Vulgar + Prejudice Johann Heinrich Lambertʼs Reverse Methods of Perspective

The Pennsylvania State University The Graduate School College of Arts and Architecture

VULGAR + PREJUDICE JOHANN HEINRICH LAMBERTʼS REVERSE METHODS OF PERSPECTIVE

A Thesis in Architecture by Berrin Terim

Submitted in Partial Fulﬁllment of Requirements for the Degree of

Master of Architecture

August 2012 The thesis of Berrin Terim was reviewed and approved by the following:

Jodi La Coe Assistant Professor of Architecture Thesis Adviser

Katsuhiko Muramoto Associate Professor of Architecture

Donald Kunze, Jr. Professor of Architecture and Integrative Arts, Emeritus

Alexandra Staub Associate Professor of Architecture Graduate program chair

*Signatures are on ﬁle in the Graduate School.

ii ABSTRACT

“I must say, though, that an appearance that absolutely never deceives us could well be something more than appearance...”

In a letter to Kant, Lambert wrote these words in order to emphasize his suggestion for a return to the perceived phenomena. His perspective treatise, in which he presented the set of rules for a ʻreverseʼ perspective method -constructing the true form from the appearance-, was mostly regarded as a further step for instrumentalization of perspective. However, within the framework of his philosophical thoughts and cosmological understandings, one can realize that his approach to perspective still embodied a symbolic way of meditation to reveal the true order of the cosmos. It aimed to reconcile manʼs relative position with the hierarchically structured universe.

iii TABLE OF CONTENTS

LIST OF ILLUSTRATIONS v

ACKNOWLEDGEMENTS vii

1)INTRODUCTION 1 “Perspectival Consciousness” and Artiﬁcial Perspective 4

2)PERSPECTIVE 6 Seeing 7 From Seeing to Comprehending 10 Constructing 19 Reverse 33

3)JOHANN HEINRICH LAMBERT 36 Brief Biography of Lambert 37 Cosmology 40 To Be or Not To Be Copernican 52 Reverse Methods of Perspective 58

4)CONCLUSION 64 Return to Phenomena & Mathematization of Appearance 65 Meditating Through Perspective 67

BIBLIOGRAPHY 69

iv LIST OF ILLUSTRATIONS

1.1 The eye as the symbol of perspective, from E. A. Petitotʼs Raisonnement sur la Perspective pour en faciliter lʼusage aux Artistes, Parma 1758. 6

1.2 An Illustration of optical correction, from Jean Martinʼs French edition of Vitruviusʼs De Architectura, 1547. (left) 8

1.3 An illustration of optical correction, from Cesare Cesarianoʼs edition of Vitruvius, De Architectura, 1521. (right) 8

1.4 An Illustration of the celestial spheres -formed via multiplication of light-, and their relation to perspectival vision, from Cesare Cesarianoʼs edition of Vitruviusʼs De Architectura, 1521. 16

1.5 Brunelleschiʼs perspective demostration, from David Lindberg, Theories of vision from al-kandi to Kepler, 1976. (The mirror is placed in half way between the building and the panel). 24

1.6 An illustration of the baptistery in Florence with the schema of the experiment, from Dalibor Vesely, Architecture in the Age of Divided Representation, 2004. 24

1.7 Illustrations of the geometrical terms and mathematical explanation of visual rays, from NellʼInstituto delle scienze publication of Leon Battista Albertiʼs, Della architettura, della pittura e della statua, 1782. 26

1.8 An Illustration of Albrecht Dürerʼs perspective construction, with the help of an eyepiece and a grid frame, from his Unterweysung der Messung, 1525. 28

1.9 Illustrations of linear perspective, from NellʼInstituto delle scienze publication of Leon Battista Albertiʼs, Della architettura, della pittura e della statua, 1782. (The central point of the perspective is determined based on the height of man, considering the position of the eye.) 31

2.1 An illustration of the free perspective drawing of the sky with a comet, from Lambertʼs Freye Perspektive, oder Unweisung, 1774. 36

v 2.2 Johann Heinrich Lambertʼs portrait, from Alberto Pérez-Gómez and Louise Pelletier, Architectural Representation and the Perspective Hinge, 1997. 37

2.3 Book cover of Cosmologische Briefe über die Einrichtung des Weltbaues, 1761. 40

2.4 An image of the proportional magnitudes of the planetary orbits, from James Jacque translation of Lambertʼs System of the World, 1800. 41

2.5 (left) A section of an artiﬁcial horizon of the globe which demonstrates the relativity of the appearance of the stars to the position of the observer, from Wrightʼs treatise, 1750. 43

2.6 (right) An image of the spherical structured galaxies of the inﬁnite universe. The eyes represent the omnipresence of God and inﬁnitely many eternal abodes, from Wrightʼs An Original Theory or New Hypothesis of the Universe, 1750. 43

2.7 An image of Lambertʼs experimental set up, demonstrating; the square of the distance of the light source to the opaque plane is equal to the ratio of number of candles, from DiLaura ed. of Lambertʼs Photometria, 2001. 49

2.8 An image of the application of the formula in 2.7 for the planets interior to earthʼs orbits, from DiLaura ed. of Lambertʼs Photometria, 2001. 49

2.9 Lambertʼs “perspectograf” in use for transferring the plan of a garden into its perspectival appearance, from Anlage Zur Perspektive, 1752. 62

vi ACKNOWLEDGEMENTS

First and foremost, I would like to thank my advisor, Jodi La Coe. Jodi is one of the greatest professors I have ever met, and probably the best advisor that could ever be. Apart from her tremendous support and valuable guidance through out the process, which cannot be disregarded by the way, I would like to gratefully acknowledge her unblemished trust in me. When Jodi first met me, I had a patch of ideas in mind but no clear path to follow. I had the enthusiasm for this “long-shot” research, but not enough courage to conduct it. I really wanted to study Johann Heinrich Lambertʼs perspective theory, but was not sure if I could ever fully understand it. Towards the end, I knew I had to “finish” this work and write this thesis, but I did not know how. All within that, Jodi always helped removing my anxiety caused by those “buts”, and brought the passion which I already had to surface, made it visible to my eyes. I thought I was blind but she made me realize that it was only dark, and I only had the light of my passion to follow. Would that be sufficient to end this journey? Jodi never answered the question. Now, when I look back, I see that she already knew I would somehow find my way out. So she just took my hand and walked with me. Sometimes she also got lost with me, however she never stopped believing in me. I donʼt know, maybe for Jodi, trusting her advisee was already a priori thing. Without her encouragement and motivation, I would never be able to come this far.

Through out the research, and also while writing the thesis, I was constantly dragged to dead-ends. It was dark and the light I had was not bright enough to illuminate far edges. In every critical turn, at every fork in the road, there was Katsu. By lighting a candle, he helped me see a little farther. He never told me which road to pick, and I did not expect him to do so either. In our five-ten minute meetings, he just showed me what would I see at the end of those roads. With his constructive suggestions, I accomplished five-ten days of work in five-ten hours. His assistance was vital for the success of this work. I would like to take this opportunity to express my gratitude to my committee member, Katsuhiko Muramoto.

Last, but not least, I would like to offer my special thanks to Donald Kunze, “the sun” of this work. It was particularly his guidance which made me realize, all that time I was walking in the night. Since I had not exposed my work in day-light, I could not have seen the full picture, until I met him. Don rose into this long and dark process towards the end.

vii To me, I was still trying to reach the end, but he showed me, in fact, I was already there. Every single detail hidden in between lines was brought to surface with his careful reading and immense knowledge. Besides, with the help of his insights I could elevate myself from my own work and re-examine it, not as the author but like a reader. I am deeply indebted to him for his invaluable support. I highly appreciate his willingness to devote his time and effort so generously to edit most of this thesis. I would like to state that I am honored to have his signature on this work.

I also need to acknowledge the help provided by my French instructor, Rebecca Laurie Weiner. Her assistance in translating the primary sources of J. H. Lambert was greatly appreciated.

I wish to avail of this opportunity, express a sense of gratitude and love to my friends. I would like to thank Sema Erten and Pelin Gultekin for their great company and tremendous help. Like the ﬁreworks in fourth of July, they always brought joy to my life and made me smile.

Finally, an honorable mention goes to my family; my father Vahit Terim, my mother Selma Terim, my brother Burak Terim and my sister Belgin Terim Cavka. I especially thank my mother for bringing early summer to my long and hard winter with her visit to US in May. I also acknowledge my sisterʼs last-minute motivation and help. In general, I am grateful for their genuine support and patience. I should admit, since the very beginning, they believed in me more than I did in myself.

viii 1) INTRODUCTION

Perspective, since ancient times until its modern interpretations, has been a mode of revealing the presence of the divine realm; a higher order, which was in general associated with the “truth.”1 In the age-old philosophical quest to realize the “truth,” the conversion of poetics to instrumentality has transformed perspectiveʼs ability to signify what was believed to be true into a transparent expression of the truth itself. In other words, perspective — particularly perspectiva artiﬁcalis, embellished with symbolic connotations to reveal the divine order — became an instrument that, surpassing its initial functions, claimed to deﬁne external reality. While poetics aimed to reconcile this higher order with the human realm, perspective isolated the subject and evolved to perfect its quantitative view of objects.

This transformation has constituted what we could accurately call “perspectival consciousness.” The realization of the geocentric world-view as a perspectival illusion became the idea of a heliocentric and, later, a center-less universe.2 This transformation discredited humanʼs imperfect, limited vision, which had been embodied in the poetic view of the cosmological order. The poetic conception of the world as a polysemous but hierarchically ordered whole was reduced to mono-layered empirical phenomena. In that respect, the evolution of scientiﬁc thought reduced value relations to concept relations. Such ideas as harmony, perfection, and the enigma of the universe were either abandoned or converted into mathematical relationships. 3

1 As it will be elaborated in the “Perspective” chapter, ancient studies on the science of sight were named under perspectiva naturalis. Further medieval interpretations of perspectiva naturalis set the philosophical framework for the Renaissance invention of perspectiva artiﬁcalis, which was a means to represent the external reality. Even though these two forms have crucial distinctions, the quest for ﬁnding the truth via visual phenomena remained consistent.

2 See the chapters on Nicholas of Cusa in, Karsten Harries, Inﬁnity and Perspective, (Cambridge, Massachusetts: The MIT Press, 2001), pp. 24-66.

3 Alexandre Koyré, From the Closed World to the Inﬁnite Universe, (Baltimore: The John Hopkins Press, 1957), p. 2.

1 The success of Copernican Revolution lay in objectifying humanityʼs natural way of seeing, mechanizing vision as a tool for understanding the true structure of the cosmos. Copernicusʼs scientiﬁc discoveries proved that the geocentric world-view was, in fact, an illusionary consequence of the perspectival vision, which naturally places the observer in the center. This realization was critical for the emergence of the new epoch, in which the evidence of knowledge no longer depended on the primacy of perception. The “heroic age” of Copernicanism would culminate in Newtonʼs consolidation of astronomy and physics.4 The victory of Newtonian science allowed the systematization of knowledge based on merely mathematical veriﬁcation.

Johann Heinrich Lambert (1728–1777) was one of the most significant figures of the Eighteenth Century. He postulated his thoughts on the world-edifice at a time when Newtonian science was regarded as the dominant ethos for solving the enigma of the universe. He was no doubt a true Copernican who had fully appreciated the significance of Newtonʼs discovery of the law of gravity. Lambert realized, through this law, that the universe could be described with a single set of rules. This unity signified the existence of unified structure as well as unified knowledge of that structure. As he stated:

The dispute which the philosophers have long ago stirred up about gravity is magniﬁcent and great, and it causes a respectful wonderment if one considers that the whole heavens are and all celestial bodies are moved by one and the same law; indeed, if no other law can take its place, this alone must be sufﬁcient to show that through it all the heavens are in a very close tie with one another, that the entire world is an interconnected whole, and that is not patched together from single, broken pieces.5

As his explanation makes clear, Lambertʼs primary concern was to establish the a priori principles of cosmic order. In that respect, he fully supported Newtonʼs discovery, since it demonstrated the possibility of a systematically structured world conception. What distinguished Lambert from his contemporaries was this: instead of relying on Newtonʼs method of empirical veriﬁcation of the behavior of the solar system, he took Newtonʼs results as a starting point. He was then able to articulate a more comprehensive view of

4 See the introduction of, Hans Blumenberg, The Genesis of The Copernican World, trans. Robert M. Wallace, (Cambridge, Massachusetts: The MIT Press, 1987), p. xlii

5 Johann Heinrich Lambert, Cosmological Letters on the Arrangement of the World-Ediﬁce, trans. Stanley L. Jaki, (Edinburgh: Scottish Academic Press, 1976), p. 66.

2 cosmic structure — one that favored the idea of a teleologically determined universe over a mechanistically determined one. To state it more explicitly, his belief in the existence of a designed cosmos was never damaged by any positive results that did not prove it so.

As he also stated, any a posteriori conditions that did not agree with his a priori presuppositions could be attributed to a lack of the proper instruments of observation, which later ages would invent. In his words:

I had to say myself all that the most incredulous will ﬁnd fault with, and he who is not entirely in the position of passing judgment on it, will take it in a stride. But there will be others, who will weigh my arguments and who will push them further through the observation and computations which I propose. I have no reason to doubt that gradually they will succeed, but until then I had to set aside the positive tone. 6

The significance of Lambertʼs work lies in his teleological assumptions about the structure of the universe, directly driven by Copernicusʼs discovery and intensified through his perspectival meditations. Even though the Copernican revolution postulated a world that was not designed for man, Lambert, to reveal the true structure of the Milky Way by following up on Copernicusʼs radical discovery, still argues for a hierarchically ordered universe.7 This hierarchy should not be mistaken directly as a distinction between divine and human, but the development of a metonymical relationship: that any small part of the universe reflects and embodies the structural organization of the larger body. This insight was by no means in conflict with Copernicusʼs replacement of the center of the world. Rather, it re-structured this replacement in terms of a higher order. In that respect, Lambert realized the revolutionary implication of Copernicusʼs success in liberating thought about the cosmos from sensual experience. This liberation will be taken up in the second chapter.

It would be naïve to argue that Lambertʼs cosmological thoughts were revolutionary, or that they have something to say about the modern views that supplanted them. However, if his philosophy of the logic of appearance is restored to its proper position — as the

6 In his letter sent to his former student Baptista von Salis with the copy of his book, dated from April 10, 1761. Quoted from the introduction of; Cosmological Letters, p. 22.

7 Blumenberg, The Genesis of The Copernican World, p, 584.

3 centerpiece of his achievements in perspective — it becomes clear that he was one of the Enlightenmentʼs most subtle and original thinkers.

“Perspectival Consciousness” and Artiﬁcial Perspective

Robert M. Wallace argues that the removal of man from the center of the cosmos had profound metaphorical signiﬁcance for the development of all philosophy. For instance, Goethe explicitly stated that losing “the enormous privilege of being the center of the universe” meant that “a world of innocence, poetry and piety, the testimony of the senses, the conviction of a poetic-religious faith ... went up in smoke.” At the same time, the new creed had “justiﬁed those who accepted it in, and summoned them to, a previously unknown, indeed unimagined freedom of thought and largeness of views.”8

In the Renaissanceʼs poetic approach to perspective, the aim was to reconcile the phenomenal reality of human perception with the true order of the celestial realm. Working from Euclidʼs idea of the cone of vision, the natural human way of seeing led to a transcendental use of geometry, actualized within a geocentric world-view. Perspectiva naturalis and the linear perspective systems of the Renaissance determined cosmic order from a central-view point; they were immune to any relativity. In Goetheʼs terms, the hegemony of the order could allow for any freedom or subjective appearances. Higher order, which was the congruence of the divine, resisted exposure to logic and mathematics; it could only be signiﬁed through the appearance.

