Multi-Scaling, Quantum Theory, and the Foundations ...

NeuroQuantology 2003; 4: 404-427 Flanagan, BJ. Multi-scaling, quantum theory, and the foundations of perception

404

Original Article

Multi-Scaling, Quantum Theory, and the Foundations of Perception

Brian J. Flanagan1 Abstract The issue of multi-scaling in neuroscientific research is examined with respect to a quantum field theoretic account of mind and brain. Key Words: multi-scaling, quantum, qualia, vision, EPR, fractal, gauge theory, M-theory NeuroQuantology 2003; 4:404-427

INTRODUCTION should like to discuss a number of important and timely issues concerning multi-scaling in neuroscience. Addressing recent philosophical work on cognitive function and the search for neural correlates of consciousness, Pereira (2001) states that this effort has “relied on the assumption of an ultimate level of description where the biological basis of cognition could be identified.” In contrast, neuroscientific research has been characterized by the “tacit assumption of multiple coexisting spatial and temporal scales that should be tied together.” Pereira discusses empirical criteria whereby we might distinguish these different scales of organization, together with related issues regarding the irreducibility of levels of description. Clearly, all of these considerations have their importance, but it is this final ‘irreducible’ issue which will most concern us. For the irreducibility of sensory qualities or qualia would seem to be telling us something crucial about their proper place in the natural world, and in what follows we will attempt to show what that lesson might be. Briefly, the argument runs as follows: We accept, as a working hypothesis, that sensory qualities are irreducible. Whereas the irreducibility of sensory qualities is often viewed as a problem for science, which has often to do with reducing complex wholes to simpler parts, we prefer instead to emphasize the fact that all theories must begin 1

Sentient technologies, Iowa City, IA, [email protected]

ISSN 1303 5150

www.neuroquantology.com


405

with primitive, undefined elements in order to avoid an infinite regression of definition. Given their utter simplicity, it seems as though sensory qualities ought to make plausible candidates for the elements of a theory T of mind and brain, insofar as being irreducible is like being elemental. By mapping sensory qualities to the elements of T, we would seem to recover a few fundamental items of phenomenology. Thus, no matter how complex T might be (it may exhibit the complexity of a human brain) it will be impossible to define T’s elements within T, for then the elements would not be elements. Just so, perhaps, are we unable to reduce the sensory qualities—the elements of perception—to anything simpler. We would therefore appear to have mirrored a durable fact of perception in the basic logic of our situation. In a similar vein, we seem to have recovered the fact that all objects of perception are either sensory qualities or configurations of qualities, just as all objects of T are either elements of T or composed of those elements. Flushed with this initial bit of encouragement, we then ask how we might square T with various threads of traditional physical theory, such as Kaluza-Klein theory, “hidden variables” theory, gauge theory, and string/M-theory. In so doing, we raise many more questions in our wake. The most fundamental question with which we The most shall concern ourselves is whether the secondary fundamental question qualities of sensory perception might find a with which we shall congenial home in the additional, internal, or concern ourselves is “hidden” spaces of these various formulations of whether the physics. In the course of our inquiry, we will have secondary qualities a look at the mathematics of perceptual fields vis-à-vis quantum fields, touching upon such of sensory perception might find a objects as vectors, tensors, fiber bundles and manifolds. We will also consider a handful of congenial home in experimental predictions and post-dictions which the additional, might serve to corroborate or contradict theory. internal, or “hidden”

spaces of these

Field theory various formulations It has been suggested (Flanagan, 2001) that the of physics ultimate level of description of mind and brain ought to be the quantum level, insofar as quantum field processes mediate all chemical and biological processes. Indeed, as is made clear by Dyson (1953), when we regard nature from a strictly physical viewpoint, “There is nothing else except these fields: the whole of the material universe is built of them.” We can sharpen our focus further by selecting the brain’s electromagnetic (EM) fields for further attention, for as Salam (1990) reminds us, “all chemical binding is electromagnetic in origin, and so are all phenomena of nerve impulses.” We reason that, if perceptual fields are “phenomena of nerve impulses,” as would seem altogether plausible, then it would seem to follow that perceptual fields are “electromagnetic in origin.” Importing quantum field theory (QFT) into mind/brain identity theory, we ask whether we might profitably identify perceptual fields with photon fields, given that both sorts of field are vector fields which coincidentally and continually co-vary. ISSN 1303 5150



406

We readily find support for some such thesis in Chalmers (1995): The pattern of color patches in a visual field, for example, can be seen as analogous to that of pixels covering a display screen. Intriguingly, it turns out that we find the same information states embodied in conscious experience and in underlying physical processes in the brain. The three-dimensional encoding of color spaces, for example, suggests that the information state in a color experience corresponds directly to an information state in the brain. We might even regard the two states as distinct aspects of a single information state, which is simultaneously embodied in both physical processing and conscious experience. So essentially what we’re suggesting is, let us substitute “EM processing” for “physical processing” in the last sentence above, and see where that gets us. Chalmer’s remarks are echoed in Feigl (1970), who underscores our meaning and sense: Certain neurophysiological terms denote (refer to) the very same events that are also denoted (referred to) by certain phenomenal terms. The identification of the objects of this twofold reference is of course logically contingent, although it constitutes a very fundamental feature of our world as we have come to conceive it in the modern scientific outlook. Using Frege's distinction between Sinn ('meaning', 'sense', 'intension'), and Bedeutung ('referent', 'denotatum', 'extension'), we may say that neuro-physiological terms and the corresponding phenomenal terms, though widely differing in sense ... do have identical referents. I take these referents to be the immediately experienced qualities, or their configurations in the various phenomenal fields. In parallel with Chalmers, we substitute “quantum field theory (QFT) terms” for Feigl’s “neurophysiological terms” and argue that these QFT field terms and the “corresponding phenomenal terms, though widely differing in sense … do have identical referents.” We also take these identical referents to be the “immediately experienced qualities, or their configurations in the various phenomenal fields.” Aside from considerations of naturalness and economy, we motivate this move, this identification of perceptual field and quantum field, by invoking the fact that quantum states are described by vectors, as are such “immediately experienced qualities” as colors and sounds. (P.M. Churchland, Clark) We are thus on a more even footing mathematically, for on the one hand we have Chalmers‘ “information” and Feigl’s “immediately experienced qualities” expressed as vectors, while on the other we have concomitant photon states, which are also expressed as vectors. To paraphrase Helmholtz, we might say that similar photonic vectors are associated, under similar conditions, with similar color vectors. We view the elementary nature of qualia as an important clue to their place in nature, reasoning that it makes a good deal of sense to place the secondary qualities among the elements of a complete quantum theory. By “complete” we have in mind the seminal paper of EPR, for whom a complete theory was one where all “elements of reality” are represented. As Russell, Schrödinger, and Austen Clark remark, the secondary qualities have no good agreed-upon place within science. Now, to be sure, one often does encounter statements in the literature to the effect that colors, e.g., are ISSN 1303 5150



