Reviewer A very kindly contacted me directly, and revealed himself to be Professor Dr. Hans-Georg Geissler of the University of Leipzig. I wrote him the following general response in January 2000, followed by responses to specific points raised by him and by the other reviewer .
Dear Professor Geissler,
First of all, I would like to thank you most profoundly for making yourself available for direct contact. I have always found the one-way anonymity and long delays of the review process a great hindrance to meaningful communication with my reviewers. I have now received a response from Psychological Review, including your own commentary. I am however disappointed in your recommendation for rejection unless substantial new material is added. The other reviewer was less kind, suggesting unconditional rejection. I enclose the full review from Psychological Review in case you would like to see it.
There was generally good correspondence between the two reviews on the major points, with which the editor was also in agreement. The general conclusion was that I have tackled an important and very interesting issue and that my approach has novelty and may have promise. However the complaint was raised that I have not developed my approach beyond the metaphor stage, and that therefore no real theory is presented. Furthermore, it was said that I failed to cite alternative approaches such as Grossberg's ART model, the PDP approach, and Gibson's resonance theory. The editor concludes that addressing these comments will require a lot of work, especially developing a theory of perception.
I can address the issue of citing alternative approaches, as discussed in the responses to specific points below. However I contest the criticism that the theory, as presented, is no theory but merely an analogy. For the fact that harmonic resonance is employed in embryological morphogenesis is not merely an analogy, but solid and concrete evidence that demonstrates that harmonic resonance both can and does serve the purpose of a representation of spatial pattern in biological systems. The hypothesis that the same principle is also active in neurocomputation is a valid and solid proposal worthy of publication, even if the exact principles and properties of resonance were to remain mysterious. In fact harmonic resonance is not mysterious, but is a well known physical phenomenon that has been investigated in considerable detail in physical systems such as standing waves in steel plates. In those systems it exhibits unique properties such as an elastic flexibility in the coding scheme, abstraction as well as reification, and rotation invariance in symmetrical resonating systems. These properties are unique to harmonic resonance, and thus illustrate a truly novel concept, not as a physical phenomenon, but as a spatial representation, and truly novel concepts are deserving at the very least of publication in the literature, whether or not they are ultimately accepted as the actual representation used in the brain.
The reviewers suggest that the theory is incomplete until I can identify the exact neural mechanisms or mathematical specification behind resonance in perception, and describe exactly how this resonance serves the computational processes of perception. However theories are validly proposed at different levels of generality, from very specific neurophysiological theories involving the mechanism of action potentials and neurotransmitter release, all the way to more general theories of computational or representational principles. In fact there have been many theories published which are at least as general and non-specific as my harmonic resonance theory, including Selfridge's Pandemonium theory, Triesman's Feature Integration Theory, Neisser's Iconic Memory Theory, Thorndyke's Schemas concept, Rosch's Prototype theory of memory, Kosslyn's theory of mental imagery, Atkinson & Schiffrin's model of memory, Gibson's theory of Direct Perception, Biederman's Geon theory, Crick's theory of quantum consciousness, Pribram's holographic theory, De Valois' Fourier theory, McClelland's Interactive Activation Model, Kirkpatrick's Simulated Annealing concept, McClelland's PDP approach, etc. All of these theories have been rightfully published in the literature even in the absence of either direct neurophysiological evidence, or complete mathematical specification (and sometimes both), because until the essential principles of operation of the brain have been established beyond a doubt, such theories enrich the discussion of possible principles and mechanisms of neurocomputation. Even if such theories are ultimately rejected, they serve the invaluable purpose of supplying a reference point, or "handle" available in all subsequent discussions on the issue, even if those references are cited only as examples of wrongful approaches. Every unique and original concept of neurocomputation deserves to be exposed to the community, to make it available to be judged on its merits by the larger community of scientists, many of whom have access to additional evidence not available to either the author or to the reviewers, which may help to either support or refute the proposed theory.
