Leonardo

Reply to Sir Ernst GombrichAuthor(s): David CarrierSource: Leonardo, Vol. 18, No. 2 (1985), pp. 126-127Published by: The MIT PressStable URL: http://www.jstor.org/stable/1577904 .

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Letters Letters Letters

Readers' comments are welcomed on texts published in Leonardo. The Editors reserve the right to shorten letters. Letters should be written in English and sent to the Main Editorial Office.

Readers' comments are welcomed on texts published in Leonardo. The Editors reserve the right to shorten letters. Letters should be written in English and sent to the Main Editorial Office.

Readers' comments are welcomed on texts published in Leonardo. The Editors reserve the right to shorten letters. Letters should be written in English and sent to the Main Editorial Office.

Comments on the Relations between Art and the Sciences: The Role of Projective

Geometry and Perspective

From its beginnings, Leonardo has paid much attention to the relations between art and the sciences. This has involved discussions of how the objectives and procedures of those two modes of human cognition resemble each other and how they differ. Methods of geometrical and arithmetic proportion have been described as ways of applying measure- ment to visual composition. A favorite topic has been the rules of projective geometry and optics, explored as means of 'correctly' representing three-dimensional space on two- dimensional surfaces. It is the insistence on this latter category of investigations that has led me again and again to ask myself: What is the raison d'etre of such studies? What are they meant to accomplish?

One can ask: What kind of image results when three-dimensional objects are projected geometrically or optically upon a flat surface? We know the answers, and we know the rules by which the results come about. One can also ask: What do people see when they look at the three-dimensional world with normal or abnormal eyes? The answer to this question is by no means simple, and it is not given by the rules of projection. What did Leon Battista Alberti believe he had accomplished when he described his rules of perspective? Did he claim that he had shown the way to make pictures that look the way the world looks to us? I do not think so. With regard to perception Alberti reasoned and worked in a pre-psychological age. He was concerned with what he knew as the physical world. To imitate nature meant to him and to his age to duplicate it in its own realm. The projective image created on a glass plate cutting Alberti's 'visual pyramid' at a right angle was a transformation of one thing of nature into another thing of nature, e.g. of a human body into a picture of that body. The eyes served to see them both, but there was no ontological difference between the two. They were denizens of the same universe of discourse.

In practice, the geometrical constructions of central perspective served the artist to produce pictures of a convergent world; but neither did the construction yield a complete optical projection (as we know it from photography) nor did it apply to all aspects of the things to be shown. Also, from the beginning, painters used the new formula only to the extent to which its effect looked right to them. No difference in principle exists in this respect between Raphael and Cezanne. In the pictorial practice of our own time, of course, the rules of central perspective are either totally ignored, or applied with varying degrees of approxi- mation, or obeyed strictly but for nonartistic technical purposes.

Comments on the Relations between Art and the Sciences: The Role of Projective

Geometry and Perspective

From its beginnings, Leonardo has paid much attention to the relations between art and the sciences. This has involved discussions of how the objectives and procedures of those two modes of human cognition resemble each other and how they differ. Methods of geometrical and arithmetic proportion have been described as ways of applying measure- ment to visual composition. A favorite topic has been the rules of projective geometry and optics, explored as means of 'correctly' representing three-dimensional space on two- dimensional surfaces. It is the insistence on this latter category of investigations that has led me again and again to ask myself: What is the raison d'etre of such studies? What are they meant to accomplish?

One can ask: What kind of image results when three-dimensional objects are projected geometrically or optically upon a flat surface? We know the answers, and we know the rules by which the results come about. One can also ask: What do people see when they look at the three-dimensional world with normal or abnormal eyes? The answer to this question is by no means simple, and it is not given by the rules of projection. What did Leon Battista Alberti believe he had accomplished when he described his rules of perspective? Did he claim that he had shown the way to make pictures that look the way the world looks to us? I do not think so. With regard to perception Alberti reasoned and worked in a pre-psychological age. He was concerned with what he knew as the physical world. To imitate nature meant to him and to his age to duplicate it in its own realm. The projective image created on a glass plate cutting Alberti's 'visual pyramid' at a right angle was a transformation of one thing of nature into another thing of nature, e.g. of a human body into a picture of that body. The eyes served to see them both, but there was no ontological difference between the two. They were denizens of the same universe of discourse.

In practice, the geometrical constructions of central perspective served the artist to produce pictures of a convergent world; but neither did the construction yield a complete optical projection (as we know it from photography) nor did it apply to all aspects of the things to be shown. Also, from the beginning, painters used the new formula only to the extent to which its effect looked right to them. No difference in principle exists in this respect between Raphael and Cezanne. In the pictorial practice of our own time, of course, the rules of central perspective are either totally ignored, or applied with varying degrees of approxi- mation, or obeyed strictly but for nonartistic technical purposes.

Comments on the Relations between Art and the Sciences: The Role of Projective

Geometry and Perspective

From its beginnings, Leonardo has paid much attention to the relations between art and the sciences. This has involved discussions of how the objectives and procedures of those two modes of human cognition resemble each other and how they differ. Methods of geometrical and arithmetic proportion have been described as ways of applying measure- ment to visual composition. A favorite topic has been the rules of projective geometry and optics, explored as means of 'correctly' representing three-dimensional space on two- dimensional surfaces. It is the insistence on this latter category of investigations that has led me again and again to ask myself: What is the raison d'etre of such studies? What are they meant to accomplish?

One can ask: What kind of image results when three-dimensional objects are projected geometrically or optically upon a flat surface? We know the answers, and we know the rules by which the results come about. One can also ask: What do people see when they look at the three-dimensional world with normal or abnormal eyes? The answer to this question is by no means simple, and it is not given by the rules of projection. What did Leon Battista Alberti believe he had accomplished when he described his rules of perspective? Did he claim that he had shown the way to make pictures that look the way the world looks to us? I do not think so. With regard to perception Alberti reasoned and worked in a pre-psychological age. He was concerned with what he knew as the physical world. To imitate nature meant to him and to his age to duplicate it in its own realm. The projective image created on a glass plate cutting Alberti's 'visual pyramid' at a right angle was a transformation of one thing of nature into another thing of nature, e.g. of a human body into a picture of that body. The eyes served to see them both, but there was no ontological difference between the two. They were denizens of the same universe of discourse.

