Mother Lode

I've been debating whether to share this next item with everyone; I decided it would be selfish to keep it to myself. (Remember the mindless seagulls in Finding Nemo? "Mine!")

Over the years, I've wondered about the wisdom of choosing color to illustrate my ideas re: secondary qualities & the foundations of quantum theory. I continue to believe that it was the best choice to start out with, given how easy it is for us to "see" the main ideas and how most of us are highly visual in our orientation to the world.

On the other hand, sounds have a certain appeal, given that there are well-known harmonic relations, already known to Pythagoras, between what we hear and the numbers associated with the media producing those sounds. And then, there are the fascinating correspondences between the vibrating strings (and membranes!) we hear and the strings of string/M-theory theory.


Well, it turns out there are all sorts of wonderful relations (rather obvious, in retrospect*) between harmonic analysis, operator theory, spectral theory, group theory, number theory, Calabi-Yau theory & Kac-Moody algebras -- far too many for me to adequately explore in my lifetime.

The math mirrors what I've been on about regarding color all this time. I couldn't be happier -- especially so in view of the fact that one could lob a stone in any direction on a college campus and, chances are, you'd bean someone with more native mathematical ability than I'll ever have.

So ... now is the way plain. But I thought I'd better leave a trail of bread crumbs for those who come after, in case I get hit by a truck tomorrow. (Heaven forfend!)

UCLA

Fields Institute

Project Euclid

Mathphyz

Oxford (PDF)

___________

Although I am only beginning to understand harmonic relations, the parallels with the mathematics of color seem clear enough. He wrote confidently.

I feel a bit foolish, looking back, wishing I'd looked into this business better years ago, but ...

I remember a desire to narrow my focus to one (relatively) simple phenomenon -- color vision -- and then see what sorts of math & physics might model the facts on hand ... and, as it were, before our eyes.

I always knew that, if I should be able to get those facts right regarding vision, the math ought to fall out naturally and apply, mutatis mutandis, to audition, olfaction, and so forth.

Lately, I'm beginning to think I wasn't wholly mistaken.

Catch a Wave

I have exciting news. I recently wrote about the AAAI’s Quantum Interaction 2008 symposium, to be held in Oxford. As with last year’s gathering in Stanford, I expect the forthcoming show will have more political impact than intellectual interest. I.e., the simple fact that the event is associated with Oxford lends an air of credibility to a field once dismissed as the province of crackpots and “quantum mystics.”

Well, the truly exciting news also comes from the UK, by way of the British Computer Society which really does appear to be getting it.

Consider the following:

This is “Can quantum information processing explain how brains work?” For, as Perus, for example, has shown, the neural net and the quantum systems formalisms are epistemologically identical, except they concern mathematically real and complex quantities respectively. These formalisms therefore differ only in the fact that quantum theory explicitly concerns complex amplitudes defining a wave mechanics capable, in principle, of describing the holographic physical informational encoding/decoding of the dimensional geometry of real objects.

Compare this with an earlier publication in Information & Cognition:

If Paul Churchland is correct about the neural implementation of matrix-valued operators, then that is rather interesting, since that is precisely the sort of mathematics we find at work at the quantum level of neural function. Which would seem to make a kind of sense, if, as we suggest, the form of neural networks follows the underlying function of those quantum processes, which mediate neural activity.

Here is another excerpt from the BCS:

It is therefore on this biological frontier of information processing, that the Group is now concentrating its investigations and programme, the success of which is regularly reported in its homepages.

These investigations show

(a) that while qubit computing research concentrates on the discrete/particle observable properties of quantum mechanical systems, usually taken to concern the eigenvalues of quantum mechanical operators, (b) that(i) quantum (rather than thermodynamically) optimally controlled chemistry [...] likely appropriate to the brain/organism’s chemically based computation, and (ii) quantum mechanical neural information processing in brains are both much more likely to involve observable gauge invariant phases of the quantum state vector.