And of course there is Gestalt theory itself, a concept that is so vague and unspecified that it is hard to even state the theory in unambiguous terms. And yet Gestalt theory has made a major contribution by alerting us to certain deeply enigmatic processes and principles in perception, most of which remain mysterious to this day. If Gestalt theory had been rejected for publication until it were more precisely specified, this would have been an incalculable loss to science, and the theory would have remained unpublished to this day. If Gestalt theory has any merit whatsoever, then any extension of Gestalt theory in the direction of greater specification of either computational or neurophysiological principles must be seen as an advance, even if much remains to be elaborated on the specifics of the theory. My own reduction of Gestalt theory to the somewhat more specified principles of Emergence, Reification, Invariance, and Multistability, is an attempt at such specification, and my Harmonic Resonance theory even offers a possible neurophysiological mechanism, with demonstrably unique properties. In fact my Harmonic Resonance theory is far from unspecified, indeed it is specified so completely that its principles of operation can be demonstrated in a real physical system composed of steel plates and oscillators, as described in the paper. This goes far beyond the computational specificity offered by many of the general theories cited above, many of which can be validly criticized on the basis that their operational principles remain unspecified, but those theories nevertheless represent valuable contributions to the debate.
The value of harmonic resonance, even if it were only a hypothesis, is seen even in your own work where you postulate some kind of resonance to account for various subtle psychophysical phenomena. But your hypothesis is itself open to the very criticism that you aim at my theory, for the phenomena you describe could also be explained in conventional neural terms, although they would probably be implausibly complex. How then can you get away with proposing a speculative resonance mechanism without presenting a complete theory, and incontravertable evidence that eliminates alternative neural network explanations? In fact the value of my harmonic resonance theory is that it offers a broader theoretical justification for harmonic resonance hypotheses such as your own, by highlighting the unique properties of harmonic resonance as a representational principle in the brain, thereby explaining why resonances such as those you postulate should be found in the brain. Contemporary neuroscience has been stagnant for decades for lack of refreshing alternative hypotheses to offer a way out of thetheoretical dead-end in which it finds itself. The trouble is that the stagnation has endured so long that a kind of "learned helplessness" has set in, such that any solution to the age-old problems is rejected out of hand as being too radical, without regard to the fact that the conventional receptive field theory is at least as inadequate as a theoretical solution to the larger issues of neural representation. Neuroscience would be immeasurably enriched by a frank discussion of the limitations of contemporary concepts, and a free discussion of as many alternative hypotheses as can possibly be explored. It is a miscarriage of the methods of science to reject alternative hypotheses even for consideration by the community merely because they have not yet been proven, especially when the conventional hypothesis has itself never been proven, and can be shown to be theoretically untenable.
The reviewers would probably be more comfortable with a complete mathematical specification of harmonic resonance rather than a verbal description of its properties as implemented in vibrating steel plates. I presume this is what you mean by your critique that sufficient rigor is missing from my presentation. The western scientific tradition has always emphasized reduction of physical systems to simpler mathematical terms, and virtually all problems in physics are traditionally addressed in that form. However this procedure can give the physicist a biased view of physical reality. For in fact the vast majority of physical systems and phenomena are far too complicated to be reduced to such analytical terms except by way of simplifying assumptions. There are certain classes of physical systems which simply do not succumb to mathematical analysis because the phenomena in question are already the simplest model of themselves, i.e. there is no way to reduce the phenomena to simpler mathematical terms without setting prohibitively restrictive constraints on the parameters of the system. In all but the simplest cases, harmonic resonance has exactly this property. And it is those very properties that represent the most interesting aspects of harmonic resonance as a representation in the brain. For example Chladni and Waller both reference work by various authors who provide mathematical solutions to the equilibrium states of various standing wave patterns found on steel plates. Also, basic physics texts offer formulae to calculate the fundamental frequency of flutes and organ pipes based on their length and diameter etc. But these analyses are an abstraction or meta-level description of the actual mechanism of harmonic resonance, which is actually a fine-grained process involving molecular interactions throughout the resonating system resulting in global effects. The mathematical solutions for steel plates have only been developed to account for the simplest of these patterns, like those for a circular or square plate, and the equations for organ pipes apply only to geometrically simple straight pipes with circular cross-section and uniform diameter along their length. This kind of analysis is invalid in the case of irregular or arbitrary shaped steel plates, or plates of non-uniform thickness, or organ pipes that are curved, or flared, or barrel-shaped, or with any other irregularity in their form. And yet it is this very flexibility that represents the most interesting aspect of the resonance. If the discussion were limited to the simple cases for which analytical solutions have been found, the theory would degenerate to a template theory, and thereby lose its most appealing properties. This is exactly what Wertheimer meant when he said that a "new mathematics" will have to be devised to account for the Gestalt properties of perception (see p. 48 of my book).