The meditating role of perspective changed when the geocentric world-view was exposed as an illusion. Copernicusʼs discovery not only removed man from the center; it made him realize that his search for truth from a (natural perspective) central position was wrong in the first place. A new consciousness, elaborated through numerous new scientific theories, relocated the earth at the same level of being with other celestial bodies. The order that had once belonged exclusively to the cosmos, was made subject to laws inherent in nature itself. This conversion radially undermined the meditating role of perspective. Perspectiveʼs infinite, boundless and homogeneous space was localized to fit within the terrestrial realm, converted to a “reality technique.” In that regard, the central point that was essential to the Renaissanceʼs adaptations of perspectiva naturalis,

8 Blumenberg, The Genesis of The Copernican World, p, xlii

4 dominated by the idea of a perfect cosmos, would change. Man and his earthly home didnʼt move, but the center did — or, worse, it disappeared entirely.

Johann Heinrich Lambert published his work on perspective in 1759, two years before his major work on cosmology. In the Eighteenth Century, the idea that linear perspective was an adequate representation of the human world had reached its limits. With Newtonʼs method of revealing truth through direct observation, appearance could be taken as a true measure of actual form as long as geometry was allowed to systematize artiﬁcial perspective. Within this Newtonian context, Lambert advocated a return to perceived phenomena, with the idea that they would reveal the truth if the drawing could be made scientiﬁcally. In La Perspective Affranchie de lʼembaras du Plan géometral, Lambert elaborated on methods to draw an object in perspective, without a pre-given geometric plan. In the eight sections of this book, he presented an “inversion method,” a technique for determining the true plan of a given perspective image of an object. Lambertʼs argument was quite original and profound: if perspective is a reversible process, it is also autonomous.9

Lambertʼs provocative theory could be regarded simply as a step in further instrumentalizing perspective. Since he had shown how perceived phenomena could be the departure point, he “nonetheless acknowledged the imminent assimilation of lived space to geometric space.” 10 This assimilation would inevitably evoke the reductionist use of perspective, to design and also to dominate the world. However, when considered against his cosmological understandings, one can realize that Lambert had, through this demonstration, functionalized appearances. While making it possible to deduce our eccentric (i.e. no longer cosmo-centric) point of view, he aimed to compensate this loss of center by locating the human within an expanded idea of the cosmos. What had been lost through perspectival instrumentalization was gained back with a ﬁrmer idea of a truth, even at the expense of making that truth inaccessible.

9 For further mathematical interpretations of artiﬁcial perspective which was culminated in Mongeʼs descriptive geometry, Lambertʼs methods technically cannot be regarded as a precursor. Nevertheless, his idea of beginning the construction directly on picture plane could be inspiring. See; Kirsti Andersen, The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge, (New York: Springer, 2007), p. 635.

10 Alberto Pérez-Gómez and Louise Pelletier, Architectural Representation and the Perspective Hinge, (Cambridge, Massachusetts: The MIT Press, 1997), p. 215.

5 2) PERSPECTIVE

Fig. 1.1. The eye as the symbol of perspective, from E. A. Petitotʼs Raisonnement sur la Perspective pour en faciliter lʼusage aux Artistes, Parma 1758.

...”Perspective Houses”, a name which reminds us that perspective was always just another word for the traditional optics of antiquity and the Middle Ages, in contrast to that more recent conception of the term which symbolically elevates perspective, as the precursor of modern “Descriptive Geometry”, to the supreme invention of a new epoch, the Renaissance. 11

11 Werner Oechslin, “Architecture, Perspective, and the Helpful Gesture of Geometry”, Daidalos 11 (1984), p. 39.

6 Seeing

Perspectiva naturalis or communis, the science of sight, was ﬁrst detailed extensively by Euclid in the Third Century BCE. In a primordial sense, it was a mathematical method for formulating the laws of natural vision and “often used as a means of grasping the physical and metaphysical structure of reality, whose essence was believed to be similar to light.”12 According to Euclid, the eye was an active participant in visual phenomena, the departure point of the visual rays (physical) that deﬁne the contour of the object to be perceived. In Optics, Euclid demonstrated that phenomena of vision in a direct relationship between the observer and the object could be studied precisely through geometry. In his geometrical interpretation, Euclid described vision as a cone with the eye as its apex and the limits of vision as its base. Objects upon which visual rays fall were, therefore, visible. Euclid went on to describe objects represented in perspective depth as “those things seen within a larger angle appear larger, and those seen within a smaller angle appear smaller, and those seen within equal angles appear to be of the same size.” 13

This primitive form of perspective acknowledged the relativity of the apparent dimensions to the angle of vision revealing the discrepancy between actual form and its appearance within an optical framework and accounting for the curvature of the eye. In order to reconcile our spheroidal optical world with actual forms, the ideal appearance of architecture was created through adjustments to the geometry of buildings.

The subjective perception of objects was elucidated in architectural, perspective, and mathematical treatises from antiquity to the modern era. The problem of perceiving straight lines as curved and curved lines as straight was explored in antique optics, art theory and philosophy, as well.14 The practice of adjusting building elements according to

12 Alberto Pérez-Gómez and Louise Pelletier, Architectural Representation and the Perspective Hinge, (Cambridge, Massachusetts: The MIT Press, 1997), pp. 12-13.

13 See Euclid, “The Optics of Euclid,” trans. Harry Edwin Burton, Journal of the Optical Society of America 35 (1945), pp. 357-372.

14 Erwin Panofsky, Perspective as Symbolic Form, trans. Christopher S. Wood. (New York: Zone Books, 1991), p. 34.

7 the rules of perspectiva naturalis — ”to compensate for the weakness of sight”15 — can be discerned in many examples of classical architecture. The need for entasis on columns, the manipulation of lettering on high architraves, and the curvature of epistyles and stylobates are some of the examples of optical corrections.

Figs. 1.2. and 1.3. An Illustration of optical correction, from Jean Martinʼs French edition of Vitruviusʼs De Architectura, 1547 (left) and an illustration of optical correction, from Cesare Cesarianoʼs edition of Vitruvius, De Architectura, 1521 (right).

The common use of optical correction in the First Century BCE was also recorded by the Roman architect, Marcus Pollio Vitruvius, in De Architectura. According to Vitruvius, it was “the most signiﬁcant technique for embodying precise ideas (poetic images) in a real building.”16 In order to achieve a desired visual effect, optical corrections were considered with respect to the position of the observer, since human perception depended on the location of the body in the world.

While Vitruvius described the exact alterations for the building elements, he immediately referred to the relationship between their speciﬁc placements and the position of the observer. His explanation of optical corrections ran parallel to Euclidʼs interpretation of

15 See the note under Figure 0.4 in Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 20.

16 Alberto Pérez-Gómez, Built upon Love: Architectural longing after ethics and aesthetics, (Cambridge, Massachusetts: The MIT Press, 2006), p.72.

8 cone of vision. Referring to extromission theories of optics, Vitruvius elaborated the direct geometrical relation of the visual angle to dimensional distortions. Therefore, he demonstrated optical adjustments accordingly. In his words:

All the elements which are to be above the capitals of the columns, that is to say, architraves, friezes, cornices, tympana, pediments, acroteria, are to be inclined towards their fronts by a twelfth part of their height; because when we stand against the fronts, if two lines are drawn from the eye, and one touches the lowest part of the work, and the other the highest, that which touches the highest, will be the longer. Thus because longer line of vision goes to the upper part, it gives the appearance of leaning backwards. When however, as written above the line is inclined to the front, then the parts will seem vertical to measure. 17

Although his demonstration for these corrections may seem technical, it should not be considered as a direct method or applicable theory for building techniques. As Kim H. Veltman points out, in antiquity optical studies focused on qualitative aspects of vision and on illusions. For the ancients, the optical adjustments of the objective measured world were meant to convey constant appearances in the subjective world of the observer. Consequently, Vitruviusʼs texts are an example of the proposed interpolation of the “mental preconceptions into the objective elements of the measured world...” Veltman also noted that “even their [ancientsʼ] quantitative ideals became entwined with qualitative concerns.”18

It should be emphasized that, in extromission theories of optics common in antiquity, vision was primarily tactile and belonging to our heterogeneous conception of space in a ﬁnite world, as experienced and perceived through all senses.

Later transformations in optical theory inverted the concept of visual perception as a tactile corporeal quality. Visual theory became an adaptation, or in other words, an imposition of perspective construction that was commonly accepted as a model for the “natural” way of seeing. The process of this adaptation inevitably reached its climax with Johann Heinrich Lambertʼs “reverse methods of perspective.” In his writings, Lambert

17 See Vitruvius, De Architectura (On Architecture), Ed. and trans. Frank Gagner. (Cambridge, Massachusetts: Harvard University Press, 1931), pp. 195, 197.

18 Kim H. Veltman, Linear Perspective and the Visual Dimensions of Science and Art. (Munich: Deutscher Kunstverlag, 1986), p.34-37.

9 called for a return to perceived phenomena examined within the boundaries of constructed perspective. The signiﬁcance of appearance in perspective construction ran parallel with his cosmological thoughts. Within the scope of his argument, reversing the process helped the realization of manʼs eccentric position in respect to the true order of the cosmos. Reversing the process between the true form and appearance advocated for the autonomy of the homologous construction. Despite the invention of linear perspective during the Renaissance, artists did not yet posit a homologous relation between true form and its appearance. The philosophical framework for that invention did not support such a systematic relationship to the truth as directly accessible in the human realm.

From Seeing to Comprehending

During the Fifteenth Century, perspective theorists diverged from further elaborations on traditional optics toward advancing a congruent mathematical discourse that was not dependent upon the innumerable complexities of visual perception.19 The Renaissance invention of perspectiva artiﬁcalis was regarded as a systematic geometric construct depicting homogeneous space; thus it was also known as costruzione legittima. This perspective was acknowledged as a new form of representation of space. In that regard, perspectival space was considered to be potentially inﬁnite and, in essence, Euclidean.20 This new conception of space has been conventionally considered as a revolution in visual representation, since it represented a radically new form of visual representation.

19 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 19.

20 Dalibor Vesely, Architecture in the Age of Divided Representation: The Question of Creativity in the Shadow of Production, (Cambridge, Massachusetts: The MIT Press, 2004), pp.112-113. Vesely also points out that during the Renaissance development of perspective, the Euclidean space could only be considered as ideal. Even during the modern transformations of science and philosophy, Euclidean space was not regarded as actual space, however, became accessible to humans.

10 To some extent, it has also been argued that perspectiva artiﬁcalis had no direct historical precedent.21

In a formal sense, there is no doubt that perspectiva naturalis and perspectiva artificalis are completely different. However, to compare these two forms based on their rather obvious technical differences is a narrow convention imposed by modern studies of history. On the one hand, it is certain that the development of artificial perspective was a revolutionary step in a modern conception of space, coinciding with the beginning of a new historical era. While on the other hand, it should also be clarified that the Renaissance invention of constructed perspective was not yet an autonomous, mathematical representation of vision.22 Discourse on perspective continued to contain inherent cultural values such as the theological and gnoseological connotations of vision as well as the symbolism of light. Renaissance authors of perspective treatises tried to reconcile this novel geometric construct of space with traditional optics; however, “their frequent incapacity to do so poignantly revealed potential contradictions inherent in their new forms of hegemonic visual representation.”23 Nevertheless, the implicit connotations of light remained consistent. Hence, as Dalibor Vesely surmises, the inquiry into theories of light can reveal a continuity between early Renaissance perspective and late medieval optics. In Veselyʼs words:

By examining Renaissance perspective against the background of the medieval philosophy of light, we can come to understand the ontology of architectural space, which is formed by light before it is structured geometrically... its

21 Ibid., p.131. For example, Hubert Damisch claims that the connection of perspectiva artiﬁcalis to perspectiva naturalis is “an unforeseeable one.” See, The Origin of Perspective, trans. John Goodman. (Cambridge, Massachusetts: The MIT Press, 1995), p.65. Martin Kemp also disregards the entailment of social and intellectual factors for artistic causation and directly relates the invention of artiﬁcial perspective to genius of Brunelleschi. See “Science, Non-Science, and Nonsense: Brunelleschiʼs Perspective,” Art History 1, no. 2 (1978), p. 135.

22 Vesely, Architecture in the Age of Divided Representation, p. 131.

23 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 16. In the literature on perspective, these contradictions were prevalently explored based on the technical assumptions of these two forms. Among those is Erwin Panofskyʼs assessment of the “angle axiom” of classical optics and the “distance axiom” of linear perspective is the most remarkable one. See Renaissance and Renascences in Western Art, (Stockholm: Almqvist & Wiksell, 1960), p. 129.

11 [philosophy of light] analysis illustrates the gradual transformation of space, connected originally with the luminosity of the visible world, into space as a pure conceptual construct. 24

A comprehensive discussion of philosophy of light is beyond the scope of this essay. However, in order to elucidate the transcendental use of geometry in early Renaissance perspective, one must acknowledge the smooth transition from medieval to Renaissance theories, that both embraced the theology of light and its mathematical interpretation through optics. As a matter of fact, this interpretation was the key to understanding divine wisdom and to ﬁnd the ʻTruth.ʼ Thus, the novel representation of space in Renaissance art was indeed guided by this notion, whereas it also turned out to be its ultimate goal.

Since antiquity, the connection between light and divine knowledge had been evident in philosophical statements, ancient mythologies, and religious literature.25 Meanwhile to comprehend or explain its nature had always been difficult. The proclivity that regarded light as an isolated entity from the rest of the materiality probably contributed to the difficulty in defining it. This ambiguity was inherent in its twofold character; lux, the invisible source of light — that could be named but not seen — and visible light — that could be seen but not easily defined.26 In that regard, light is either a concept, which can be envisaged, or an entity, which can be perceived. In other words, because of its twofold character, light can both respond to our senses and still remain in the domain of our intellect. This interpretation of light refers directly to humanityʼs double-sided manner to understand the nature. Evidently, both approaches coexist but cannot be easily reconciled.

The tension between visible light and lux was in accord with the tension between our sensible uncertainty and intelligible experience. Thus, such tension could be overcome with the help of representational symbols, which could “also reveal light to be a disclosure of the essential nature of things, the true exemplum of their intelligibility.”27

24 See Architecture in the Age of Divided Representation, p. 6.

25 See note 21 in Charles King McKeon, A Study of the Summa philosophiae of the Pseudo- Grosseteste, (New York: Columbia University Press, 1948), p. 157.

26 Vesely, Architecture in the Age of Divided Representation, p. 114.

27 Ibid., p. 114.

12 Probably the earliest and the most comprehensive interpretation of the link between intelligibility and light was postulated by Plato in Republic. As David Lindberg points out, Western meditations on light-imagery were commonly founded on this text.28 Hence the reﬂections in Platoʼs analogy of the cave were present in further metaphysical studies of light — which reached its climax during the thirteenth century. Charles McKeon interprets Platoʼs famous analogy as: “The Form of the Good is here represented as the sun of the intelligible world; or the Form of the Good is to the intelligible world as the sun is to the visible world. Or it is the source of intelligibility and truth.”29 Based on this assumption, the study of light could be the only means to understand the form of the good — referred to a higher being — which was inherited in the intellect. Thus, Plato also denotes that a process analogous to vision of the imperfect material world could reveal the structure of eternal forms.30 Further studies of light particularly within the framework of Christian philosophy, would replace the form of the good with the divine, considering “vision as an analogy by which to comprehend the process of cognition.”31

Therefore, the study of physical light in medieval optics had something more than an interest in natural science, although during the Middle Ages it was considered as the most fundamental of all natural sciences. It was a search for truth.32 Accordingly, it was certain that the inherent meaning of optics was actually cosmological — this understanding was a key to cosmology — in the ﬁrst place. Elaborating on this original meaning, the studies of optics during the Thirteenth Century aimed to reveal the essence of creation.

28 David C. Lindberg, Theories of Vision from al-Kandi to Kepler (Chicago: University of Chicago Press, 1976), p. 95.

29 Charles King McKeon paraphrases from Plato, Republic, 508 B-C, 509 B and 517 C, in A Study of the Summa philosophiae of the Pseudo-Grosseteste, (New York: Columbia University Press, 1948), p. 157.

