Leonardo

Correction: The Art of Raymond Jonson, PainterAuthor(s): Paul RéSource: Leonardo, Vol. 16, No. 4 (Autumn, 1983), p. 334Published by: The MIT PressStable URL: http://www.jstor.org/stable/1574985 .

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viewed from this theoretically correct position is a separate, more difficult question.

John L. Ward Art Department,

FAA, University of Florida,

Gainesville, FL 32611, U.S.A.

CORRECTION: THE ART OF RAYMOND JONSON

I wish to note a correction in my review of The Art of Raymond Jonson, Painter in Leonardo 16, 72 (1983). The second sentence of my text should read, "Not only has he been central in helping nonrepresentational art to gain recognition in New Mexico, but his works are an important contribution to modern art." Perhaps the death of Raymond Jonson in May 1982 will help stimulate the long overdue appreciation of his work.

Also, I am most pleased to hear that Leonardo is continuing. The high quality of interaction that it encourages between people of diverse disciplines, cultures, and beliefs is important to the health of the modern world.

Paul Re 10533 Sierra Bonita Ave. NE,

Albuquerque, NM 87111, U.S.A.

COMMENT ON ARTIFICIAL INTELLIGENCE

Wilson's essay about artificial intelligence (Leonardo 16, 15, 1983) interested me because I know so little about this field, my own expertise being limited to the other end of the stick, natural stupidity. In my reading, I thought I recognized some common threads.

To illustrate Wilson's sinister labeling of work as showing imaginative poverty and/or an infatuation with computer technology for its own sake, he chose (along with one of his own) a work of mine, a spatially quantized image transformation of a colored photograph of Ralph Nader (see Fig. 2), although Wilson calls it a transformation into digitized blocks. Well it may be, although I think not. Not one whit of information from the original was ever transformed, at any point, into a number. The elapsed time for transformation was equal to the time it takes light to travel about six centimeters in a vacuum. How much digitizing is possible in that amount of time?

Image transformations of this sort fall into a general category of optical puzzles of which, perhaps, caricatures are a special subset. Their "prolific production" is due, I think, not to a poverty of imagination, but to a certain societal usefulness, ranging from the arresting of attention in connection with marketing products to scientific investigation of the brain processes that engender perception and recognition, and hemispheric function. Such images can titillate the retinas, amuse the psyche, and cause both the lay and instructed viewer to have some useful introspective thoughts about illusion.

Ed Manning 875 East Broadway,

Straftord, CT 06497, U.S.A.

A COMMENT ON RAUSCHENBACH'S PAPER

In recent years the pictorial practice of 'inverted perspective' has aroused renewed attention because it contradicts the cherished traditional belief that in representational image-making artists draw "what they see". Boris V. Rauschenbach's article on this subject [1] shows that certain basic concepts, indispensable for any such discussion, are still insufficiently or incorrectly defined.

First of all, 'seeing' means more than one thing. It should be clear by now that seeing does not refer to the optical projections on the retinas of the eyes. Approximations to retinal images play a role as one of the components of perception, but no known variety of visual experience simply coincides with retinal projection. Most percepts differ from it profoundly. What, then, is 'seeing'? It may mean the usual and spontaneous way in which humans and animals look at their

viewed from this theoretically correct position is a separate, more difficult question.

John L. Ward Art Department,

FAA, University of Florida,

Gainesville, FL 32611, U.S.A.

CORRECTION: THE ART OF RAYMOND JONSON

I wish to note a correction in my review of The Art of Raymond Jonson, Painter in Leonardo 16, 72 (1983). The second sentence of my text should read, "Not only has he been central in helping nonrepresentational art to gain recognition in New Mexico, but his works are an important contribution to modern art." Perhaps the death of Raymond Jonson in May 1982 will help stimulate the long overdue appreciation of his work.

Also, I am most pleased to hear that Leonardo is continuing. The high quality of interaction that it encourages between people of diverse disciplines, cultures, and beliefs is important to the health of the modern world.