Physical systems that defy mathematical characterization are often addressed numerically, using computer simulations. This is the approach used for example to predict the behavior of the atmosphere, which is approximated by quantization of the system in space and time to tiny local elements which are simple enough to be treated as a single point. However this approach too has its limits, for the quantization in space and time inevitably introduce inhomogeneities into the system. For example a computer model that simulates the interactions between vibrating molecules of air in an organ pipe must begin with a subdivision of that pipe into discrete cells or "voxels" (volume pixels), but the rectilinear nature of that grid of voxels introduces artifacts due to the fact that vertically and horizontally adjacent voxels in the grid are closer than diagonal or other pixels. Since resonance is such a fine-grained phenomenon that operates in an essentially continuous analog medium, it is impossible to accurately simulate the phenomenon in a digital simulation with any confidence that the simulation is correct in any but the simplest possible cases, to say nothing of the enormous computational load of an iterative algorithm operating on volumetric data. The case of harmonic resonance is even more problematic for numerical simulations than a model of the atmosphere, because atmospheric parameters such as temperature, pressure, and humidity tend to diffuse amorphously into adjacent regions in a relatively simple manner, so that these parameters can be computed fairly accurately by considering only nearest neighboring regions. In the case of standing wave pattern in a resonating system on the other hand, the local value of the pattern (i.e. whether a particular point is a node or anti-node of the standing wave) depends on the configuration of the entire resonating system as a whole, and cannot be even approximated from the values of adjacent regions of the system, for resonance does not simply diffuse between adjacent points in the system, but is influenced by the entire configuration of the system as a whole. The very fact that harmonic resonance exhibits this Gestalt-like nature, and the fact that these kinds of systems are so difficult to characterize both mathematically and computationally, provides all the more reason to investigate these phenomena as a possible property of biological computation, to account for exactly those aspects of perception which have defied characterization in more abstracted terms. If this work must be done "by analogy" using vibrating steel plates, that does not in any way invalidate the results, for the vibrating steel plate is itself a computational mechanism, albeit one whose operational principles are radically different from any known computational device, and therefore the "output" of the steel plate is no different in principle from the output of a computer simulation. The fact that resonance exhibits similar properties whether expressed as a physical, electrical, chemical, or acoustic resonance shows that resonance is a general principle that transcends any particular physical instantiation, and thereby represents a higher order organizational principle of physical matter. Considered as a computational paradigm, harmonic resonance has unique emergent properties that cannot be meaningfully reduced to an equivalent Turing machine description. This alone makes harmonic resonance unique in the literature of neurocomputational principles. The message of Gestalt theory is that it is exactly this kind of unconventional enigmatic computational principle that should be sought out in the brain.
The reviewers suggest that the theory is incomplete without a more detailed statement of the specific role that resonance plays in perception. In fact I have developed such a theory for vision, which was the focus of my thesis work, and I have submitted it for publication on several occasions. Specifically, I have identified a number of visual illusory phenomena which cannot be plausibly explained using conventional neural network models such as those proposed by Grossberg, without invoking implausibly large combinatorial assemblies of neural elements. I show that these same phenomena are explained by a harmonic resonance mechanism in a very simple homogeneous medium using a very simple computational architecture, whose emergent complexity is due to the resonance phenomenon itself, rather than to the complexity of the computational architecture. On every occasion these papers have been rejected for publication. The major reason given was that in a model of perceptual processes, the reviewers considered it inappropriate to introduce a completely novel and unconventional form of neurocomputation as the central mechanism to account for the phenomena addressed. Such a radical departure from conventional concepts of neurocomputation is a subject deserving of central focus, and that is exactly what I have attempted in the present submission, in which I propose to challenge the concept of the neuron doctrine itself, and replace it with a general concept of a harmonic resonance representation. After this paper is published, (if it ever gets that far!) then I can resubmit my model of visual perception making reference to this paper, to justify the use of the unconventional harmonic resonance mechanism. If I were to attempt a paper to address both harmonic resonance and visual illusory phenomena, the paper would quickly grow to excessive length, and cover too great a theoretical scope for a single paper, and thus be rejected on that basis. I enclose a copy of my rejected paper on "Orientational Harmonics" as an explanation for visual illusory phenomena, as well as excerpts from my thesis work, to show how the theory does indeed make specific predictions in the visual domain, but that this is a subject in itself that is difficult to squeeze into a single paper, let alone to attempt to justify the harmonic resonance principle as well as model the illusory visual phenomena. There are some ideas which are just too big to fit into a single paper.
