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Friday, January 25, 2008

Yverse: A New Model of the Universe


A new model of the universe?

Actually, yeah.

It starts out with the familiar concept of the "multiverse," which is mainly associated with the many-universes interpretation of quantum theory.

According to one verbalization of the multiversal interpretation of quantum theory, every time a quantum-random "choice" is made (say, an electron spins up instead of down), there is a "branching" into two possible universes: one where the electron spins up, another where it spins down.

Similarly, if a bus drives at you while you're walking across the street, there may be two possible universes ahead of you: one where you get flattened, and another where you don't. (Actually, there are a lot of other choices going on in your life too, so it's more accurate to say there is one set of universes where you get flattened and another where you don't).

The collection of all these possible universes is known as the "multiverse."

In fact the language of "choice" used in the above description of the multiverse is a bit suspect. It's more accurate to say that corresponding to each possible state of the electron (up/down) once it is coupled with the external environment (so that it decoheres), there is a set of branches of the multiverse, and leave the ambiguous and misleading language of "choice" out of it.

Anyway, the multiverse is fascinating enough, but it's just the beginning.

It's easy enough to think of multiple possible multiverses. After all, there could be a multiverse in which Ben Goertzel never existed at all, in any of its branches.

One way to think about backwards time travel, for instance, is as a mechanism for selecting between multiverses. If you go back in time and change something, then you're effectively departing your original multiverse and entering a new one.

So, we can think about a multi-multiverse, i.e. a collection of multiverses, with a certain probability distribution over them.

I don't posit this hypothesis all that seriously, but I'm going to throw it out there anyway: It seems possible to conceive of consciousness as a faculty that facilitates movement between multiverses!

Well, I guess you can see where all this is going.

If there's a multi-multiverse, there can also be a multi-multi-multiverse. And so on.

But that is not all -- oh no, that is not all ;-)

What about the multi-multi-...-multi-multiverse?

I.e. the entity Yverse so that

Yverse = multi-Yverse

??

Math wonks will have already inferred that I chose the name Yverse because of the Y-combinator in combinatory logic, which is defined via

Yf = f(Yf)

In other words

Yf = ...ffff...

(where the ... goes on infinitely many times)

So the Yverse is the (Y multi-) universe ...

In the Yverse, there are multiple branches, each one of which is itself a Yverse....

Two Yverses may have two kinds of relationship: sibling (two branches of the same parent Yverse) or parent-child.

Backwards time travel may jolt you from one Yverse to a parent Yverse. Ordinary quantum decoherence events merely correspond to differences between sibling Yverses.

If there is a probability distribution across a set of sibling Yverses, it may be conceived as an infinite-order probability distribution. (A first-order probability distribution is a distribution across some ordinary things like numbers or particles, or universes. A second-order probability distribution is a distribution across a set of first-order probability distributions. Well, you get the picture.... An infinite-order probability distribution is a probability distribution over a set of infinite-order probability distributions. I've worked out some of the math of this kind of probability distribution, and it seems to make sense.)

What use is the Yverse model? I'm not really sure.

It seems to be an interesting way to think about things, though.

If I had more time for pure intellectual entertainment, I'd put some effort into developing a variant of quantum theory based on Yverses and infinite-order probabilities. It seems a notion worth exploring, especially given work by Saul Youssef and others showing that the laws of quantum theory emerge fairly naturally from the laws of probability theory, with a few extra assumptions (for instance, in Youssef's work, the assumption that probabilities are complex rather than real numbers).

And reading Damien Broderick's excellent book on psi, "Outside the Gates of Science," got me thinking a bit about what kinds of models of the universe might be useful for explaining psi phenomena.

Yes, quantum theory is in principle generally compatible with psi, so one doesn't need wacky ideas like Yverses to cope with psi, but it's fun to speculate. It seems to me that for quantum theory to account for psi phenomena would require some really far-out long-range quantum-coherence to exist in the universe, which doesn't seem to be there. So in my view it's at least sensible to speculate about how post-quantum physics might account for psi more sensibly.

This babbling about psi leads back to my wacko speculation above that consciousness could be associated with action in the multi-multiverse. In the Yverse model, the idea becomes that consciousness could be associated with action in the parent Yverse.

Could the difference between physical action and mental action be that the former has to do with movement between sibling Yverses, whereas the latter has to do with movement between parent and child Yverses?

Well I'll leave you on that note --

I've gone pretty far "out there", I guess about as far as it's possible to go ;-> ....

(Unless I could work Elvis into the picture somehow. I thought about it, but didn't come up with anything....)