Now compare this with the text from Information & Cognition:

So why have the secondary properties not been put forward heretofore to occupy these “hidden” variables and extra dimensions? Part of the answer must lie in the fact that colors and sounds have historically been excluded from the physical world, even though they demonstrably co-vary with other physical parameters. Another part of the answer is contained in an observation from Wittgenstein, where he writes that “the things that are most important for us are hidden from us by their simplicity and familiarity.” And then, of course, the dimensions of color and sound and so forth are different from the dimensions of traditional spacetime; they are more like the “internal” dimensions of gauge theory or the compactified (very small) dimensions of string/M-theory — and like these more traditional physical dimensions, the dimensions of color and sound are tangent to the points of spacetime, suggesting that colors and sounds might be amenable to the mathematics of fiber bundles.

Or the following:

Such questions raise many another in their wake — just what is color space, e.g.? Note that we can make a natural mapping from the spectral colors to a color sphere, where Newton’s color wheel runs around the circumference, with black and white at the poles. Or such a mapping could be made with red, green and blue for the axes of a unit sphere in Hilbert space. We could then easily map those color vectors to the photonic vectors with which they are associated, remembering that these “physical” vectors recapitulate the mathematics of colors under vector addition and multiplication. Then, any operation upon the photonic vector would naturally correspond to a rotation of the color vector, in a direct analogy with the mathematics of gauge theory and quantum theory generally.

Further on, the BCS article brings up the De Broglie wave as a plausible hypothesis. This is quite exciting, since it’s a short, logical hop from there to Bohm’s work on hidden variables (HVs), which, as is also argued in the Information & Cognition piece, are just what we need to incorporate secondary qualities into the formalism of quantum theory.

So it seems to me that we are now finally beginning to get somewhere. (Though it’s possible I may be biased.)

Quantum Interaction 2008

Well, I'm happy to see Oxford getting on board. Or, I should be happy, but I'm not. The odious toads in charge of the event made a point of stating that travel funds are not available to such as I.

Last year, they told me that I was behind several grad students for consideration. So, not only did they not honor me for my groundbreaking and ongoing efforts in a field whereof I am one of the founding fathers, they arrogate to themselves the power to determine my stature in their stuffy little world -- these clueless buffoons who are only now beginning to dimly comprehend what I knew 30 years ago.

Well! I feel much better.

Reverse Casimir Effect

Off-topic again, but pretty darn cool!

At the risk of sounding like 20/20 hindsight, I suspected something of the sort might be possible.

Let me now venture to say that I believe this new technology might well have... extraordinary implications for space flight, and quite possibly FTL travel.

OK, so that's as far out on a limb as I go, these days.

Superfractals

And just in case you still think I'm out of my gourd...

I've just now picked up a fascinating new book: Superfractals, by mathematician Michael F. Barnsley. It is all to do with fractals, chaos theory, iterated function sets (IFS), topology, code space and probability.

In the beginning (pg. 4), he writes: "I think that just over the horizon, in the direction in which this book points, there is an unambiguous, new branch of geometry that combines colour and space."

I Can See It, Now

A bit off-topic, but... What will computing look like in the future?

Project Looking Glass



I found this while learning about a wonderful new work from James Burke:


Knowledge Web



Where I also learned about this wicked cool technology:


PersoanlBrain



All thanks to those nice people at IPTV.

Mindful Universe

Henry Stapp's work in this field is among the best and most advanced. I'm pleased to see that he has a new book out and that it's actually getting a thoughtful review -- along with the usual, predictable reactions from the uninformed.

Stapp writes very well and his views are grounded in a thorough understanding of both classical and quantum physics. Although I differ with him on a few basic points, his ideas regarding perceptual states and quantum states will, I firmly believe, prove to stand the test of time. Lockwood and I arrived at the same set of conclusions -- all of us independently of one another.