30 This analogy was the fundamental guide for medieval science that enabled attempts to comprehend celestial forms through direct visual phenomena. It was the belief in this analogy that precipitated the ʻdiscoveryʻ of Renaissance perspective. Lindberg, Theories of Vision from al-Kandi to Kepler, p. 95.

31 Ibid., p. 96.

32 A. C. Crombie states this interpretation for Robert Grossesteste, but it was the case for all ʻscientistʼ of middle ages. See, Robert Grosseteste and the Origins of Experimental Science 1100-1700, (Oxford: Clarendon Press, 1953), p. 128.

13 The study of Euclidean Optics during the middle ages was a propaedeutic to the study of mathematical and philosophical theories of light.33 In this particular subject, the aim to understand the nature of light was not merely an empirical concern, but a path leading to intelligible, celestial worlds. Especially with the Christian interpretation of Neoplatonic philosophy, connotations of light and intelligibility were extended to divine wisdom. As a phenomenon of the ineffable one, light was regarded as God; therefore, it was also reconciled with the source of creation.34 Particularly in Christian literature, the interpretation of light as the first form that stimulated creation was present in St. Augustineʼs writings. In De trinitate (fifth century A.C), Augustine elucidates the self- diffusion of light as it “multiplies itself from a single point and forms a finite sphere, firmament (sphaera lucis), matter becomes dimensional.” 35 In this explanation, the firmament presents the image of a spherical boundary in which the expanded matter reaches its finite limits.36 Running parallel with Augustineʼs interpretation, studies on cosmogony of light in medieval optics elaborated on the story of creation and, therefore,

33 Vesely, Architecture in the Age of Divided Representation, pp. 6, 118. Euclidʼs Optics was not only limited to the nature of light but also involved the functioning and anatomy of the eye, since seeing was generally taken for granted as an active process. Considering the eye as an active participant of vision is a component of the extromission theories, which were postulated by both Euclid and Plato. Contrary to this assumption, tenth-century Arab scientists, Al-Hazen and Avicenna, advanced intromission theories of vision, influenced by Democritusʼ atomism and Aristotleʼs thoughts. Intromission theory asserted the eye as a passive receptor, which receives light from external objects. In the Thirteenth Century, sources on optics originating in the East were distributed to some extent in the west — though the authors were not given any credit. Among thirteenth-century scientist-philosophers, Robert Grosseteste and Roger Bacon were clearly influenced by Al-Hazenʼs texts, although they never accepted his intromission theories. J. V. Field, The Invention of Infinity: Mathematics and Art in the Renaissance, (New York: Oxford University Press, 1997), pp. 6-7. See also Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, pp. 12-13. For a broad discussion, See; Lindberg, Theories of Vision from al-Kandi to Kepler. During the Renaissance, discussion of extromission and intromission theories was mentioned to some extent in perspective treatises, but the debate about the direction of the light rays did not have an explicit conclusion. However, such an argument was not the main concern of the artists, in the first place. For either way, visual rays between the object and the eye would follow a particular geometry and form the cone of vision. Thus, the Renaissance artistsʼ primary interest was to develop a coherent discourse based on static geometry rather than on the direction of the vectors.

34 Vesely, Architecture in the Age of Divided Representation, p. 114.

35 Quoted from; Ibid., p. 122. For more information on the Chrisitian interpretation of light, See, In the City of God 10. 2, Augustine quotes John 1:6-9. Cf. De trinitate 13. 1.

36 Ibid., See note 37, in p. 407.

14 formed the framework in which the mathematical annotation of light was stimulated. Above all, thirteenth century philosopher Robert Grossestesteʼs explanation was remarkable, since his understanding established a qualitative approach in dialectical reasoning, therefore “led to the formation of a qualitatively articulated world.” 37 In his short treatise on metaphysics of light, De Luce, which he signed as the “Bishop of Lincoln,” Grosseteste says:

... light is more exalted and of a nobler and more excellent essence than all corporeal things. It has, moreover, greater similarity than all bodies to the forms that exist apart from matter, namely, the intelligences. Light therefore is the first corporeal form. Thus light, which is the first form created in first matter, multiplied itself by its very nature an infinite number of times on all sides and spread itself out uniformly in every direction. In this way it proceeded in the beginning of time to extend matter which it could not leave behind, by drawing it out along with itself into a mass the size of the material universe. 38

As evident in their metaphysical studies, Grosseteste and other thirteenth-century perspective theorists considered light as the first form of corporeality that does not have a body. Because of its nature, it is self-diffusive. An infinite multiplication of itself in every direction could help light to extend matter and gives rise to the formation of the material world.39 Based on this understanding, light is not merely a form of the intellect that belongs to the domain of the divine, or a means to illuminate the world from outside, but “it is [also] an active power (virtus activa), which structures the world from inside and is seen as a primary source of both the differentiation and the unity of the world.”40 Since it was regarded as “common to all things in the universe from the lowest of the elements, earth, up to and including the firmament,”41 it was appreciated as the symbol of the continuity between the terrestrial and celestial worlds, between divine and human existences. In short, Grossetesteʼs interpretation of cosmogony of light established a principle of continuity in the world.

37 Ibid., p.114.

38 Robert Grosseteste, On Light (De Luce), trans. Clare C. Riedl (Milwaukee: Marquette University Press, 1978), pp. 10-11.

39 Lindberg, Theories of Vision from al-Kandi to Kepler, p. 97.

40 Vesely, Architecture in the Age of Divided Representation, p. 121.

41 See the introduction written by the translator in Grosseteste, On Light (De Luce), p. 6.

15 Fig. 1.4. An Illustration of the celestial spheres -formed via multiplication of light-, and their relation to perspectival vision, from Cesare Cesarianoʼs edition of Vitruviusʼs De Architectura, 1521.

However, it is crucial to emphasize that, this principle of continuity cannot be considered as akin to Galileoʼs speculations. By rejecting the superiority of heavens, Galileoʼs science stimulated the transformation of the universe into a whole comprised of similar components under the control of universal laws.42 Even though, it might be possible that the homogenization of the celestial and terrestrial worlds was inspired by Grossetesteʼs interpretation of the role of light in the formation of continuous space,43 the hypothetical premises of homogeneous space in seventeenth-century science was not fully in accord with his understanding of ʻcontinuity.ʼ In Grossetesteʼs metaphysics, the expansion of light to form the spheres is a gradual process, in which each step the actualization and perfection of form (spherical boundary) decrease (ﬁgure 1.4). It is formed by a continuity of the expansion of light, but the quantity of the corporeal matter in each sphere and its

42 Pérez Gómez, Architecture and the Crisis of Modern Science, p. 311.

43 Dalibor Vesely states that Grosseteste was likely to be the ﬁrst to postulate such continuity and he speculates on the possibility that he might have had inﬂuence on further accomplishments in science. See Architecture in the Age of Divided Representation, p. 122 and see the note 42 on p. 408.

16 qualitative aspect differs in every rarefaction. Therefore, it is not a homogeneous space but a continuous one structured hierarchically from the circumference to the center. In Grossetesteʼs explanation, the most perfect form is the outermost part of the sphere, the firmament, since it was created by the very first matter. It contains nothing else but first matter in its composition, thus it is the simplest of all bodies.44 After the outermost sphere is actualized, the light of the firmament diffuses itself to the center. “Each represent a region rarefied by the action of light; once the limit of possible rarefaction is reached, a new sphere is formed. This process of propagation continues through the perfect, incorruptible celestial spheres and culminates in the imperfect, corruptible domain of the sublunar terrestrial spheres identified with the four elements.”45 In his words:

The form (species) and perfection of all bodies is light, but in the higher bodies it is more spiritual and simple, whereas in the lower bodies it is more corporeal and multiplied. Furthermore, all bodies are not of the same form (species) even though they all proceed from light, whether simple or multiplied, just as all numbers are not the same in form (species) despite the fact that they are all derived from unity by a greater or lesser multiplication.46

In Grossetesteʼs interpretation of the materialization of the universe, we see a clear dialectical reasoning for the hierarchical differentiation between the heavenly and earthly bodies. Even tough, all thirteen spheres — nine heavenly and four earthly47 — are formed by the diffusion of light, the qualitative aspect of the bodies, whether spiritual or corporeal, are dependent on the quantity of matter, whether simple or multiplied. It is interesting that Grosseteste explains such reasoning through an analogy based on numbers, directly referring to mathematics, the science constructed to reveal the structure of the intelligible things. In De Luce, Grosseteste explains the formation of ﬁnite spheres and differentiation of each through mathematics.48 But he does not exactly

44 Grosseteste, On Light (De Luce), p 13.

45 Vesely, Architecture in the Age of Divided Representation, p. 122.

46 Grosseteste, On Light (De Luce), p. 15.

47 Ibid.

48 In Grossestesteʼs explanation, light does not have a body. However, through an infinite multiplication of itself, light forms finite matter. Accordingly, the first finite and actualized sphere is the firmament, which has the largest circumference, therefore it is the least dense one. As the light propagates from the outermost sphere to the center, the spheres that are actualized in each step owns a smaller circumference than the former. As the circumference area decreases, the density of the sphere increases, since it is assumed that all spheres have a finite amount of matter in it. See, Ibid., p. 14.

17 suggest the inquiry of mathematics or geometry for further studies of the bodies.49 Among the notable perspective theorists of the next generation, Roger Bacon would elaborate on this dialectical understanding and make a clearer argument on the necessity of mathematics to comprehend terrestrial phenomena, since it was regarded as in direct relation to celestial. In Baconʼs words:

It is plain, therefore, that celestial things are known by means of mathematics, and that a way is prepared by it to things that are lower. That, moreover, these terrestrial things cannot be learned without mathematics, is clear from the fact that we know things only through the causes, if knowledge is to be properly acquired, as Aristotle says. But celestial things are the causes of terrestrial. Therefore these terrestrial things will not be known without a knowledge of celestial, latter cannot be known without mathematics. Therefore a knowledge of these terrestrial things must depend on the same science.50

Reflections of the medieval optics in Renaissance perspective theories could be defined to some extent based upon the connotations of mathematical and geometrical interpretation of light. However, these connotations were not merely a technical aid on which to found the new representation. They were an expected outcome of a larger cosmological and philosophical framework. This framework was established by postulating light as the common matter in creation of the universe. The assumption of common matter inevitably diminished the conventional boundary between supra-lunar, celestial, and sub-lunar, terrestrial, realms. Though the world was postulated as hierarchically structured, a belief in ʻcontinuityʼ was critical “for there to be a unified vision of reality that could, in the future, be represented perspectivally. The most important consequence of the new vision was that it became possible to see the presence of celestial order in terrestrial phenomena more directly.”51

49 In his other book, De lineis, angulis et ﬁgures, Grosseteste praises mathematics and geometry for the comprehension of natural phenomena. He says that, “all causes natural effects must be expressed by means of lines, angles and ﬁgures for otherwise it is impossible to grasp their explanation.” See Edward Grant, ed., A Source Book in Medieval Science. (Cambridge, Massachusetts: Harvard University Press, 1974) p. 385.

50 Roger Bacon, Opus Majus, trans. Robert Belle Burke. (New York: Russell & Russell Inc., 1962), p.129

51 Vesely, Architecture in the Age of Divided Representation, pp. 122-3.

18 Constructing

Although the Renaissance invention of constructed perspective, perspectiva artificalis, had crucial differences from medieval optics, the quest for finding the truth via visual phenomena remained consistent.52 Renaissance artists were aware of the optical studies conducted during the Middle Ages53 and their further studies on geometrical structure of vision elevated the discourse of perspective to representation. This elevation, in general, is rightly marked as a revolution. The philosophical framework that enabled such a revolution was predominantly under the influence of medieval optics, which established continuity between human and divine realities. This continuity, on one hand, was constituted in metaphysics by postulating light as the common matter in the creation of both celestial and terrestrial realms. On the other hand, it was also evident in the epistemology of light, which advanced a strong connection between divine intellect, intelligible things and the human mind. By sustaining associations of light and intelligibility, this connection was articulated as the irradiance of divine light on intelligible things and its reflection on the human mind. A clear example of this interpretation can be seen in Grossetesteʼs philosophy, which acknowledged that “all human knowledge stemmed from a spiritual irradiance of uncreated light.”54 In accordance with this understanding, Grosseteste explained divine illumination as a “spiritual light which is

52 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 31.

53 Optical studies conducted during the thirteenth century culminated in the complete synthesis of Roger Baconʼs work as developed further by his two young contemporaries, Witelo and John Pecham. These two ﬁgures cannot be claimed as Baconʼs disciples, since they were inﬂuenced by many other sources and authorities, including Euclid, Aristotle, Augustine, Avicenna, and Grosseteste. Nevertheless, both of their thoughts were almost entirely structured on Baconʼs synthesis. Although there is no concrete evidence whether Witelo or Pecham had any personal contact with Bacon, there is ample chance that Witelo had access to Baconʼs treatise via the papal Curia in Viterbo, since Witelo visited the Curia a year after Baconʼs texts were received and dispatched. In Pechamʼs case, he and Bacon were fellow residents of the Franciscan monastery in Paris in the early 1260s. It is highly possible that Pecham had read Baconʼs manuscripts and/ or discussed his perspective studies with him in person. After Pecham and Witelo, the development of the medieval optics stalled during the fourteenth century. Save a few texts reexamining the perspective tradition, there arose few original treatises. Among those was Blasius of Parmaʼs work entitled, Questiones Super Perspectivam, consisting of 24 questions on Pechamʼs Perspectiva Communis. A copy of this treatise was brought to Florence in 1424, by Paolo Toscanelli. See Lindberg, Theories of Vision from al-Kandi to Kepler, pp. 116-152.

54 Georges Duby continued, “were it not the sin makes the body opaque, the soul would be able to perceive the blaze of divine love.” See The Age of the Cathedrals: Art and Society 980-1420, (Chicago: The University of Chicago Press, 1981), p. 147.

19 shed upon intelligible things and the eye of mind (oculus mentis), and which has the same relation to the interior eye (ad oculum interiorem) and to intelligible things as the corporeal sun has to the bodily eye (ad oculum corporalem) and to visible things.”55

As evident in this statement, Grosseteste explained the continuum of divine illumination on intelligible things and the ʻeyeʼ of the mind through an analogy. To him this process was analogous to the irradiance of the physical light and its perception by the corporeal eye.56 Such analogies that emphasized the twofold character of light — which can either be a conceptual constituent of the intellect or, regarding its corporeity, could be perceived through senses — were present since antiquity. However, the motivation to reconcile these two manners was also inherited in the strong belief in the same analogy. Since Plato, it is important to remember that the only modus to discover the ʻform of the goodʼ — divine — could be through the studies of physical light and phenomena of corporeal vision. The reason for taking for granted such an approach as the only modus, was probably the enigmatic operation of sight and the ineffable nature of light. In particular, the difﬁculty of deﬁning the nature of light inevitably elevated its unknown essence from the rest of the material world. Thus, such elevation enabled the assumption that its essence was congruent to the intelligible. To quote Grosseteste again: “... light is more exalted and of a nobler and more excellent essence than all corporeal things. Moreover, it has greater similarity than all bodies to the forms that exist apart from matter, namely, the intelligences.”57 Based on this understanding and precedent analogies, we can see that there was an established continuum between corporeal light, vision and the intellect, “on the grounds that they all share the same source of light and participate in the same sequence of illuminations.”58 This was the philosophical framework inherited from

55 See the quote in A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700, (Oxford: Clarendon Press, 1953), p. 130.

56 He elaborated on this analogy in his book De veritate as follows, “Therefore it is true, as Augustine attests, that no truth is perceived except in the light of the supreme truth. But just as inﬁrm corporeal eyes do not see colored bodies unless they are illuminated by the light of the sun (however, they cannot gaze on the light of the sun itself, but only as radiated onto colored bodies), so the inﬁrm eyes of the mind do not perceive truths themselves except in the light of the supreme truth; however, they cannot gaze on the supreme truth itself, but only in conjunction with and irradiation upon true things.” Quoted from David C. Lindberg, Theories of Vision from al-Kandi to Kepler, p. 96.

