a third version after 1286, which included the lives of Saint Louis and Philippe III. In other words, one of the centres that helped to inspire the new realism of Gothic art, also inspired a tendency to record past and contemporary history. All this becomes the more striking when one recalls that Jean Fouquet's version of this same Chronicle of Saint Dénis (1458, now Paris, Bibliothèque Nationale), was one of the first examples of (nearly correct) perspectival art in a French manuscript.

    Bishop Geoffrey of Chartres was a personal friend of Abbot Suger. Geoffrey visited Suger at Saint-Denis in 1130, 1137, 1140 and assisted him at the consecration of the new cathedral of Saint-Denis on 11 June 1144. So, from the outset, there were close links between Saint-Denis and Chartres, which became the two key centres of early Gothic architecture and art.

    Most descriptions of the Gothic focus on a new interest in light, a fascination with stained glass windows and a new emphasis on realistic sculpture. Mâle has suggested that the reasons for this new realism could be related to the crusades which led some French noblemen to settle in Greece. We know from Abbot Suger himself that he was personally well acquainted with the cultural heritage afforded by Rome. Speaking of columns, for instance, he noted: "we might obtain them from Rome (for in Rome we had often seen wonderful ones in the Palace of Diocletian and other Baths)". Hence the new realism would mainly be due to a re-discovery of Ancient Greek and Roman examples which, in the French context, became integrated within elaborate typological parallels between the Old and the New Testaments focussing on the Life of Christ.

    More was involved, however. The Gothic period introduced a new approach to story-telling. In terms of stained-glass windows, for example, Brisac noted that the Childhood of Christ on the interior of the west front at Chartres (1150) was:

the earliest surviving example of a composition made up of three illustrated compartments at each level, and it contains a very comprehensive treatment of this period of Christ's life and also of two later events: his Baptism and the Entry into Jerusalem. Some episodes are dealt with in a sequence of several compartments. There are six, for example, in the case of the Adoration of the Magi.

    These themes were continued when Chartres was rebuilt between 1194 and 1240. By the time of the Sainte-Chapelle (1243-1248), a single Story of Esther and Ahaseurus was "told in one hundred and twenty-nine scenes" which, Brisac claimed, made it lose "its narrative precision." In the next century this apparently changed again:

Legendary windows, for example, with multiple medallions, allowed stories to be told with extraordinary narrative diffuseness, whereas in the fourteenth century only the most salient events of their subject's life were portrayed; in the case of saints, for example, it would be their meeting with Christ or their conversion to Christianity, one of their miracles and finally their glorious death. All the subsidiary episodes are dispensed with and the "reading" of the window becomes much easier.

    All this becomes the more intriguing because Gombrich has suggested that the pictorial revolution which led to linear perspective had its roots in a new approach to narrative. We would suggest that this change in narrative first occured in France rather than Italy and began seriously in the century from 1150 to 1250, which is usually associated with Gothic art and architecture. In other words, paradoxically, in the French Gothic emerged basic ingredients essential for the Italian Renaissance: not just a new commitment to realism but a whole new approach to narrative. To understand this we need to look briefly at the new subject matter of stories in the stained-glass windows and relate this to new themes in literature of the time. Then we shall stand back to look more globally at changes in the six centuries from 1000 to 1600.

New Subjects in Windows and Walls

    A closer look at the the interior stained glass windows and the exterior sculptures of the great cathedrals, reveals other aspects of their novelty. Besides introducing new realism into representations of the Life of Christ, their subject matter was increasingly about the lives of the saints, donors, recent champions of the faith and early founders of Christianity in the North. For example, when Canterbury cathedral burned in 1174, the new church had a series illustrating the lives of archbishops of Canterbury, such as Saint Dunstan and Saint Alphège, who lived around 1000. The Trinity and the Corona Chapels contained scenes from the Life of Thomas à Becket, who was murdered in the cathedral in 1170. When Chartres burned in 1194, one of the most impressive windows was dedicated to the life of Charlemagne. When the cathedral at Rouen was burned by a fire in 1200, the sculptures on the doors recorded the lives of Saint Romain, who had been bishop of Rouen from 626 to 638, and Saint Ouen, who was pope from 641 to 684. The great cathedral at Reims, had stained glass windows (c.1160's or after) dedicated to the Life of Saint Nicaise, martyred by the Vandals in 407 and the Life of Saint Remi, who first baptized Clovis and his Franks in 498. When the cathedral was rebuilt after the great fire in 1210, these stories were integrated into the sculptures over the doorways of the North facade of the transept. The Sainte Chapelle (1243-1248), ostensibly about Old and New Testament parallels, emphasized a continuity between Biblical royalty and the Capetian dynasty, as embodied by Saint Louis, founder of the chapel. One set of windows was dedicated specifically to the history of relics of the passion of Christ and traced their lineage right through the Middle Ages. The images of the stained glass windows dovetailed with those in the illuminated manuscripts and hence it is not surprising to find that one of the most impressive proto-perspectival scenes is subsequently found in the Lives and Miracles of Saint-Louis from the collection of Jeanne de France (Paris, BN, ms. fr. 2829, fol 11v.).

    For the pre-history of perspective, this seemingly simple shift in subject matter was of the greatest importance. As long as the Old or New Testament, and particularly the Life of Christ remained the chief topics, artists were challenged to represent places they had never visited and persons they had never seen. To represent Christ very realistically could be seen as too personal or even blasphemous. To represent the space in which he moved in terms of local geography could equally be seen as blasphemous. When the subject matter shifted to the life of a saint, particularly a local saint, these restrictions diminished greatly. It is no-coincidence therefore that most examples of proto- and early perspective involve cycles from the lives of saints rather than the Life of Christ (notwithstanding, as we have discussed elsewhere, that particular scenes from his life such as the Annunciation were very important). Some examples of such cycles are Giotto's Life of Saint Francis (Assisi), Massacio and Masolino's Life of Saint Catherine (Rome, San Clemente), Masolino's Life of Saint John the Baptist (Castiglione D'Olona) and Ghirlandaio's Life of Saint Francis (Florence, Santa Trinità).

    Donor portraits played a special role in this shift of subject matter that prepared the way for perspective narrative. Here again, Gothic art set the stage for that which the Renaissance developed. In early examples, such as Canterbury (1180), donors were typically guilds such as the furriers or goldsmiths and identified generically as such. In the course of the thirteenth and fourteenth centuries, the role of the donor became increasingly personalized to the point that they represented individual portraits. Initially donors were represented in separate spaces or peripheral to scenes in the Life of Christ or the life of a saint. Increasingly they becam