Monday, October 29, 2007

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.)