57 Robert Grosseteste, On Light (De Luce), p. 10.

58 Vesely, Architecture in the Age of Divided Representation, p. 124.

20 medieval perspectiva that directly influenced the Renaissance approach to artificial perspective. Within this conjecture, Renaissance art aimed to find out the divine order in direct visual phenomena.

In that regard, the connection of the divine intelligence to human apprehension could only be realized within the domain of studies of light and vision. In other words, light was the medium that revealed the essence of nature, enabled it to be visible to human eye, and consequently penetrated by human knowledge. Acknowledging this connection, the possibility of comprehending the divine through the directly perceived realm could only be “motivated by the conviction that senses give us real knowledge of reality and that it is light which makes the knowledge real, because it simultaneously affects the visual ﬁeld and vision itself.”59 Therefore, for Renaissance artists, the Aristotelian doctrine which advanced a direct relation between ʻseeingʼ and ʻknowingʼ was inspiration. Hence, during the Fifteenth and Sixteenth Centuries, perspective studies were inherently conducted based on the synesthetic perception of the observer.60

Accordingly, during the Renaissance, space could not be considered as an objectified medium, in isolation from the rest of human reality. Perspective drawings intended to demonstrate the established continuum between corporeal vision and divine intellect. In that regard, seemingly autonomous structure of Renaissance perspective was a means to meditate through the geometrical interpretation of corporeal sight, in order to participate in the divine order. As a matter of fact, in early perspective treatises, it was explicit that the vision occurred in a finite world61 and the space represented on the canvas could only be regarded as ʻpotentiallyʼ infinite. Particularly, homogeneous and potentially boundless space visualized in perspective drawings was not only the result, but the main purpose of perspective construction. That was to bring the homogeneity and boundlessness of divine realm, which is foreign to direct experience, to limited human understanding.62 Thus, the ultimate desire of Renaissance perspective was “to recognize

59 Ibid.

60 See Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, pp. 19, 25-7.

61 Regarding, in particular, Albertiʼs treatise De Pictura. See; Ibid., p. 12.

62 Panofsky, Perspective as Symbolic Form, pp. 30-31.

21 the presence of light, intelligibility, and order — that is, the divine reality — in the human world and to make it accessible to ﬁnite human understanding.”63

Based on the context presented here, it cannot be possible to agree with the traditional understanding of the Renaissance invention of linear perspective, which regards it as a new representation of space. Such understanding could only be acceptable for representing the modern conception of the universe, postulated by Newton as a priori, homogeneous, absolute and independent space.64 Newtonian science was founded on absolute premises of an inﬁnite universe, and, when Newtonʼs doctrines became the dominant ethos after the Seventeenth Century, the a priori concept of homogeneous space turned out to be the domain of natural actions, which could be explored via direct observation. Hence, this homogeneous space was meant to be collided with humanityʼs ʻnaturalʼ way of seeing. However, it should be emphasized that such an instrumentalization of perspective in order to directly ʻobserveʼ the ʻtruth,ʼ is fundamentally different from the intentions of both medieval optics and the Renaissance art, which aimed to have access to the ʻtruthʼ in limited human understanding via the connotations of vision and light. For the Renaissance, it is evident that artists were seeking to obtain “true knowledge through vision;”65 however, during the Fifteenth Century, the understanding of true knowledge was not reduced to positivist premises that can only be obtained through objective or disembodied analyses — which would be the case for the modern science. “For the [Renaissance] arts, knowledge involved personal orientation in a speciﬁc cultural context, including its metaphysical (mythical) and theological dimensions.”66

Therefore, to actualize legitimate construction of linear perspective, a priori concepts of ʻmodernʼ space were not a precondition. In the Fifteenth Century context, cosmological world-view was not suitable for formation of representations based on hypothetical premises. After all, with reference to the connotations of medieval metaphysics, the world was not postulated as homogeneous but continuous. Thus, the novelty of the new representation was inherited in the hierarchically distinct cosmological continuity between

63 Vesely, Architecture in the Age of Divided Representation, p. 134.

64 Ibid., p. 139.

65 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 31.

66 Ibid.

22 imperfect terrestrial and perfect celestial realms, and in the epistemologically established continuum between visual phenomena and the divine realm. Within this conjecture it became possible to bring the divine order, which was established in the language of mathematics, into human sight. The ultimate motivation that precipitated the ʻinventionʼ of linear perspective was, therefore, intended to reconcile the divine order with imperfect human realm.

When considered against this context, one can realize that Filippo Brunelleschiʼs perspective experiments were not intended to discover a method for merely depicting visual objects, but to demonstrate “the possibility of a new link between visible reality and its ultimate source in the divine truth.”67 Thus, the experiments were a means to search for truth. Regarding the implicit relationship between vision and divine intellect, this new link could be manifested via the geometrical interpretation of light (or vision, since their essence was believed to be similar).68 Through the visual experiments, which led him to set down “...properly and rationally the reductions and enlargements of near and distant objects as perceived by the eye of man...,”69 Brunelleschi, in fact, aimed to display the presence of truth in the visible world. In that sense, the vision of a congruent space, derived from the geometric structure of the visual pyramid, was in accord with the perspectival organization of a directly visible world.70

Brunelleschiʼs symmetrical representation of the Baptistery (1420), is credited as the ﬁrst example of a systematic perspective construction (ﬁgure 1.6). About its construction method, the commentaries are divergent, whether Brunelleschi depicted the building based on sensory impression or geometrically derived its perspective structure from orthographic drawings. For instance, it was Giorgio Vasari who stated that Brunelleschiʼs construction was derived from a ground plan and an elevation, although there is no documentary proof that he did so. Besides, it is important to note that Brunelleschiʼs

67 Vesely, Architecture in the Age of Divided Representation, p. 144.

68 Also, as Leonardo Da Vinci states, “in the practice of perspective the same rules apply to light and to the eye.” See, Leonardo Da Vinci, The Notebooks of Leonardo Da Vinci, vol. 1, ed. Jean Paul Richter, (New York: Dover Publications, 1970), p. 45.

69 Antonio Manetti, The Life of Brunelleschi, ed. and trans. Howard Saalman and Catherine Enggass, (University Park, PA: Pennsylvania State University Press, 1970), p. 42.

70 Vesely, Architecture in the Age of Divided Representation, pp. 143-4.

23 experiments were mostly intuitive.71 While the construction technique was not mentioned in his biography — written by his disciple Antonio Manetti — the experimental set-up to verify the “correctness” of the image was explicitly noted. After Brunelleschi finished the painting, he pierced a peephole in the center of the panel, where the vanishing point was placed (figure 1.5). He asked the viewer to place his eye at the back of the panel, “...with the one hand bringing it [the panel] close to the eye, and with the other holding a mirror opposite, so that there the painting came to be reflected back...”72 The most important feature of this critical positioning was the predetermined distance between the viewer and the mirror. The ratio of the height of the actual building to the viewing distance, supposed to be the same as the ratio of the height of the panel to the distance between the observer and the mirror. This proportional setting was crucial in order to verify the “correctness” of the perspective image. In that regard, as Manetti also insisted, Brunelleschiʼs construction was in accord with rules of linear perspective.73

Figs. 1.5. and 1.6. Brunelleschiʼs perspective demonstration in which the mirror is placed in half way between the building and the panel, from David Lindberg, Theories of vision from al-kandi to Kepler, 1976 (left), and an illustration of the baptistery in Florence with the schema of the experiment, from Dalibor Vesely, Architecture in the Age of Divided Representation, 2004 (right).

71 See Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, pp. 25-7.

72 Manettiʼs description was partially quoted from John White, Birth and Rebirth of Pictorial Space, 2nd ed. (London: Faber & Faber, 1967), p. 116.

73 See Linberg, Theories of Vision from al-Kandi to Kepler, p. 148; White, Birth and Rebirth of Pictorial Space, pp. 116-7. See also Rudolf Wittkower, “Brunelleschi and ʻProportion in Perspectiveʼ,” Journal of the Warburg and Courtauld Institutes 16 (1953), pp. 275-91.

24 The significance of Brunelleschiʼs experience was inherited in the proportional relation between the actual context and its perspective representation on the panel.74 The fact that the experiment was controlled mathematically does not imply that Brunelleschi anticipated a homogeneous space for the conception of the building. It is exactly the opposite. Taking into account the relation of the actual distance — between the observer and the building — to the viewing distance — between the observer and the mirror — verifies that the context was a prerequisite in order to represent the building. Besides, the perspective was constructed based on the eye as a single fixed point, but this point was not specifically determined in the geometric order. These facts clearly display that the perspective image was regulated based on the heterogeneity of lived space, which was still the space of architecture and its representation during the Renaissance.75

The so-called invention of linear perspective was achieved through a physical demonstration. It was fifteen years later when Leon Battista Alberti wrote the first theoretical work on the subject, De Pictura (On Painting), and, among many other important perspective practitioners, he dedicated his treatise especially to Brunelleschi. What Alberti explained in his book did not propose anything new to established knowledge of linear perspective, but it was significant since he articulated the problems of subject matter in the language of mathematics.76

Alberti began his treatise by clarifying that his explanation and use of mathematical terms were sufﬁcient to help painters to understand the basics for perspective construction. He distinguished paintersʼ approach to perspective from mathematiciansʼ by clearly stating that, “Mathematicians measure with their minds alone the forms of things separated from all matter. Since we wish the object to be seen, we will use a more sensate wisdom.” In addition, he asked the reader to consider him “not as a mathematician but as a painter writing of these things.”77 However, through out the book, he examined the issues of perspective solely in mathematical terms; therefore, he sounded more like a

74 Vesely, Architecture in the Age of Divided Representation, pp. 144-5.

75 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 26.

76 Vesely, Architecture in the Age of Divided Representation, p. 147.

77 On Painting, trans. and intro. John R. Spencer, rev. ed. (New Haven: Yale University Press, 1966), p. 43.

25 mathematician than a painter.78 What Alberti meant by “sensate wisdom” was to leave behind the theoretical framework of medieval optics and turn to practice for the sake of mastery. It is more understandable when one considers that Albertiʼs primary goal was to teach to those who aim to have mastery in painting. In order to achieve that, Alberti treated perspective as a practical science, which was in some sense similar to Descartesʼ favor of his practical philosophy over the speculative philosophy taught in the Schools.79

Fig. 1.7. Illustrations of the geometrical terms and mathematical explanation of visual rays, from NellʼInstituto delle scienze publication of Leon Battista Albertiʼs, Della architettura, della pittura e della statua, 1782.

In that regard, Alberti considered only the mathematical aspect of vision and ignored its further philosophical connotations since they were “quite useless” for his scope. For instance, while explaining the geometry of visual rays and their places in the visual pyramid, he avoided discussing their direction, “whether these rays come from the eye or

78 Vesely, Architecture in the Age of Divided Representation, p. 147.

79 Harries, Inﬁnity and Perspective, p. 71.

26 the plane.”80 Through out the text, he was not even consistent with one direction, since, in both ways the geometry of the rays would remain the same.81 Physiology and psychology of vision were highly considered within the mathematical interpretation of vision in medieval optics, and they would also be acknowledged in further theoretical studies of artiﬁcial perspective. In this early work, however, Albertiʼs concern was limited with the autonomous structure of perspective construction, concerning the position of the eye to the object to be seen. In that respect, he only inherited the geometry of cone/pyramid of vision from ancient optics, particularly from Galen and Euclid,82 and he elaborated on the construction through the proportional interpretation of that particular geometry.

In accord with the pyramid of vision, linear perspective was regarded as “a window on the world.” 83 It was Alberti who introduced the term as a means to frame the scene, which he intended to paint.84 Theoretically, among its many recent interpretations,85 it was elucidated in its most comprehensive and contextual sense, as “punctual ontological

80 Spencer ed., On Painting, p. 46.

81 Ibid., p. 103 (note 18)

82 Thomas Frangenberg, “The Image and the Moving Eye: Jean Pélerin (Viator) to Guidobaldo del Monte,” Journal of the Warburg and Courtauld Institutes 49 (1986), pp. 150-171. John R. Spencer claims that, before Alberti, vision was believed to take the form of a cone. This assumption was based on the stoic statement by Euclid, which Spencer quotes as “They [the stoics] hold that we see when the light between the visual organ and the object stretches in the form of a cone...” According to Spencer, Alberti intentionally replaced this form with a pyramid since, “By substituting the pyramid for a cone Alberti made the one-point perspective system possible, for in pyramidal vision the size of the object seen varies as the height of the observerʼs eye and the distance to the object.” See Spencer ed., On Painting, p. 103 (note 18). However, in ancient and medieval optics, there was no clear distinction between a cone or a pyramid. The form supposed to have a triangular section, one point at the eye and the base, whether circular or rectangular, on the surface. Therefore, as David Lindberg suggests, “...there is no reason to suppose that Alberti intended any more than to continue the medieval tradition.” See the note 8 in, Theories of Vision from al-Kandi to Kepler, pp. 263-4. See also Vesely, Architecture in the Age of Divided Representation, pp. 411-2 (note 70), and Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 398 (note 15).

83 Alberto Pérez-Gómez and Louise Pelletier, “Architectural Representation Beyond Perspectivism,” Perspecta 27 (1992), pp. 20-39.

84 The entire quotation is “I inscribe a quadrangle of right angles, as large as I wish, which is considered to be an open window through which I see what I want to paint.” (Spencer ed., On Painting, p. 56)

85 For a broad discussion on the theoretical interpretations of Albertiʼs “window” deﬁnition, see Joseph Masheck, “Albertiʼs Window,” Art Journal 50 (Spring 1991), pp. 34-41.

27 epiphanies whose degree of geometric abstraction was a considerable innovation.” 86 This explanation is significant since it clarifies that, fifteenth-century studies on perspective did not propose nor accomplish a systematic geometrization of pictorial depth.

On the other hand, technically, the window was conceived as a painterʼs panel in which the painting occurs as a planar cross section through the pyramid of vision.87 As seen in ﬁgure 1.8, Albrecht Dürerʼs perspective machine is an example of this method of depicting the external reality precisely by cutting a section — which is, in this case, demonstrated in the form of the physical grid frame — through the vision.

Fig. 1.8. An Illustration of Albrecht Dürerʼs perspective construction, with the help of an eyepiece and a grid frame, from his Unterweysung der Messung, 1525.

The eye — considered as the apex of the cone of vision — is connected to the asunder points within the space to be represented. The relative distances of these visual rays determine the apparent positions of the corresponding points and yield the apparent dimensions in the image.88 Since the perspective image was regarded as an exact section through the pyramid of vision, its construction depended on Euclidean laws of proportional and similar triangles. In De Pictura (On Painting), Alberti repeats the deﬁnition of proportional triangles, which is: “...those whose sides and angles contain a ratio to each other.” Then, he explains the visual pyramid as a composition of these triangles. Based on this statement, he asserts that quantities that are equally distant to the cross section, cannot make any alteration in the picture since these are similar — in

86 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 21.

87 Lindberg, Theories of Vision from al-Kandi to Kepler, p. 150., See also; Panofsky, Perspective as Symbolic Form, pp. 27-28.

88 Panofsky, Perspective as Symbolic Form, p. 28.

28 terms of proportion — in every equidistant division. Therefore, “every cross-section of the visual pyramid which is equidistant to the plane of the thing seen will be proportional to that observed plane.” 89

Constructing a perspective image, based on the geometry of vision, does not directly suggest the determination of foreshortening with respect to distance. There are other ways to control the foreshortening. However, Alberti preferred to use this relatively easy method, which was simple to understand and to apply: a sectional projection in which the appearance was established proportionally to distance.

