Physics in Mind: a Quantum View of the Brain
_______________
Loewenstein, p.238
And here we are. This is a good read, offering many fascinating nuggets of information and insight. In my own efforts, I have largely focused on finding a physically plausible account of mind & brain, and so I am especially grateful for all the material from physiology and biophysics, whereof the author was a professor at Columbia. I now have many new points of departure for further thought and research, thanks to Loewenstein's lively book, and for that I thank him.
That said...
I have a few serious reservations concerning a number of his remarks, but will concentrate on several crucial points, and that briefly, so as not to be a complete ingrate.
Let us revisit Freeman Dyson for a moment: "There is nothing else except these [quantum] fields: the whole of the material universe is built of them."
So to those who question the relevance of quantum theory to the brain (and at the risk of being snarky), I'm inclined to ask what it is about "nothing" that they don't understand? Let's move on.
Loewenstein then goes on to paraphrase one of Schrodinger's remarks on color.
Well, no lesser a luminary than Hermann Weyl tells us that colors behave like vectors, as do photons. Colors might then be supposed to add like vectors, and so they do. The analogy is reliable and exact, allowing us to manufacture TV screens where the vast majority of the colors we see are metamers or mixtures of RGB. Don't take my word for it.
Finally, we read: "The physicist is right, of course; color is not a thing of the world outside but of the one inside us."
The physicists are wrong, of course—most of them. Mach was exceptional:
And so with Pauli (PDF):
Schrödinger also demurred on this issue; see the "Third Lecture: The Part of the Human Mind," in his Interpretation of quantum mechanics.
How do we restore "red and yellow, sweet and hot"? What might Pauli's "psychophysical unitary language" look like? Somewhat surprisingly, we already an answer in Heisenberg's matrix formulation of quantum theory. Happily, our answer is thoroughly grounded in daily observation.
Now, in a way, we have only restated myriad observations in a slightly formal language. Thus, we get up in the morning and things look, sound, taste and feel the way they generally do. Where there are differences, we find physical causes for those differences. Thanks to Heisenberg, however, we can say all this without leaving his formulation of quantum theory. Isn't that interesting? From a physical standpoint, it is naturally immaterial whether the operator fields in question are inside or outside the brain, thus mooting the supposedly "subjective" character of sensory data.
It is well worth noting that we typically model neural nets via the same math. Perhaps this is just because neural processes are mediated by operator fields—acting upon sensory state vectors?
Returning to the bit about how "color is not a thing of the world outside but of the one inside us," this begs an epochal question, what Hume and Leibniz already understood as the central problem of materialist thinking.
Well, of course, materialism carried the day—because it worked! Up until the moment when we try to frame a science of perception. We are then met with an incomplete description of reality.
Enter EPR:
Where are we? As we know from Maxwell, Weyl, Schrodinger and Feynman, colors behave like vectors. Which are dual to differential forms.
This is interesting, since what we perceive are colored areas—and in light of those dualities which unite the different flavors of string theory into M-theory. Moreover, Weyl tells us that colors respect a projective vector geometry and these dualities have their provenance in projective geometry. The immediate upshot being this: Every true theorem we can state about colors and vectors implies another true theorem about colors and forms. More general implications might be glimpsed in a pregnant remark by Wittgenstein:
Dirac mentioned just now that phase enters the picture when discussing superposition. This is also suggestive, given that lights (and sounds) of different phases reliably produce interference phenomena resulting in different colors (and sounds).
Curiously, phase is just what gauge theory is all about. In gauge theory (which would more accurately be called phase theory), we have an interesting parallel with M-theory's extra dimensions—viz., internal spaces—where important physical symmetries hold sway.
Now, it is of the greatest importance to note that the secondary properties respect these symmetries, as a moment's reflection will disclose. Thus, an astronaut in a closed spaceship cannot say, judging from the appearances of the secondary properties, whether he is in uniform motion or at rest, or whether he is accelerating or in a gravitational field.
Cao ties a number of these considerations together for us.
Notice that assigning colors (and the other secondary properties) to the "hidden" variables and/or extra dimensions one of the chief objections to these theories, viz., if such extra dimensions or variables exist, why do we not "see" them? The answer being that we do observe them, everywhere, all the time—but they have been veiled from our sight by ancient dogma, but also for reasons found in Wittgenstein: "The aspects of things that are most important for us are hidden(!) because of their simplicity and familiarity."
In closing, I'd like to mention how pleased I am to see that these various points are percolating throughout the academic world, inasmuch as these notions were once beyond the lunatic fringe—or, as I like to say, my personal comfort zone. Now, as promised, I have kept my remarks brief and so skipped over many important issues in the foregoing, but again, I've been at this for a long time and so if the reader is desirous of further instruction, she is directed here.