Paul Re 10533 Sierra Bonita Ave. NE,

Albuquerque, NM 87111, U.S.A.

COMMENT ON ARTIFICIAL INTELLIGENCE

Wilson's essay about artificial intelligence (Leonardo 16, 15, 1983) interested me because I know so little about this field, my own expertise being limited to the other end of the stick, natural stupidity. In my reading, I thought I recognized some common threads.

To illustrate Wilson's sinister labeling of work as showing imaginative poverty and/or an infatuation with computer technology for its own sake, he chose (along with one of his own) a work of mine, a spatially quantized image transformation of a colored photograph of Ralph Nader (see Fig. 2), although Wilson calls it a transformation into digitized blocks. Well it may be, although I think not. Not one whit of information from the original was ever transformed, at any point, into a number. The elapsed time for transformation was equal to the time it takes light to travel about six centimeters in a vacuum. How much digitizing is possible in that amount of time?

Image transformations of this sort fall into a general category of optical puzzles of which, perhaps, caricatures are a special subset. Their "prolific production" is due, I think, not to a poverty of imagination, but to a certain societal usefulness, ranging from the arresting of attention in connection with marketing products to scientific investigation of the brain processes that engender perception and recognition, and hemispheric function. Such images can titillate the retinas, amuse the psyche, and cause both the lay and instructed viewer to have some useful introspective thoughts about illusion.

Ed Manning 875 East Broadway,

Straftord, CT 06497, U.S.A.

A COMMENT ON RAUSCHENBACH'S PAPER

In recent years the pictorial practice of 'inverted perspective' has aroused renewed attention because it contradicts the cherished traditional belief that in representational image-making artists draw "what they see". Boris V. Rauschenbach's article on this subject [1] shows that certain basic concepts, indispensable for any such discussion, are still insufficiently or incorrectly defined.

First of all, 'seeing' means more than one thing. It should be clear by now that seeing does not refer to the optical projections on the retinas of the eyes. Approximations to retinal images play a role as one of the components of perception, but no known variety of visual experience simply coincides with retinal projection. Most percepts differ from it profoundly. What, then, is 'seeing'? It may mean the usual and spontaneous way in which humans and animals look at their

viewed from this theoretically correct position is a separate, more difficult question.

John L. Ward Art Department,

FAA, University of Florida,

Gainesville, FL 32611, U.S.A.

CORRECTION: THE ART OF RAYMOND JONSON

I wish to note a correction in my review of The Art of Raymond Jonson, Painter in Leonardo 16, 72 (1983). The second sentence of my text should read, "Not only has he been central in helping nonrepresentational art to gain recognition in New Mexico, but his works are an important contribution to modern art." Perhaps the death of Raymond Jonson in May 1982 will help stimulate the long overdue appreciation of his work.

Also, I am most pleased to hear that Leonardo is continuing. The high quality of interaction that it encourages between people of diverse disciplines, cultures, and beliefs is important to the health of the modern world.

Paul Re 10533 Sierra Bonita Ave. NE,

Albuquerque, NM 87111, U.S.A.

COMMENT ON ARTIFICIAL INTELLIGENCE

Wilson's essay about artificial intelligence (Leonardo 16, 15, 1983) interested me because I know so little about this field, my own expertise being limited to the other end of the stick, natural stupidity. In my reading, I thought I recognized some common threads.

To illustrate Wilson's sinister labeling of work as showing imaginative poverty and/or an infatuation with computer technology for its own sake, he chose (along with one of his own) a work of mine, a spatially quantized image transformation of a colored photograph of Ralph Nader (see Fig. 2), although Wilson calls it a transformation into digitized blocks. Well it may be, although I think not. Not one whit of information from the original was ever transformed, at any point, into a number. The elapsed time for transformation was equal to the time it takes light to travel about six centimeters in a vacuum. How much digitizing is possible in that amount of time?