I am also quite intrigued by his ideas regarding the Quantum Zeno Effect (QZE) in relation to William James' thoughts on the selective role of attention.

Herewith an excerpt from the review:

Henry Stapp is well known for his complex theoretical discourses on the nature of the mind and brain. A distinguished quantum physicist at Lawrence Berkeley National Laboratory, Stapp has been exploring these topics for over 50 years. The Mindful Universe represents the latest effort in his ongoing crusade to convince the cognitive and neurosciences that the transition away from classical physics and towards quantum theory is long overdue. Stapp’s core argument is that cognitive and brain scientists are stuck in a paradigm of classical physics which is outdated and inaccurate. The text is carefully crafted to make his point from several complimentary directions, as well as to briefly refute other contemporary theorists who advocate alternative positions. While Stapp considers this a book for the lay reader, it is definitely not mass market material. There are far fewer equations than in many of his other writings, but any serious reader will find a basic understanding of contemporary consciousness and quantum theory helpful before picking up this text. The book opens with chapters presenting the core tenets from the Copenhagen and von Neumann interpretations of quantum theory, often in the words of their founders along with commentary from Stapp. His wider view of quantum theory is summed up well by the following passage:

The original form of quantum theory is subjective, in the sense that it is forthrightly about relationships among conscious human experiences, and it expressly recommends to scientists that they resist the temptation to try to understand the reality responsible for the correlations between our experiences that the theory correctly describes. (p. 11)

In these opening chapters he diligently works to establish the case that most of these powerful thinkers strongly believed in a causal gap within quantum theory that makes it an open system into which free choice can enter. Citing the fact that “purposeful action by a human agent has two aspects” (p. 23) he draws heavily on theories involving “…the interplay between the psychologically and physically described components of mind-brain dynamics, as it is understood within the orthodox (von Neumann-Heisenberg) quantum framework” (p. 15).

From Science & Consciousness Review

Respect our authority

Respect our authority: Wikipedia

The quantum mind theory is founded on the premise that quantum theory is necessary to fully understand the mind and brain, particularly concerning an explanation of consciousness. This is considered a minority opinion in science.

(Of course, the bulk of academia is traditionally a generation behind the real innovators. Given the safety to be found in numbers, we momentarily lapse into the colloquial to advise the dedicated pedant and dutiful careerist to make (as it were) like a lemming.)

We are accustomed to regarding as real those sense perceptions which are common to different individuals, and which therefore are, in a measure, impersonal. The natural sciences, and in particular, the most fundamental of them, physics, deal with such sense perception. (Einstein)

Indoctrination

A key argument underlying the quantum mind thesis is that classical mechanics cannot fully explain consciousness. Proponents have suggested that quantum mechanical phenomena, such as quantum entanglement and superposition, may play an important part in the brain's function, and could form the basis of an explanation of consciousness.

(Quite a gasper, as the learned reader will readily acknowledge.)

There is nothing else except these [quantum] fields: the whole of the material universe is built of them. (Dyson)

The quantum mind thesis does not as yet have any evidence to confirm its validity, but some role of quantum processes in consciousness has not been completely ruled out.

(Of course, given that the brain just is a set of quanta, it would seem to follow that consciousness just might have something to do with those quanta, but for the moment a select committee of gibbering idiots would seem to serve as arbiters of majority opinion.)

Sufficient understanding of the operation of the brain could prove the proposition false.

(Ya think?)

Ongoing Debacle

The main argument against the quantum mind proposition is that the structures of the brain are much too large for quantum effects to be important.

(Gosh, aren't black holes pretty darn big?)

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. (Umezawa)

It is impossible for coherent quantum states to form for very long in the brain and impossible for them to exist at scales on the order of the size of neurons.

Any physical system is completely described by a normalized vector (the state vector or wave function) in Hilbert space. All possible information about the system can be derived from this state vector by rules ... (Byron & Fuller)

(On the other hand, plant cells use quantum coherence and superposition on a daily basis, but our brain cells are clearly not quite so sophisticated as those found in your average eggplant.)

