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vision-that which we actually see, namely the physical world. When Israel Rosenfield entitled his review of Vision as Seeing through the brain’ he could have just as easily entitled it as ‘Seeing through visual metaphors’ (Rosenfield, 1984).

Although Marr spends little time describing the evolutionary context in which he places his theory of vision, his explicit invocation of the evolutionary purposes of seeing among animals provides a realistic framework.

The usefulness of a representation depends upon how well suited it is to the purpose for which it is used. A pigeon uses vision to help it navigate, fly, and seek out food. Many types of jumping spider use vision to tell the difference between a potential meal and a potential mate . . Human vision, on the other hand, seems to be very much more general, although it clearly contains a variety of special-purpose mechanisms that can, for example, direct the eye toward an unexpected movement in the visual field or cause one to blink or otherwise avoid something that approaches one’s head too quickly (Marr. 1982; p. 32).

Marr’s theory of vision can be expanded into an evolutionary knowledge process by viewing the visual metaphors invoked in the second level of explanation to choose representations and algorithms as mediators between the brain and the environment. Visual metaphors describe the evolutionary mechanism by which visual, computable processes ‘fit’ the biological purposes of animals and humans. Of course, visual metaphors cannot be found in individual neurons or at present in collections of them. Visual metaphors are rational reconstructions of a process. And this was the great discovery of David Marr and his colleagues-that an explanatory account of vision could not rest upon the actions of neurons or lists of features alone. An explanatory account of vision requires not only a multi-level explanation constrained by the physical world, but as part of those levels, a computational component at the second level. I have suggested that this crucial second level could also be understood as involving visual metaphors to determine the choices or representations and algorithms and to mediate between the brain and the environment.

References MacCormac. E. R. (1985). A Cognitive Theorj~ of Meraphor. Cambridge, Massachusetts: MIT

Press (Bradford Books). Marr, D. (1982).Vision. New York: W.H. Freeman. Mandelbrot, B. (1983). The Fracral Geometry o/Nature. New York: W.H. Freeman. Rosenfield, I. (1984). Nerr York Rev. Books, October I I, pp. 53-55.

E. R. MacCormac Ofice of the Governor,

Raleigh, North Carolina, USA

The great chain of perception: a response to David Marr’s Vision by Frederick Turner The appearance of David Marr’s book Vision marks the midpoint ofthe assault on the last great conceptual barrier left in science: that between biology and psychology. With Newton, the wall between physics and mathematics was breached; with Dalton, that between chemistry and physics; with Watson and Crick, that between biology and chemistry. Now it looks as if the final distinction between the physical and the spiritual is about to fall.

Significantly, one breakthrough in Marr’s book is its seizing of the initiative, its going on the offensive. Instead of trying passively to describe the mechanism of a given element

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of vision, he finds out what it is for, defines the hypothetical mechanism by its function, and actively tries to build a model of one. This trope of experimental method can be compared with the most fertile research at the borders of matter, which involves the creation of new particles, and the most fertile research at the borders of life, which involves the creation of chimeric and unprecedented forms of life. We find out by creating; a wise passiveness is not enough by itself and takes its appropriate place only as a phase in the creative process. Knowledge is active synthesis, not a heap of facts.

One of the delights of Marr’s book is that it shows the same process of active synthesis at work in the visual system itself. Here, I must in all sympathy and understanding take issue with one aspect of Marr’s rhetoric. He describes the output of visual information processing as the ‘objective’ ‘physical’ properties of the ‘real world’. Defined functionally, this will do very well. But Marr himself suggests that other animals see things that we do not see. He insists that the ‘virtual lines’ that we construct as part of our ‘primal sketch’ (with only inferential justification) are just as real for the visual system as ‘objective’ ones. He states that we ‘assume’ the continuity of objects in time (an assumption some animals do not make). And indeed the core of his argument is that what is presented to the rest of the brain by the visual system is a ‘description’, not raw ‘objective’ sense data. Thus, his subtext is surely that we construct the visual world rather than merely recover it. If the words ‘objective’, ‘physical’, and ‘real world’ can carry the content of ‘constructed description’, then my objection disappears, and I for one would be content with such a redefinition. But I am not sure that Marr’s fidelity to the scientific assumption of a real world independent of how it is measured and perceived by its components would let him go that far.