Image transformations of this sort fall into a general category of optical puzzles of which, perhaps, caricatures are a special subset. Their "prolific production" is due, I think, not to a poverty of imagination, but to a certain societal usefulness, ranging from the arresting of attention in connection with marketing products to scientific investigation of the brain processes that engender perception and recognition, and hemispheric function. Such images can titillate the retinas, amuse the psyche, and cause both the lay and instructed viewer to have some useful introspective thoughts about illusion.

Ed Manning 875 East Broadway,

Straftord, CT 06497, U.S.A.

A COMMENT ON RAUSCHENBACH'S PAPER

In recent years the pictorial practice of 'inverted perspective' has aroused renewed attention because it contradicts the cherished traditional belief that in representational image-making artists draw "what they see". Boris V. Rauschenbach's article on this subject [1] shows that certain basic concepts, indispensable for any such discussion, are still insufficiently or incorrectly defined.

First of all, 'seeing' means more than one thing. It should be clear by now that seeing does not refer to the optical projections on the retinas of the eyes. Approximations to retinal images play a role as one of the components of perception, but no known variety of visual experience simply coincides with retinal projection. Most percepts differ from it profoundly. What, then, is 'seeing'? It may mean the usual and spontaneous way in which humans and animals look at their

viewed from this theoretically correct position is a separate, more difficult question.

John L. Ward Art Department,

FAA, University of Florida,

Gainesville, FL 32611, U.S.A.

CORRECTION: THE ART OF RAYMOND JONSON

I wish to note a correction in my review of The Art of Raymond Jonson, Painter in Leonardo 16, 72 (1983). The second sentence of my text should read, "Not only has he been central in helping nonrepresentational art to gain recognition in New Mexico, but his works are an important contribution to modern art." Perhaps the death of Raymond Jonson in May 1982 will help stimulate the long overdue appreciation of his work.

Also, I am most pleased to hear that Leonardo is continuing. The high quality of interaction that it encourages between people of diverse disciplines, cultures, and beliefs is important to the health of the modern world.

Paul Re 10533 Sierra Bonita Ave. NE,

Albuquerque, NM 87111, U.S.A.

COMMENT ON ARTIFICIAL INTELLIGENCE

Wilson's essay about artificial intelligence (Leonardo 16, 15, 1983) interested me because I know so little about this field, my own expertise being limited to the other end of the stick, natural stupidity. In my reading, I thought I recognized some common threads.

To illustrate Wilson's sinister labeling of work as showing imaginative poverty and/or an infatuation with computer technology for its own sake, he chose (along with one of his own) a work of mine, a spatially quantized image transformation of a colored photograph of Ralph Nader (see Fig. 2), although Wilson calls it a transformation into digitized blocks. Well it may be, although I think not. Not one whit of information from the original was ever transformed, at any point, into a number. The elapsed time for transformation was equal to the time it takes light to travel about six centimeters in a vacuum. How much digitizing is possible in that amount of time?

Image transformations of this sort fall into a general category of optical puzzles of which, perhaps, caricatures are a special subset. Their "prolific production" is due, I think, not to a poverty of imagination, but to a certain societal usefulness, ranging from the arresting of attention in connection with marketing products to scientific investigation of the brain processes that engender perception and recognition, and hemispheric function. Such images can titillate the retinas, amuse the psyche, and cause both the lay and instructed viewer to have some useful introspective thoughts about illusion.

Ed Manning 875 East Broadway,

Straftord, CT 06497, U.S.A.

A COMMENT ON RAUSCHENBACH'S PAPER

In recent years the pictorial practice of 'inverted perspective' has aroused renewed attention because it contradicts the cherished traditional belief that in representational image-making artists draw "what they see". Boris V. Rauschenbach's article on this subject [1] shows that certain basic concepts, indispensable for any such discussion, are still insufficiently or incorrectly defined.