Erwin Panofsky directs our attention to the distinction between Euclidʼs understanding of visual distortions — based on the angle axiom — and Renaissance practice of perspective construction —based on the distance axiom. According to Euclidʼs eighth theorem, parallel objects which are equally large and unequally distant from the eye, are not seen proportionally to their distances. The relative size of apparent objects could be determined by the measure of the angle of vision rather than the distance of the object form the eye. Therefore, there was an awareness that the magnitudes of the objects could only be expressed through a spherical — not a planar — cut in the cone of vision and could only be studied in degrees of an angle or an arc — not in measurements of linear length. For instance, Leonardo Da Vinci, who already criticized Albertiʼs method because it was not doing justice to human vision, worked on spherical section of visual pyramid and projection of the image on a concave surface, for his optical studies. However, he did not use this for construction of artiﬁcial perspective since he did not have a uniﬁed theory for both. 90

In Albertiʼs work, human vision was reduced to one stable point — the eye; however this point was not determined in the geometric order of construction. The autonomous structure proposed did not consider an embodied observer. In that regard, as Alberti also stated, the appearance of the objects was subject to relativity. This statement suggests

89 Spencer ed., On Painting, pp. 52-53.

90 See Panofsky, Perspective as Symbolic Form, p.35. See also Allen S. Weiss, Mirrors to Inﬁnity: The French Formal Garden and 17th century Metaphysics. (New York: Princeton Architectural Press, 1995), p. 35. For more information on Leonarda da Vinci, see; Martin Kemp, “Leonardo and the Visual Pyramid,” Journal of the Warburg and Courtauld Institute 11 (1977), pp. 128-149; Frangenberg, “The Image and the Moving Eye: Jean Pélerin (Viator) to Guidobaldo del Monte,” p. 154; and Damisch, The Origin of Perspctive, p. 35

29 that perception, represented via geometric order, would remain the same as long as the size and place of every element would change in proportion to the initial situation. In his words:

... if the sky, the stars, the sea, mountains and all bodies should become -should God so will- reduced by half, nothing would appear to be diminished in any part of us. All knowledge of large, small; long, short; high, low; broad, narrow; clear, dark; light and shadow and every similar attribute is obtained by comparison.91

Disembodied nature of Albertiʼs perspective portrays an autonomous structure, which was regulated based on the placement of the picture plane; however, this placement was not systematized, yet. During the sixteenth century, increasing interest in the empirical aspect of this phenomenon would suggest a systematic approach, which would only take place as mathematical explanations in theoretical treatises with almost no reference to practice of artificial perspective.92 In an effort to embody perspective, in order to represent pictorial depth, Albertiʼs initial structure must be interpreted through imagination. In order to exhibit the potential reconciliation of the divine order with imperfect human realm, regular geometry of perspectival space had to be considered within the phenomenal conditions of our concrete world. In that respect, Albertiʼs perspective construction cannot be considered as a method for “pictorial representation of the visible world. …At this stage, the correct or legitimate construction (costruzione legittima) is only a formal representation of space twice removed from reality, first through disembodiment and second as a two-dimensional projection.” 93 As seen in figure 1.9, Albertiʼs perspective method does not properly present the three dimensionality of perspectival space. In this construction, the spatial matrix created, is limited with horizontal projection of a two-dimensional structure into three-dimensional space.

91 Spencer ed., On Painting, p. 54.

92 Pérez-Gómez and Pelletier, “Architectural Representation Beyond Perspectivism,” p. 25.

93 Vesely, Architecture in the Age of Divided Representation, p. 139.

30 Fig. 1.9. Illustrations of linear perspective, from NellʼInstituto delle scienze publication of Leon Battista Albertiʼs, Della architettura, della pittura e della statua, 1782. (The central point of the perspective is determined based on the height of man, considering the position of the eye.)

The enchantment of ﬁfteenth century artists with early linear perspective did not achieve a geometric systematization of pictorial depth nor could be regarded as an instrument for the process of architectural creation. The notion of architectural creation belonged to the world of everyday experience, which was revealed in qualitatively distinct, heterogeneous places and could be explored through poetic narratives. Therefore, Renaissance architects were not ready to accept the homogeneous space of perspectiva artiﬁcalis as a medium to understand the three-dimensionality of a building. With De Pictura, Alberti aimed to enlighten painters about this legitimate construction; but, in his work on architecture, De Architectura, which was published later, there was no trace of these new

31 ideas.94 Since, the concept of homogeneous space could only be congruous for the regular motions of the heavenly bodies in the supra-lunar realm.95

It is certain that later perspective theorists sought to visualize homogeneous and potentially infinite space; yet, it is crucial to emphasize that in the Renaissance context, space was “still a part of the phenomenal reality in which it cannot be treated in isolation from the conditions of its embodiment.”96 In that regard, the representation of homogeneous and infinite space — which could only be congruent for the regular motions of heavenly bodies — cannot be considered as totally absolute, distant from corporeality of human vision. In Albertiʼs work, this corporeality was totally abstracted and presented only within the limits of geometry. This truly geometric interpretation, which led to an autonomous structure, can only be considered as a technical precursor of further development of systematic geometrization. Nonetheless, theoretically, Albertiʼs approach was heavily under the influence of medieval tradition. For instance, John White, clearly displays this fact through Piero Della Francescaʼs explanation for the necessity of artificial perspective. In Pieroʼs words:

... since one part of any quantity is always closer to the eye than the another, and the nearer part always appears under a greater angle in relation to the ﬁxed limits, and because it is not possible for the intellect by itself to judge their measurements, that is to say how great the nearer and how great the more distant, therefore I say that perspective is necessary, which discerns all the quantities proportionally like a true science, showing the diminution of any quantity by means of lines.97

The evaluation of the relationship between the apparent quantity and the angle of vision was inherited from Alhazenʼs and John Peckhamʼs works. Their notes on other antique sources were recorded in the Renaissance as a patch of quotes by Lorenzo Ghiberti in his Third Commentary.98 Pieroʼs statement suggests that the axiomatic relation between

94 Oechslin, “Architecture, Perspective, and the Helpful Gesture of Geometry”, p. 40.

95 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 21.

96 Vesely, Architecture in the Age of Divided Representation, p. 139.

97 White, Birth and Rebirth of Pictorial Space, p. 129.

98 Ghibertiʼs unﬁnished work was generally considered a return to perspectiva naturalis of ancient and medieval science. However, his contribution ultimately led to a reconciliation of the new science of Alberti, whom he respected, with phenomenal aspects of optics.

32 ʻseeingʼ and ʻknowingʼ can be fulﬁlled when the knowledge of distance is involved in the process of understanding what is seen. As White claims: “The same conception of sight underlies Albertiʼs insistence that there must be some rule whereby this knowledge of the painted object can be passed on to the beholder before it can ʻappear like the real.ʼ It is the knowledge of the actual size which gives meaning to the appearance in the eye.” Therefore, it is suggested that the scientiﬁc painter has to be concerned with the actual size.99

It is incorrect to assume that this recommendation discloses the homology between plan, elevation, and perspective drawing. In the Renaissance, the concern with true form and its appearance did not yet result in a systematic approach, in which to construct the image, as the entire system is required to be deﬁned in plan and in elevation where the former determines the width while the latter determines the height of the perspectival projection. This correspondence was sure to be realized in the experience of a building.100 However, such realization was not yet considered as instrumental, but transcendental, a means for reconciling the imperfect human sight with true form.

Reverse

The Renaissance context, in which the Brunelleschiʼs legitimate construction of linear perspective could be actualized, was far from Newtonian, but eventually that context would change to the point when it was assumed that humanity was living in a linear perspectival world. This philosophical shift produced a sharp end to the type of perspective inquiry which culminated the theoretical approach to perspective. An examination of the amount and the quality of the treatises produced during the Renaissance reveals that space was not an objectified medium that can be represented in autonomy for the Renaissance authors and artists. It would be a lengthy process to finally postulate space as infinite, absolute and homogeneous.

Perspectiva artiﬁcialis was considered to be a geometric construct but was approached as a symbolic way of revealing the order of the cosmos until the end of the Seventeenth

99 White, Birth and Rebirth of Pictorial Space, p. 129.

100 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 27.

33 Century. As a consequence of the Scientific Revolution, the concept of hierarchical structure to the world was replaced with a vision of the infinite universe. It was assumed that there was no further need for interpretation to reveal the order of things, since order was believed to be constituted in nature itself. Therefore, perspective, which was cultivated with symbolic connotations of light and vision, lost its privilege position in scientific discourse and was relegated to an instrument to depict the observed phenomena. In this regard, perspective was considered as truly natural.

However, within the framework of the natural perspective, Johann Heinrich Lambert investigated the transcendent capacity of perspective; reminiscent of the former signiﬁcance of perspective was, in fact, cosmological. In his perspective treatise, La Perspective Affranchie, he devoted a chapter on a ʻreverseʼ construction method for examining perspective images, which he called Des Regles inverfes de la Perspective. Lambert presents a set of rules to attain the true dimensions of a form from a given perspective. At ﬁrst glance, such an approach can be considered as a further step for the instrumentalization of perspective. However, it should be emphasized that Lambertʼs perspective theory was complementary to his studies on cosmology.

His cosmological thoughts were framed with by teleological assumptions based upon the perfection of Godʼs creation. His conception of the universe was finite. His understanding of the cosmological structure was hierarchically ordered. His speculative thoughts on the world edifice were grounded in his unblemished trust in analogy. Accepting the sun as the center of the solar system, which is a part of the Milky Way, led him to conclude that the whole structure of the universe was grounded on a center — to him, it was a massive dark body — that holds the whole sub-systems together. In order to reveal the true structure of this system, he proposed ʻappearanceʼ as a means to grasp the perspectival image of the celestial bodies. Acknowledging the distinction between true structure and its ʻappearance,ʼ Lambert reversed the procedure of perspective construction. In his perspective theory, he considers ʻappearanceʼ as a starting point in his search for the truth. He is aware of the deceptive quality of ʻappearanceʼ dependent upon the subjective nature of perception. Nevertheless, he points out the limits of human capability and emphasizes that human perception should be considered in understanding the order of the world. Therefore, he concludes that although objective observations are primarily significant in order to reach the truth. A partial, subjective perception would impede the

34 ability to achieve this goal. To Lambert, the subjectivity of ʻappearanceʼ is not a problem, it was the very symbol of the world ediﬁce.

35 3) JOHANN HEINRICH LAMBERT

Fig. 2.1. An illustration of the free perspective drawing of the sky with a comet, from Lambertʼs Freye Perspektive, oder Unweisung, 1774.

“...I must say, though, that an appearance that absolutely never deceives us could well be something more than mere appearance....”101

101 Quoted from Lambertʼs letter to Kant, dated from Oct. 13, 1770. See; Immanuel Kant, Correspondence, ed. and trans. Arnulf Zweig, (Cambridge: Cambridge University Press, 1999), p. 79.

36 Brief Biography of Lambert

Fig. 2.2. Johann Heinrich Lambertʼs portrait, from Alberto Pérez-Gómez and Louise Pelletier, Architectural Representation and the Perspective Hinge, 1997.

Johann Heinrich Lambert (1728-1777) was one of the most interesting ﬁgures of the eighteenth century. Karsten Harries calls him “one of the most thoughtful representatives of the enlightenment.”102 Today, published studies of Lambert present him with the anecdote of his inauspicious entry into the mainstream of European intelligencia. In March 1764, Lambert, the son of a poor tailor, was introduced to Frederick the Great,

102 Inﬁnity and Perspective, p. 303.

37 King of Prussia, the Royal Patron of the Prussian Academy of Sciences in Berlin. As a prospective member of the Academy, Lambert was seated in a room intentionally darkened to avoid the possible prejudice the King might have in encountering the unusual-looking candidate. When the King arrived and was introduced to Lambert, the candidateʼs words made an unusual impression. The Prussian King asked the man, whom he could barely see, “Would you do me the favor of telling me in what sciences you are specialized?” “— In all of them” was the answer from the dark silhouette. “Are you also a skillful mathematician?” the King continued. “— Yes” the silhouette answered, without elaborating. The King proposed one more question to the laconic candidate, “Which professor taught you mathematics?” “— I myself,” replied Lambert. “Are you therefore another Pascal?” “— Yes, Your Majesty.” That night, at dinner, the King remarked that he had just met the greatest blockhead in the world. Nonetheless, more than a year later, the blockhead would be inducted into the Academy.103

As in this anecdote, Lambert was usually described by his contemporaries in a way that prevail the Eighteenth Centuryʼs admiration of Socrates. He was odd-looking, did not seem to suit in the polite society with his unmatched clothes, loud laughter and silly jokes. However, in Lichtenberg words: “But under this bizarre exterior the finest qualities of the heart and the intellect lay hidden….”104 His description resembles the image of an absent-minded philosopher, reduced from the burden of traditional approaches. For instance, Copernicus (the astronomer whom Lambert admired above all others), too, was distanced from “the centers of the scientific culture.” The image fits the tradition that those who are authentic searcher of truth are lonely, introverted, willing to submit themselves before all others to what they find. In that respect, just as Copernicus had liberated his thoughts from traditional prejudices, Lambert, too, set himself free from the prejudices of his age, and opened his mind through imagination. It was his firm trust in his own thoughts rather than the proclaimed accomplishments of his scientifically progressive contemporaries that led him to present one of the most interesting but speculative accounts of the new order of the cosmos.105

103 Cosmological Letters, p. 1.

104 Blumenberg, The Genesis of The Copernican World, p. 528.

105 Harries, Inﬁnity and Perspective, p. 302.

38 As a self-educated scientist, Lambert was interested in many fields of science — hygrometry, meteorology, photometry, pyrometry. Thanks to his pioneering studies on the physics of light, advanced by his books, Photometria and Pyrometria, he is frequently credited for original accomplishments in pure mathematics and geometry. He proved the irrationality of e, the numerical basis of natural logarithms. He also ascertained the irrationality of π, the ratio of the circumference of a circle to its diameter. He came close to formulating a non-Euclidean geometry. He made significant advances in the field of cartography. Contemporary cartographers still use Lambertʼs projections, which are parallel, conic and central. His treatise on perspective was closely related to his studies of cartography, since perspectiva artificialis had been theoretically tied to cartographic studies since the Sixteenth Century.106 However, his theory of perspective had a more historically significant impact on his cosmological studies and philosophical speculations.

He was the ﬁrst to introduce phenomenology as a branch of science, as a ﬁeld that studies “the logic of appearances.” This work has not been seriously considered as a forerunner of modern phenomenology phenomenology, developed mainly by Husserl. Nonetheless, the strong links connecting perspective and human perception in Lambertʼs work are strong enough to suggest that Lambert was simply “born too soon.”

Although today Lambert is now mostly celebrated by mathematicians and illumination engineers rather than philosophers, he was a well-respected philosopher in his day. His early writings on philosophy were admired by Kant, so much so that Kant thought of dedicating his works Critique of Pure Reason to him. Kantʼs and Lambertʼs thoughts on cosmology were similar in many ways — they both considered the phenomena of the Milky Way as a perspectival problem, for example. But, while Kant advocated the inﬁnity of universe, Lambert insisted on ﬁnite boundaries. Nevertheless, Kant acknowledged Lambertʼs work in his Theory of Heavens in such a way that guaranteed Lambertʼs place in the history of cosmological science of the Eighteenth Century.107

106 Louise Pelletier, “Johann Heinrich Lambertʼs natural perspective,” in Halina Dunin-Woyseth & Jan Michl (Eds.), Towards a Disciplinary Identity of the Making Professions: The Oslo Millennium Reader, Research Magazine, no.4 (2001), p. 76.

107 Blumenberg, The Genesis of The Copernican World., p. 578.

39 Cosmology

Fig. 2.3 Book cover of Cosmologische Briefe über die Einrichtung des Weltbaues, 1761.

...Cosmological Letters dates from 1749. Right after supper I went to my room, contrary to my habit then, and from my window I looked at the starry sky, especially the Milky Way. I wrote down on a quarto sheet the idea that occurred to me then, that the Milky Way could be viewed as an ecliptic of the ﬁxed stars and it was this note I had before me when I wrote the Letters in 1760.108

108 Quoted from Lambertʼs letter to Kant, dated from Nov. 13, 1765. See; Immanuel Kant, Correspondence, ed. and trans. Arnulf Zweig, (Cambridge: Cambridge University Press, 1999), p. 79.

