Monday, January 22, 2007

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.