407

identical with the frequency or wavelength of the light with which they are associated. Such statements are typically made en passant, however, with nothing like a reasonable explanation of how such an identification might fit the relevant data. Much more convincing is the work of Schrödinger, PM Churchland, and Lockwood, who propose a vector space model of colors (or of qualia in general). As Feynman notes in his Lectures, colors add and multiply like vectors, and it is well worth noting that this mathematics is put to practical use in color TVs and computer monitors. Once we take hold of the vectorial aspect of qualia, we can then ask how we might coordinate the “secondary vectors” with their associated state vectors. Continuing in this line of thought, and keeping in view the manifest symmetries of the secondary qualities, we are then led to a picture much like that found in Kaluza-Klein theory, in gauge theory, and in string/M-theory, where “internal” and/or “compactified” spaces appear to be required in order to account for the standard “phenomenology“ of particle physics. Might the secondary qualities find a natural fit among the sorts of additional spaces that pop up in mainstream physical theory? Note for the time being that the secondary qualities have one obvious factor in favor of such a coordination, namely that these qualities intersect the space-time coordinates of perceptual events. Or as Wittgenstein put it, “A speck in the visual field, though it need not be red must have some color; it is, so to speak, surrounded by color-space. Notes must have some pitch, objects of the sense of touch some degree of hardness, and so on." Where are we? If there is nothing to the brain but its constituent fields, then it seems to follow by a ready consequence that Feigl’s neurophysiological terms ought to reduce to field terms. We then inquire whether perceptual fields are perhaps identically photon fields. Put like that, the question induces a bit of ontological vertigo, but as Lockwood reminds us, something like this thesis was put forward by both Bertrand Russell and the early Gestalt psychologists. With a view to the dizzying, abstract heights of the prospect before us, we will call upon a number of trustworthy guides to help us along—illustrious philosophers, mathematicians, and scientists who have mapped out the route before us and planted signposts along the way. To begin again, we argue that color vectors, considered as “immediately experienced qualities” together with their configurations in the visual field, ought to map to photonic vectors and their configurations in a photon field. So vectors get mapped to vectors, and fields to fields. What could be simpler? Are these mappings identities, though? And what might such identities entail for physical theory? Clearly, we must attend a number of related issues and concerns. By way of lending a measure of plausibility to these notions, we remark the fact that our visual field, for example, regularly and predictably co-varies with the photon field that stimulates our retinal receptors, and so with those fields which constitute the visual cortex. Moreover, the color vectors of the visual field add together in parallel with the superposition of their associated state vectors—predictably, reliably, and really quite quantifiably. Now, to be sure, one of the recurrent criticisms often leveled against the whole “quantum mind” movement is that quantum effects can be safely ignored because such effects are “washed out” by the wet, noisy environment of the brain. But this criticism ISSN 1303 5150



408

cannot stand, because if physics is to be believed, the brain and sense organs just are quantum processes, and any "washing out" that might occur simply results from losing sight of this fact. Another charge often made is that quantum theory only applies in the realm of the microscopic, but this complaint does not fare any better (Umezawa, 1993): There have been many models based on quantum theories, but many of them are rather philosophically oriented. The article by Burns ... provides a detailed list of papers on the subject of consciousness, including quantum models. The incorrect perception that the quantum system has only microscopic manifestations considerably confused this subject. As we have seen in preceding sections, manifestation of ordered states is of quantum origin. When we recall that almost all of the macroscopic ordered states are the result of quantum field theory, it seems natural to assume that macroscopic ordered states in biological systems are also created by a similar mechanism. Multiscaling and self-similarity In thinking about those "ordered states" known as neurons, we are drawn to the fact that dendritic processes appear to be aptly captured by the mathematics of fractals. As is well-known, one of the hallmarks of fractal patterns consists in their self-similarity across spatial and temporal scales. This consideration brings us around again to Pereira and multi-scaling: Perhaps the meso-level of neural form follows the micro-level of quantum function? Perhaps the quantum level embodies the initial conditions upon which the organism exhibits sensitive dependence? Such notions would seem to dovetail nicely with the outlook found in Pribram (1991), where he writes that “the mathematical formulations that have been developed for quantum mechanics and quantum field theory can go a long way toward describing neural processes due to the functional organization of the cerebral cortex.” Further support for a quantum-mechanical foundation of neural function stems from Heisenberg’s operator formalism, where we also find matrices acting upon vectors (Dirac, 1966). Considering Patricia Churchland's criticism of Penrose & Hameroff, it is somewhat ironic, then, to note our own agreement with Paul Churchland (1989) in respect of (a) neural implementations of matrix operations on (sensory) input vectors; and (b) the observation, apropos the work of Pellionisz and Llinas, that the cerebellum’s job is “the systematic transformation of vectors in one neural hyperspace into vectors in another neural hyperspace”; and that (c) “the tensor calculus emerges as the natural framework with which to address such matters”; and (d) the characterization of phenomenal properties as vectors.*2 On a biological view, the picture which emerges is that of brains evolving so as to exploit quantum processes. If there is nothing to the brain but quantum fields, then it seems as though the evolving organism would have no other choice but to avail itself of quantum processes. Are perceptual fields identically photon fields? Perhaps. Perceptual fields vary mechanically with those photon fields which excite our various receptor neurons. A 2

Since having submitted this article I have been reminded that both Churchlands have written in support

of these ideas. ISSN 1303 5150



409

cone captures photons corresponding to light of 590 millimicrons wavelength and the observer sees an "event" at a corresponding point in space-time. But having coordinated the event in four dimensional space-time does not exhaust the observed properties of that event, which also manifests a yellow color. Yet as Schrödinger (1959) tells us, “yellow” has no place in the official lexicon of the physicist. We have raised the question of whether the quantum level might embody the initial conditions upon which the organism exhibits sensitive dependence. Implicit in the picture sketched herein is an account of neural coding, where the sensory receptors superpose the state vectors of their respective stimuli on the neural impulses triggered by those stimuli, which impulses then act as a sort of carrier wave, bearing this vector "information" downstream to the thalamic, Now, to be sure, one cortical, and other regions for processing. As has of the recurrent often been noted, however, one neural impulse criticisms often looks much like another, so this notion would seem to encounter immediate difficulties. But if leveled against the the brain exhibits sufficiently sensitive dependence whole “quantum on its sensory input vectors, then it seems to mind” movement is follow that we are, perhaps, not looking at neural that quantum effects impulses with sufficient resolution.3 If there is nothing to the brain and sense can be safely organs but their constituent fields, then there is ignored because essentially no physical problem so far as getting such effects are multiple spatial and temporal scales to coexist—the meso and macro levels of “washed out” by the description turn out to be only different ways of wet, noisy speaking about large collections of quantum fields. environment of the Nonetheless, there are excellent reasons for brain paying close attention to these larger scales above the ground floor of the quantum. In the first place, there is a clear sense in which the brain’s constituent fields are ordered at various spatio-temporal scales, from the brain down to its various modules, and on down to the individual neurons, dendrites, synapses, and finally to the fields themselves, where the rubber of the organism meets the pavement of its environment. Focusing our view by varying degrees of magnification reveals levels of organization not otherwise apparent. In the second place, these various levels of organization coexist at widely different time scales. Thus, while all chemical processes are mediated by photons (Feynman, 1985) we ourselves do not move at the speed of light, but at a relatively glacial rate. Yet clearly all our spatial and temporal levels “cohere” into a living organism. The picture that springs to mind is that of a clockwork, where larger and smaller gears move at different rates but mesh to produce orderly behavior. In the case of the organism, is the whole perhaps governed by an atomic clock of some kind? Of course, unlike a clockwork, organisms move at different 3

I have also recently been apprised of work which suggests that neural events previously regarded as “noise” actually constitute complex signals: http://www.columbia.edu/cu/21stC/issue-4.2/lerner.html ISSN 1303 5150