In practice, the geometrical constructions of central perspective served the artist to produce pictures of a convergent world; but neither did the construction yield a complete optical projection (as we know it from photography) nor did it apply to all aspects of the things to be shown. Also, from the beginning, painters used the new formula only to the extent to which its effect looked right to them. No difference in principle exists in this respect between Raphael and Cezanne. In the pictorial practice of our own time, of course, the rules of central perspective are either totally ignored, or applied with varying degrees of approxi- mation, or obeyed strictly but for nonartistic technical purposes.

In the meantime, expositions by psycho- logists, philosophers and other theorists dwell all too often in a curious no-man's land. For instance, in discussions of whether the straight edges of physical things are seen as curved, it is often not clear whether the author is concerned with projections on the retinae of the eyes-in which case the problem is one of geometrical optics-or with ways the world looks to us-in which case the answers will vary depending on what is being observed by whom and in what attitude. Nevertheless, much theory tends to deal with the task of artists as though they were intent on producing mathematically correct projections. This, however, has never been the case. The artist's task is a visual task. He wishes to create a world that looks the way he wants it to look. Geometrical constructions are only one means of going about this task, but artistically they are no more valid than purely intuitive compositions of space.

Understandably, theorists prefer to deal with geometrically definable procedures for the pictorial representation of space. But such endeavors strike me as exercises in the void. The kinds of art and artists they describe do not exist. An image of the world made up of crooked edges is as good as one made of straight or curved ones if it fits the artist's vision, and none of them calls for scientific justification.

It is true, however, that the ways in which such visions take shape are by no means arbitrary. They obey rules of style, psycho- logical rules of expression and vision, which can be described and reduced to principle. It is this kind of scientific analysis that I would like to recommend to the acute minds of our theorists. Analyzing what artists really do when they represent things in space rather than what they might do if they were engaged in some construction business would help to close the gap between scientific endeavor and artistic invention.

Rudolf Arnheim 1133 South Seventh Street

Ann Arbor, Michigan 48103, U.S.A.

Comment on "Theoretical Perspectives on the Arts, Sciences and Technology"

The space at my disposal does not allow me to take issue with Norman Bryson's theories, but I can at least assure the reader that I do not hold the views which Professor Carrier attributes to me in the Theoretical Perspectives section of Leonardo 17, No. 4 (1984). I have never entertained "a theory of representation as illusion" and have frequently warned against this facile misinterpretation of the title of Art and Illusion. In fact, I have written in the Preface to The Sense of Order (1979) that I have

In the meantime, expositions by psycho- logists, philosophers and other theorists dwell all too often in a curious no-man's land. For instance, in discussions of whether the straight edges of physical things are seen as curved, it is often not clear whether the author is concerned with projections on the retinae of the eyes-in which case the problem is one of geometrical optics-or with ways the world looks to us-in which case the answers will vary depending on what is being observed by whom and in what attitude. Nevertheless, much theory tends to deal with the task of artists as though they were intent on producing mathematically correct projections. This, however, has never been the case. The artist's task is a visual task. He wishes to create a world that looks the way he wants it to look. Geometrical constructions are only one means of going about this task, but artistically they are no more valid than purely intuitive compositions of space.

Understandably, theorists prefer to deal with geometrically definable procedures for the pictorial representation of space. But such endeavors strike me as exercises in the void. The kinds of art and artists they describe do not exist. An image of the world made up of crooked edges is as good as one made of straight or curved ones if it fits the artist's vision, and none of them calls for scientific justification.

It is true, however, that the ways in which such visions take shape are by no means arbitrary. They obey rules of style, psycho- logical rules of expression and vision, which can be described and reduced to principle. It is this kind of scientific analysis that I would like to recommend to the acute minds of our theorists. Analyzing what artists really do when they represent things in space rather than what they might do if they were engaged in some construction business would help to close the gap between scientific endeavor and artistic invention.

Rudolf Arnheim 1133 South Seventh Street

Ann Arbor, Michigan 48103, U.S.A.

Comment on "Theoretical Perspectives on the Arts, Sciences and Technology"

The space at my disposal does not allow me to take issue with Norman Bryson's theories, but I can at least assure the reader that I do not hold the views which Professor Carrier attributes to me in the Theoretical Perspectives section of Leonardo 17, No. 4 (1984). I have never entertained "a theory of representation as illusion" and have frequently warned against this facile misinterpretation of the title of Art and Illusion. In fact, I have written in the Preface to The Sense of Order (1979) that I have

In the meantime, expositions by psycho- logists, philosophers and other theorists dwell all too often in a curious no-man's land. For instance, in discussions of whether the straight edges of physical things are seen as curved, it is often not clear whether the author is concerned with projections on the retinae of the eyes-in which case the problem is one of geometrical optics-or with ways the world looks to us-in which case the answers will vary depending on what is being observed by whom and in what attitude. Nevertheless, much theory tends to deal with the task of artists as though they were intent on producing mathematically correct projections. This, however, has never been the case. The artist's task is a visual task. He wishes to create a world that looks the way he wants it to look. Geometrical constructions are only one means of going about this task, but artistically they are no more valid than purely intuitive compositions of space.

Understandably, theorists prefer to deal with geometrically definable procedures for the pictorial representation of space. But such endeavors strike me as exercises in the void. The kinds of art and artists they describe do not exist. An image of the world made up of crooked edges is as good as one made of straight or curved ones if it fits the artist's vision, and none of them calls for scientific justification.

It is true, however, that the ways in which such visions take shape are by no means arbitrary. They obey rules of style, psycho- logical rules of expression and vision, which can be described and reduced to principle. It is this kind of scientific analysis that I would like to recommend to the acute minds of our theorists. Analyzing what artists really do when they represent things in space rather than what they might do if they were engaged in some construction business would help to close the gap between scientific endeavor and artistic invention.

Rudolf Arnheim 1133 South Seventh Street

Ann Arbor, Michigan 48103, U.S.A.

