(First posted at Lifeboat Foundation.)

We have had a lot of offhand discussion about building minds and understanding the future here. But all of that rests on a foundation of assumptions about what the mind and the future actually are. This past month..., well, it is possible to surprise even an old guy with some startling new wrinkles -- if we don't get lost in the foggy world of empty DC-style pedigrees and hermeneutics.

Long ago, folks like Aristotle told us that "mind" or consciousness as we know it is basically just a matter of "form," of patterns of organization defined over "substance" or hardware. Some of you associate that with Dan Dennett, who has pushed the idea that mind equals brain equals patterns of atoms in the brain. Dennett's choice of words was unfortunate at times, but the basic idea that mind is a matter of patterns defined over a physical substrate still makes sense. When real life experience tells us that our minds don't follow the mundane version of "what you see is what you get," some folks would choose to go nuts, while others would recognize that "substance" is not limited to atoms and that we can still try to understand natural law even when it gets weird.

OK, that's past. We take it for granted.

What I have begun to appreciate for the past few months is that this is not the true picture. And yes, this has something to do with my re-examining of quantum mechanics. Consciousness, in a quantum mechanical universe, does not really fit the Aristotelian picture. Perhaps Plato will have the last laugh here.

Many of you know about the "multiverse," a concept due to Everett and Wheeler, ably carried on by David Deutsch of Oxford (a bit less ably by Bohm and Hiley). In their version of quantum field theory, the cosmos is made up of an infinite continuum of the kinds of object we call "universes", all existing in parallel. In this view... when we ask what the future will be... we should remember that ALL possibilities will actually occur, in reality, with varying probability strength.

Everett tried to prove that this picture LEADS TO the usual Copenhagen picture of measurement, of "the collapse of the wave function," but he did not quite succeed in proving this -- because it isn't true! The work of David Deutsch is the real foundation of quantum computing as it is now known to science. Quantum computing is also necessary to building the most powerful type of mind, whether "natural" or 'artificial," possible in this cosmos.

But I never really believed in the Everett picture. It seems unnecessarily complicated, and it entails some really strange kludges, like assuming an infinite number of space dimensions but still only one time dimension. There are other ways to go. As a proper follower of Occam's Razor, I have tried hard to get back to Einstein's prohgram, back to reality, back to understanding just how much we could predict and explain by assuming just three space dimensions and one time dimension, governed by nonlinear partial differential equations. I have sought a "theory of everything' which could be expressed in a single equation, a "Lagrangian,' and I even have a specific candidate Lagrangian in my notes.

But... well... those nonlinear PDE can do a lot more than even I used to imagine.

Even a universe governed by nonlinear PDE can do things which are very strange, in a way which changes the proper assumptions about mind and the future themselves.

I have two new papers coming out this month, one in the International Journal on Bifurcation and Chaos, and one in a Russian mathematics journal, giving different aspects of this, as well as a new experiment which really should be reporting out in a couple of weeks (delayed due to byproducts of the ongoing reorganization of the US government).

The IJBC paper discusses (among other things) three theories of physics -- Feynmann path (the most orthodox of orthodox in quantum theory today),

a new stochastic path formulation (which I call stochastic realism), and -- briefly -- the PDE possibility which is mathematically just a limiting case of stochastic path.

And yes, the latter two are abject heresy this week -- except that new experiments may say otherwise.

I have studied what stochastic realism really predicts in detail for experiments involving two or three entangled photons... versus the usual old Copenhagen version of quantum mechanics... and this has led me to a deeper understanding

of Feynmann path as well.

In essence, stochastic path and Feynmann path both appear to say that reality is just 3+1 dimensional, not at all like the multiverse theory. One future, and one future only. We would picture our minds as patterns over the fields in three-dimensional space.

But no, not so.

Both Feynmann path and stochastic realism are grounded in something I would call "scenarios" rather than "paths". (Feynmann used the term "path" \when he started out, thinking of a small number of point particles, but folks like Schwinger pushed towards thinking of functions of space-time.) You can think of a scenario X as a set of possible values for all of the fields of physics, over all points in space and time. In a way, all of Feynmann physics can be summarized in the model

psi(X) = (1/Z) product {space x,time t} e**(iL(x,t,X)),

where psi is the probability amplitude of scenario X, where L is called "the Lagrangian function," and where Z is just a real number chosen to make the resulting probabilities add up to one. In stochastic realism, I just assume:

pr(X)=(1/Z) product {x,t} e**(L(x,t,X)) -- just like ordinary Markov Random Fields,

used in AI for decades. (I think Laveen Kanal started that.) MRF are not new, but

what's new is the proof that we can explain all the known two-photon experiments this way, WITHOUT assuming any "collapse of the waver functoi\\ion" -- as in some papers I have at arxiv.org. With three photons, we can test for stochastic realism versus the old Copenhagen stuff.

What really hit me this path month... is the realization that

MIND IS ATTACHED TO SCENARIOS, NOT TO REALITY ITSELF.

What's more, even the "conservative" Einstein view, as the limiting case of stochastic realism, actually implies all the same weirdness as full stochastic realism and Feynmann! In all these systems, consciousness or mind is attached to "scenarios,' and "our" future is just a matter of other possible scenarios.

A bit like Pogo: I finally found reality, but it's not us. Mind as we know it

is a matter of forms and organization of SCENARIOS... almost like those

science fiction novels where lots of simulations are going on in parallel.

And so... the complexity of an entire multiverse seems to be compressed into

a single 3+1-D continuum, in all three types of model... so in a sense, David Deutsch gets the last laugh. I think of this as the "Jack in the box" universe,

mathematically "simple," but, due to the incredible power of Lagrangian variational mathematics... an emergent effect just like a multiverse! Time tracks and all..

not for reality itself, but for shadows like us. (I suppose Zelazny might feel a bit vindicated.) EVEN for the Einstein-type universe!

And yes, there are operational consequences of many kinds, including consequences for the design of more powerful computing systems...

but some of the consequences I am just now beginning to assimilate.

It's really amazing how rich the emergent behavior can be of one Lagrangian one could write out in half a page...

Best of luck,

Paul

(As of now, no longer an employee of the US government.)

P.S. Could it be that NONE of these three theories -- Feynmann path, stochastic realism or PDE -- is true? Certainly. But the stochastic path and PDE theories are the simplest one could hope to devise, consistent with the two-photon and three-photon experiments. If the true 'law of everything" is different, that probably means that there are ADDITIONAL complications -- but all of THIS weirdness is pretty much unavoidable. I really wasn't planning to try to vindicate Plato this year... but.. some things need to be faced up to.

P.S. Could it be that NONE of these three theories -- Feynmann path, stochastic realism or PDE -- is true? Certainly. But the stochastic path and PDE theories are the simplest one could hope to devise, consistent with the two-photon and three-photon experiments. If the true 'law of everything" is different, that probably means that there are ADDITIONAL complications -- but all of THIS weirdness is pretty much unavoidable. I really wasn't planning to try to vindicate Plato this year... but.. some things need to be faced up to.

I see where you corrected one typo, but there are still a couple lurking in the above.

ReplyDelete"artificial," not 'artificial,"

Einstein's program not Einstein's prohgram

"collapse of the wave function" not "collapse of the waver functoi\\ion"

this past month not this path month

I guess I can't suppress the copy editor in me.

Zelazny vindication would be amazing indeed.

Allen Taylor