This does not imply that classical mechanics can explain consciousness, but that quantum effects including superposition and entanglement are insignificant.

To monochromatic light corresponds in the acoustic domain the simple tone. Out of different kinds of monochromatic light composite light may be mixed, just as tones combine to a composite sound. This takes place by superposing simple oscillations of different frequency with definite intensities. (Weyl)

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)

The second principle of color mixing of lights is this: any color at all can be made from three different colors, in our case, red, green, and blue lights. By suitably mixing the three together we can make anything at all, as we demonstrated ...

Further, these laws are very interesting mathematically. For those who are interested in the mathematics of the thing, it turns out as follows. Suppose that we take our three colors, which were red, green, and blue, but label them A, B, and C, and call them our primary colors. Then any color could be made by certain amounts of these three: say an amount a of color A, an amount b of color B, and an amount c of color C makes X:

X = aA + bB + cC.

Now suppose another color Y is made from the same three colors:

Y = a'A + b'B + c'C.

Then it turns out that the mixture of the two lights (it is one of the consequences of the laws that we have already mentioned) is obtained by taking the sum of the components of X and Y:

Z = X + Y = (a + a')A + (b + b')B + (c + c')C.

It is just like the mathematics of the addition of vectors, where (a, b, c ) are the components of one vector, and (a', b', c' ) are those of another vector, and the new light Z is then the "sum" of the vectors. This subject has always appealed to physicists and mathematicians. In fact: Schrödinger wrote a wonderful paper on color vision in which he developed this theory of vector analysis as applied to the mixing of colors. (Feynman)

This looks vaguely familiar...

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. (Weyl)

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. (Wittgenstein)

Probably just a coincidence...

Calabi-Yau space, from Elegant Universe

Quantum chemistry is required to understand the actions of neurotransmitters, for example.

(Now, as any half-learned buffoon can tell you, quantum chemistry reduces to quantum physics, but we seem to be in short supply of same and so it might seem as though we must make do with the distinguished assembly of slobbering imbeciles already cited. Happily, however, we have a deeply learned buffoon standing by in case of just such an emergency.)

In fact, biologists are trying to interpret as much as they can about life in terms of chemistry, and as I already explained, the theory behind chemistry is quantum electrodynamics. (Feynman)

However, this does not preclude the possible existence of mechanisms by which quantum effects could influence the state of larger structures.

A Quantum Neural Network Computes Entanglement

(Since those larger structures also consist of quanta, this would seem a safe bet.)

... all chemical binding is electromagnetic in origin, and so are all phenomena of nerve impulses. (Salam)

Fractals are self-similar under changes of spatio-temporal scales.

Does neural form follow quantum function?

The text of this volume claims 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. (Pribram)

One well-known critic of the quantum mind is Max Tegmark. Based on his calculations, Tegmark concluded that quantum systems in the brain decohere quickly and cannot control brain function, "This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way."

(On the other hand, Pauli believed that quantum mechanics would inform a future theory of mind & brain. Whom to believe -- Tegmark, or one of the founders of quantum theory? Hmm, that is a puzzler. I wonder what would happen if we opened a book and looked up what those other guys thought?)

Bohr suggests that thought involves such small amounts of energy that quantum- theoretical limitations play an essential role in determining its character. (Bohm)

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 its justification exclusively to the totality of the sense impressions which we associate with it. (Einstein)

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 ... (Weyl)

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. (EPR)

Anyone dissatisfied with these ideas may feel free to assume that there are additional parameters not yet introduced into the theory which determine the individual event. (Born)


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 comes 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. (Schrödinger)

Thus, the task is, not so much to see what no one has yet seen; but to think what nobody has yet thought, about that which everybody sees. (Schrödinger)


Since matter clearly influences the content of our consciousness, it is natural to assume that the opposite influence also exists, thus demanding the modification of the presently accepted laws of nature which disregard this influence. (Wigner)

.