Comment on "Theoretical Perspectives on the Arts, Sciences and Technology"

The space at my disposal does not allow me to take issue with Norman Bryson's theories, but I can at least assure the reader that I do not hold the views which Professor Carrier attributes to me in the Theoretical Perspectives section of Leonardo 17, No. 4 (1984). I have never entertained "a theory of representation as illusion" and have frequently warned against this facile misinterpretation of the title of Art and Illusion. In fact, I have written in the Preface to The Sense of Order (1979) that I have

been "needled by the assumption that I wished to equate art with illusion" and extended my analysis to purely formal configurations including their analogies with music. Even earlier, in Illusion in Nature and Art, published jointly with R. L. Gregory (1973), I pointed out that the title of my Mellon Lectures underlying Art and Illusion had been "The Visible World and the Language of Art" and that the change in title was merely made in the interest of brevity. Thus it really will not do for Professor Carrier to construe a convenient contrast between my alleged "notion of art as illusion" and Bryson's reliance on semiotic theories. In a recent number of the Art Journal (Summer 1984, p. 164), I acknowledged the early influence which Karl Buehler's Sprachtheorie (1934) had on my development; witness also my extensive review of Charles Morris, Signs, Language and Behavior in the Art Bulletin of 1949 (pp. 68-75). If the reader cares to look at p. 120 of Art andIllusion he will find me making use of the linguistic notion of 'distinctive features' in a discussion of board games, which "allow us to study articulation, the creation of distinctions without the intrusion of the problem of likeness or representation". I have continued these trends of thought in various papers of my volume The Image and the Eye (1982), notably in a contribution to the International Conference on the Semiotics of Art at Ann Arbor, Michigan, where, on p.282, the interested reader can also find Professor Nelson Goodman's comments which he kindly allowed me to publish. Unhappily, I was forced to clarify these matters yet again in "Representation and Misrepresentation", Critical Inquiry, December 1984, where I explained why I do not consider the study of image making to be co-extensive with aesthetics. This study (which includes maps, facsimiles, stage sets and holographs) does not only permit but compels us to deal with questions of resemblance and even of illusion, however marginal these may usually be to art. It is precisely because my interests are not confined to either representational or non- representational art that I must regard the visual creations of all ages and cultures as my province and am bound to see my own age in the perspective of this millennial history.

E. H. Gombrich 19 Briardale Gardens

London NW3 7PW, U.K.

Reply to Sir Ernst Gombrich

No books in my working library are more frequently reread than the works of Sir Ernst Gombrich, whose texts provide me, and many other scholars, with a vision of what art history may accomplish. Long ago, when I was a graduate student, Professor Gombrich took the time and trouble to discuss in considerable

been "needled by the assumption that I wished to equate art with illusion" and extended my analysis to purely formal configurations including their analogies with music. Even earlier, in Illusion in Nature and Art, published jointly with R. L. Gregory (1973), I pointed out that the title of my Mellon Lectures underlying Art and Illusion had been "The Visible World and the Language of Art" and that the change in title was merely made in the interest of brevity. Thus it really will not do for Professor Carrier to construe a convenient contrast between my alleged "notion of art as illusion" and Bryson's reliance on semiotic theories. In a recent number of the Art Journal (Summer 1984, p. 164), I acknowledged the early influence which Karl Buehler's Sprachtheorie (1934) had on my development; witness also my extensive review of Charles Morris, Signs, Language and Behavior in the Art Bulletin of 1949 (pp. 68-75). If the reader cares to look at p. 120 of Art andIllusion he will find me making use of the linguistic notion of 'distinctive features' in a discussion of board games, which "allow us to study articulation, the creation of distinctions without the intrusion of the problem of likeness or representation". I have continued these trends of thought in various papers of my volume The Image and the Eye (1982), notably in a contribution to the International Conference on the Semiotics of Art at Ann Arbor, Michigan, where, on p.282, the interested reader can also find Professor Nelson Goodman's comments which he kindly allowed me to publish. Unhappily, I was forced to clarify these matters yet again in "Representation and Misrepresentation", Critical Inquiry, December 1984, where I explained why I do not consider the study of image making to be co-extensive with aesthetics. This study (which includes maps, facsimiles, stage sets and holographs) does not only permit but compels us to deal with questions of resemblance and even of illusion, however marginal these may usually be to art. It is precisely because my interests are not confined to either representational or non- representational art that I must regard the visual creations of all ages and cultures as my province and am bound to see my own age in the perspective of this millennial history.

E. H. Gombrich 19 Briardale Gardens

London NW3 7PW, U.K.

Reply to Sir Ernst Gombrich

No books in my working library are more frequently reread than the works of Sir Ernst Gombrich, whose texts provide me, and many other scholars, with a vision of what art history may accomplish. Long ago, when I was a graduate student, Professor Gombrich took the time and trouble to discuss in considerable

been "needled by the assumption that I wished to equate art with illusion" and extended my analysis to purely formal configurations including their analogies with music. Even earlier, in Illusion in Nature and Art, published jointly with R. L. Gregory (1973), I pointed out that the title of my Mellon Lectures underlying Art and Illusion had been "The Visible World and the Language of Art" and that the change in title was merely made in the interest of brevity. Thus it really will not do for Professor Carrier to construe a convenient contrast between my alleged "notion of art as illusion" and Bryson's reliance on semiotic theories. In a recent number of the Art Journal (Summer 1984, p. 164), I acknowledged the early influence which Karl Buehler's Sprachtheorie (1934) had on my development; witness also my extensive review of Charles Morris, Signs, Language and Behavior in the Art Bulletin of 1949 (pp. 68-75). If the reader cares to look at p. 120 of Art andIllusion he will find me making use of the linguistic notion of 'distinctive features' in a discussion of board games, which "allow us to study articulation, the creation of distinctions without the intrusion of the problem of likeness or representation". I have continued these trends of thought in various papers of my volume The Image and the Eye (1982), notably in a contribution to the International Conference on the Semiotics of Art at Ann Arbor, Michigan, where, on p.282, the interested reader can also find Professor Nelson Goodman's comments which he kindly allowed me to publish. Unhappily, I was forced to clarify these matters yet again in "Representation and Misrepresentation", Critical Inquiry, December 1984, where I explained why I do not consider the study of image making to be co-extensive with aesthetics. This study (which includes maps, facsimiles, stage sets and holographs) does not only permit but compels us to deal with questions of resemblance and even of illusion, however marginal these may usually be to art. It is precisely because my interests are not confined to either representational or non- representational art that I must regard the visual creations of all ages and cultures as my province and am bound to see my own age in the perspective of this millennial history.