But this is a minor issue, of the letter not of the spirit. The spirit of Marr’s book is one of excitement, fun, elegance, and joy-to use his words. Part of Marr’s subtext is that in the process of research, just as in the integrative operations of the visual system, esthetic criteria are a sure guide to truth-parsimony, richness, unity, simplicity in complexity, harmony, and above all, hierarchical organization. Only constructs that meet these qualifications can generate predictions and testable hypotheses: a species or a science which produces such constructs is likely to survive because it out-predicts its rivals. The world is how its survivors see each other; and survivors survive by seeing the world beautifully. Might it be that in the remarkable correspondence between the ‘difference of Gaussians’ constant that defines the spatial receptive field of the size-tuned image filters, and the V 2G operator that generates the ‘zero crossings’ (the atoms of visual perception), a constant of about 1.6, we have encountered once more our old friend the ‘golden ratio’? That the ratio between excitatory and inhibitory space constraints at the most primal neural level is that same ratio that Kelly and Lefebvre have discovered between positive and negative ethical judgments?

The golden ratio is derived by comparing two successive terms of that series of numbers(1, 1,2,3,5,8, 13,21,34,55,89,144 . . . ) which is generated by the most simple mathematical feedback system. Feedback systems tend to produce hierarchies in which the highest and most recent elements subsume and summarize the lower and older ones. Simple feedback systems do this in terms of magnitude (increasing size or increasing closeness to a limit), and complex feedback systems do this in terms of increasing richness of information and subordination of function, as in the case of fetal cell division.

Marr’s central concept is essentially hierarchy. The reason why we did not understand the visual system before was that for some reason-I suspect political/cultural-we wanted the various operations of visual/neural processing to stand in a democratic relationship with each other, as equal technicians, so to speak, working together in a big

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undifferentiated mass, observed by a godlike ‘I’. But it turns out that the subjective unity, simplicity, and elegance of sight is merely the apex of an enormous stratified pyramid of functions, of delegated authority modified by the option to override, which is not observed by ‘I’ but constitutes ‘I’.

And as Philip Sidney points out in The Defense of Poetry, the idea of hierarchy is inseparably bound up with the idea of purpose (or, as its lower levels, ‘function’). Marr’s conception of vision as the active solution of information-processing problems, his insight that we must know what a piece of the visual system is for before we can find out how it works, is the logical expression of his notion of functional hierarchy. Without hierarchy there is no purpose. Purposes are served; and, we might add, no purpose, no meaning, no coherent view of the world, no world. As Marr says, vision is symbolic from its very earliest stages.

The human eye and visual cortex routinely retrace the whole course of the evolution of the universe in about the half-second it takes to construct its 3-D model of the visual world. It begins on the stochastic, probabilistic level of the most primitive and ancient components of the universe-the elementary particles, the photons that were all there during the first moment of the ‘big bang’. In succession the eye constructs regularities, elementary orientations, edges, surfaces, color, texture, motion, stereoscopic solids, enduring objects flexibly or rigidly existing in time, with their own sources of light and motion; recapitulating the feedback process of evolution whereby atoms, molecular solids, crystals, life forms, and sentient entities were produced.

Indeed, the main body of Marr’s book follows exactly this schedule and concludes with a highly reflexive and personal dialogue, with the most exciting suggestions about artificial intelligence. If we were to follow his example and structure the process of our research according to the logic of its content, we might find ourselves radically trans- forming the whole structure of the academy itself.

Frederick Turner University of Texas at Dallas, Richardson, TX 75083, USA

Comments on David Marr’s 20/20 Vision by Robert Sekuler Near the start of this remarkable book, David Marr inquires into the purpose of vision. Before considering the wisdom of his answer, let me explain my own purpose in reviewing this book, which has already commanded so many excellent and thoughtful reviews.

As you will see, this will not be yet another synopsis of Marr’s book or yet another commentary on it. Others have already done far too good a job. Instead, since Marr himself pointed out the utility of analyzing any complex terrain at several different scales, I will attempt a large-scale view of the book. Though this scale may seem to obscure the book’s many significant details, it does throw certain broader aspects of Marr’s approach into high relief. These few, broader aspects are particularly interesting because they promise to change the future direction of research into vision.

Starting at a very large scale indeed, Marr’s book encourages us to ask, ‘what is vision for?’ Or, putting the question as Marr preferred, ‘what does it mean, to see? These basic, almost naive, questions are paramount. The answers one selects animate one’s entire approach to vision.

Go back in time nearly three centuries to Bishop George Berkeley. In A New Theory of Vision (1709), Berkeley wrote that vision was designed to allow animals to ‘foresee . . . the damage or benefit which is like to ensue, upon the application of their own bodies to this