40 Fig. 2.4. An image of the proportional magnitudes of the planetary orbits, from James Jacque translation of Lambertʼs System of the World, 1800.

When he started writing his Cosmological Letters (published a year later), Lambert had only a single piece of paper with him, on which he had made his initial notes on the appearance of the Milky Way. Throughout the process, he avoided nurturing thoughts from earlier scholarship, to avoid jeopardizing the ﬂow of his Letters, structured as a ﬁctional correspondence between him and his — imaginary — colleague.109 Twelve years after the publication, Lambert wrote to Johann Lorenz Böckmann, to explain how this manner of writing made every response into a step to elevating the argument to the next

109 Even numbered letters are Lambertʼs responses while the odd numbered are his colleagueʼs.

41 level.110 Thus, in this “artiﬁcially engendered dialogue situation,” Lambertʼs thoughts were not just presented but also developed, and more of them were produced.111 In the same letter, he also noted that, lacking access to his sources, he was not able to quote recent data that could have supported his argument.112

The significance of Lambertʼs writing process is two-fold. On one hand, it emphasizes the originality of his Cosmological Letters; on the other hand it demonstrates its speculative essence. For the first case, we should remember that Lambert was not the first scientist to regard the phenomena of the Milky Way as a perspectival problem. This issue was first considered by Thomas Wright in his An Original Theory or New Hypothesis of the Universe, published in 1750. Wright anticipated Lambertʼs idea that the irregular distributions of the stars in the Milky Way were a result of our eccentric point of view (Figure 2.5). Wright acknowledged Keplerʼs ideal circular form as a theoretical a priori, which suggested that the galaxy could either be formed as a ring or a spherical shell of stars. According to him, since our standpoint is in the solar system —already inside this ring or sphere — stars would appear to be situated on a flat disk. Wright perspectivally thought that the disk could be the two-dimensional foreshortened view of their true circular form. Therefore, he concluded that the seemingly irregular structure of the stars, could not be more than a false appearance of a true order, since “the guiding principle, for Wright, [was] manifestly the metaphysical need for a well-ordered arrangement of the world that is all-encompassing, even if it is painstakingly concealed for man.” 113 Wrightʼs a priori concept was determined by un-scientific, esthetic-theological considerations. To

110 Böckmann (Boeckmann) was a professor of physics and mathematics in Karlsruhe. See; note 39 in Cosmological Letters, p. 202.

111 Lambert explains how his manner of writing helped developing his ideas, in his letter to Johann Lorenz Böckmann, dated from Mar. 7, 1773. In the text, this is quoted from Blumenbergʼs paraphrase. See The Genesis of the Copernican World, p. 577.

112 Same letter, paraphrased from; Jakiʼs introduction in Cosmological Letters, p. 8. Jaki also notes that these sources were; “the Magellanic Clouds, the explanation by Maupertuis of the various visual shapes of ʻnebulous starsʼ”, and some articles in the Mémoires of the Academy of Sciences in Paris on the pale light in Orion”. The former was published in 1742 and in this work Maupertius claimed that the reason of the different appearances of nebulous stars could be their “ﬂattened oval” shape. The latter studies were mostly concerned with the changeability of the appearance of the nebulae. See; note 40 and 41, pp. 202-3.

113 Blumenberg, The Genesis of the Copernican World, p. 531. See also; Stanley L. Jaki, The Milky Way: An Elusive Road for Science, (New York: Science History Publications, 1972), pp. 183-221.

42 him, well-ordered structure of the world “would serve as a mirror image of a moral and spiritual order centered in God (Figure 2.6).” 114

Fig. 2.5. A section of an artificial Fig. 2.6. An image of the spherical horizon of the globe which structured galaxies of the infinite demonstrates the relativity of the universe. The eyes represent the appearance of the stars to the omnipresence of God and infinitely position of the observer, from many eternal abodes, from Wrightʼs treatise, 1750. Wrightʼs An Original Theory or New Hypothesis of the Universe, 1750.

Wrightʼs theory was not well received by his contemporaries and, running contrary to more progressive ideas, not conﬁrmed by later quantitative analysis. His theological a priori proved to be the main obstacle to realizing the true form of our galaxy, which would be compared to a disk or grindstone.115 Since his cosmological studies were driven by his theological convictions, Wright never discovered the new methods that would have led to

114 Jaki, The Milky Way, p. 184.

115 Ibid., p. 183.

43 a corrected theory.116 Nevertheless, he was the ﬁrst after Copernicus to attempt a comprehensive hypothesis about the structure of our galaxy.

Lambert remained unaware of Wrightʼs work until 1761, when, during his visit to Nürnberg, he was told that an Englishman had already written about the arrangement of the ﬁxed stars in a way that approximated Lambertʼs more detailed analysis.117 Like Wright, Lambert was also guided by his belief in a hierarchically structured universe. However, while Wright placed God in the center of his perspectival cosmos, Lambertʼs references to God were indirect.

In Lambertʼs understanding, the cosmos necessarily had the most perfect structure since it was the product of an “all-wise Creator.”118 Following the logic of creation and divine rule, the systems of the universe had to have a hierarchical order. “Order and hierarchy were synonymous for Lambert with purpose, and this in turn was one of the basic truths that in Lambertʼs eyes were self-evident and provided a necessary framework for valid reasoning.” 119 Thus, Lambertʼs guiding principles were teleological. For instance, his hypothesis for the motion of the ﬁxed stars and his arguments for the necessity for the existence of multiple planets and satellites were intended to demonstrate that there was no part of the cosmic space created without underlying divine purpose. Another key aspect of this teleological view was that no other part of the universe could be habitable. God had placed Adam and Eve on earth as a primary alignment of his divine plan. This thesis was not critical for Lambertʼs explanation for the construction of the cosmos, but it was theologically central to the idea of stability.120 If all celestial bodies were theoretically suitable for life, it would not be possible for them to “undergo any major transformations

116 In 1784, when William Herschel conducted his truly quantitative observations, through his advanced telescope, he displayed that a theological priori was not the guiding principle of the structure of the universe. In his ﬁrst publication on the construction of the heavens, he criticized those who were still representing the universe as a hollow globe, with the observer at the center and the starry heavens on the periphery, ﬁlling in the inner surface. See; Blumenberg, The Genesis of the Copernican World, pp. 531-2.

117 Lambertʼs letter to Kant, dated from Nov. 13, 1765. See; Immanuel Kant, Correspondence, ed. and trans. Arnulf Zweig, (Cambridge: Cambridge University Press, 1999), p. 79.

118 Cosmological Letters, p. 41.

119 Ibid., p. 6.

120 Blumenberg, The Genesis of The Copernican World, p.548.

44 either with respect to their orbits or to their physical constitution.”121 In Lambertʼs view, the whole structure of the universe was a priori ruled by harmony. Every part had to act in accord with, and reﬂect the logic of, the whole.

Lambertʼs Cosmological Letters was mostly regarded as speculative, because his explanation of cosmic order universe was based solely on his teleological a prioris, with only anecdotal support. Lambert did not receive much of response from his more empiricist colleagues, even though he had expected them at least to be aroused by his ambitious tone. This general disinterest actually revealed a key aspect of his work. According to Lambert cosmology was “a science not only of the parts but also of the whole.”122 Lambertʼs quantitative observations could determine only the existence of phenomena; they could not discover reasons. It would not be naïve to speculate that Lambert was sensitive to empirical scienceʼs resistance to the methods and presuppositions of philosophical conjecture.123 His work on cosmology led him to believe that the process of thought played a direct and key role in comprehending the correct order inherent in the cosmos.

While, in the general approach of positive science, teleological a prioris were acceptable as a central starting point — a terminus a quo — to ground natureʼs subsequently specific and diverse laws, Lambertʼs cosmological speculation regarded teleology as the end point — the terminus ad quem — which could retroactively influence the discovery of new principles and procedures. Lambert clarified that “cosmological proofs” were not like geometrical ones, which require no proof. In his work, these proofs were already legitimized by the purpose of creation. The proof and the a priori principle of creation, put in terms of a teleological end point, were one and the same. The scientist was obliged by belief in a divine plan to accept the coincidence of these beginning and end points, but he was free — an empowered by the teleological insight — to conduct quantitative observations.124 Lambertʼs bold statement, while displaying his confidence in his Letters,

121 Cosmological Letters, p. 9. Since Copernicus put the earth in motion, it was widely debated whether the earth could become a subject to possible collisions. In the Letters, Lambert also presented this concern as his colleagueʼs doubts in the ﬁrst letter. See Cosmological Letters, p. 57.

122 Ibid., p. 10.

123 Blumenberg, The Genesis of the Copernican World., p. 537.

124 Cosmological Letters., pp. 46-7.

45 acknowledged empirical scienceʼs drift away from philosophical speculation. With his Letters, Lambert sought to establish the primacy of speculation about the cosmological order. As he states in his letter to Tobias Mayer:

But you will ﬁnd indeed, Sir, that it was necessary to appeal to some experimental evidence in order not to demand of the readers to believe in proofs which are simply cosmological. These kinds of proofs are not yet fashionable and several who tried them out, have failed. It remains to be seen whether these letters have a better luck.125

Since Copernicus, scientific agenda were driven by empirical evidence gatherd via telescopes. These studies, however, did not lead to any major new hypotheses about the arrangement of the cosmos.126 Until the mid-Eighteenth Century, there were only a few significant discoveries: (1) the discovery of the outermost sphere of the fixed stars, the existence of which was already considered in ancient studies and (2) the realization that the fixed starsʼ motions were an illusion, that the stars were not “mounted inside the enclosure of a sphere.” This view was replaced by the realization that the fixed stars were irregularly distributed in space, and that their distances to the Earth were proportional to their apparent magnitudes. In that respect, both Lambertʼs and Wrightʼs studies appeared at a time when “space had gained depth but lost structure.” Contextually, they were in between two great accomplishments of the modern astronomy, “the constructive description of the solar systems and the disclosure of order in the universe of the fixed stars.”127

In the preface of his Letters, Lambert summed up the current situation of cosmological studies. He criticized contemporary scientistsʼ over-reliance on instruments and their unwillingness to accept and employ a priori concepts about the structure of the universe:

While more recent astronomers are very anxious to put in order the sphere of our solar system and to assign each comet its orbit, and to determine in advance its eventual return, hardly any attempt has been made to find out something probable on the arrangement and position of the fixed stars. What has been done in this respect was that one tried to figure out how distant the nearest of them is from the sun. Undoubtedly, one can hardly infer from this arrangement which

125 The letter is dated from Mar. 24, 1761. Quoted from; Cosmological Letters, p. 20.

126 Blumenberg, The Genesis of the Copernican World, p. 531.

127 Ibid., pp. 530-1.

46 they have with respect to one another. The measurements in this connection do not reach far enough and one must therefore necessarily employ general considerations which, though they do not possess geometrical precision, can nevertheless be brought to a rather high degree of probability.128

Lambertʼs major work on cosmology is best described by the translator of the book, Stanley L. Jaki. As he states: “On a cursory look it seems to have been motivated by his preoccupation with comets, but its true wellspring was a vision of the universe as a totality of hierarchically ordered systems of stars.”129 To build on this comment, I should emphasize that this vision was significantly influenced by the science of perspective. Lambertʼs early fascination with realizing the oblique view of the Milky Way did not immediately lead him directly to cosmological studies. His first concern was to reconcile the idea of the hierarchically structured cosmos with manʼs eccentric position. He aimed to understand the phenomena of cosmological appearance with respect to the position of the observer. Before writing his Cosmological Letters, he had first to develop his ideas about perspective and light. While perspective led him to understand the general rules for dealing with the disparity between actual form and appearances, the quantitative relation of reception of light to the distance of its source led to its complement. Together, Lambertʼs two fields of interest prepared the way for his teleological cosmology.

On this basis, it is easy to see how Lambertʼs speculations were never very far from his scientific considerations. Since Lambert did not present his early studies as empirical verifications, but solely as teleological a priori considerations, the implicit connection between his cosmology and early mathematical studies went generally unnoticed. However, it is clear that his teleological ideas evolved closely in relation to his scientific preoccupations. Cosmological Letters actually acted as a meditator between his scientific background and his philosophical conjectures. As he stated: “In that section of Photometrie130 which deals with the light and distance of fixed stars I have incidentally

128 Cosmological Letters, p. 45.

129 Ibid., p. 6.

130 The name of the section is “On the light of the ﬁxed stars and their distance”, which is placed under chapter 6, titled as “In which the illumination of the planetary system is subjected to calculation”. See; Johann Heinrich Lambert, Photometry or on the Measure and Gradations of Light, Color and Shade, trans. David L. DiLaura, (New York: Illuminating Engineering Society of North America, 2001).

47 remarked, I believe, that one can represent to oneself their distribution in cosmic space in a most reasonable manner.”131

Considered from an astronomical perspective, the Letters was a further elaboration of the significant section on the fixed stars. However, regarding the whole context of the work from a philosophical perspective, it was a preparation for “his systematic discussion of epistemology, and especially of the role of teleological considerations.”132 When examined against his studies on perspective, one can realize how Lambertʼs methodology, in his understanding of cosmological science, was meant to replace (Newtonian) empirical verification with phenomenal experience — so much so that, in order to comprehend the cosmos, not only in parts but as a whole, Lambert realized that man had to rely on the whole appearance of the cosmos. It was in particular his reverse methods of perspective, elucidated in the next section, that proved critical, since it displayed how the apparent scene constituted a departure point for deducing true structure.

Lambertʼs return to perceived phenomena resulted in his independent discovery of the true arrangement of the stars in the Milky Way.133 Early theories on the arrangement of the ﬁxed stars proposed a correspondence between distance and apparent magnitudes. Based on this view, stars were assumed to be homogeneously distributed in an inﬁnite universe. However, this view would require every part of the sky to be as bright as the Milky Way.134 Lambert was aware of the disparity between the appearance of the galaxy and the formula proposed for its arrangement. In terms of the standpoint of the observer, he re-examined the small stars in this band, which appeared to very close to each other. The distance between them was hard to calculate because they were so far away from earth. However, as he stated: “The stars cannot be, I thought, are not so close together as to touch one another. They ought lie behind one another, and the rows of stars should

131 Cosmological Letters, p. 45. Hans Blumenberg interprets that Lambert referred to his early scientiﬁc work in order to be accepted. See; Blumenber, The Genesis of The Copernican World, p. 526.

132 Ibid., p. 9.

133 Jaki, The Milky Way, p. 200.

134 He particularly opposed Chéseaux who is a forerunner of Olbers. See; Jaki, The Milky Way, p. 200. See also; Photometry, p. 391.

48 throughout the Milky Way be many times longer than outside it .... In brief, the edifice of fixed stars is not spherical but flat and very much so.”135

The mathematical knowledge required to support his argument was already established in his major work on the physics of light, Photometrie (1760). In this work, Lambert quantitatively explained the interaction of the light source, material and visual systems136 (Figure 2.7 ). On this basis, he examined the relation between ﬁxed stars, celestial bodies and their distances from our earth (Figure 2.8).

Fig. 2.7. An image of Lambertʼs experimental set up, Fig. 2.8. An image of the application demonstrating the square of the distance of the light of the formula in Figure 2.7 for the source to the opaque plane is equal to the ratio of planets interior to earthʼs orbits. number of candles. Photometria, 2001. Photometria, 2001.

Contrary to the “ideal form” and “homogeneous distribution” assumptions, Lambert asserted that the apparent structure of the universe was the closest to its true order. As he claimed: “In my judgement, the system of the fixed stars, as it appears to us, is not all spherical but round and flat, and I therefore submit that the Milky Way is a sort of ecliptic of the fixed stars.”137 Lambert also clarified that this ecliptic was not a perfect shape, either. It had an uneven contour because of its formation of many irregularly distributed

135 Cosmological Letters, p. 121. In the previous letter, it is also mentioned that the distances of the nearest stars to the earth, were at least as far as the distances in between small stars of the Milky Way. See, p.118.