E. H. Gombrich 19 Briardale Gardens

London NW3 7PW, U.K.

Reply to Sir Ernst Gombrich

No books in my working library are more frequently reread than the works of Sir Ernst Gombrich, whose texts provide me, and many other scholars, with a vision of what art history may accomplish. Long ago, when I was a graduate student, Professor Gombrich took the time and trouble to discuss in considerable

LEONARDO, Vol. 18, No. 2, pp. 126-129, 1985 LEONARDO, Vol. 18, No. 2, pp. 126-129, 1985 LEONARDO, Vol. 18, No. 2, pp. 126-129, 1985 Pergamon Press Ltd.

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0024-094X/85 $3.00+0.00 126 126 126

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detail my reading of his research. In my "Gombrich on Art Historical Explanations" (Leonardo 16, No. 2 (1983) pp.91-96) and in a book, Artwriting, which will soon be forthcoming, I show, I hope, that I have learned from his kind responses to my writing. Since I have gained so much from him, nothing would be more ungracious than to quarrel with him now, particularly about the precise interpretation of his work. I hope therefore, that my few, brief remarks may contribute positively to an ongoing debate which, modelled on Sir Karl Popper's theory of scientific experimentation, may lead us all closer to the truth.

My goal in providing a commentary to Dr Norman Bryson's remarks was to indicate one perspective on his semiotic theory of art. As the reference in the second footnote indicates, I do not accept entirely Bryson's theory, nor do I agree with his reading of Art andIllusion. Here, then, I present my own reading of Gombrich's work, which differs, I believe, from Bryson's..

Art andIllusion contains two lines of thought which are difficult to bring together. On one hand, Gombrich does seem to say that some naturalistic representations are illusions. For example, he writes: "While standing in front of a painting by Jan van Eyck we...believe he succeeded in rendering the inexhaustible wealth of detail that belongs to the visible world" (p.220). "Only in extreme cases...are the illusions of art illusions about our real environment. But they are illusions all the same..." (p.277). "...under the hands of a great master the image becomes translucent" (p.389). Not only in the title, I would think, is a theory of representation as illusion entertained. On the other hand, many other passages focus on the role of convention in representation and explicitly deny that artworks are illusions. For example: "We rarely get into situations where the eye is actually deceived..." (p.246). Here is one way that these two lines of thought might be made consistent with one another. Gombrich argues that "we can train ourselves to switch between readings, but we cannot hold conflicting interpretations" (p.236; see also p.6). So it seems possible to maintain both that representations may be seen as illusions and that they can also, when we switch readings, be viewed as visual signs. If many readers of Art and Illusion have been tempted by the identification of representation with illusion, perhaps that is because they find it difficult to understand how we actually do switch between readings. Michael Podro's "Fiction and Reality in Painting" (Poetik und Hermeneutik Bd. X (Wilhelm Fink Verlag: Munich, 1983): pp.225-237) offers a challeng- ing discussion of this problem.

I admire Gombrich's efforts in the papers mentioned in his letter and other work since Art and Illusion to carry further the study of this difficult problem. His books and articles have taught me, a philosopher by training, to be skeptical of the belief that the techniques of philosophy can solve these problems. The lesson I draw from his work, and from such other well known texts as Anthony Blunt's "Illusionistic Decoration in Central Italian Painting of the Renaissance" (Journal of the Royal Society of Arts, April 1959: pp.309-326)

detail my reading of his research. In my "Gombrich on Art Historical Explanations" (Leonardo 16, No. 2 (1983) pp.91-96) and in a book, Artwriting, which will soon be forthcoming, I show, I hope, that I have learned from his kind responses to my writing. Since I have gained so much from him, nothing would be more ungracious than to quarrel with him now, particularly about the precise interpretation of his work. I hope therefore, that my few, brief remarks may contribute positively to an ongoing debate which, modelled on Sir Karl Popper's theory of scientific experimentation, may lead us all closer to the truth.

My goal in providing a commentary to Dr Norman Bryson's remarks was to indicate one perspective on his semiotic theory of art. As the reference in the second footnote indicates, I do not accept entirely Bryson's theory, nor do I agree with his reading of Art andIllusion. Here, then, I present my own reading of Gombrich's work, which differs, I believe, from Bryson's..

Art andIllusion contains two lines of thought which are difficult to bring together. On one hand, Gombrich does seem to say that some naturalistic representations are illusions. For example, he writes: "While standing in front of a painting by Jan van Eyck we...believe he succeeded in rendering the inexhaustible wealth of detail that belongs to the visible world" (p.220). "Only in extreme cases...are the illusions of art illusions about our real environment. But they are illusions all the same..." (p.277). "...under the hands of a great master the image becomes translucent" (p.389). Not only in the title, I would think, is a theory of representation as illusion entertained. On the other hand, many other passages focus on the role of convention in representation and explicitly deny that artworks are illusions. For example: "We rarely get into situations where the eye is actually deceived..." (p.246). Here is one way that these two lines of thought might be made consistent with one another. Gombrich argues that "we can train ourselves to switch between readings, but we cannot hold conflicting interpretations" (p.236; see also p.6). So it seems possible to maintain both that representations may be seen as illusions and that they can also, when we switch readings, be viewed as visual signs. If many readers of Art and Illusion have been tempted by the identification of representation with illusion, perhaps that is because they find it difficult to understand how we actually do switch between readings. Michael Podro's "Fiction and Reality in Painting" (Poetik und Hermeneutik Bd. X (Wilhelm Fink Verlag: Munich, 1983): pp.225-237) offers a challeng- ing discussion of this problem.

I admire Gombrich's efforts in the papers mentioned in his letter and other work since Art and Illusion to carry further the study of this difficult problem. His books and articles have taught me, a philosopher by training, to be skeptical of the belief that the techniques of philosophy can solve these problems. The lesson I draw from his work, and from such other well known texts as Anthony Blunt's "Illusionistic Decoration in Central Italian Painting of the Renaissance" (Journal of the Royal Society of Arts, April 1959: pp.309-326)

detail my reading of his research. In my "Gombrich on Art Historical Explanations" (Leonardo 16, No. 2 (1983) pp.91-96) and in a book, Artwriting, which will soon be forthcoming, I show, I hope, that I have learned from his kind responses to my writing. Since I have gained so much from him, nothing would be more ungracious than to quarrel with him now, particularly about the precise interpretation of his work. I hope therefore, that my few, brief remarks may contribute positively to an ongoing debate which, modelled on Sir Karl Popper's theory of scientific experimentation, may lead us all closer to the truth.