First of all, 'seeing' means more than one thing. It should be clear by now that seeing does not refer to the optical projections on the retinas of the eyes. Approximations to retinal images play a role as one of the components of perception, but no known variety of visual experience simply coincides with retinal projection. Most percepts differ from it profoundly. What, then, is 'seeing'? It may mean the usual and spontaneous way in which humans and animals look at their environment for the purpose of identification and orientation. Such perception, to be useful, must correspond closely to the shapes and environment for the purpose of identification and orientation. Such perception, to be useful, must correspond closely to the shapes and environment for the purpose of identification and orientation. Such perception, to be useful, must correspond closely to the shapes and environment for the purpose of identification and orientation. Such perception, to be useful, must correspond closely to the shapes and

spatial relations of the physical world. But seeing may also mean focusing one's perception on the projective aspects of the visual image-a rarely practiced attitude, limited to observers in certain experiments on visual perception and to artists intent on mechanically realistic representation. Such an approach comes closest to, but never duplicates, optical projections. There are, finally, references to 'what the artist sees' for the purpose of his work. Such percepts are highly individual ways of grasping and interpreting the structure of visual objects in relation to particular intentions and stylistic requirements. In theoretical discussion it is indispensable to make clear what meaning is referred to when one talks about seeing. The term 'seeing correctly' makes sense only when the meaning of seeing is specified. A bicyclist must see correctly if he wants to survive, but such correctness could have been irrelevant or even disturbing for Matisse when he perceived what he needed for his paintings.

Similarly, images are seldom intended to represent retinal projections. For scientific purposes it matters what such projections look like. Psychologists need to find out how projections compare to the physiological processes they cause in the nervous system and to the corresponding percepts in visual experience. Elsewhere images serve two purposes. They convey information about properties of the physical world. Maps, blueprints, or scientific illustrations are of this nature. Or they render significant aspects of visual experience for the purposes of the sight-seer, the magazine reader, the artist, etc. Neither of these types of images is necessarily dependent on faithful optical projection. For example, a picture constructed according to the geometrical rules of central perspective may look like the real world to persons brought up in a congenial tradition, and it may or may not provide the factual information or aesthetic expression sought by certain viewers. But it does not reproduce the optical projections in the human eye [2]. In theoretical discussion we cannot decide whether or not certain kinds of images are correct unless we know their purpose.

There is also the phenomenon of perceptual constancy, commonly but incorrectly defined as the tendency to adapt projective sizes and shapes to those of the corresponding visual objects. Constancy is the perceptual tendency to perceive sizes and shapes according to the simplest visual structure available in the stimulus situation. Its effect may or may not correspond to the 'objective' properties of the physical models. For example, the spatial illusions created by certain architects or stage designers or shown in the well-known demonstrations of Adalbert Ames make use of constancy to mislead viewers as to the actual physical situation [3].

Rauschenbach mentions that perceptual constancy is strongest for the range close to the viewer. This is true but far from self-explanatory, since projective distortion, as every photographer knows, is greatest, not smallest, at close range. Perhaps the explanation can be found in a remote source, the sculptor Hildebrand's book, The Problem of Form (1893) [4]. It is now rarely read but was most influential in its time. Hildebrand pointed to the distinction between near view and distant view and maintained that only the latter affords a truly unified visual image because it can be surveyed with minimum eye movement. At close range, the eyes and even the head of the viewer must shift at wide angles to cover the visual field. This makes for multiple vistas, much less integrated in a compelling image than the distant view. It seems plausible to me that this considerable freedom from one uncontested projective image enables the inherent tendency toward simplest structure to be most effective; whereas at the distant view the much more unified image powerfully imposes projection and thus reduces constancy.