410

rates at different times. Then, too, we live in a quantum universe distinctly unlike Newton’s. Our clockwork picture, while perhaps a helpful heuristic, is clearly out of date in important respects. At any rate, it seems clear that all parts of an organism must move in space and time “in synch” with one another. Given the fractal character of dendritic arborizations, it seems plausible to suppose that both the brain (and, perhaps, the organism as a whole) might cohere by way of self-similarity across its spatio-temporal levels, one level sitting nested inside another like the fractal equivalent of the famous Russian dolls called matryoshka. On such a view, the optic nerve, for example, with its central bundle of axons and its branches to the retina at one end and the visual cortex at the other, looks curiously self-similar to the axons and dendritic branches of its constituent neurons (and perhaps also to the microtubule structures within the individual neurons). These ideas are obviously somewhat speculative at the moment, but they appear to have a degree of plausibility and are clearly subject to observation and falsification. There are, moreover, a few substantial papers touching upon similar conceptions (Prusinkiewicz, 1993; Qiao et al., 1999; Teich et al., 1997; Liu et al., 2000; Caserta et al., 1995).4 Pereira (2001) proposes an empirical criterion for determining the existence of multiple levels of organization in a system: “If experimental access to two levels of description requires two different technical strategies and tools, then they constitute two levels of organization; but if only one methodology gives experimental access toboth levels, they are merely levels of description.” Here one is immediately reminded of Bohr’s well-known views on complementarity and of his insistence on specifying the total experimental arrangement when speaking of the properties assigned to a system. It would seem quite plausible to suppose that, in addition to different levels of description, two different methodologies in the neurosciences might well reveal two different but complementary aspects of the system under study. Where that system is a conscious organism, the epistemology of neuroscience shades into classical mind/body philosophy. For certainly the most famous among the “complementary” aspects of the conscious brain must be the “mental” and the “physical.” On a mind/brain identity theory, these “dual” aspects of the system might be seen as complementary descriptions of a more fundamental unity, in analogy with wave and particle, perhaps, or matter and energy. In the tradition of William James and Bertrand Russell, then, “mind” and “matter” resolve into different ways of talking about the same stream of experience. In a similar vein, Feigl's phenomenal fields and Chalmers’ information states resolve into different ways of talking about quantum fields and their states. History teaches us Mach (1970) would seem to agree with such a "dual" view of colors—typically regarded as “mental” entities: The great gulf between physical and psychological research persists only when 4

I have recently been delighted to learn of Pellionisz’ work on fractal models of neurons: http://usa-siliconvalley.com/inst/pellionisz/89_fractal/89_fractal.html ISSN 1303 5150



411

we acquiesce in our habitual stereotyped conceptions. A color is a physical object as soon as we consider its dependence, for instance, upon its luminous source, upon temperatures, upon spaces, and so forth. When we consider its dependence upon the retina it is a psychological object, a sensation. It is interesting to note in light of recent developments in string/M-theory that in Mach, the duality of mind and brain becomes a matter merely of dual descriptions of the same (color) phenomena. For what John Schwarz has dubbed the "second superstring revolution" arose from the recognition that the various competing formulations of string theory were, in fact, different versions of the same "M" theory, where M stands for "matrix," (or possibly "magic"). If, as Mach argues, colors and other secondary qualities are indeed physical properties, then a complete theory of everything ought to account for these qualities in a natural manner. In this wise it is a curious fact that, like its stringy progenitors, M-theory requires additional spatial dimensions in order for the theory to work. For on the one hand we have the secondary qualities, looking for a decent home in physical theory, and on the other these additional dimensions in M-theory, which (as in Kaluza-Klein theory) are typically thought to be vanishingly small because we do not observe them. Also of interest in this connection to contemporary physics is the use of “empirical” in Pereira’s criterion for determining the existence of multiple levels of organization in a system. Insofar as “empirical” means “based on observation,” we are drawn to another curious fact, remarked by Russell, that all our “objective” science is ultimately justified with respect to “subjective” experience. As Clark (1993) points out in his work on Sensory Qualities, it is now possible to quantifiably predict which “subjective” color samples will be matched by a given individual once that person’s “basis vectors” in color space have been determined. It is hard to miss the formal analogy with the prediction of a “physical” body’s future position in four-dimensional space-time, which analogy would seem to go a long way toward dispelling the “subjective” view of colors—and this is an essential point, because colors, together with the other secondary qualities, have long been considered “mental” entities in large part because of their supposedly “subjective” character, as Burtt (1954) tells us: Swept on by the inherent necessities of this mathematical metaphysic, Galileo, like Kepler, was inevitably led to the doctrine of primary and secondary qualities, only with the Italian genius the doctrine appears in a much more pronounced and developed form. Galileo makes the clear distinction between that in the world which is absolute, objective, immutable, and mathematical; and that which is relative, subjective, fluctuating, and sensible. … The Copernican astronomy and the achievements of the two new sciences must break us of the natural assumption that sensed objects are the real or mathematical objects. They betray certain qualities, which, handled by mathematical rules, lead us to a knowledge of the true object, and these are the real or primary qualities, such as number, figure, magnitude, position and motion … The reality of the universe is geometrical; the only ultimate characteristics of nature are those in terms of which certain mathematical knowledge becomes possible. All other qualities, and these are often far more prominent to the senses, are secondary, ISSN 1303 5150



412

subordinate effects of the primary. Of the utmost moment was Galileo’s further assertion that these secondary qualities are subjective. In Kepler there had been no clear statement of this position; apparently for him the secondary qualities were out there in the astronomical world, like the primary, only they were not so real or fundamental. Now, being more or less "real" is akin to being more or less pregnant, but Burtt is not far from the mark. Here is what Galileo actually wrote: “Hence I think that these tastes, odors, colors, etc., on the side of the object in which they seem to exist, are nothing else than mere names, but hold their residence solely in the sensitive body …” Newton also opined that colors as perceived do not exist in light itself: “For the Rays (of light) to speak properly are not colored. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Color. ... in the Rays they are nothing but their Dispositions to propagate this or that Motion into the Sensorium, and in the Sensorium they are Sensations of those Motions under the form of Colors.” Locke gets the credit for naming the distinction between primary and secondary qualities (Burtt):

These I call original or primary qualities of the body, which I think we may observe to produce simple ideas in us, viz., solidity, extension, figure, motion or rest, and number. Secondly, such qualities which in truth are nothing in the objects themselves, but powers to produce various sensations in us by their primary qualities, i.e. by the bulk, figure, texture, and motion of their insensible parts, as color, sounds, tastes, etc., these I call secondary qualities. (Burtt) Locke writes that secondary qualities are “nothing in the objects themselves” but "powers to produce various sensations" in us by the operation of primary qualities. Boyle seems to have wavered on this issue: But now we are to consider, that there are de facto in the world certain sensible and rational beings that we call men; and the body of man having several external parts, as the eye, the ear, etc., each of a distinct and peculiar texture, whereby it is capable of receiving impressions from the bodies about it, and upon that account is called an organ of sense; we must consider, I say, that these sensories may be wrought upon by the figure, shape, motion, and texture of bodies without them after several ways, some of those external bodies being fitted to affect the eye, others the ear, others the nostrils, etc. And to these operations of the objects on the sensories, the mind of man, which upon the account of its union with the body perceives them, gives distinct names, calling the one light or color, the other sound, the other odor, etc. … whereas indeed there is in the body to which these sensible things are attributed, nothing of real and physical, but the size, shape, and motion or rest of its component