My goal in providing a commentary to Dr Norman Bryson's remarks was to indicate one perspective on his semiotic theory of art. As the reference in the second footnote indicates, I do not accept entirely Bryson's theory, nor do I agree with his reading of Art andIllusion. Here, then, I present my own reading of Gombrich's work, which differs, I believe, from Bryson's..

Art andIllusion contains two lines of thought which are difficult to bring together. On one hand, Gombrich does seem to say that some naturalistic representations are illusions. For example, he writes: "While standing in front of a painting by Jan van Eyck we...believe he succeeded in rendering the inexhaustible wealth of detail that belongs to the visible world" (p.220). "Only in extreme cases...are the illusions of art illusions about our real environment. But they are illusions all the same..." (p.277). "...under the hands of a great master the image becomes translucent" (p.389). Not only in the title, I would think, is a theory of representation as illusion entertained. On the other hand, many other passages focus on the role of convention in representation and explicitly deny that artworks are illusions. For example: "We rarely get into situations where the eye is actually deceived..." (p.246). Here is one way that these two lines of thought might be made consistent with one another. Gombrich argues that "we can train ourselves to switch between readings, but we cannot hold conflicting interpretations" (p.236; see also p.6). So it seems possible to maintain both that representations may be seen as illusions and that they can also, when we switch readings, be viewed as visual signs. If many readers of Art and Illusion have been tempted by the identification of representation with illusion, perhaps that is because they find it difficult to understand how we actually do switch between readings. Michael Podro's "Fiction and Reality in Painting" (Poetik und Hermeneutik Bd. X (Wilhelm Fink Verlag: Munich, 1983): pp.225-237) offers a challeng- ing discussion of this problem.

I admire Gombrich's efforts in the papers mentioned in his letter and other work since Art and Illusion to carry further the study of this difficult problem. His books and articles have taught me, a philosopher by training, to be skeptical of the belief that the techniques of philosophy can solve these problems. The lesson I draw from his work, and from such other well known texts as Anthony Blunt's "Illusionistic Decoration in Central Italian Painting of the Renaissance" (Journal of the Royal Society of Arts, April 1959: pp.309-326)

detail my reading of his research. In my "Gombrich on Art Historical Explanations" (Leonardo 16, No. 2 (1983) pp.91-96) and in a book, Artwriting, which will soon be forthcoming, I show, I hope, that I have learned from his kind responses to my writing. Since I have gained so much from him, nothing would be more ungracious than to quarrel with him now, particularly about the precise interpretation of his work. I hope therefore, that my few, brief remarks may contribute positively to an ongoing debate which, modelled on Sir Karl Popper's theory of scientific experimentation, may lead us all closer to the truth.

My goal in providing a commentary to Dr Norman Bryson's remarks was to indicate one perspective on his semiotic theory of art. As the reference in the second footnote indicates, I do not accept entirely Bryson's theory, nor do I agree with his reading of Art andIllusion. Here, then, I present my own reading of Gombrich's work, which differs, I believe, from Bryson's..

Art andIllusion contains two lines of thought which are difficult to bring together. On one hand, Gombrich does seem to say that some naturalistic representations are illusions. For example, he writes: "While standing in front of a painting by Jan van Eyck we...believe he succeeded in rendering the inexhaustible wealth of detail that belongs to the visible world" (p.220). "Only in extreme cases...are the illusions of art illusions about our real environment. But they are illusions all the same..." (p.277). "...under the hands of a great master the image becomes translucent" (p.389). Not only in the title, I would think, is a theory of representation as illusion entertained. On the other hand, many other passages focus on the role of convention in representation and explicitly deny that artworks are illusions. For example: "We rarely get into situations where the eye is actually deceived..." (p.246). Here is one way that these two lines of thought might be made consistent with one another. Gombrich argues that "we can train ourselves to switch between readings, but we cannot hold conflicting interpretations" (p.236; see also p.6). So it seems possible to maintain both that representations may be seen as illusions and that they can also, when we switch readings, be viewed as visual signs. If many readers of Art and Illusion have been tempted by the identification of representation with illusion, perhaps that is because they find it difficult to understand how we actually do switch between readings. Michael Podro's "Fiction and Reality in Painting" (Poetik und Hermeneutik Bd. X (Wilhelm Fink Verlag: Munich, 1983): pp.225-237) offers a challeng- ing discussion of this problem.

I admire Gombrich's efforts in the papers mentioned in his letter and other work since Art and Illusion to carry further the study of this difficult problem. His books and articles have taught me, a philosopher by training, to be skeptical of the belief that the techniques of philosophy can solve these problems. The lesson I draw from his work, and from such other well known texts as Anthony Blunt's "Illusionistic Decoration in Central Italian Painting of the Renaissance" (Journal of the Royal Society of Arts, April 1959: pp.309-326) and Sven Sandstroem, Levels of Unreality: Studies in Structure and Construction in Italian Mural Painting During the Renaissance (Uppsals, 1963) is that only careful study of concrete examples will advance the analysis. For that reason, I can only regret that

and Sven Sandstroem, Levels of Unreality: Studies in Structure and Construction in Italian Mural Painting During the Renaissance (Uppsals, 1963) is that only careful study of concrete examples will advance the analysis. For that reason, I can only regret that

and Sven Sandstroem, Levels of Unreality: Studies in Structure and Construction in Italian Mural Painting During the Renaissance (Uppsals, 1963) is that only careful study of concrete examples will advance the analysis. For that reason, I can only regret that

and Sven Sandstroem, Levels of Unreality: Studies in Structure and Construction in Italian Mural Painting During the Renaissance (Uppsals, 1963) is that only careful study of concrete examples will advance the analysis. For that reason, I can only regret that

Gombrich has not yet taken issue with the details of Bryson's examples. Would not doing so now carry the debate forward?

David Carrier Department of History and Philosophy

Carnegie-Mellon University Pittsburgh, PA 15213

U.S.A.