As far as 'inverted perspective' is concerned, I have seen no persuasive demonstration that it can occur in optical projection, although I believe that Patrick A. Heelan has recently made that claim [5]. Nor does Rauschenbach's unhappily lopsided Fig. Id on page 29 of his article strike me as a likely product of perceptual constancy, which, as I mentioned, is a tendency toward simplest structure. Instead I suggest that it is useless and misleading to search for the origin of divergent perspective or other systems of spatial representation in either the optics of vision or the perception of the physical environment. Rather such systems are solutions of specific formal problems arising in the media themselves, that is, in painting, architecture, and occasionally in sculpture. This contention is, to my mind, a special aspect of a much more fundamental problem of visual representation. It was for the sake of this more general and much more important problem that I published the article cited by Rauschenbach [6]. I would like to restate here as

spatial relations of the physical world. But seeing may also mean focusing one's perception on the projective aspects of the visual image-a rarely practiced attitude, limited to observers in certain experiments on visual perception and to artists intent on mechanically realistic representation. Such an approach comes closest to, but never duplicates, optical projections. There are, finally, references to 'what the artist sees' for the purpose of his work. Such percepts are highly individual ways of grasping and interpreting the structure of visual objects in relation to particular intentions and stylistic requirements. In theoretical discussion it is indispensable to make clear what meaning is referred to when one talks about seeing. The term 'seeing correctly' makes sense only when the meaning of seeing is specified. A bicyclist must see correctly if he wants to survive, but such correctness could have been irrelevant or even disturbing for Matisse when he perceived what he needed for his paintings.

Similarly, images are seldom intended to represent retinal projections. For scientific purposes it matters what such projections look like. Psychologists need to find out how projections compare to the physiological processes they cause in the nervous system and to the corresponding percepts in visual experience. Elsewhere images serve two purposes. They convey information about properties of the physical world. Maps, blueprints, or scientific illustrations are of this nature. Or they render significant aspects of visual experience for the purposes of the sight-seer, the magazine reader, the artist, etc. Neither of these types of images is necessarily dependent on faithful optical projection. For example, a picture constructed according to the geometrical rules of central perspective may look like the real world to persons brought up in a congenial tradition, and it may or may not provide the factual information or aesthetic expression sought by certain viewers. But it does not reproduce the optical projections in the human eye [2]. In theoretical discussion we cannot decide whether or not certain kinds of images are correct unless we know their purpose.

There is also the phenomenon of perceptual constancy, commonly but incorrectly defined as the tendency to adapt projective sizes and shapes to those of the corresponding visual objects. Constancy is the perceptual tendency to perceive sizes and shapes according to the simplest visual structure available in the stimulus situation. Its effect may or may not correspond to the 'objective' properties of the physical models. For example, the spatial illusions created by certain architects or stage designers or shown in the well-known demonstrations of Adalbert Ames make use of constancy to mislead viewers as to the actual physical situation [3].

Rauschenbach mentions that perceptual constancy is strongest for the range close to the viewer. This is true but far from self-explanatory, since projective distortion, as every photographer knows, is greatest, not smallest, at close range. Perhaps the explanation can be found in a remote source, the sculptor Hildebrand's book, The Problem of Form (1893) [4]. It is now rarely read but was most influential in its time. Hildebrand pointed to the distinction between near view and distant view and maintained that only the latter affords a truly unified visual image because it can be surveyed with minimum eye movement. At close range, the eyes and even the head of the viewer must shift at wide angles to cover the visual field. This makes for multiple vistas, much less integrated in a compelling image than the distant view. It seems plausible to me that this considerable freedom from one uncontested projective image enables the inherent tendency toward simplest structure to be most effective; whereas at the distant view the much more unified image powerfully imposes projection and thus reduces constancy.

As far as 'inverted perspective' is concerned, I have seen no persuasive demonstration that it can occur in optical projection, although I believe that Patrick A. Heelan has recently made that claim [5]. Nor does Rauschenbach's unhappily lopsided Fig. Id on page 29 of his article strike me as a likely product of perceptual constancy, which, as I mentioned, is a tendency toward simplest structure. Instead I suggest that it is useless and misleading to search for the origin of divergent perspective or other systems of spatial representation in either the optics of vision or the perception of the physical environment. Rather such systems are solutions of specific formal problems arising in the media themselves, that is, in painting, architecture, and occasionally in sculpture. This contention is, to my mind, a special aspect of a much more fundamental problem of visual representation. It was for the sake of this more general and much more important problem that I published the article cited by Rauschenbach [6]. I would like to restate here as