136 Ibid., p. v.

137 Photometry, p. 391.

49 star systems. For instance our solar system was not on its main stream but placed at the edge of it.138

To Lambert, apparent irregularity of the distribution of the cosmic bodies was not a concern for the true order of the universe. In his view, the manifestation of the perfect structure was not inherited in the form but in the arrangement of its constituents. As it was stated by his correspondent in Cosmological Letters: “I will no longer be taken aback by the irregular shape of the Milky Way. The order consists in the arrangement of these orbits even though it may remain hidden to us for a long time because we lack number and measure for the determination of so enormous spaces and times. Meanwhile, one can safely conclude that this arrangement is not in the least less real, for order and perfection necessarily extend throughout the world.”139

Lambert elaborated his early thoughts on the Milky Way in his Letters, such that it turned out to be a particular model for his further analogous interpretation of the structure of the universe. In his words:

We ﬁnd ourselves in one such system and I count into it all stars that are visible to us and lie outside the Milky Way as well as the larger ones that cover that arch of the sky. I set each such system similar to our solar system in the sense that all ﬁxed stars or suns which belong to it move around a common center, and I would be inclined to believe that all these systems, or the whole Milky Way, have a common center around which they move.140

It should be reminded that, when Lambert wrote on the arrangement of the world-edifice, the Aristotelian and Scholastic understanding of the unity of the cosmos had already been devastated, first by Copernicus and then, more thoroughly, by Newton. The infinite world of Newton was mainly constituted of void. “Not only were the heavenly spaces..., but even the so-called ʻsolid bodiesʼ were full of void,” in which the occupation of “matter” property was an infinitesimal part of the space. From the micro to the macro scale, these “matter” properties were freely distributed and moving to each other according to the law of attraction. Newton could not find the possible agent of this force, thus he explained the phenomena only in mathematical terms, even by disregarding its physical aspect. The

138 Jaki, The Milky Way, p. 201.

139 Cosmological Letters, p. 119.

140 Cosmological Letters, p, 111.

50 universal application of the law was the only possible clue for the unity in this new concept of the universe. As Lambert also highly appreciated; “it was the same set of laws which governs all the motions in the inﬁnite universe: that of an apple which falls to the ground and that of the planets which move around the sun.” 141

In the Eighteenth Century, the universe was yet considered as one world, but with “any physically fulﬁllable sense”. The implementation of unity was required to legitimize the immensity of the new order.142 Within this conjecture, Lambert aimed to extend the concept of unity in a physical sense. In accord with his teleological priori, he proposed an analogical construction principle for the cosmos. In his analogy, the visible hierarchical order between the satellites, planets and the sun, including the Milky Way, became a model for constructing the invisible parts of the universe. He continued to explain his method for expanding the systems toward a complete whole:

You will see from this Sir, that I make my conclusions on the basis of analogy. Thus, for instance, the satellites belong to the planets, these to the sun, the sun to its system, and this to the system of the whole Milky Way. Farther our eyes do not reach and I leave it undecided whether the Milky Way visible to us still belongs to uncounted others and forms with these a whole system. 143

Analogically, since the centralized solar system was present in that hierarchy, the whole structure was proposed to have a central organization. The planets were at the center of the satellitesʼ orbits, and meantime, they were also in constant motion, following a sun- centered pattern. The solar system as well as the other star systems became constituents of a higher order, the galaxy. Lambert did not determine the ﬁnal number of steps, since no human vision, or any possibly optical instrument that could extend human vision, were able to reach the farthest edges of the cosmos. However, he clearly stated that the end of the process would reveal a massive, dark body to be the center of the whole system.144 For Lambert, the immense universe had to have ﬁnite boundaries.

141 For further information on this, See; Koyré, Newtonian Studies, pp. 14-5.

142 Ibid.

143 Ibid.

144 Lambert explains the reason for not leaving the center empty according to the law of gravity. He asserted that, there supposed to be a massive source for attraction to keep the whole system in equilibrium. See; Cosmological Letters, p. 168

51 Hans Blumenberg uses the term “Copernican Comparative” for Lambertʼs thought-form, which implies “applying the Copernican pattern of the solar system, with the body with the greatest mass at the center of the motion of other bodies, over and over again, as the structural principle for solving all the problems in construction of the universe.” Lambertʼs analogical interpretation is a clear example of this understanding.145 However, in the Letters, Lambertʼs constant references to the “chief astronomer” of the new world brings forward further connotations of this expression.

To Be or Not to Be Copernican

How unconcerned was the good Ptolemy with his resting earth, and how quiet his followers remained until Copernicus came and began to lead the earth around the sun! But now the situation is more complicated, and Copernicus might not even be too proud of his triumph should he know that we must now be concerned that a comet might come and drag along the earth beyond the ﬁxed stars, or at least would drown, crush, choke, burn all of us and, what is even worse than such calamities, would make us fearful of philosophers. I soon wished that comets had again their old signiﬁcance and would presage wars and all calamities, which hit us anyhow and are less universal than such effects that threaten not only single countries but the whole earth and come in much more unexpected manner than do all wars 146

In the ﬁrst letter of the book, Lambertʼs correspondent stated his concern about the new conception of the movements of the celestial bodies, against the consciousness of the age. The once ineffable motions of heavenly bodies, which had been regarded as signs for possible human actions on the earth, were radically being transformed into mathematically explicable concepts. In this mathematization, the earth was brought to

145 His speculations on the existence of more planets and satellites were guided by his analogical construction principle and they were proved to be correct after his death, in Herschelʼs observations. Even after the conﬁrmation of some of his hypothesis, Lambertʼs Letters were still disregarded. It is important to emphasize that Lambert cannot be regarded as a forerunner of any further discoveries in modern astronomy. Stanley L. Jaki presents the correspondence between Lambertʼs speculations and scientiﬁc observations of Herschel. See; Cosmological Letters, pp. 33-9.

146 Cosmological Letters, p. 57.

52 same level with celestial bodies, and thus it became possible subject for the earth to directly interact.

The clear cut of the hierarchical order between celestial and terrestrial realms had been the limit for pre-Copernican science. Science had considered only the phenomenal reality of the terrestrial world. The Enlightenment undermined the distinction between these two realms and expanded the territory of the world of physical action to include the whole universe. However, the science of the new age was not successful in translating between signs and phenomena. It could formally examine the physical bodies and their movements in quantitative terms. Movements of the heavenly bodies — formerly the basis of scientiﬁc and religious signiﬁcance — lost their ability to signify essence. Mathematics limited cosmic individuality and subordinated the peculiarities of stars and planets to a single cause, gravity. Mathematics, as a language, was unable to replace the astronomical and astrological explanations of natural phenomena, placing them far beyond the human experience. Therefore, “what can no longer be a sign became a possible agent” of cosmic actions.147

Human knowledge was subjected to a massive shock. Once, the truth that belonged to the celestial bodies was accessible through symbolic means. Perspective provided a model for extracting this truth. Unmasking the illusion of a geocentric world seemed to leap toward a greater truth. However, this leap involved a loss of order. With the loss of the signiﬁcative power of the heavens, earthly bodies no longer enjoyed the “divine gap” between earth and cosmos, across which the idea of law had been born. Cosmic bodies and earthly bodies, bound by the same mechanical laws, tended toward the objectivity of those laws. Subjectivity, at a loss to ﬁnd its basis in the higher order of the cosmos, fell victim to a causality of objects. Causality, a universal objective basis, became more important than sign-generated mandates emanating from the heavens.148

This transformation also created a crisis for scientiﬁc thinking. Was the idea of a world run by the Newtonian God, according to “His free will,” viable?149 Lambert noted that, the philosophers of his time (with no hesitation) accepted Newtonʼs authority, but Netwonʼs

147 Blumenberg, The Genesis of The Copernican World, p. 553.

148 Ibid.

149 Koyré, From the Closed World to the Inﬁnite Universe, p. 276.

53 scientiﬁc laws seemed to contradict the purpose of creation. As he stated: “the [commonly accepted calculation] which one ﬁnds in so many writings is copied so readily and without inquiry, and in all likelihood this would happen less frequently if the authority of Newton, who gave us only casual computation, would not serve as a substitute for reason.”150

Lambert didnʼt directly identify the specifics of these concerns in his response. He was aware of loss of significative power with the acceptance of universal physical law and the fear that this created, but he firmly believed in the greater value of a hierarchically ordered world, where the loss of Godʼs determinative will was compensated by the harmony within the hierarchy. In Lambertʼs view, the reason for the problems of the current age lay not Copernicusʼs discovery but in the predictions of later philosophers — predictions which were by no means loyal to Copernicus. By taking earth from rest to motion, Copernicus was not making at a target of possible collisions. The true case was exactly opposite: he elevated the earth to the status of a celestial body, adapted to the full system of causalities and balances.151 As I elaborated in the previous section, such causality itself could not belong to the phenomena of the world. It could only be that which could be manipulated by the philosopher to create fear. Thus, fear could only be a product of human understanding, or the lack thereof.

I hope that you will now ﬁnd less reason to be angry with the brave Copernicus for having dislocated the earth from its rest, because you see that each comet can do that, and that perhaps several had produced various changes in that connection. You can also understand from this that we are perhaps not yet Copernican enough, inasmuch as I am not of the opinion that we become such by assuming that the earth can in the long run become the satellite of a comet. 152

Blumenbergʼs expression of “Copernican Comperative” also implies another connotation of Lambertʼs statement, “we are perhaps not yet Copernican enough.” In Blumenbergʼs words, it implies that ”the fundamental Copernican principle of putting in question and penetrating the illusion of the observerʼs being located in the center of the universe had not yet been applied sufﬁciently radically to the problems that present themselves in the

150 Cosmological Letters, p, 83

151 Blumenberg, The Genesis of The Copernican World, p. 555.

152 Cosmological Letters, p. 62.

54 astronomy.” 153 In Lambertʼs view, philosophersʼ speculations about the possibility of chaos were again central.

What Lambert aimed to emphasize was that the predictions of the later age could possibly have occurred before Copernicusʼs discovery. What Copernicus did was no more than a realization of a universal condition. In this respect, Copernicus was not necessarily liberated from the historical perspective, the “traditional understanding” of the universe as hierarchy. He did not refute this tradition; rather, he posited manʼs eccentric position and set in motion the intellectual basis needed for a perspectival consciousness as the basis for truth.

In Lambertʼs first letter, where he represented the fear of possible physical perils threatening Copernicusʼs de-centered earth, he was also referring to the problems of subjecting consciousness to the new strictures of scientific thought. In the perspectival model, truth was never reachable. When consciousness was brought into play, science opened up a possible mode of access. But, whereas the perspectival model placed mankind at the bottom of a single line of approach, the “upper reaches” of which lay beyond the senses and human reason, science had opened up the forbidden regions but provided too many false turns along the way. One wrong turn opened up an illusionary truth that multiplied and trapped the thinker. As Lambert put it, such a process is clear only in the first stages.154

The fact that new knowledge leads to new questions and doubts is after all simply “the common road along which we come from one truth to another.” In that respect each step does not reach any end but only lead to others. “Posteriority is no conclusion for the person whom the truth is not promised and for whom its own lifespan becomes a mere episode in a process that seems never to be able to guarantee that a present will ever be anything but an episode in relation to the truth.” 155 Within the conjecture of this dilemma, Lambertʼs reliance on teleology, evident in his Letters as an a priori stopgap for the lack of the proof, should be considered in this context of postponement. By no means, a priori presuppositions or a posteriori results would be sufﬁcient to determine the truth solely,

153 Blumenberg, The Genesis of The Copernican World, p. 526.

154 Cosmological Letters, p. 56.

155 Blumenberg, The Genesis of The Copernican World, p. 554.

55 but both be helpful in reaching it. While the former would set the path to follow, the latter would verify each step. In that regard, Lambertʼs departure point was to postulate the general framework in which every step was supposed to lead to a larger system of the same hierarchical structure visible to all.

Analogy is not sufﬁcient to determine truth with certainty, but it provides an inducement for conjecturing the truth and ﬁnding it out completely by means of experiments and investigations serving that purpose. This is where its use is distinguished from its misuse. The extent to which this distinction was precisely observed in the Cosmological Letters, I leave to people of keener vision to judge, as long as my intention of using analogy in moderation and correctly granted.156

In the thought-form of a “Copernican Comparative,” Lambert ﬁrmly believed in the hierarchical order of the universe centralized in a massive, stable, dark body. Just as further observations later disproved the sun-centered system of Copernicus, Lambert was sure that reaching that body would take centuries, maybe an eternity. We would not be able to reach it, or perhaps reaching it would require becoming “more Copernican.” At that point, the paradox of being increasingly skeptical about the notion of center while insisting ever more on its importance overwhelmed Lambertʼs correspondent towards the end of the Letters. As he stated: “Now we will be once more Copernican enough, or we will never be, or we should have never become one, for I am completely at a loss ….”

The significance of Copernican Revolution was inherited in refutation of humanʼs perspectival model of cosmological structure. However, this did not amount to a true liberation from the intellectual inheritance of perspectivalism. Copernicus postulated the new cosmological structure in contrast to human perception, but in keeping with humanityʼs traditional understanding of a perception. In other words, Copernicus achieved a liberation from sensual experience. His sun, the center of the physical universe, occupied the intellectual center as a “consciousness” for perception, an intellectual basis of perspective. In accord with the “hierarchy of perspective,” he constructed a higher order of appearance. Further studies of the Milky Way showed the need for a further step — a redefinition of formʼs relation to appearance — to be taken to re-configure our relationship to the gradually shifting point of center.157 To be a true Copernican, one had to be aware of this situation. As one approached the problem of the

156 Lambertʼs response to J. Wegelinʼs letter, quoted from, Ibid., p. 555.

157 Harries, Inﬁnity and Perspective, p. 303.

56 center with an increasing confidence, the center seemed to magically distance itself from the understanding. Lambert explained the complexity of each step and difficulty in finding manʼs relation to the core of the truth:

How much the world is reversed! First, the earth was at rest. Then it started moving and the sun stood still. Now it, too, moves and the body of the fourth rank rests. But it, too, will be disturbed and rest will belong to the body of the ﬁfth, and so forth until the order comes to the last [body] which is at rest not hypothetically but in fact.

Lambert geometrically applied the gradual shift of the center to the problem of perceiving cosmological order. Each step creates new complications. As he continues:

If the earth is at rest, we stay with spherical astronomy to which all the phenomena of the heavens must be reduced. This happens through a translation from astronomical language into the common idiom. If the sun is at rest, we have to do this [translation in connection] with our planets, satellites, and comets, and we speak of ellipses and hyperbolas alone. Should one go on, it becomes the turn of our neighboring suns or ﬁxed stars, and there come new ellipses and hyperbolas, and the language extends to cycloids of the ﬁrst degree. Upon these there will follow cycloids of the second, third, and subsequent degrees. 158

Under the overwhelming complexity of locating the central body, Lambert raised the possibility of anarchy among the cosmic bodies. However, the common ground of his teleological a priori, combined with the unity established by the law of gravity, reminded him of the need for some higher power, never yet conceived, to govern the evident harmony of the cosmos. Rather than open up such a daunting theological-scientiﬁc issue, Lambert favored taking the Copernican path, in which a single, central, dark body served as both ground and cause. In that understanding it was certain that the possibility of ﬁnding the truth may have turned into its impossibility. But, for Lambert, it was worth it to follow this path, whatever its perils. His analogical method, technologically cursed by its generation of new problems with every partial solution, was at least theoretically clear. Examining the visible would always be simpler than imagining the invisible. As Lambert stated:

The simple order is the apparent one. In fact what can appear more orderly than the daily course, the rise and the setting of the sun and of each ﬁxed star? Once a day the whole heavens turn around the earth, and at night the moon seems to

158 Cosmological Letters, p. 175.

57 be the leader of the whole host of stars. If one takes enough time and leisure to look into this scene carefully, small deviations begin to show. The moon wanders backward from star to star, and the planets, too, begin to show that they follow their own mind, strongly as they may be dragged on by the general stream. To remove this disorder the observer begins to think Copernican and brings planets and comets into such an order that could not be of greater excellence. But gradually the ﬁxed stars, too, show that they are not dead masses but have their own life and motion. This is a new reason to view also the [Copernican] order of planets as ﬁctitious and to conclude once and for all that the true order is the most complicated one and will never be reached by us. 159

If humans can never reach the ideal of true order, Lambert aimed to construct at least a part of it by meditating on the apparent order, via the analogy of perspective. In this historical context, then, Lambertʼs reverse methods of perspective are more comprehensible, since he aimed to start from perceived phenomena to realize the eccentric position of the observer.