ISSN 1303 5150



413

particles. (Burtt) In another passage, however, Boyle writes that the sensible qualities “Have an absolute being irrelative to us; for snow, for instance, would be white, and a glowing coal would be hot, though there were no man or any other animal in the world …” The conception of colors as “mental” properties has persisted down the centuries, as related by Schrödinger (1959): If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electromagnetic waves of wavelength in the neighborhood of 590 millimicrons. If you ask him: But where does yellow come in? he will say: In my picture not at all, but these kinds of vibrations, when they hit the retina of a healthy eye, give the person whose eye it is the sensation of yellow. Bertrand Russell relates the usual scientific view of these matters, as noted by Einstein (1970). Here is what Russell wrote: We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow, are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself. Thus science seems to be at war with itself: when it means to be most objective, it finds itself plunged into subjectivity against its will. Einstein replies: Apart from their masterful formulation these lines say something which had never previously occurred to me. For, superficially considered, the mode of thought of Berkeley and Hume seems to stand in contrast to the mode of thought in the natural sciences. However, Russell's just cited remark uncovers a connection: If Berkeley relies upon the fact that we do not directly grasp the "things" of the external world through our senses, but that only events causally connected with the presence of "things" reach our sense-organs, then this is a consideration which gets its persuasive character from our confidence in the physical mode of thought. At the foundations of the "physical mode of thought" we find this famous dichotomy between, on the one hand, the physical, “primary” properties of mass, extension in space, and duration in time, and on the other the mental, subjective, “secondary” properties of color and sound and so forth. Clark (1993) helps us draw a direct line from the early empiricists to the present: The world as described by natural science has no obvious place for colors, tastes, or smells. Problems with sensory qualities have been philosophically and scientifically troublesome since ancient times, and in modern form at least since Galileo in 1623 identified some sensory qualities as characterizing nothing real in the objects themselves . . . The qualities of size, figure (or shape), number, and motion are for Galileo the only real properties of objects. All other qualities revealed in sense perception—colors, tastes, odors, sounds, and so on—exist only in the ISSN 1303 5150



414

sensitive body, and do not qualify anything in the objects themselves. They are the effects of the primary qualities of things on the senses. Without the living animal sensing such things, these 'secondary' qualities (to use the term introduced by Locke) would not exist. Much of modern philosophy has devolved from this fateful distinction. While it was undoubtedly helpful to the physical sciences to make the mind into a sort of dustbin into which one could sweep the troublesome sensory qualities, this stratagem created difficulties for later attempt to arrive at some scientific understanding of the mind. In particular, the strategy cannot be reapplied when one goes on to explain sensation and perception. If physics cannot explain secondary qualities, then it seems that any science that can explain secondary qualities must appeal to explanatory principles distinct from those of physics. Thus are born various dualisms. Symmetry Let us linger a moment longer over the supposed subjectivity of such “immediately experienced” qualia as greenness, hardness, and coldness, for those attributes of secondary qualities which prompt us to label them as “subjective” would seem to be telling us important things about the physics and the mathematics of these qualities. To look forward a bit: Our visual field discloses to us parallel lines which converge in the distance, and our pictorial artists have learned how to employ the laws of perspective in order to render a realistic scene. Poincaré (1913) broadens the scope of these ideas for us: "Perceptual space is only an image of geometric space, an image altered in shape by a sort of perspective ..." It is rather as though our visual fields respect a projective geometry. Before we converge on this point, however, let us ponder the following business from Weyl, which ought to help dispel the notion, prominent in loose discourse, that our “subjective“ impressions are somehow less trustworthy than the “objective“ view of the natural sciences: The immediately experienced is subjective but absolute; no matter how cloudy it may be, in this cloudiness it is something given thus and not otherwise. To the contrary, the objective world which we continually take into account in our practical life and which science tries to crystallize into clarity is necessarily relative; to be represented by some definite thing (numbers or other symbols) only after a system of coordinates has been arbitrarily introduced into the world. We said at an earlier place, that every difference in experience must be founded on a difference of the objective conditions; we can now add: in such a difference of the objective conditions as is invariant with regard to coordinate transformations, a difference that cannot be made to vanish by a mere change of the coordinate system used. ... Who desires the absolute, must take subjectivity, the ego for which things exist, into the bargain; who is urged towards the objective cannot escape from the problem of relativity! (My emphasis) With Weyl’s words in mind, we consider that, other things being equal, the color of a thing remains invariant or symmetric with respect to coordinate transformations. ISSN 1303 5150



415

Thus, other things being equal, the color of a laser light (say) does not change because the earth rotates, or because the solar system goes sailing along in space-time. This fact is highly suggestive, for the other secondary qualities also appear to respect these fundamental symmetries and it is just this sort of symmetry which informs the foundations of relativity, quantum theory, and gauge theory generally. We raised the possibility just now that the secondary qualities might inhabit the sorts of additional spatial dimensions required by M-theory. It is also quite suggestive, then, to recall that the symmetries of these additional spatial dimensions are thought to manifest themselves in gauge symmetries. Now, it would take us too far afield here to furnish an introduction to gauge theory. Happily, however, many educated readers are familiar with the ideas of general relativity, where curvature of the space-time continuum is shown to be what we know as gravity. And it is just this kind of picture which we find in gauge theory. Cao (1988) surveys the parallels: Now let me turn to the central topic, the geometrization of fundamental physics. The starting-point here is the geometrization of gravity: making Poincaré symmetry local removes the flatness of space-time and requires the introduction of some geometrical structures of space-time, such as [the] metric, affine connection, and curvature, which are correlated with gravity. For other fundamental interactions, which, it is believed, can be described as gauge interactions, we find that the theoretical structures of the corresponding theories are exactly parallel to that of gravity. There are internal spaces: phase space, for electromagnetism, which looks like a circle; isospace which looks like the interior of a three-dimensional sphere; color space for [the] strong interaction, etc. The internal space defined at each space-time point is called a fibre, and the union of this internal space with space-time is called fibre-bundle space. Moving along on this line, the familiar Doppler shift in a photon’s color might be viewed as a change of phase in the photon’s gauge-theoretic internal space. (Which would appear to require a significant enlargement, or completion.) Remarkably, if we map the spectral colors to the unit sphere, the picture of the Doppler shift which emerges is that of an external gravitational (velocity) field rotating the color vector, a picture intriguingly like that found in gauge theory and its representation in fiber bundle theory. In our own time, with lessons learned from non-Euclidean geometry, we reflexively ask, what happens if we replace the postulate handed down to us from Galileo et al., and assert that colors and sounds are every bit as primary as extension in space and duration in time? More specifically, we wonder: If the secondary qualities of color and sound and so forth inhere in matter itself, then where in our various physical formalisms might we plug them in? Our physics is deeply informed by Riemannian geometry, and so the following remarks by Riemann (1857) ought to help us along: so few and far between are the occasions for forming notions whose specialization’s make up a continuous manifoldness, that the only simple notions whose specializations form a multiply extended manifoldness are the positions of perceived objects and colors. … ISSN 1303 5150



416

Definite portions of a manifoldness, distinguished by a mark or a boundary, are called Quanta … And so with Weyl (1922): The characteristic of an n-dimensional manifold is that each of the elements composing it (in our examples, single points, conditions of a gas, colors, tones) may be specified by the giving of n quantities, the "co-ordinates," which are continuous functions within the manifold. Riemann tells us that both the "positions of perceived objects and colors" form manifolds. Weyl tells us that the elements of both sorts of manifold are specified by their coordinates. Minkowski aids us in bridging these two manifolds: We will try to visualize the state of things by the graphic method. Let x, y, z be rectangular co-ordinates for space, and let t denote time. The objects of our perception invariably include places and times in combination. Nobody has ever noticed a place except at a time, or a time except at a place. … The multiplicity of all thinkable x, y, z, t systems of values we will christen the world. It is well worth remarking that Minkowski speaks of visualizing the state of things, and refers above to the “objects of our perception,” for it is in relation to perception that mathematics acquires physical content. Moreover, to paraphrase his next sentence, nobody has ever seen a place except at a time and except but that place was colored, so Weyl’s color manifold would appear to intersect Minkowski’s space-time manifold, requiring us to assign a color coordinate to each x, y, z, t coordinate. Then, once we consider that any speck in the visual field may have a different color from any of its neighbors, it seems to follow that a copy of color space ought to sit over (fiber over) every such speck, and so again we have parallels between the visual field and the physics and mathematics of the quantum field. With the foregoing firmly in mind, we consider that space-time is thought to be a four-dimensional manifold, and that extension in space and duration in time are encoded in the metric of that manifold, whose curvature tensor is equal to the gravitational tensor, together with a multiplicative factor. Now we recall that Kaluza & Klein discovered that, by adding an additional dimension to the manifold, all of EM could be seen to flow from this new, improved metric. Kaluza thought that this extra dimension might be very small, since we do not “see” it. But every point of space-time is "seen," in fact, to intersect an additional manifold, viz., the manifold of colors. And so, mutatis mutandis, with the other sensory modalities. Furthermore, as Einstein makes explicit, our picture of the "external" world rests on sense data: I believe that the first step in the setting of a "real external world" is the formation of the concept of bodily objects and of bodily objects of various kinds. Out of the multitude of our sense experiences we take, mentally and arbitrarily, certain repeatedly occurring complexes of sense impression (partly in conjunction with sense impressions which are interpreted as signs for sense experiences of others), and we attribute to them a meaning—the meaning of the bodily object. Considered logically this concept is not identical with the totality of sense impressions referred to; but it is an arbitrary creation of the human (or animal) mind. On the other hand, the concept owes its meaning and ISSN 1303 5150