spatial relations of the physical world. But seeing may also mean focusing one's perception on the projective aspects of the visual image-a rarely practiced attitude, limited to observers in certain experiments on visual perception and to artists intent on mechanically realistic representation. Such an approach comes closest to, but never duplicates, optical projections. There are, finally, references to 'what the artist sees' for the purpose of his work. Such percepts are highly individual ways of grasping and interpreting the structure of visual objects in relation to particular intentions and stylistic requirements. In theoretical discussion it is indispensable to make clear what meaning is referred to when one talks about seeing. The term 'seeing correctly' makes sense only when the meaning of seeing is specified. A bicyclist must see correctly if he wants to survive, but such correctness could have been irrelevant or even disturbing for Matisse when he perceived what he needed for his paintings.

Similarly, images are seldom intended to represent retinal projections. For scientific purposes it matters what such projections look like. Psychologists need to find out how projections compare to the physiological processes they cause in the nervous system and to the corresponding percepts in visual experience. Elsewhere images serve two purposes. They convey information about properties of the physical world. Maps, blueprints, or scientific illustrations are of this nature. Or they render significant aspects of visual experience for the purposes of the sight-seer, the magazine reader, the artist, etc. Neither of these types of images is necessarily dependent on faithful optical projection. For example, a picture constructed according to the geometrical rules of central perspective may look like the real world to persons brought up in a congenial tradition, and it may or may not provide the factual information or aesthetic expression sought by certain viewers. But it does not reproduce the optical projections in the human eye [2]. In theoretical discussion we cannot decide whether or not certain kinds of images are correct unless we know their purpose.

There is also the phenomenon of perceptual constancy, commonly but incorrectly defined as the tendency to adapt projective sizes and shapes to those of the corresponding visual objects. Constancy is the perceptual tendency to perceive sizes and shapes according to the simplest visual structure available in the stimulus situation. Its effect may or may not correspond to the 'objective' properties of the physical models. For example, the spatial illusions created by certain architects or stage designers or shown in the well-known demonstrations of Adalbert Ames make use of constancy to mislead viewers as to the actual physical situation [3].

Rauschenbach mentions that perceptual constancy is strongest for the range close to the viewer. This is true but far from self-explanatory, since projective distortion, as every photographer knows, is greatest, not smallest, at close range. Perhaps the explanation can be found in a remote source, the sculptor Hildebrand's book, The Problem of Form (1893) [4]. It is now rarely read but was most influential in its time. Hildebrand pointed to the distinction between near view and distant view and maintained that only the latter affords a truly unified visual image because it can be surveyed with minimum eye movement. At close range, the eyes and even the head of the viewer must shift at wide angles to cover the visual field. This makes for multiple vistas, much less integrated in a compelling image than the distant view. It seems plausible to me that this considerable freedom from one uncontested projective image enables the inherent tendency toward simplest structure to be most effective; whereas at the distant view the much more unified image powerfully imposes projection and thus reduces constancy.

As far as 'inverted perspective' is concerned, I have seen no persuasive demonstration that it can occur in optical projection, although I believe that Patrick A. Heelan has recently made that claim [5]. Nor does Rauschenbach's unhappily lopsided Fig. Id on page 29 of his article strike me as a likely product of perceptual constancy, which, as I mentioned, is a tendency toward simplest structure. Instead I suggest that it is useless and misleading to search for the origin of divergent perspective or other systems of spatial representation in either the optics of vision or the perception of the physical environment. Rather such systems are solutions of specific formal problems arising in the media themselves, that is, in painting, architecture, and occasionally in sculpture. This contention is, to my mind, a special aspect of a much more fundamental problem of visual representation. It was for the sake of this more general and much more important problem that I published the article cited by Rauschenbach [6]. I would like to restate here as

spatial relations of the physical world. But seeing may also mean focusing one's perception on the projective aspects of the visual image-a rarely practiced attitude, limited to observers in certain experiments on visual perception and to artists intent on mechanically realistic representation. Such an approach comes closest to, but never duplicates, optical projections. There are, finally, references to 'what the artist sees' for the purpose of his work. Such percepts are highly individual ways of grasping and interpreting the structure of visual objects in relation to particular intentions and stylistic requirements. In theoretical discussion it is indispensable to make clear what meaning is referred to when one talks about seeing. The term 'seeing correctly' makes sense only when the meaning of seeing is specified. A bicyclist must see correctly if he wants to survive, but such correctness could have been irrelevant or even disturbing for Matisse when he perceived what he needed for his paintings.