Comments on "A Visual Aid for Artists with Retinitis Pigmentosa ('Tunnel Vision')"

Apart from the obvious usefulness of the use of the two mirrors to correct 'tunnel vision', Leonardo 17, No. 3 (1984), the optical arrangement can be very useful for people who like to stand back from their picture, but are hampered by limited studio space. In case the artist only wished to view the painting without actually working on it, a single small mirror can be mounted on the wall behind the artist, and he or she can look into it to see the picture from about double the distance of the unaided eye.

This last arrangement has a fascinating historical precedent, the experiment made by Brunelleschi, the pioneer of perspective drawing, in the 1460s. To give a lifelike impression of his painting of the Baptistry of Florence Cathedral, he asked the viewer to look through a small hole drilled through the actual painting (a small panel held in one hand) while seeing the reflection of the painting in a mirror held in the other hand [1]. Not a very practical arrangement for the practicing artist!

In my own work I find that sometimes looking through an old detached zoom lens gives a wide overall view of the picture, and then suddenly zooming in on a particular area gives a very vivid impression, helping link up the part to the whole.

One last remark concerning the small mirror of the pair mentioned in the article: a front- coated mirror would be more expensive, but it would give a much sharper image, specially of thin lines, since a front mirror will not give the annoying double reflection caused by the glass used in conventional, back-coated mirrors.

REFERENCES AND NOTES

1. Samuel Y. Edgerton, Jr., The Renaissance Rediscovery of Linear Perspective (New York: Harper & Row, 1975).

Vladimir Tamari 1-27-11 Shimmachi

Setagaya-Ku Tokyo

Japan 154

Comments on "Drawing for Designing"

I read Peter Lloyd-Jones's article, Leonardo 17, No. 4 (1984), with great interest, as I am in the process of finalizing a teaching method in three-dimensional basic design devised along similar lines of thought. The key idea of the article can be summarized by Mr Lloyd- Jones's statement that "a design is 'discovered' or invented by variations in decisions during the process of construction itself'.

Gombrich has not yet taken issue with the details of Bryson's examples. Would not doing so now carry the debate forward?

David Carrier Department of History and Philosophy

Carnegie-Mellon University Pittsburgh, PA 15213

U.S.A.

Comments on "A Visual Aid for Artists with Retinitis Pigmentosa ('Tunnel Vision')"

Apart from the obvious usefulness of the use of the two mirrors to correct 'tunnel vision', Leonardo 17, No. 3 (1984), the optical arrangement can be very useful for people who like to stand back from their picture, but are hampered by limited studio space. In case the artist only wished to view the painting without actually working on it, a single small mirror can be mounted on the wall behind the artist, and he or she can look into it to see the picture from about double the distance of the unaided eye.

This last arrangement has a fascinating historical precedent, the experiment made by Brunelleschi, the pioneer of perspective drawing, in the 1460s. To give a lifelike impression of his painting of the Baptistry of Florence Cathedral, he asked the viewer to look through a small hole drilled through the actual painting (a small panel held in one hand) while seeing the reflection of the painting in a mirror held in the other hand [1]. Not a very practical arrangement for the practicing artist!

In my own work I find that sometimes looking through an old detached zoom lens gives a wide overall view of the picture, and then suddenly zooming in on a particular area gives a very vivid impression, helping link up the part to the whole.

One last remark concerning the small mirror of the pair mentioned in the article: a front- coated mirror would be more expensive, but it would give a much sharper image, specially of thin lines, since a front mirror will not give the annoying double reflection caused by the glass used in conventional, back-coated mirrors.

REFERENCES AND NOTES

1. Samuel Y. Edgerton, Jr., The Renaissance Rediscovery of Linear Perspective (New York: Harper & Row, 1975).

Vladimir Tamari 1-27-11 Shimmachi

Setagaya-Ku Tokyo

Japan 154

Comments on "Drawing for Designing"

I read Peter Lloyd-Jones's article, Leonardo 17, No. 4 (1984), with great interest, as I am in the process of finalizing a teaching method in three-dimensional basic design devised along similar lines of thought. The key idea of the article can be summarized by Mr Lloyd- Jones's statement that "a design is 'discovered' or invented by variations in decisions during the process of construction itself'.

Gombrich has not yet taken issue with the details of Bryson's examples. Would not doing so now carry the debate forward?

David Carrier Department of History and Philosophy

Carnegie-Mellon University Pittsburgh, PA 15213

U.S.A.

Comments on "A Visual Aid for Artists with Retinitis Pigmentosa ('Tunnel Vision')"

Apart from the obvious usefulness of the use of the two mirrors to correct 'tunnel vision', Leonardo 17, No. 3 (1984), the optical arrangement can be very useful for people who like to stand back from their picture, but are hampered by limited studio space. In case the artist only wished to view the painting without actually working on it, a single small mirror can be mounted on the wall behind the artist, and he or she can look into it to see the picture from about double the distance of the unaided eye.

This last arrangement has a fascinating historical precedent, the experiment made by Brunelleschi, the pioneer of perspective drawing, in the 1460s. To give a lifelike impression of his painting of the Baptistry of Florence Cathedral, he asked the viewer to look through a small hole drilled through the actual painting (a small panel held in one hand) while seeing the reflection of the painting in a mirror held in the other hand [1]. Not a very practical arrangement for the practicing artist!

In my own work I find that sometimes looking through an old detached zoom lens gives a wide overall view of the picture, and then suddenly zooming in on a particular area gives a very vivid impression, helping link up the part to the whole.

One last remark concerning the small mirror of the pair mentioned in the article: a front- coated mirror would be more expensive, but it would give a much sharper image, specially of thin lines, since a front mirror will not give the annoying double reflection caused by the glass used in conventional, back-coated mirrors.

REFERENCES AND NOTES

1. Samuel Y. Edgerton, Jr., The Renaissance Rediscovery of Linear Perspective (New York: Harper & Row, 1975).

Vladimir Tamari 1-27-11 Shimmachi

Setagaya-Ku Tokyo

Japan 154

Comments on "Drawing for Designing"

I read Peter Lloyd-Jones's article, Leonardo 17, No. 4 (1984), with great interest, as I am in the process of finalizing a teaching method in three-dimensional basic design devised along similar lines of thought. The key idea of the article can be summarized by Mr Lloyd- Jones's statement that "a design is 'discovered' or invented by variations in decisions during the process of construction itself'.

Gombrich has not yet taken issue with the details of Bryson's examples. Would not doing so now carry the debate forward?