Lambertʼs “Reverse Method” of Perspective

To be true Copernican, one should always be aware of the decentralized point of view in the order of the cosmos. In Lambertʼs case, since he ﬁrmly believed that in this purposeful arrangement, not only the earth but also other cosmic bodies had to be inhabited, there was a variety of different standpoints that could be taken by observers, and therefore different appearances, all requiring consideration.

As mentioned earlier, Lambert also advocated the habitability of the comets in order to include them in the universeʼs harmonious structure; therefore, they would not undergo major transformations that could threaten the cosmic ediﬁce. Comets, Lambert argued, were “created for the purpose of viewing the ediﬁce of heavens, the position of each sun, the plane and course of their planets, satellites, and comets in their whole interconnectedness.” 160 Because comets were moving from one sun to another, the viewpoints of their possible inhabitants were subject to a greater change than was the

159 Ibid., p. 178.

160 See; Cosmological Letters, p. 73.

58 case for humans. Their observations would take place over the long duration of their cosmic travel. Each new position would happen “when their habitat was on the point of seeking a new path around a sun to observe that sky from a new angle. They would need centuries to reconcile their varying views. They would be “immortals” in comparison to humans, for their experience would require eons to complete.161

Teleological understanding again comes into play when Lambert explains how the temporality of every living being is based on the purpose of their existence in the world. Since the inhabitants of comets had the chance to observe the sky from different points of view, they theoretically had access to a perfect knowledge of the whole structure of the universe. Our earth is also in motion but cannot travel to other suns. As humans we are only able to visualize the cosmos from our particular, decentralized point of view. Compared to the denizens of comets, the human view is more stable. To realize the whole structure and therefore meaning of the cosmos is impossible for humans. Manʼs life is an episode in the process of knowing the truth.

When Lambert described the denizens of other cosmic bodies, he contrasted humansʼ inability to imagine an intelligent creature that did not have particular parts resembling a man. “If we go far [enough], we add some wings because we feel that we lack the ability to ﬂy.”162 Though he implied that the shape of extra-terrestrialsʼ bodies could be outside of our ability to imagine, he insisted that they needed to have eyes, since this is the primary organ by which we know the world.163 In Lambertʼs words:

I will not thereby say that all inhabitants of all worlds must have eyes like ours. There can be more ways by which images of visible things present themselves to the soul of thinking creatures, much accustomed as we are to consider necessary the refraction of light and the image on the retina. The nature of light, its effects, the partnership between soul and body either are not known to us as yet, or are known only insofar as we receive the impressions which light makes on us, and we seek to ﬁll in the rest which through conclusions to which we have as yet no other bases than the ones which we postulate through seeing. 164

161 Ibid.

162 Ibid., p. 92.

163 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 193.

164 Cosmological Letters, p., 93.

59 This expression is signiﬁcant, because it reveals Lambertʼs approach to the axiomatic relationship between seeing and knowing, which, with his understanding of perspective consciousness, was about to take a new form. Within the boundaries of artiﬁcial perspective, Lambert asserted the homology of lived space and geometric space, by suggesting for a return to perception, phenomenal reality. In the decentralized point of view, it was the appearance of appearance that led to truth, and in order to reach it, Lambert functionalized appearances.

During the eighteenth century, natural philosophy of Newton was generally accepted in Europe. The absolute premises of his science, although contradicting human experience, were regarded as inherited in the nature itself. Within that conjecture, the absolute concepts of the perspectival space were imposed onto lived space. Direct observation was regarded as the key to understand the order of the world, and in that respect, perspective was assumed to be humanityʼs natural way of seeing. Within that, however, a return to phenomenal reality was not suggested yet. It was a linear and one way mode which postulated a systematic correspondence starting from the true structure and ending in its appearance.

Aristotelian understanding of a direct relation between seeing and knowing was doubted ever since the Copernican Revolution had proved that appearances were decisive. However, the presumption of homogeneous space in Newtonian science, which diminished the hierarchical difference between everyday experience and a higher order, also precipitated the reversibility of this one way examination of a true structure and its appearance. Since the space of everyday life was geometrized, the appearance could no longer signify a true order, but both could systematically co-exist within that matrix. In that respect, Lambertʼs suggestion for a return to perceived reality would also clearly take place within than matrix. The systematic approach which disregarded the phenomenal reality in the ﬁrst place, could now be used as an instrument to analyze perception in mathematical terms. This understanding, on one hand was a clear approval of the systematic relation between truth and appearance. On the other hand, it adverted the homology of the space of everyday life and the space of representation. Once this homology was taken for granted, the reversability of perspective construction was one more step to take, which was ﬁrmly postulated by Lambertʼs “Inverse Methods of Perspective.” If humanity was living in a world constructed according to the laws of linear perspective, then it was supposed to be possible to return to perceived reality to deduce

60 true structure. Metaphorically, our true but decentralized position in the structure of the cosmos could be realized through analysis of appearance. The solution he proposed was geometric.

After his 1749 observation of the Milky Way, Lambert carried his early observation to a sophisticated level, which led him to comprehend the picture of the universe, through the rules of perspective. It is not a coincidence that his fascination with realization of the oblique view of the Milky Way did not immediately advance him to cosmological studies. He ﬁrst developed his ideas about perspective. In 1752, he wrote his unpublished manuscript on perspective, entitled Anlage zur Perspektive, which was a preliminary version of his major work on the subject, Freye Perspektive (1759), which was published also in German Die Freye Perspektive. This manuscript starts with: “Visible things often present themselves to our eyes in a very different form than they actually have.” 165 This understanding was the departure point for Lambert.

In Lambertʼs studies, true structure of an object and its appearance was ﬁrst elaborated, not only as a systematic relation in between but as a precedent for two methods of representation; parallel projection and perspective. He explained that while parallel projection is necessary to understand the “tactile” reality of the object, perspective refers only to visual appearance. In this distinction, the parallel projection, as a way to represent the tactile reality, should be regarded within the Euclidean axiom that parallel lines never meet. In the natural way of seeing, parallel lines seem to converge; and, in perspective drawings, they are represented as meeting at a point. In his Anlage Zur Perspektive, Lambert presented his “perspectograf” machine (ﬁgure 2.9), which transferred the geometrical plan into its perspective representation as a means of understanding the systematic relationship connecting them. “Useless as a practical drawing tool — the perspectograph could project only the plan of an object, with no regard for its elevation — it demonstrated nonetheless an explicit relationship between the visual reality and the tactile appearance of the world by projecting the orthogonal plan into the converging appearance of a perspective view.”166

165 Blumenberg, The Genesis of the Copernican World, p. 533.

166 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 196.

61 Fig. 2.9. Lambertʼs “perspectograf” in use for transferring the plan of a garden into its perspectival appearance, from Anlage Zur Perspektive, 1752.

Perspective machines that postulated a systematic correspondence between orthogonal drawings and perspective images had been used in the Renaissance and, later, in the Seventeenth Century. However, Lambertʼs adaptation was particularly signiﬁcant, since conceptually his was also reversible. Four years after he ﬁnished his manuscript, he noted on his Monatsbuch “The problem of the art of perspective [has been] inverted.” 167 His interest in the homology between the tactile reality and its visual image would be elaborated further in his main work on the subject.

In his Freye Perspektive, Lambert elaborated on the method of drawing perspectivally without a pre-given plan. In the ﬁrst section of the work, Lambert repeated the same phrase he used in his previous work, to indicate that his study of perspective would be determined by the rules of optics. The expression “free perspective” implied drawing an object by directly looking at it.

167 Blumenberg, The Genesis of The Copernican World, p. 534.

62 Lambert uses the term optics and perspective in a different sense than it was used in this essay so far, yet his different use also reveals the same connection that was postulated earlier. According to Lambert optics is not only a science that studies visual rules but “proscribes appearances, and insists instead on truth so as to disclose the mistake that could deceive the eye.” 168

168 La Perspective affranchie, p. 120. Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 209.

63 4) CONCLUSION

Renaissance perspective converted perspectiva naturalis, the ancient Euclidean formalization of the “natural way of seeing,” to “artiﬁcial perspective,” not just in the service of creating more realistic illusionary spaces in painting and drawing, but to reconcile the phenomenal experience of human sight with the divine intellect — more speciﬁcally in order to realize the place of the celestial in the human world. In that respect, human perception was realized as embodying the way man understood his place in its hierarchal order — central but imperfect. Renaissance perspective aimed to incorporate the perfection of the heavens within human visuality. This transcendental use of geometry was based on the cone of vision but regulated according to the order of heavens. It was the examination of phenomenal reality within the rules established by perspective.

On one hand, “perspectival consciousness” devastated the anthropocentric model used to elevate perspectiva naturalis to perspectiva artiﬁcalis. On the other hand, it inevitably diminished the symbolic connotations of artiﬁcial perspective, by postulating the earth being on as same level with celestial bodies.

The Copernican revolution discredited humanityʼs “natural way of seeing” since it was decisive in understanding the cosmological order. The new order was postulated by a seeming liberation from the phenomenal aspect of perspectival vision. Yet, it did not truly escape from perspectival thinking. As Karsten Harries states: “What Copernicus presented as the truth turned out to be not an escape from appearance altogether, but only a step toward a higher order appearance.”169 In that regard, the idea of a central arrangement for the order of the cosmos was an inescapable aspect of perspectival thinking. As a good Copernican, Lambert also elaborated on his perspective theory within the limits of intellectual rules of perspective.

The Enlightenmentʼs decentralized point of view could no longer have any interest in the phenomenal aspect of perspectival vision. Even though earth was elevated to the same level with other celestial bodies, man was not able to regard the other cosmic bodies as phenomena, just as living in an inﬁnite world doesnʼt make comprehension of inﬁnity any

169 Harries, Inﬁnity and Perspective, p. 303.

64 easier. The phenomenal aspect of human vision was no longer relative to the position of the earth in the universe. For a view of the true structural organization of the cosmos, man had to be conscious of his phenomenal position and the limits of his sight.

The transcendental use of geometry that linked the phenomenal aspect of human sight with celestial realm was relieved of its symbolic obligations when these two realms became one. Because the idea of hierarchical order was discredited, the geometry of perspective — a means of mediation — was systematized as the unique means of relating appearance to true form. In other words, the represented world and the real world were juxtaposed in the new order of the cosmos.170 Consequently, and most dramatically, the distinction between perspectiva naturalis and artiﬁcialis — the way we see the world and the way we represent it — was blurred. Artiﬁcial perspective was transformed into a kind of mechanistic vision and was imposed on humans as a more natural way of seeing than persectiva naturalis.

Return to Phenomena & Mathematization of Appearance

Lambert presented his perspective theory within the limits imposed by mechanistic vision. According to him, the rules of artiﬁcial perspective were natural to human eye. The distinction between appearances and true forms could be regarded as a systematic relation within the rules of perspective. His ﬁrm belief in mechanistic vision made him realize that perspective construction could be reversed. If one could construct a perspective view from any given plan and elevation, then one could also deduce true dimensions of a given object from its perspective image.

Within this conjecture, Lambert suggested a return to perceived phenomena. This move was critical because the Copernican revolution had led to a distinction between the phenomenal aspects of perspective and perspectival thinking in general. The former had already been re-evaluated, because the Renaissance realized that human senses were decisive in understanding the order of the cosmos. The new order could be realized only through a “perspectival consciousness,” because the Renaissance believed that

170 Louise Pelletier, “Johann Heinrich Lambertʼs natural perspective,” in Halina Dunin-Woyseth & Jan Michl (Eds.), Towards a Disciplinary Identity of the Making Professions: The Oslo Millennium Reader, Research Magazine, no.4 (2001), p.82.

65 humanity had not been able to perceive the world by any other means. Lambertʼs cosmological thoughts, and within them his understanding of appearance, were also developed in perspectival thinking. His “Copernican Comparative” model (Blumenbergʼs term) for the universe predetermined a constant consciousness of our eccentric point of view. In his centrally organized conception of the universe, man was not in the center, but was part of a system that had a center unknown to him. In that respect, systematized relations between appearances and true forms could help one to deduce his position within the whole system. Acknowledging the autonomous structure of perspective construction, Lambert suggested reversing the process, starting with appearance.

Significantly, before Lambert, the philosophical-theological idea of removing man from the center was developed by manipulating the rules of artificial perspective. In the Seventeenth Century, our decentralized universe was represented through “decisive” aspects of artificial perspective, in which the observer was re-centered within a new system of meaning. Lambert focused his speculations on how the homology of appearance and true form was related to their “true” relation. According to Lambert, the rules that applied to world of representations applied to the world of true forms. As he put it himself, while in the art of perspective “the thing is to grasp the mechanism of illusions so that one can produce them, cosmology has to reverse the process by using this knowledge for the purpose of discovering illusions to which we could be subject as a result of our standpoint and our motions in the universe” [emphasis mine].171

In that respect, Lambertʼs understanding of perceived phenomena was already an appearance that could be examined by following the mathematical rules of perspective. Therefore, his suggestion for starting perspective construction directly from the appearance cannot be regarded as an extension of the Renaissance idea of perspective, in which the rules for regulating the phenomenal aspect of vision were based on the order of heavens. In Lambertʼs use, the geometry of artiﬁcial perspective was disconnected from its initial meanings — that particular geometry was already embodied by the rules of mechanic vision, which he advocated as a tool for understanding the true structure of the objects and, metaphorically, as a means of determining our position in the cosmological order.

171 Blumenbergʼs inerpretation of Lambertʼs quote. See; The Genesis of The Copernican World, p. 534.

66 His proposal for a return to perceived phenomena inevitably assimilated the space of everyday life within the precisions of geometric space.172 By postulating perspective construction as a reversible process, Lambert reduced the enigma of vision to its geometrical properties, which by no means can resemble the way humans actually perceive the world. In the Nineteenth Century, however, this reduced mechanical vision would become an instrument of truly predictive visualization.173 Perspective would become a tool for design and thus would be used as a mode to dominate our world.

Meditating through Perspective

Pérez-Gómez and Pelletier: “For Lambert, ʻnatural perspectiveʼ was more than a set of phenomena that explains vision and representation of objects: it was a metaphor for explaining the structure of the universe. As in his cosmology, the observer in his perspective theory occupied a relative position that was not assumed to be at the center....”174 My studies have been in full agreement with this statement, but it should also be added that, in this metaphor, appearance was functionalized in order to grasp a “true order.” Lambertʼs mathematical explanation of perceived phenomena, both in his perspective theory and also in his cosmological thoughts, postulated a system in which not only did appearances account for the way we see the world; upon closer examination, appearance itself was the agent that led us to be able to deduce the true structure of the world. His theories about mechanistic vision and, therefore, his assimilation of lived and geometric space, regarded appearance as function. The consequences of this approach still haunts us, since we believe ourselves able to dominate the world without understanding its essence.

In this regard, we should not forget Dalibor Veselyʼs important proviso: “The truth is that we donʼt live in a perspectival world, and there is no evidence to suggest that anybody

172 Pérez-Gómez and Pelletier, Architectural Representation and the Perspective Hinge, p. 215.

173 Ibid.

174 Ibid., p. 214.

67 ever did. There are levels of reality that we cannot appropriate, represent, or even affect and thereby determine the nature of the world in which we live.”175

175 Dalibor Vesely, Architecture in the Age of Divided Representation: The Question of Creativity in the Shadow of Production, (Cambridge, Massachusetts: The MIT Press, 2004), p. 149.

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