________
* In Göttingen in 1925-26 Werner Heisenberg and Erwin Schrödinger created the theory of quantum mechanics. In Heisenberg's theory the physical fact that certain atomic observations cannot be made simultaneously was interpreted mathematically to mean that the operations which represented these operations were not commutative. Since the algebra of matrices is non-commutative, Heisenberg together with Max Born and Pascual Jordan represented each physical quantity by an appropriate (finite or infinite) matrix, called a transformation; the set of possible values of the physical quantity was the spectrum of the transformation. (So the spectrum of the energy of the atom was precisely the spectrum of the atom.)
Schrödinger, in contrast, advanced a less unorthodox theory based on his partial differential wave equation. Following some initial surprise that Schrödinger's "wave mechanics" and Heisenberg's "matrix mechanics"—two theories with substantially different hypotheses—should yield the same results, Schrödinger unified the two approaches by showing, in effect, that the eigenvalues (or more generally, the spectrum) of the differential operator in Schrödinger's wave equation determine the corresponding Heisenberg matrix. Similar results were obtained simultaneously by the British physicist Paul A. M. Dirac. Thus interest in spectral theory once again became quite intense.
Steen, "Highlights in the History of Spectral Theory," American Mathematical Monthly 80 (1973) 359-381.
by Werner Loewenstein
When Physics World published a list of the five biggest unanswered questions in physics earlier this year in its 25th anniversary special issue, "What is consciousness?" was not on it. The reason for its exclusion seemed, at the time, straightforward: although the nature of consciousness is one of the toughest conundrums of modern science, it is not one that is commonly associated with physics. Biology and neuroscience, yes. Philosophy, certainly. Perhaps even art or poetry. But not, for the most part, physics.
In his book Physics in Mind: a Quantum View of the Brain, author Werner Loewenstein sets out to convince readers otherwise, and thereby "sink into oblivion" the idea that "biology is biology, and physics is physics, and never the twain shall meet". The result is, in the words of our reviewer Seth Lloyd "an intellectual rollercoaster ride" that takes in ideas about the nature of time, evolution, electrochemical signalling, information theory and, ultimately, quantum computing – a burgeoning field that Loewenstein believes may hold vital clues to the problem of consciousness.
So there it is. We cannot leave out the bewildering quantum world from our naturalistic accounts of higher brain processes. lest we risk missing the mark. And as we grope our way through the web of the brain for clues to the mechanisms of consciousness, we must keep a weather eye out for quantum phenomena, even if they are strange, as quantum phenomena inevitably are.
Loewenstein, p.238
And here we are. This is a good read, offering many fascinating nuggets of information and insight. In my own efforts, I have largely focused on finding a physically plausible account of mind & brain, and so I am especially grateful for all the material from physiology and biophysics, whereof the author was a professor at Columbia. I now have many new points of departure for further thought and research, thanks to Loewenstein's lively book, and for that I thank him.
That said...
I have a few serious reservations concerning a number of his remarks, but will concentrate on several crucial points, and that briefly, so as not to be a complete ingrate.
Let us revisit Freeman Dyson for a moment: "There is nothing else except these [quantum] fields: the whole of the material universe is built of them."
So to those who question the relevance of quantum theory to the brain (and at the risk of being snarky), I'm inclined to ask what it is about "nothing" that they don't understand? Let's move on.
But before anything else, we must define what we mean by a color. Though it is one of our most common perceptions, color is not something easily explained. Try to define, or even describe, a color, and you discover how quickly you run into a tautology. One naturally looks to physics in this case.As was already known to Aristotle, every theory must begin with a list of undefined elements in order to avoid an infinite regression of definition. The question arises naturally: What if colors are among nature's elements? Though somewhat jarring, this move would seem to handle this difficulty at one stroke. We might then ask, in a parallel with Riemann, what sort of space-time geometry might arise from including colors as its elements. We get a pointer here from the master himself, in his famous lecture on the foundations of geometry.
[So] few and far between are the occasions for forming notions whose specializations make up a continuous manifold, that the only simple notions whose specializations form a multiply extended manifold are the positions of perceived objects and colors.Riemann
Loewenstein then goes on to paraphrase one of Schrodinger's remarks on color.
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.Lowenstein then asserts that "There is no physics reason why two spots, one lit by a single wavelength and the other by a mixture, should look exactly alike. No physics theory will predict that."
Well, no lesser a luminary than Hermann Weyl tells us that colors behave like vectors, as do photons. Colors might then be supposed to add like vectors, and so they do. The analogy is reliable and exact, allowing us to manufacture TV screens where the vast majority of the colors we see are metamers or mixtures of RGB. Don't take my word for it.