David Carrier Department of History and Philosophy

Carnegie-Mellon University Pittsburgh, PA 15213

U.S.A.

Comments on "A Visual Aid for Artists with Retinitis Pigmentosa ('Tunnel Vision')"

Apart from the obvious usefulness of the use of the two mirrors to correct 'tunnel vision', Leonardo 17, No. 3 (1984), the optical arrangement can be very useful for people who like to stand back from their picture, but are hampered by limited studio space. In case the artist only wished to view the painting without actually working on it, a single small mirror can be mounted on the wall behind the artist, and he or she can look into it to see the picture from about double the distance of the unaided eye.

This last arrangement has a fascinating historical precedent, the experiment made by Brunelleschi, the pioneer of perspective drawing, in the 1460s. To give a lifelike impression of his painting of the Baptistry of Florence Cathedral, he asked the viewer to look through a small hole drilled through the actual painting (a small panel held in one hand) while seeing the reflection of the painting in a mirror held in the other hand [1]. Not a very practical arrangement for the practicing artist!

In my own work I find that sometimes looking through an old detached zoom lens gives a wide overall view of the picture, and then suddenly zooming in on a particular area gives a very vivid impression, helping link up the part to the whole.

One last remark concerning the small mirror of the pair mentioned in the article: a front- coated mirror would be more expensive, but it would give a much sharper image, specially of thin lines, since a front mirror will not give the annoying double reflection caused by the glass used in conventional, back-coated mirrors.

REFERENCES AND NOTES

1. Samuel Y. Edgerton, Jr., The Renaissance Rediscovery of Linear Perspective (New York: Harper & Row, 1975).

Vladimir Tamari 1-27-11 Shimmachi

Setagaya-Ku Tokyo

Japan 154

Comments on "Drawing for Designing"

I read Peter Lloyd-Jones's article, Leonardo 17, No. 4 (1984), with great interest, as I am in the process of finalizing a teaching method in three-dimensional basic design devised along similar lines of thought. The key idea of the article can be summarized by Mr Lloyd- Jones's statement that "a design is 'discovered' or invented by variations in decisions during the process of construction itself'.

Two elements are essential in this phrase: "variation in decisions", which can be defined as experiments or experiencing, and "con- struction", by which we usually mean some kind of three-dimensional delineation. This delineation is characterized by one or more

Two elements are essential in this phrase: "variation in decisions", which can be defined as experiments or experiencing, and "con- struction", by which we usually mean some kind of three-dimensional delineation. This delineation is characterized by one or more

Two elements are essential in this phrase: "variation in decisions", which can be defined as experiments or experiencing, and "con- struction", by which we usually mean some kind of three-dimensional delineation. This delineation is characterized by one or more

Two elements are essential in this phrase: "variation in decisions", which can be defined as experiments or experiencing, and "con- struction", by which we usually mean some kind of three-dimensional delineation. This delineation is characterized by one or more

well-defined structures which are conceptually conditioned by some kind of systematic approach achieved by the integration of rational thinking and intuitive sensing. In support to the validity of his approach, Lloyd- Jones describes a brief account of some of his students' works. These works are three- dimensional, expressed via axonometric drawings or tectonic objects.

I find it difficult hence to understand why the author employs the term 'drawing' in describing his method. In my opinion, 'modeling' would be a more suitable term. Modeling in itself is a means intended to make possible the realization of 'constructive forethoughts'. I agree with the author that certain kinds of correlations are necessary in order to reach this realization. The question is: why limit students to the use of matrix correlations only?

The final stage in Lloyd-Jones's method is presented as an escape into a 'phantastic architecture'. Is this a compensation, an opportunity to revolt against rectangular limitations?

I believe that this experiment has the poten- tial to achieve more than just some sort of visual pattern. In my view, modeling is a tech- nique that helps transform space ideas from abstract statements into concrete realizations. In order to fulfil this task, modeling has to be enriched by some kind of well-defined content dimensions, formulated as conditions, sit- uations, constraints or demands. This content might be of a functional nature (use-struc- ture), contextual nature (environmental, historical), material nature, or combinations of any of these dimensions.

In no case can design survive, let alone develop, by creating patterns and types for their own sake. The 'raison d'etre' of design in general, and design education in particular, is to create a presence whose meaning and structure are legible, easily understood, employed and enjoyed.

It seems to me that the method presented in Mr Lloyd-Jones's paper can offer answers to the questions I have raised. Therefore a more detailed description of the course, and how Peter Lloyd-Jones developed it, would be helpful to those, like myself, who are interested in the subject.

Alex Mailer Technion Institute of Technology

Technion City, Haifa 3200 Israel

well-defined structures which are conceptually conditioned by some kind of systematic approach achieved by the integration of rational thinking and intuitive sensing. In support to the validity of his approach, Lloyd- Jones describes a brief account of some of his students' works. These works are three- dimensional, expressed via axonometric drawings or tectonic objects.

I find it difficult hence to understand why the author employs the term 'drawing' in describing his method. In my opinion, 'modeling' would be a more suitable term. Modeling in itself is a means intended to make possible the realization of 'constructive forethoughts'. I agree with the author that certain kinds of correlations are necessary in order to reach this realization. The question is: why limit students to the use of matrix correlations only?

The final stage in Lloyd-Jones's method is presented as an escape into a 'phantastic architecture'. Is this a compensation, an opportunity to revolt against rectangular limitations?

I believe that this experiment has the poten- tial to achieve more than just some sort of visual pattern. In my view, modeling is a tech- nique that helps transform space ideas from abstract statements into concrete realizations. In order to fulfil this task, modeling has to be enriched by some kind of well-defined content dimensions, formulated as conditions, sit- uations, constraints or demands. This content might be of a functional nature (use-struc- ture), contextual nature (environmental, historical), material nature, or combinations of any of these dimensions.

In no case can design survive, let alone develop, by creating patterns and types for their own sake. The 'raison d'etre' of design in general, and design education in particular, is to create a presence whose meaning and structure are legible, easily understood, employed and enjoyed.

It seems to me that the method presented in Mr Lloyd-Jones's paper can offer answers to the questions I have raised. Therefore a more detailed description of the course, and how Peter Lloyd-Jones developed it, would be helpful to those, like myself, who are interested in the subject.