Similarly, images are seldom intended to represent retinal projections. For scientific purposes it matters what such projections look like. Psychologists need to find out how projections compare to the physiological processes they cause in the nervous system and to the corresponding percepts in visual experience. Elsewhere images serve two purposes. They convey information about properties of the physical world. Maps, blueprints, or scientific illustrations are of this nature. Or they render significant aspects of visual experience for the purposes of the sight-seer, the magazine reader, the artist, etc. Neither of these types of images is necessarily dependent on faithful optical projection. For example, a picture constructed according to the geometrical rules of central perspective may look like the real world to persons brought up in a congenial tradition, and it may or may not provide the factual information or aesthetic expression sought by certain viewers. But it does not reproduce the optical projections in the human eye [2]. In theoretical discussion we cannot decide whether or not certain kinds of images are correct unless we know their purpose.

There is also the phenomenon of perceptual constancy, commonly but incorrectly defined as the tendency to adapt projective sizes and shapes to those of the corresponding visual objects. Constancy is the perceptual tendency to perceive sizes and shapes according to the simplest visual structure available in the stimulus situation. Its effect may or may not correspond to the 'objective' properties of the physical models. For example, the spatial illusions created by certain architects or stage designers or shown in the well-known demonstrations of Adalbert Ames make use of constancy to mislead viewers as to the actual physical situation [3].

Rauschenbach mentions that perceptual constancy is strongest for the range close to the viewer. This is true but far from self-explanatory, since projective distortion, as every photographer knows, is greatest, not smallest, at close range. Perhaps the explanation can be found in a remote source, the sculptor Hildebrand's book, The Problem of Form (1893) [4]. It is now rarely read but was most influential in its time. Hildebrand pointed to the distinction between near view and distant view and maintained that only the latter affords a truly unified visual image because it can be surveyed with minimum eye movement. At close range, the eyes and even the head of the viewer must shift at wide angles to cover the visual field. This makes for multiple vistas, much less integrated in a compelling image than the distant view. It seems plausible to me that this considerable freedom from one uncontested projective image enables the inherent tendency toward simplest structure to be most effective; whereas at the distant view the much more unified image powerfully imposes projection and thus reduces constancy.

As far as 'inverted perspective' is concerned, I have seen no persuasive demonstration that it can occur in optical projection, although I believe that Patrick A. Heelan has recently made that claim [5]. Nor does Rauschenbach's unhappily lopsided Fig. Id on page 29 of his article strike me as a likely product of perceptual constancy, which, as I mentioned, is a tendency toward simplest structure. Instead I suggest that it is useless and misleading to search for the origin of divergent perspective or other systems of spatial representation in either the optics of vision or the perception of the physical environment. Rather such systems are solutions of specific formal problems arising in the media themselves, that is, in painting, architecture, and occasionally in sculpture. This contention is, to my mind, a special aspect of a much more fundamental problem of visual representation. It was for the sake of this more general and much more important problem that I published the article cited by Rauschenbach [6]. I would like to restate here as forcefully as I can that true progress in our understanding of visual representation will be hampered until we decide on a paradigmatic forcefully as I can that true progress in our understanding of visual representation will be hampered until we decide on a paradigmatic forcefully as I can that true progress in our understanding of visual representation will be hampered until we decide on a paradigmatic forcefully as I can that true progress in our understanding of visual representation will be hampered until we decide on a paradigmatic

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