[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.Dirac
Finally, we read: "The physicist is right, of course; color is not a thing of the world outside but of the one inside us."
The physicists are wrong, of course—most of them. Mach was exceptional:
A color is a physical object a soon as we consider its dependence, for instance, upon its luminous source, upon temperatures, and so forth. When we consider, however, its dependence upon the retina [...], it is a psychological object, a sensation. Not the subject matter, but the direction of our investigation, is different in the two domains.
And so with Pauli (PDF):
For the invisible reality, of which we have small pieces of evidence in both quantum physics and the psychology of the unconscious, a symbolic psychophysical unitary language must ultimately be adequate, and this is the far goal which I actually aspire. I am quite confident that the final objective is the same, independent of whether one starts from the psyche (ideas) or from physis (matter). Therefore, I consider the old distinction between materialism and idealism as obsolete.
Schrödinger also demurred on this issue; see the "Third Lecture: The Part of the Human Mind," in his Interpretation of quantum mechanics.
What this something is cannot be said; by calling it matter or field or whatnot, we just give it a name. The relevant point is that it is not supposed to have any other properties but geometrical configuration, changing in time according to certain "laws of nature." It is not in itself yellow or green, sweet or cold. If parts of it appear to us so, there is no hard, indubitable fact to make this judgment true or false.
This view is strongly supported by our analysis of actual experimental procedure, and it is attractively simple. It carries us comfortably a long way, indeed so long, that we may have forgotten its artificiality, when we meet the obstacles that it renders unsurmountable. So it is better to ask the naive but very pertinent question right away: how do red and yellow, sweet and hot come in at all? Once we have removed them from our "objective reality," we are at a desperate loss to restore them. We cannot remove them entirely, because they are there, we cannot argue them away. So we have to give them a living space, and we invent a new realm for them, the mind, saying that this is where they are, and forgetting the earlier part of the story—all that we have been talking about till now—is also in the mind and nowhere else. But deeming it to be something else—objective reality—we run against the unanswerable question: how does matter act on mind, to produce in it the sensory qualities—and also how does mind act on matter, to move it at will? These questions cannot, so I believe, be answered in this form, and they owe their embarrassing form precisely to our having posited an objective reality which is a pure geometrical scheme of thought and deprived of everything real given by experience.In his article in Scientific American, Chalmers has provided a modern take on this position.
How do we restore "red and yellow, sweet and hot"? What might Pauli's "psychophysical unitary language" look like? Somewhat surprisingly, we already an answer in Heisenberg's matrix formulation of quantum theory. Happily, our answer is thoroughly grounded in daily observation.
Similar light produces, under like conditions, a like sensation of color. ~HelmholtzWe can both broaden and tighten this remark with a little help from Heisenberg and say that the same state vector, acted upon by the same (matrix) operator(s), produces the same spectrum of colors—as well as the other secondary properties. Feynman helps us out with an easy lesson:
If you take a physical state and do something to it—like rotating it, or like waiting for some time t—you get a different state. We say, "performing an operation on a state produces a new state." We can express the same idea by an equation:
|_{}> = A|_{}>.
The new state has a perfectly predictable spectrum—and this is a key point because, as the mathematician Steen (PDF) reminds us, "The mathematical machinery of quantum mechanics became that of spectral analysis...," which is just the matheematics of matrices and vectors.*An operation on a state produces another state. The operator A stands for some particular operation. When this operation is performed on any state, say |_{}>, it produces some other state |_{}>.
Now, in a way, we have only restated myriad observations in a slightly formal language. Thus, we get up in the morning and things look, sound, taste and feel the way they generally do. Where there are differences, we find physical causes for those differences. Thanks to Heisenberg, however, we can say all this without leaving his formulation of quantum theory. Isn't that interesting? From a physical standpoint, it is naturally immaterial whether the operator fields in question are inside or outside the brain, thus mooting the supposedly "subjective" character of sensory data.
It is well worth noting that we typically model neural nets via the same math. Perhaps this is just because neural processes are mediated by operator fields—acting upon sensory state vectors?
Returning to the bit about how "color is not a thing of the world outside but of the one inside us," this begs an epochal question, what Hume and Leibniz already understood as the central problem of materialist thinking.
Besides, it must be confessed that Perception and its consequences are inexplicable by mechanical causes; that is to say, by figures and motions. If we imagine a machine so constructed as to produce thought, sensation, perception, we may conceive it magnified— to such an extent that one might enter it like a mill. This being supposed, we should find in it on inspection only pieces which impel each other, but nothing which can explain a perception. It is in the simple substance, therefore,—not in the compound, or in the machinery,—that we must look for that phenomenon [...]Leibniz
Well, of course, materialism carried the day—because it worked! Up until the moment when we try to frame a science of perception. We are then met with an incomplete description of reality.