417

its justification exclusively to the totality of the sense impressions which we associate with it. Might the spaces of secondary qualities map to additional spaces in physical theory? On such a view, our sensory receptors might be seen to embody operators which project out those secondary vectors which characterize the different sensory fields. One sort of projection operator and you get a characteristic (eigen) color vector; another sort of projection (corresponding to a given stimuli resonance and neural resonator), yields a characteristic sound. It is just like Heisenberg’s operator formalism for QM, extended to include the secondary properties. Moreover, and somewhat obviously, we can extend Bohr's correspondence principle in the same way, merely by taking note of which secondary vectors are associated with which stimulus eigenvectors and projection operators. Irreducible Elements of Reality Where are we? Since Riemann’s time we have learned that light comes to us in those quanta called photons, as described by state vectors. As Schrödinger (1959) and Feynman (1963) tell us, colors are also described by vectors. As P. M. Churchland (1989) has argued, the other secondary properties have a natural vector description, too. So, again, we ask: Where in our various physical formalisms might we plug in the secondary qualities? Let us further attend the nature of these qualities or properties. One of the most salient features of the secondary qualities is their apparent irreducibility. Thus, e.g., Wittgenstein (1977): “When we’re asked “What do ‘red’, ‘blue’, ‘black’, ‘white’ mean?” we can, of course, immediately point to things which have these colors,—but that’s all we can do: our ability to explain their meaning goes no further.” We find the same point made in Maxwell (1993):

When a beam of light falls on the human eye, certain sensations are produced, from which the possessor of that organ judges of the color and luminance of the light. Now, though everyone experiences these sensations and though they are the foundation of all the phenomena of sight, yet, on account of their absolute simplicity, they are incapable of analysis, and can never become in themselves objects of thought. If we attempt to discover them, we must do so by artificial means and our reasonings on them must be guided by some theory. (My emphasis). Russell & Whitehead (1970) make matters precise: “Thus “this is red,” “this is earlier than that,” are atomic propositions.” Notice that Russell and Whitehead have just now put the temporal coordinates of events on something like the same primitive footing as the “color coordinates” of events. Pursuing this line of thought we might reflect, in the spirit of relativity, that our measurements of color, like our measurements of mass, space, and time, are dependent on the observer’s state of motion—as is readily seen in the “red-shift” phenomenon. Note, however, that mass, space, and time are not regarded as subjective for being observer dependent. As with the standard clocks and measuring rods of relativity, what is needed to firmly ground the secondary qualities in "objectivity" are something like ISSN 1303 5150



418

the color plates of Maxwell or the standard color values maintained by the CIE. Or we might employ lasers or tuning forks, tuned to a single frequency. In this fashion we can proceed in the spirit of Heisenberg, and simply assign secondary vectors to the characteristic (eigen) state vectors associated with the frequencies of lasers and tuning forks. Fortified by the foregoing, we remember with Aristotle that every theory must have a number of undefined elements in order to avoid an infinite regression of definition. It seems to make a certain amount of sense, then, to take the secondary properties and make them the elements of a completed physics. For the sake of argument, then, suppose we interpret the elements of a formal theory T (of a very general nature) as Feigl’s “immediately experienced qualities.” Say T has a sufficiently rich structure so as to allow T to frame statements about itself within itself, a la Gödel. It follows that T will be unable to define its elements—for if it could, its elements would not be elements. Are we similarly unable to define the elements of our experience, the “immediately experienced qualities” in respect of anything simpler? Is this basic fact of experience an artifact of the fundamental logic of our brains, sense organs, and of matter generally? Well, perhaps, but recall that Einstein, Podolski, and Rosen (1935) also considered that there might be additional “elements of reality” not yet countenanced by quantum mechanics (QM). The inclusion of these elements would make QM “complete.” The seminal work of EPR has engendered a thriving cottage industry in the foundations of quantum theory (Auletta). What is missing from the many clever ideas that have been put forward in this field is the recognition that the exclusion of the secondary qualities from the formalisms of physics constitutes prima facie evidence of the incompleteness of that science—and all others which are based upon it. For the secondary qualities are given to us in observation, and observation furnishes us with the empirical content of science. If we are serious about grounding science in observation, then the "observable" status of the secondary qualities ought to be at least on par with (and even take precedence over) more purely rationalistic considerations. (If it should turn out that the secondary qualities are one and the same as the "hidden variables" of quantum theory, then this would constitute a wonderful irony, of epic proportions, given that these variables are only "hidden" in plain view.) As is well known, however, the results of numerous ingenious experiments by Aspect et al., seem to have ruled out any such “local” hidden variables. On the other hand, more recent experiments appear to have borne out the existence of “nonlocal” entanglement in QM systems. Consider then that the secondary properties are nonlocal in a ready sense: Two photons of equal energy will exhibit identical wavelengths and frequencies. We expect that two photons of equal energy will also manifest identical colors for standard observers, even though those photons and observers be light-years distant from one another. Being of equal energy, frequency, and wavelegth, we expect that the two photons will also be of equal color. So in some sense two photons can occupy the same “point” in color space, even though they might be far apart in ordinary four-dimensional space-time. Are nonlocal influences propagated via the space of secondary properties? It strikes one as a question conceivably open to experimental test. ISSN 1303 5150



419

Notice that if we regard colors as vectors, then in order to test the equality of two color vectors we must “parallel transport” them in order to see whether they match up side-by-side. But since space-time is curved by the presence of matter, and since this curvature influences the degree of red-shift experienced by photons, we see that, in order to parallel transport the color vectors associated with the photons, we must avail ourselves of the mathematics of tensors and connections employed in relativity and in gauge theory generally. Pursuing this line of reasoning, we might again consider that, for an observer in the same reference frame, we do not expect a red laser light to change colors as the earth turns on its axis, or as the local system goes flying along through interstellar regions. No, we fully expect the laser light to remain red for the observer at rest. It is rather as though the “red” vector is invariant or symmetric under the Poincaré group of rotations and translations in space-time—suggesting, in the light of Noether's theorem, the existence of a conserved charge. And so, by implication, with the other secondary qualities. This feature troubled me until recently, when I came upon an article by Polyakov (1998) et al., which argues for increasing the number of such charges in M-theory on quite different grounds. If we follow this path a step further, and agree to assign a photon’s color to a gauge-theoretic “internal” space, we might expect to find further mathematical analogies by way of the mathematics of connections and fiber bundles; thus, again, if we assign the spectral colors to a unit sphere, then gravitational red-shift might be seen to perform a generalized rotation of the photon’s internal state vector in such a manner as to point more towards “red.” At a glance, this assignation of secondary colors to the internal spaces of photons would seem to capture a few important facts from phenomenology, such as Wittgenstein's speck in the visual field, which, "though it need not be red must have some color.” Moreover, such a speck can not have more than one color all over at the same time. This latter item from elementary epistemology, taken together with the vector character of color, recapitulates one of the central features of Hilbert space which makes it so well suited for modeling QM, viz., its vectors are "mutually exclusive and jointly exhaustive" (Hughes, 1989). Getting back to gauge theory, let us attend Atiyah (1979): We shall now recall the data of a classical theory as understood by physicists and then reinterpret them in geometrical form. Geometrically or mechanically we can interpret this data as follows. Imagine a structured particle, that is a particle which has a location at a point x of R4 and an internal structure, or set of states, labeled by elements g of G. Let’s not worry too much about the machinery of fiber bundle theory for now, but simply regard colors and other secondary qualities as sets of states (governed by some group G) and compare Atiyah with Lockwood (1989): Take some range of phenomenal qualities. Assume that these qualities can be arranged according to some abstract n-dimensional space, in a way that is faithful to their perceived similarities and degrees of similarity—just as, according to Land, it is possible to arrange the phenomenal colors in his three-dimensional color solid. Then my Russellian proposal is that there exists, within the brain, some physical system, the states of which can be arranged in ISSN 1303 5150