Alex Mailer Technion Institute of Technology

Technion City, Haifa 3200 Israel

well-defined structures which are conceptually conditioned by some kind of systematic approach achieved by the integration of rational thinking and intuitive sensing. In support to the validity of his approach, Lloyd- Jones describes a brief account of some of his students' works. These works are three- dimensional, expressed via axonometric drawings or tectonic objects.

I find it difficult hence to understand why the author employs the term 'drawing' in describing his method. In my opinion, 'modeling' would be a more suitable term. Modeling in itself is a means intended to make possible the realization of 'constructive forethoughts'. I agree with the author that certain kinds of correlations are necessary in order to reach this realization. The question is: why limit students to the use of matrix correlations only?

The final stage in Lloyd-Jones's method is presented as an escape into a 'phantastic architecture'. Is this a compensation, an opportunity to revolt against rectangular limitations?

I believe that this experiment has the poten- tial to achieve more than just some sort of visual pattern. In my view, modeling is a tech- nique that helps transform space ideas from abstract statements into concrete realizations. In order to fulfil this task, modeling has to be enriched by some kind of well-defined content dimensions, formulated as conditions, sit- uations, constraints or demands. This content might be of a functional nature (use-struc- ture), contextual nature (environmental, historical), material nature, or combinations of any of these dimensions.

In no case can design survive, let alone develop, by creating patterns and types for their own sake. The 'raison d'etre' of design in general, and design education in particular, is to create a presence whose meaning and structure are legible, easily understood, employed and enjoyed.

It seems to me that the method presented in Mr Lloyd-Jones's paper can offer answers to the questions I have raised. Therefore a more detailed description of the course, and how Peter Lloyd-Jones developed it, would be helpful to those, like myself, who are interested in the subject.

Alex Mailer Technion Institute of Technology

Technion City, Haifa 3200 Israel

well-defined structures which are conceptually conditioned by some kind of systematic approach achieved by the integration of rational thinking and intuitive sensing. In support to the validity of his approach, Lloyd- Jones describes a brief account of some of his students' works. These works are three- dimensional, expressed via axonometric drawings or tectonic objects.

I find it difficult hence to understand why the author employs the term 'drawing' in describing his method. In my opinion, 'modeling' would be a more suitable term. Modeling in itself is a means intended to make possible the realization of 'constructive forethoughts'. I agree with the author that certain kinds of correlations are necessary in order to reach this realization. The question is: why limit students to the use of matrix correlations only?

The final stage in Lloyd-Jones's method is presented as an escape into a 'phantastic architecture'. Is this a compensation, an opportunity to revolt against rectangular limitations?

I believe that this experiment has the poten- tial to achieve more than just some sort of visual pattern. In my view, modeling is a tech- nique that helps transform space ideas from abstract statements into concrete realizations. In order to fulfil this task, modeling has to be enriched by some kind of well-defined content dimensions, formulated as conditions, sit- uations, constraints or demands. This content might be of a functional nature (use-struc- ture), contextual nature (environmental, historical), material nature, or combinations of any of these dimensions.

In no case can design survive, let alone develop, by creating patterns and types for their own sake. The 'raison d'etre' of design in general, and design education in particular, is to create a presence whose meaning and structure are legible, easily understood, employed and enjoyed.

It seems to me that the method presented in Mr Lloyd-Jones's paper can offer answers to the questions I have raised. Therefore a more detailed description of the course, and how Peter Lloyd-Jones developed it, would be helpful to those, like myself, who are interested in the subject.

Alex Mailer Technion Institute of Technology

Technion City, Haifa 3200 Israel

Comment on "The Fourth Dimension and Non-Euclidean Geometry in Modern Art"

One of the most striking characteristics of modern art is its unequivocal rejection of perspective. We believe that this rejection is an unjustified prejudice that originated, at least in part, from a conceptual blunder.

This blunder was the belief that one could infer from the fact that the world might be mathematically describable as four-dimen- sional and non-Euclidean such general notions as that the world is irrational, that truth is relative, that knowledge is conventional, and so on. In modern art, this belief led to the conclusion that the three-dimensional visual reality provided by our sense of sight, and best captured up to that time by classical perspective, was completely deceitful and should be abandoned. At least, such was the conclusion drawn by many modernist artists, critics and historians.

Comment on "The Fourth Dimension and Non-Euclidean Geometry in Modern Art"

One of the most striking characteristics of modern art is its unequivocal rejection of perspective. We believe that this rejection is an unjustified prejudice that originated, at least in part, from a conceptual blunder.

This blunder was the belief that one could infer from the fact that the world might be mathematically describable as four-dimen- sional and non-Euclidean such general notions as that the world is irrational, that truth is relative, that knowledge is conventional, and so on. In modern art, this belief led to the conclusion that the three-dimensional visual reality provided by our sense of sight, and best captured up to that time by classical perspective, was completely deceitful and should be abandoned. At least, such was the conclusion drawn by many modernist artists, critics and historians.

Comment on "The Fourth Dimension and Non-Euclidean Geometry in Modern Art"

One of the most striking characteristics of modern art is its unequivocal rejection of perspective. We believe that this rejection is an unjustified prejudice that originated, at least in part, from a conceptual blunder.

This blunder was the belief that one could infer from the fact that the world might be mathematically describable as four-dimen- sional and non-Euclidean such general notions as that the world is irrational, that truth is relative, that knowledge is conventional, and so on. In modern art, this belief led to the conclusion that the three-dimensional visual reality provided by our sense of sight, and best captured up to that time by classical perspective, was completely deceitful and should be abandoned. At least, such was the conclusion drawn by many modernist artists, critics and historians.

Comment on "The Fourth Dimension and Non-Euclidean Geometry in Modern Art"

One of the most striking characteristics of modern art is its unequivocal rejection of perspective. We believe that this rejection is an unjustified prejudice that originated, at least in part, from a conceptual blunder.

This blunder was the belief that one could infer from the fact that the world might be mathematically describable as four-dimen- sional and non-Euclidean such general notions as that the world is irrational, that truth is relative, that knowledge is conventional, and so on. In modern art, this belief led to the conclusion that the three-dimensional visual reality provided by our sense of sight, and best captured up to that time by classical perspective, was completely deceitful and should be abandoned. At least, such was the conclusion drawn by many modernist artists, critics and historians.

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