Enter EPR:
In attempting to judge the success of a physical theory, we may ask ourselves two questions: (1) “Is the theory correct?” and (2) “Is the description given by the theory complete?” It is only in the case in which positive answers may be given to both of these questions, that the concepts of the theory may be said to be satisfactory. The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience...
Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.
Where are we? As we know from Maxwell, Weyl, Schrodinger and Feynman, colors behave like vectors. Which are dual to differential forms.
This is interesting, since what we perceive are colored areas—and in light of those dualities which unite the different flavors of string theory into M-theory. Moreover, Weyl tells us that colors respect a projective vector geometry and these dualities have their provenance in projective geometry. The immediate upshot being this: Every true theorem we can state about colors and vectors implies another true theorem about colors and forms. More general implications might be glimpsed in a pregnant remark by Wittgenstein:
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.
Dirac mentioned just now that phase enters the picture when discussing superposition. This is also suggestive, given that lights (and sounds) of different phases reliably produce interference phenomena resulting in different colors (and sounds).
Curiously, phase is just what gauge theory is all about. In gauge theory (which would more accurately be called phase theory), we have an interesting parallel with M-theory's extra dimensions—viz., internal spaces—where important physical symmetries hold sway.
Now, it is of the greatest importance to note that the secondary properties respect these symmetries, as a moment's reflection will disclose. Thus, an astronaut in a closed spaceship cannot say, judging from the appearances of the secondary properties, whether he is in uniform motion or at rest, or whether he is accelerating or in a gravitational field.
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. ~Wittgenstein
Cao ties a number of these considerations together for us.
Now let us 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 metric, affine connection, and curvature, which are correlated with gravity.
The internal space defined at each space-time point is called a fiber, and the union of this internal space with space-time is called fiber-bundle space. Then we find that the local gauge symmetries remove the 'flatness' of the fiber-bundle space since we assume that the internal space directions of a physical system at different space-times points are different.
So the local gauge symmetry also requires the introduction of gauge potentials, which are responsible for the gauge interactions, to connect internal directions at different space-time points. We also find that the role the gauge potentials play in fiber-bundle space in gauge theory is exactly same as the role the affine connection plays in curved space-time in general relativity.
Identifying antipodal points on the projective sphere, but assigning them a
180-degree phase difference, recovers the fact that colors a + (-a) = 0,
where "0" means "no light" or "darkness," thus completing the vector space,
the other axioms of closure, etc. being obviously met.
Notice that assigning colors (and the other secondary properties) to the "hidden" variables and/or extra dimensions one of the chief objections to these theories, viz., if such extra dimensions or variables exist, why do we not "see" them? The answer being that we do observe them, everywhere, all the time—but they have been veiled from our sight by ancient dogma, but also for reasons found in Wittgenstein: "The aspects of things that are most important for us are hidden(!) because of their simplicity and familiarity."
In closing, I'd like to mention how pleased I am to see that these various points are percolating throughout the academic world, inasmuch as these notions were once beyond the lunatic fringe—or, as I like to say, my personal comfort zone. Now, as promised, I have kept my remarks brief and so skipped over many important issues in the foregoing, but again, I've been at this for a long time and so if the reader is desirous of further instruction, she is directed here.
________
* In Göttingen in 1925-26 Werner Heisenberg and Erwin Schrödinger created the theory of quantum mechanics. In Heisenberg's theory the physical fact that certain atomic observations cannot be made simultaneously was interpreted mathematically to mean that the operations which represented these operations were not commutative. Since the algebra of matrices is non-commutative, Heisenberg together with Max Born and Pascual Jordan represented each physical quantity by an appropriate (finite or infinite) matrix, called a transformation; the set of possible values of the physical quantity was the spectrum of the transformation. (So the spectrum of the energy of the atom was precisely the spectrum of the atom.)
Schrödinger, in contrast, advanced a less unorthodox theory based on his partial differential wave equation. Following some initial surprise that Schrödinger's "wave mechanics" and Heisenberg's "matrix mechanics"—two theories with substantially different hypotheses—should yield the same results, Schrödinger unified the two approaches by showing, in effect, that the eigenvalues (or more generally, the spectrum) of the differential operator in Schrödinger's wave equation determine the corresponding Heisenberg matrix. Similar results were obtained simultaneously by the British physicist Paul A. M. Dirac. Thus interest in spectral theory once again became quite intense.
Steen, "Highlights in the History of Spectral Theory," American Mathematical Monthly 80 (1973) 359-381.
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