420

some n-dimensional state space ... And the two states are to be equated with each other: the phenomenal qualities are identical with the states of the corresponding physical system. In essence, then, we are asking whether we might profitably assert that the states of the secondary qualities are identical with the internal states of the corresponding physical system, where the physical system is an ordered photon flux. How might such a move help us out with the larger mind/body problem? Phenomena of nerve impulses Let us widen our field of view with a bit more help from Lockwood (1989): Consciousness, in other words, provides us with a kind of ‘window’ on to our brains, making possible a transparent grasp of a tiny corner of a material reality that is in general opaque to us, knowable only at one remove. The qualities of which we are immediately aware, in consciousness, precisely are some at least of the intrinsic qualities of the states and processes that go to make up the material world-more specifically, states and processes within our own brains.

The psychologist Pribram … has made an interesting attempt to revive an idea originally put forward around the turn of the century by the Gestalt psychologists: namely that it is certain fields, in the physicist’s sense, within the cerebral hemispheres, that may be the immediate objects of introspective awareness ... What it would amount to, in terms of the present proposal, is that we have a ‘special’ or ‘privileged’ access, via some of our own brain activity, to the intrinsic character of, say, electromagnetism. Put like that, the idea sounds pretty fanciful. But make no mistake about it: whether about electromagnetism or about other such phenomena, that is just what the Russellian view ostensibly commits one to saying. Why does it sound “pretty fanciful” to say that we have a “‘special’ or ‘privileged’ access, via some of our own brain activity, to the intrinsic character of, say, electromagnetism”? If the brain and sense organs just are field processes, then it seems fairly clear that EM processes must be first on our list if we wish to see whether we can identify quantum fields with perceptual fields. Hearkening back to Russell and Einstein, we ask, how does the EM field get hooked up to “the greenness of grass, the hardness of stones, and the coldness of snow”? In reply, we have suggested that the states of internal spaces of gauge theory might correspond to phenomenal states which range over these secondary qualities. Now, while it is true that our suggestion is somewhat novel, it is not entirely unprecedented; as we have just noted, Lockwood and Russell have pursued a similar line of reasoning, and there is a hint of it in Weyl (1922): “Colors are thus “really” not even aether-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time.” It would appear to be a small step to take from Weyl’s remarks to the internal spaces of gauge theory—or indeed to the additional spatial dimensions of M-theory, or Kaluza-Klein theories generally. Can we ISSN 1303 5150



421

adduce further evidence in support of such an idea? Let us look at Dirac on the superposition of quantum states: When a state is formed by the superposition of two other states, it will have properties that are in some vague way intermediate between those of the original states and that approach more or less closely to those of either of them according to the greater or less 'weight' attached to this state in the superposition process. The new state is completely defined by the two original states when their relative weights in the superposition process are known, together with a certain phase difference, the exact meaning of weights and phases being provided in the general case by the mathematical theory. We now reflect on the fact that, if we assign color vectors to the unit sphere, with red, green and blue for its principal axes, then Dirac's remarks apply equally well to the mixture of two or more colors, in respect of projective geometry, as noted by Weyl (1934): Mathematics has introduced the name isomorphic representation for the relation which according to Helmholtz exists between objects and their signs. I should like to carry out the precise explanation of this notion between the points of the projective plane and the color qualities … One the one side, we have a manifold S1 of objects—the points of a convex section of the projective plane—which are bound up with one another by certain fundamental relations, R, R', ...; here, besides the continuous connection of the points, it is only the one fundamental relation: "The point C lies on the segment AB." In projective geometry no notions occur except such as are defined logically on this basis. On the other side, there is given a second system S2 of objects—the manifold of colors—within which certain relations R, R', ... prevail which shall be associated with those of the first domain of objects by equal names, although of course they have an entirely different intuitive content. Besides the continuous connection, it is here the fundamental relation : "C arises by mixture from A and B"; let us therefore express it somewhat strangely by the same words we used in projective geometry: "The color C lies on the segment joining the colors A and B." ... In this sense the projective plane and the color continuum are isomorphic with one another. Every theorem which is correct in the one system S1 is transferred unchanged to the other S2. A science can never determine its subject matter except up to an isomorphic representation. The idea of isomorphism indicates the self-understood, insurmountable barrier of knowledge. It follows that toward the "nature" of its objects science maintains complete indifference. This for example what distinguishes the colors from the points of the projective plane one can only know in immediate alive intuition ... Weyl returns to this topic in another work (1949): "Thus the colors with their various qualities and intensities fulfill the axioms of vector geometry if addition is interpreted as mixing; consequently, projective geometry applies to the color qualities." At the end of the same passage he makes for us what must be a quite pregnant remark: "Epistemologically it is not without interest that in addition to ordinary space there ISSN 1303 5150



422

exists quite another domain of intuitively given entities, namely the colors, which forms a continuum capable of geometric treatment." If we now map the projective plane to the unit sphere, we not only recapitulate the behavior of colors under the operation of mixing, we do so in a way that mirrors not only the mathematics of standard QM, but also complex projective character of the Calabi-Yau spaces of M-theory (Hubsch). Since a speck in the visual field may be any color, it is rather as though each speck in the visual field is somehow tangent to the space of colors. To simplify the physical situation we might, with Schrödinger, note that light of 590 mn is associated with yellow. We might say that photons of a given energy manifest a characteristic (eigen) color vector. On one view, it is as though photons carry these color vector states along with them in their travels through space-time. But this is a pregnant image, leading us back to Atiyah (1979) and the mathematics of fiber bundles: Imagine a structured particle, that is a particle which has a location at a point x of R4 and an internal structure, or set of states, labeled by elements g of G. We then consider the total space P of all states of such a particle. In general we conceive of the internal spaces Gx and Gy for x ≠ y as not being identified and so we draw the picture of P as a collection of "fibers." ... Now we can imagine an external field imposed which has the effect of distorting the relative alignment of the fibers so that no coherent identification is possible between the Gx at different points. However we assume that Gx and Gy can still be identified if we choose a path in R4 from x to y. In more physical terms we imagine the particle moving from x to y and carrying its internal space with it. Consider two photons at x and y, with “internal spaces Gx and Gy for x ≠ y as not being identified …” Say that spectral color vectors are the “set of states, labeled by elements g of G.” Are spectral colors (and secondary qualities generally) perhaps “irreducible” representations of some group not presently incorporated into our standard model? Now “imagine an external [gravitational] field imposed which has the effect of distorting the relative alignment of the fibers so that no coherent identification is possible between the Gx at different points.” According to Einstein’s equivalence principle, an external gravitational field can also shift a photon’s color. If we assign all color vectors to an (internal) unit sphere, the red-shift could be given an intuitive interpretation as a rotation of the color vector. Atiyah continues (1979): In Minkowski space such a motion would take place along the world line of the particle. This identification of fibers along paths is called "parallel transport." If we now imagine two different paths joining x to y then there is no reason for the two different parallel transports to agree and they are assumed to differ by multiplication with a group element, which could be viewed as a generalized "phase shift." This phase shift is interpreted as produced by the external field. In geometrical terms it is viewed as the total "curvature" or distortion of the fiber bundle over the region enclosed by the two paths. Proceeding with our analogy, two photons of different colors would differ by a gauge-theoretic “phase shift.” Again, to compare two photons with one another, the ISSN 1303 5150



