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Tuesday, March 25, 2008

Quantum Voodoo in "Classical" Systems?

Way way back in the dark ages, when I was 19 years old and in my second year of grad school, I wrote a paper called "Holistic Indeterminacy" and submitted it to the journal Mind.

The basic idea was that, in some cases, very complex "classical" physical systems might literally display the same kind of indeterminacy associated with quantum systems.

The paper was printed out crappily on a dot matrix printer with dimly printed ink, and written in a not terribly professional way. It got rejected, and I've long since lost the thing. Furthermore, I never since found time to write up the ideas in the paper again. (Had there been a Web back then I would have posted the thing on my website, but this was the mid 1980's ... if I recall correctly, I hadn't even sent an email yet, at that point. I might actually have the paper on some old floppy disk in the basement, but odds are the data's long corrupted even if the disk is still around...).

But anyways ... please pardon these reminisces of an old man!! ... these old ideas of mine came up today in a conversation I was having with a friend over lunch, so I figured I'd take a few minutes to type them into a blog post (way less work than a paper!).

In fact these ideas are far more topical now than in the 1980's, as quantum computing is these days finally becoming a reality ... along with macroscopic quantum systems and all sorts of other fun stuff....

Partly because of these advances, and partly because the ideas have had decades to pervade my brain, I think I can now express the idea a bit more crisply than I did back then.

Still, it's a freaky and speculative train of thought, which I am not fully convinced makes any sense.

But at very least, it's some amusing hi-fi sci-fi.....

The basic idea is as follows.

Premise: Quantum logic is the logic of that which, in principle, cannot be observed. Classical logic is the logic of that which can, in principle, be observed.

The above may sound odd but it's not my idea -- it's the conclusion of a lot of work in quantum physics and the quantum theory of measurement, by serious physicists who understand such things far better than I do. It's way clearer now than it was in the mid 80's, though it was known to all the cool people even then....

Now is where things start to get weird. I want to make the above premise observer-dependent in a manner different from how quantum theory does it. Namely, I want to introduce an observer who, himself, has a finite capacity for understanding and observation -- a finite Kolmogorov complexity, for example.

This leads to my

Modest proposal: An observing system should use quantum logic to reason about anything that it, as a particular system, cannot in principle observe.

There are some things that a worm cannot observe, because it is just a worm; but I can observe. From the perspective of the worm, I suggest, these things should be reasoned about using quantum logic.

Similarly, there are some things that I cannot observe, in principle, because I am just a little old me.

Yes, I could potentially expand myself into a dramatically greater being. But, then that wouldn't help ME (i.e., my current self) to observe these things ... it would just help {some other, greater guy who had evolved out of me} to observe these things.

Of course, you can't step into the same river once ... and there is not really any ME that is persistent beyond an individual moment (and there are no individual moments!). But you can talk about a class of systems, and you can say that some observables are simply NOT observable by any system within that class. So systems within that class need to reason about these observables using quantum logic.

Where does complexity come into the picture? Well, among the things I can't in principle observe, are patterns of more complexity than can fit in my brain.

And among the things my deliberatively conscious mind can't in principle observe, are patterns of more complexity than can fit within its own very limited capacity.

So, if we interpret "quantum logic is the logic of things that can't in principle be observed" subjectively, as applying to particular real-world observing systems (including subsystems like the deliberatively conscious component of a human brain), then we arrive at the funky conclusion that maybe we should reason about each others' minds using quantum logic ... or maybe even, that we should reason about our own unconscious using quantum logic....

Funny idea, hmmm?

Way back when I wrote down some mathematics embodying these notions, but I don't feel like regenerating that right now. Although I'm a bit curious to see whether it had any validity or not ;-)

What made me think of this today was a discussion about consciousness, and the possibility (raised by the friend I was talking to) that some sort of wacky quantum voodoo is necessary to produce consciousness.

Maybe so. On the other hand, it could also be that any system complex enough to display the kind of rich deliberative consciousness we humans do, is complex enough that humans need to reason about it using quantum logic ... because in principle we cannot observe its dynamics (without becoming way more complex than we are, hence losing our self-ness...).

Ahhh... well I'll get back to doing the final edits on the Probabilistic Logic Networks book now ...

5 comments:

Vladimir Nesov said...

Ben, how is it different from good old probabilistic logic that has classical logic (and computation) as special cases? You'd need to know which things you can't know in order to selectively reason about them in different logic...

Anonymous said...

im glad to see im not the only one who has pondered this kind of thinking, you've done it well, keep it up!!

Benjamin said...

Nesov: Probabilistic logic is different from quantum logic. Quantum logic lacks a distributive law, for one thing. Alternately, you can do quantum theory by preserving classical logic but moving to complex-number rather than real-number probabilities (cf Youssef). In any case, weird stuff.

Anonymous said...

Dear Ben, as food for thought in this direction please see Ignacio Matte Blanco's seminal work, The Unconscious as Infinite Sets; with perhaps the work of Gotthard Guenther on multivalued logics as _not_ intepreted relative to probabilities nor simple true-falsehood relations, as entrée -- or at least his immensely pithy "A logic is the metaphysical self-definition of a subject" as sauce; and if appetite permits, a veritable trolley of deserts can be recommended. Respectfully, Lauri

p.s. "metaphysical" in the above quotation ought be understood as nearer that alluded to by Wheelerian "pregeometry", than the hand-waving of postmodernists, modern or otherwise.

Anonymous said...

Both quantum logic and probalistic logic seem to be special cases of topological logic. Basically, you can define a logic on either anything that has a group structure (for quantum logic, this is complex projective space; for probablistic logic, this is just a simplex) or anything that has a metric structure.

A simple, and easy-to-understand review is givein in the wikipedia article "quantum finite state machine".

http://en.wikipedia.org/wiki/Quantum_finite_automata