You may or may not find the above arguments convincing. In any case I get the sense that the other reviewer will almost certainly not be convinced. But there is a deeper issue involved here. In discussions with colleagues on this issue I often hear the comment that if this theory has any validity, then surely I can devise some kind of "experimenta crucis" that will determine unambiguously which theory is correct. However the real problem is that what I am proposing is not merely a new theory of neurocomputation, but a new paradigm, i.e. I am questioning the very basis of modern neuroscience and the assumptions on which it is built. This will become abundantly clear if you take a little time to browse through my book, which I enclose also. In his book "The Structure of Scientific Revolutions", Kuhn (1970) explains the difficulty of presenting new paradigms to an audience committed to an older one. Kuhn observes (p. 156) "if a new candidate for paradigm had to be judged from the start by hard-headed people who examined only relative problem-solving ability, the sciences would experience very few major revolutions. ... But paradigm debates are not really about relative problem-solving ability ... Instead, the issue is which paradigm should in the future guide research on problems many of which neither competitor can yet claim to resolve completely. A decision between alternate ways of practicing science is called for, and in the circumstances that decision must be based less on past achievement than on future promise. ... A decision of that kind can only be made on faith. ... Something must make at least a few scientists feel that the new proposal is on the right track, and sometimes it is only personal and inarticulate aesthetic considerations that can do that."
(Kuhn p. 93) "Like the choice between competing political institutions, that between competing paradigms proves to be a choice between incompatible modes of community life. Because it has that character, the choice is not and cannot be determined merely by the evaluative procedures characteristic of normal science, for those depend in part upon a particular paradigm, and that paradigm [itself] is at issue. When paradigms enter, as they must, into a debate about paradigm choice, their role is necessarily circular. Each group uses its own paradigm to argue in that paradigm's defense. ... This issue of paradigm choice can never be unequivocally settled by logic and experiment alone."
In the present context, one issue of contention between paradigms is whether phenomena observed on a steel plate are merely analogies, or a demonstration of a new computational principle, and therefore a valid demonstration of possible neurocomputational principles in the brain. Another issue is whether the somewhat vaguely defined properties of emergence and other Gestalt qualities are valid evidence for some kind of holistic computational principle in the brain that is hler 1923 p. 64) "Natural sciences continually advance explanatory hyptotheses, which cannot be verified by direct observation at the time when they are formed nor for a long time thereafter. Of such a kind were Ampincompatible with the Neuron Doctrine paradigm. The answer to these questions cannot be proven one way or the other, because conventional neural network models can always be re-formulated to account for any particular Gestalt property in question, the problem is that such architectures become so complicated and elaborate as to be completely implausible. But neurophysiological plausibility is itself a "personal and inarticulate aesthetic consideration" that depends much more on your initial assumptions than it does on any evidence or reasoned argument. And the question of whether resonance on a steel plate is merely an analogy is a matter of what we consider to be valid methods of our science. If a theory must be reduced to analytical and mathematical terms in order to be considered rigorous, then we will be forever denied the possibility of investigating principles and mechanisms revealed by Gestalt theory that in principle resist characterization in analytical terms. Gestalt theory suggests that this restriction would forever close any investigation of the real computational principles behind perception.
It is on this basis that I appeal to you to let this paper see the light of day, even if you are not personally convinced of the validity of the theory, in order to allow other scientists the opportunity to decide for themselves whether they consider the concept to be valid. I am not afraid of hard work, and I would be happy to do whatever is necessary to get this paper published. However I get the feeling that what I am being asked to do is impossible in principle, due to the nature of the phenomena in question. My first reaction when I read the review was to just give up, and resubmit to another journal. However your kind offer to contact you directly prompted me to send you this appeal. If you are swayed by the above arguments and are willing to revise your criticism that "no theory is presented", then I will respond to Psychological Review with the above stated argument, and with a new version of the paper that incorporates the specific changes outlined below, in an attempt to induce the editor and the other reviewer to also change their minds. If on the other hand you are not convinced by the above argument, and continue to consider the theory as no theory, then I will have to resubmit elsewhere, in the hope that at least a few scientists feel that the new proposal is on the right track. Should this theory eventually be shown to be valid, I hope that history will not record your name among those narrow minded scientists who are incapable of thinking outside of their own paradigmatic box.
Sincerely,
Steve Lehar