The reviewer misreresents Köhler's commentary. Köhler does not accept the validity of the criticism, but explicitly rejects it as invalid. Köhler: [p. 224, Meridan Books edition, 1959] "In answering this objection we should be clear about its meaning. It is not said that the theory [of isomorphism] makes unconvincing assumptions about the psychophysical correlates of phenomenal data; rather, it is maintained that actually there are no such assumptions at all. I cannot accept this criticism."

For example when we perceive a square, isomorphism maintains that a square-like data structure must be physically present in our brain. The neural representation need not be an exact replica of the percept, but merely "similar in all respects"; for example the rectangular faces of the squashed cubes depicted in Figure 16 (C) above (see point 6:) are isomorphic to perceived squares, even though they are not themselves square. The above criticism holds therefore that "squareness" describes only the nature of the percept, but does not apply to its neural representation; that describing the neural representation as "square-like" is merely a verbal solution, that actually makes no statement about the specific properties of that representation. Could it not be said, for example, that an abstract node labeled "square" could also be called isomorphic to the square percept?

Köhler replies that isomorphism makes the explicit statement that "macroscopic physical states rather than microscopic events" are the correlates of perceptual experience, which is a positive hypothesis, not merely a verbal solution. I have made this point even more explicit by relating isomorphism to Information Theory, by stating that the information encoded in the neurophysiological mechanism must be equal to the information observed in the subjective percept. By this definition it is now clear that the squashed squares in Figure 16 (C) are indeed isomorphic with perceived squares, but an abstract "square" node would not, since the former encodes the exact spatial arrangement of the percept (in depth-compressed form) while the latter encodes no spatial extent.

Köhler's explicit field-theory model was not devised to escape the above criticism, as the reviewer suggests, as that criticism can be shown to be invalid without experimental evidence. If the thesis of isomorphism is accepted, then a detailed description of the properties of the subjective percept is also a description of the information encoded neurophysiologically. This means that a perceptual model that quantifies the nature of the subjective percept has direct relevance to the nature of the neurophysiological representation of perception, i.e. that perceptual modeling is valid. Furthermore, we have available to us today a resource that was not available to Köhler, which is the digital computer which, together with dynamic systems algorithms as proposed by Grossberg, offers a means to express the dynamic transformation of the sensory stimulus into a spatial percept in an explicit quantitative manner that goes way beyond a mere verbal description. The concept of perceptual modeling is my own contribution, made possible by this computational resource.

As for the matter of testable predictions, the perceptual model offers a more reliable means of matching psychophysical data, since psychophysics measures specifically the subjective percept, rather than the corresponding neurophysiological representation. It is impossible to say, for example, which kind of neural model of spatial representation is supported or refuted by a spatial percept such as the Necker cube, or the Ehrenstein illusion, although such evidence is often evoked to support such models. In the absence of exact knowledge of the mapping between the neural state and its corresponding subjective experience, all such comparisons are actually invalid. A perceptual model on the other hand must represent the Necker cube or the Ehrenstein illusion in a fully spatial manner, because that is the observed nature of the percept. As such, it is the perceptual model, not the neural nodel that offers testable predictions of psychophysical data.

As to the utility of the perceptual model, such a model would indeed be merely an illusory solution if the subjective percept were a subjective manifestation without neurophysiological counterpart. Is it not odd that this reviewer objects so vehemently to the latter statement, and yet appears to suggest that the subjective percept is illusory? Does the reviewer really not see the contradiction in this view? These comments of the reviewer are in my view representative of the current confusion in vision modeling circles, which is exactly why a review of these fundamental assumptions is so vitally essential. If a full surface reification is observed perceptually, then the neurophysiological representation corresponding to that percept must explicitly encode the information manifest in that percept; i.e. it must encode every point on every perceived surface in depth. This conclusion has relevance to both perceptual and to neural models of perception.

As to the problem that "it remains to be shown whether such dynamics are definable in principle...", this statement merely explains that the model presented here is a conceptual rather than a mechanistic model, presented specifically to root out fundamental contradictions inherent in the conventional approach. The necessity of this preliminary stage of defining the goals and methods of the general modeling approach is highlighted by the manifest contradictions implicit in the conventional approach. While the computational feasability of the proposed approach remains to be demonstrated with a more specific formulation of the model, the general approach outlined here has the distinct merit that it highlights and circumvents the fundamental contradictions inherent in the neural modeling approach.

Both general approaches, the conventional and the Gestalt approach, remain to be defined in more explicit terms. The difference between them is that the conventional view is simpler to implement computationally, at least locally at the single cellular level, but fails to address the more global aspects of perception; so we are left with a computational description of what supposedly occurs in certain neurons, which may or may not have any relevance to perception. The perceptual modeling approach on the other hand offers a better global model of perception, although by its nature its mechanism is more difficult to characterize and to simulate computationally. This difficulty itself is evidence of the insufficiency of current neurocomputational concepts for explaining perception.