423

two must undergo “parallel transport.” Thus it seems again as though spectral colors respect the basic mathematics of both relativity and gauge theory generally, a conclusion also argued by Schrödinger (1920). Now, although there would seem to be intriguing parallels between the phenomenology of spectral colors and the mathematics of gauge theory, the analogies do not end there. As Cao makes clear, and as Witten (1987) points out elsewhere, there are obvious correspondences between the internal spaces of gauge theory and the “compactified” (very small) spaces of M-theory as well as the “hidden variables” of EPR, Bohm et al. Thus, the symmetries of the additional spaces of string/M-theory are thought to manifest themselves as gauge symmetries; in this connection we recall that the color of an object is invariant or symmetric under translations and rotations in space-time (and also reflections and dilatations). Again, in parallel with Kaluza-Klein theory, the additional spatial dimensions of M-theory are usually thought to be very small because we do not “see” them. Whereas we are simply suggesting that we do, in fact, observe these additional dimensions. We consider that these additional dimensions, which are supposedly “hidden” by their tiny size, might well be occupied by the secondary properties of color and sound and so forth, but that these properties have been neglected thus far because of their putative status as “mental” entities. (This, in spite of the glaring fact that these sensory qualities define manifolds which intersect space-time as given in observation.) If the secondary qualities do, in fact, occupy the kinds of additional spaces which crop up in these various formulations, we would have quite a remarkable instance of the truth of Wittgenstein’s remark to the effect that the things that are most important for us—viz., the secondary qualities—are hidden from us by their simplicity and familiarity. In framing our discussion, we have availed ourselves of a number of striking analogies and parallels between perceptual fields and quantum fields. In seeking to model nature, we look for such plausible correspondences between the terms of the model and the phenomena to be modelled. So saying, we have drawn attention to the fact that both perceptual fields and photon fields are vector fields which co-vary in a predictable, mechanical, quantifiable manner. Moreover, neural networks are often modelled by matrices operating upon input vectors, which picture is much like that given in Heisenberg's operator formalism for QM, prompting us to consider the possibility that the form of neural processes follows QM function. Furthermore, the fractal character of dendritic processes would tend to support such a conclusion, given the self-similarity of fractals under changes of spatio-temporal scale (a conclusion pregnant with implications with respect to the conformal group of space-time transformations, incidentally). Other parallels present themselves: • Prominent physical theories require additional spaces. • Secondary qualities require a proper home in physical theory. • Secondary qualities manifest the kinds of symmetries known to determine the evolution of the QM state vector. • Fiber bundle theory appears to capture the phenomenology of both sensory perception and quantum theory. ISSN 1303 5150



424

•

Colors appear to require projective spaces, whereas the Calabi-Yau spaces of string/M-theory are thought to be projective. We are then naturally moved to consider a picture wherein a copy of color space “sits over” (is “fibered over”) every x, y, z, t coordinate in the visual field—a picture remarkably like that found in Kaluza-Klein theory, gauge theory, and string/M-theory. Is this correspondence a coincidence? Or is it telling us something important? Well, gauge theory is the least controversial of the bunch, and is well developed mathematically, allowing us look at the machinery of the theory and see whether further correspondences can be found. Arguably the most significant correspondence consists in the manifest symmetries of color and the other secondary qualities. Thus, for example, the color of a thing does not change for being translated or rotated in space-time (and similarly for reflections and dilatations). As Weinberg (1987) tells us, these kinds of symmetries determine the evolution of the state vector, and so we have a direct means whereby the secondary qualities enter the causal realm. Moreover, the symmetries of the additional spaces of M-theory are thought to manifest themselves as gauge symmetries, a consideration which further deepens the possible relevance of these "secondary" symmetries. Further, the symmetries of the secondary qualities appear to obey group relations like those thought to govern elementary particle physics. We can make this latter point explicit. For clearly, in the case of color, one color added to another always yields a color, so closure under addition is satisfied. As Feynman points out in his Lectures, colors respect associativity. Moving on, “darkness” or “no light” might be taken for the “zero” of the group. Adding “no light” to any color leaves that color unchanged, and so we have a natural identity element under addition which leaves every element unchanged. Finally, a photon of any given color, when added to a photon of identical frequency and color, but of opposite phase, gives us back the identity element. Notice that once we factor in the relative phases of photons we are already on our way to gauge theory, which, as Yang notes, really ought to be called phase theory. How else might gauge theory help us decide whether colors might inhabit an “internal” space? Let us have look at Atiyah's prescription for a generalized particle theory based on Maxwell's equations, and see whether we can meet his criteria: If one were to search ab initio for a non-linear generalization of Maxwell's equations to explain elementary particles, there are various symmetry properties one would require. These are (i) external symmetries under the Lorentz and Poincaré groups and under the conformal group if one is taking the rest-mass to be zero, (ii) internal symmetries under groups like SU(2) or SU(3) to account for the known features of elementary particles, (iii) covariance or the ability to be coupled to gravitation by working on a curved space-time. So far as the first criterion goes, it seems fairly evident that, other things being equal, the secondary qualities of an object do not change upon being translated or rotated in space-time, and so respect Poincaré symmetry. Given the well-known Doppler effect for color and sound, it seems clear that these qualities ISSN 1303 5150



425

respect Lorentz symmetry in a reliable manner. In respect of the second criterion, we have shown how colors might be viewed as the occupants of a gauge-theoretic internal space which respect the group requirements of closure, an identity element, inverse operation, and so forth. Moreover, if the spectral colors are mapped to the unit sphere, with R, G, & B for principal axes, then all other colors are obtained by suitable combinations of these three color vectors, making SU(3) a plausible candidate for the relevant group. In considering the third criterion, we know that color is also Dopplered by gravitation, and so "couples" to curved space-time. Moreover, we can confidently predict that sound waves and thermal radiation ought to Doppler in the presence of higher levels of gravity (equivalently, velocity), and we know that tactile pressure is a function of the relative velocity of observer and observed. It must be admitted, however, that the case of the chemical senses is altogether unclear to the author at this writing. Apology We have explored a number of possible avenues of research just now, asking whether (1) quantum fields constitute the ultimate level of description of biological systems; and (2) this ultimate level is nested within higher levels of organization by way of the kinds of self-similarity found in neural structures; and (3) this lowest level embodies the initial conditions upon which the brain exhibits sensitive dependence. In pursuing our inquiry, we have attempted to sharpen a thesis set forth in Chalmers and Feigl by coordinating perceptual fields with photon fields. In so doing, we have pursued the possibility that the irreducibility of the secondary qualities flows from their elemental character and that, being fundamental, they might therefore find residence at the foundations of physical theory, perhaps in (1) the internal state spaces of gauge theory, and/or (2) the additional spatial dimensions of string/M-theory and Kaluza-Klein theory, and/or (3) hidden variables theory. Given the status of our inquiries at this time, we have only barely discerned how such a picture might be made to work. Clearly,we have raised many more questions and concerns than we can begin to address, let alone answer in a reasonable space. We have made extensive use of analogies and parallels between perceptual states, vectors, and fields and physical states, vectors, and fields. These analogies and parallels are obviously far from conclusive, and are intended rather to motivate the argument, and to stimulate further thought and research upon these questions. The author is under no illusions as to the possibility that he has, in part, or perhaps altogether, missed the lesson to be learned from these analogies, and there is no doubt but that more clever minds might arrive at different conclusions altogether. Then again, formal mathematical parallels between two realms of experience have yielded rich results in the past. Thus, to take a few well known examples, we have Einstein's demonstration that gravity is very like a curved space-time manifold, and Weyl's recognition of the formal analogies between gravity and EM, which led to gauge theory. Thus emboldened, we hold out the possibility that the seeds planted here might also come to fruition.