Harvard, huh?

Steven Pinker has been explaining how the mind works. Heaven help us.

In an article for Time, he writes:

Some mavericks, like the mathematician Roger Penrose, suggest the answer might someday be found in quantum mechanics. But to my ear, this amounts to the feeling that quantum mechanics sure is weird, and consciousness sure is weird, so maybe quantum mechanics can explain consciousness.

Maybe if Prof. Pinker were to actually learn something about quantum theory, his impressions of it might cease to be so weird.

OK, once again, kids: The brain just is a collection of quantum fields. See Dyson's article in Scientific American, where he states, with the simplicity of genius, that:

There is nothing else except these [quantum] fields: the whole of the material universe is built of them.

So, if the mind is connected to the brain, as would seem plausible, how could it not be related to quantum theory? Is the brain not a part of the material universe? Does Prof. Pinker have an alternative physics to propose?

Another thing:

The Hard Problem, on the other hand, is why it feels like something to have a conscious process going on in one's head--why there is first-person, subjective experience. Not only does a green thing look different from a red thing, remind us of other green things and inspire us to say, "That's green" (the Easy Problem), but it also actually looks green: it produces an experience of sheer greenness that isn't reducible to anything else.

I encountered the Hard Problem many years ago, before Chalmers gave it that name. Stymied by the hardness of the "hard problem," I eventually took a radical step, of revolutionary implications: I did some research.

Come to find out, everyone from Democritus to Galileo to Newton to Helmholtz to Riemann, Maxwell,* Einstein, Schrodinger and Weyl wrote about color.

So did Russell and Whitehead, in their monumental work on the logical foundations of mathematics, Principia Mathematica. They wrote: "Thus 'this is red,' 'this is earlier than that,' are atomic propositions."

Well, all right: If colors are truly elemental, why not quit trying to reduce them to simpler entities? Why not take nature at her word and regard colors (along with the other secondary qualities) as elemental?

Are there other mathematical aspects to color? Indeed there are. My radical departure from tradition soon revealed that Grassmann, Maxwell, Weyl and Feynman all tell us that colors behave like vectors, whereas wavelengths, being lengths, are scalars.

Weyl goes further and tells us that the laws of projective vector geometry apply to color.

And that's kind of interesting, in light of what Wittgenstein had to say:

A speck in the visual field, though it need not be red must have some colour; it is, so to speak, surrounded by colour-space. Notes must have some pitch, objects of the sense of touch some degree of hardness, and so on.

Why is this interesting? Well, because every speck in the visual field must be some color and it may be a different color from any of its neighbors. So what?

Well, in order to provide a mechanical model of this fact of experience, we are moved along a natural path toward fiber bundle theory, where to each point in space we associate a tangent space, like so, where the individual spheres look like this.

But where else do we find projective vector spaces fibering over space-time? Precisely in the Calabi-Yau spaces of M-theory. Moreover, the symmetries and phase relations of colors lead us along an easy path to gauge theory.

Finally, once one accepts that colors and sounds and so forth are elemental physical entities, they begin to look like EPR's missing "elements of reality," or, "hidden variables."

So we kill multiple birds with one stone. Needless to add, perhaps, the ideas on view above really do come down to a radical departure from tradition and no doubt the old guard will kick and scream on their way out the door. So there's another bit of fun to add to the mix.

________________

*Then, too, if Dr. Dennett had consulted Maxwell, he might have learned that his objection was answered by Maxwell's color plates. For, given that all experience of the world is subjective, how is objective science possible? The most instructive reply comes by way of Einstein's clocks and measuring rods -- objective standards upon which we can all agree. Notice that, in order to compare two color vectors, we must "parallel transport" one to the other. If one vector encounters a gravitational field along the way, it will be Dopplered, undergoing a kind of phase shift.