ISSN 1303 5150



426

References Atiyah MF. Geometry of Yang-Mills Fields, Pisa, Italy: Accademia Nazionale Dei Lincei Scuola Normale Superiore 1979; 7-9 Auletta G. Foundations and Interpretation of Quantum Mechanics, London: World Scientific. 2001. Burtt EA. The Metaphysical Foundations of Modern Science, Garden City, NY: Doubleday Anchor Books, 1954; 83-4, 181-2, 235-6 Cao Tian-Yu. Gauge Theory, in H. Brown and R. Harré, eds., Philosophical Foundations of Quantum Field Theory, Oxford University Press, 1988;124 Caserta F., et al., Determination of Fractal Dimension of Physiologically Characterized Neurons in 2-Dimensions and 3-Dimensions. Journal of Neuroscience Methods 1995; 56 (2): 133-144 Chalmers DJ. Puzzle of Conscious Experience. Scientific American, December, 1995;85 Churchland PM. A Neurocomputational Perspective, Cambridge, MA: MIT Press, 1989;100 Clark A. Sensory Qualities, Oxford, Clarendon Press, 1993;6 Dirac PAM. Principles of Quantum Mechanics, Oxford, Clarendon Press, 1966;67-68 Dyson FJ. Field Theory. Scientific American, 1953;188;62 Einstein A, Podolsky B and Rosen N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review 1935;47: 777 Einstein A. On Russell’s Theory of Knowledge’, Philosophy of Bertrand Russell, in Schilpp, ed., LaSalle, IL: Open Court, 1971;281-3 Feigl H. Mind-body, not a pseudo problem. In Mind-Brain Identity Theory, in C.V. Borst, ed., New York, NY: St. Martin's Press, 1970; 38 Feynman R. Lectures on Physics, Menlo Park, CA: Addison-Wesley, 1963;35-36 Feynman R. QED: The Strange Theory of Light and Matter. Princeton, NJ: Princeton University Press, 1985;7-8 Flanagan B. Are Perceptual Fields Quantum Fields?' Information & Cognition, v.3, n.3, available on-line: http://www.marilia.unesp.br/atividades/extensao/revista/v3/artigo2.html, 2001. Flanagan B. ‘Notes Toward a Theory of Artificial Sentience’ from Advances in Intelligent Robotics Systems, SPIE Cambridge Symposium on Optical and Optoelectronic Engineering, Nov 1987 Hubsch T. Calabi-Yau Manifolds, London: World Scientific 1994. Hughes RIG. The Structure and Interpretation of Quantum Mechanics, Cambridge, MA: Harvard University Press, 1989; 83-84 Hume DA Treatise of Human Nature, Oxford University Press, 1968; 226-231 Liu GP., et al. Spectral calculations of Hamiltonian for a quantum fractal network. Journal of Wuhan University of Technology 2000;15 (3): 33-40 Lockwood M. Mind, Brain and the Quantum. Cambridge, MA: Basil Blackwell Ltd., 1989;172 Mach E. Analysis of Sensations. G. N. A. Vesey, ed., Body and Mind. Allen & Unwin, 1970;176 Maxwell JC. Theory of the Perception of Colors. In David L. MacAdam, ed., Colorimetry-Fundamentals. SPIE, 1993; 14 Newton I. Opticks. Toronto, CA: Dover, 1952. Pereira A. Coexisting Spatio-Temporal Scales in Neuroscience. Minds and Machines 2001; 11(4): 457-465 Poincaré H. The Foundations of Science. New York, NY: The Science Press, 1913;66-80 Polyakov AM., et al. Gauge theory correlators from non-critical string theory. Physics Letters B ISSN 1303 5150



427

1998; 428 (1-2): 105-114 Pribram K. Brain and Perception. Hillsdale, NJ: Lawrence Erlbaum, 1991; 277 Prusinkiewicz P. Modeling and Visualization of Biological Structures. In Proceeding of Graphics Interface 1993, pp. 128-137, available on-line: http://www.cpsc.ucalgary.ca/projects/bmv/papers/vismodels.gi93.html Qiao B., et al. General formalism for the spectral decomposition of the Hamiltonian in a quantum fractal network. Journal of Physics A 1999;32 (30): 5585-5598 Riemann GFB. On the Hypotheses Which Lie at the Bases of Geometry. Nature 1857; 8:183-4 Russell B and Whitehead AN. Principia Mathematica, London, England: Cambridge University Press, 1970;15 Salam A. Unification of Fundamental Forces. Cambridge University Press, 1990;10 Schrödinger E. Outline of a Theory of Color Measurement for Daylight Vision. In Selected Papers on Colorimetry-Fundamentals, David L. MacAdam, ed., Bellingham, WA: SPIE, 1959; 72-96 Schrödinger E. Mind and Matter. Cambridge University Press, 1959;88-9 Teich MC., et al. Fractal character of the neural spike train in the visual system of the cat. Journal of the Optical Society of America A 1997;14 (3): 529-546 Umezawa H. Advanced Field Theory. New York, NY: American Institute of Physics, 1993;132 Weyl H. Mind and Nature, Philadephia, PA: University of Pennsylvania Press, 1934;18-9 and 75-6 Weyl H. Philosophy of Mathematics and Natural Science. Princeton University Press, 1949;70-1 Weyl H. Space Time Matter. Dover, 1922;3-4, 84 Witten E. Search for a Realistic Kaluza-Klein Theory. In Modern Kaluza-Klein Theories, Thomas Applequist, et al., eds. Reading, MA: Addison-Wesley, 1987; 279-280 Wittgenstein L. Tractatus Logico-Philosophicus. Atlantic Highlands, NJ: Humanities Press, 1974;9-11 Wittgenstein L. Remarks on Color. University of California Press, 1977;11

NEUROSCIENCE | QUANTUM PHYSICS Copyright 2003

ISSN 1303 5150


Multi-Scaling, Quantum Theory, and the Foundations ...

Multi-Scaling, Quantum Theory, and the Foundations ...

Suggest Documents

QUANTUM PROBABILITY THEORY AND THE FOUNDATIONS OF ...

Information and the foundations of quantum theory

Quantum theory: Reconsideration of foundations

Quantum theory: Reconsideration of foundations

On the foundations of quantum theory

Foundations of Rational Quantum Field Theory, I

Quantum theory: undulating foundations, uncertain ... - viXra.org

Foundations for proper-time relativistic quantum theory

Quantum probability and the foundations of quantum

Multiscaling

Multiscaling and joint multiscaling description of the atmospheric wind ...

HPS/PHIL 687 Historical Foundations of the Quantum Theory

Quantum Annealing-Foundations and Frontiers

Experiment and the foundations of quantum physics

Foundations for Relativistic Quantum Theory I - Google Sites

Foundations for Relativistic Quantum Theory I: Feynman's ... - arXiv

Foundations of Two-Dimensional Conformal Quantum Field Theory

Dynamic Multiscaling in Turbulence

Moral Foundations Theory

Foundations of Garside Theory

Quantum Probability and Quantum Information Theory

String theory, quantum gravity and quantum groups

Foundations in Theory

Mathematical foundations of quantum information: Measurement and ...