-- (semi-relevant, rambling) P.S. Those who are interested in my AI work may be interested to know that I don't consider any of these funky speculations contradictory to the idea of creating AI on digital computers. The whole connection between probability, complex probability, quantum theory, determinism and complexity fascinates me -- and I consider it extremely poorly understood. For example, I find the whole notion of "determinism" in very complex systems suspect ... in what sense is a digital computer program determinate relative to me, if I lack the computational capability to understand its state or predict what it will do? If I lack the computational capability to understand some thing X, then relative to my own world-view, should X be modeled according to complex rather than real probabilities, in the vein of Yousseffian quantum probability theory? I suspect so. But I won't pursue this any more here -- I'll leave it for a later blog post. Suffice to say, for now, that I have a feeling that our vocabulary for describing complex systems, with words like "determinate" and "random", is woefully inaccurate and doesn't express the really relevant distinctions.

6 comments:

LĂșcio said...

Ben, I am OVERJOYED to discover that you have a blog and, better yet, that you are a frequent poster! I have just added it to my rss feeds!

Your concept of defining consciousness as a capacity to go back-and-forward in time (supposing that I got it :) is intriguing. Somehow it makes me remember of those conjectures by Penrose about consciousness being the capacity for beyond-Turing computation. I feel that I have to think about what happens to a Turing Machine if it "knows" future states of itself. (Or google the work of someone who thought about that. :)

Tom Buckner said...

I followed the Amazon link to Damien Broderick's book pn PSI, and copied this blurb:
"He concludes that while the evidence for various kinds of psi phenomena is strong, there are unknown (and possibly unknowable) factors that make classical, reductionist methods of testing it unpredictable and irreproducible (the reason, he suspects, that the CIA gave up on such research in 1995)."

This actually dovetails with what I suspect about the interaction of our consciousness with the Multiverse. (Though I don't know the form or forms the Multiverse or Verses may take, I have taken Multiverses to be a reality for well over twenty years; seems to me the writing was on the wall long before it was widely taken seriously).

Where PSI, remote viewing, ESP, or whatever Magick may be concerned: I myself have had no irrefutably Unexplainable experiences; however, certain people I trust completely have reported such experiences; yet it's not as if they could vouchsafe watertight evidence to me. I strongly suspect some aspects of an observer-created universe do in fact exist. However, I think that severe causality violations are inherently private, as in Tegmark's Quantum Suicide thought experiment. We, in other words, have some control over what universe we experience. How much control? That is to be discovered by experiment; but the results may be available only to you. This also accords with the observations of millennia of sages: 'the Tao that can be told is not the true Tao.'

Suppose that there are a certain subset of universes that contain the pattern corresponding to your brain in its present state, including all your beliefs and memories and sensory experiences. If you deliberately alter what is in that pattern, does this affect what subset of universes you could actually inhabit? If the Multiverse or Y-Verse, or what have you, is indeed a pattern of information or a data field in some sort of running simulation, why wouldn't you have some ability to navigate within it?

I keep coming back to the question of what ultimate field all this transfinite shuffling could happen on. Even if we could experimentally verify various aspects of Multiverses, we must hit a wall somewhere; the analogy I keep thinking of is that we are like stick men drawn on a chalkboard. Even once we have learned everything we can about the chalk and slate and we've decoded everything written on the board, there we are: unable to jump off the board and discover where chalk and slate come from, or anything else about this very complex world outside our chalkboard.

David said...

Hi Ben,

What probability do you assign the possibility of psi phenomena being real?

Also, can you outline how you think using complex probabilities would ever give better answers than real-valued probabilities? And wouldn't this violates Jaynes' proofs?

Mitchell said...

Ben, there are many, many people who have set out to "explain" quantum theory by saying "it's just classical probability theory, changed in some way". But the problem is always that the proposed change ruins the comprehensibility of the classical theory. To take the very simplest example, it is possible to formulate quantum mechanics in terms of quasiprobabilities which are negative as well as positive. A pseudo-explanation which then used this as a launchpad would say, "Quantum mechanics is now understood! It just means that probabilities can be negative as well as positive." And if one were to say, "But what the hell is a negative probability?", the response would be, "That's just how nature is. We just have to accept that there is such a thing, even though it is contrary to our primate intuitions" - blah blah blah. Saul Youssef's work, so far as I can see, is all about explaining quantum theory as a Bayesian theory of complex probabilities, and is therefore completely subject to this criticism - it is a purely formal pseudo-explanation, unless he can say what a "complex probability" is. People become so wrapped up in formalizations and axiomatizations that they forget that a formalization is only as good as its fidelity to the thing represented. Altering a comprehensible formalism to a new one which represents we know not what, and then saying everything is now explained, gets it all backwards.

US 0 said...

A universe simulation running inside a universe simulation

"What we don't know may exist, you can't rule out the possibility. Anything and everything may exist." one can say. But if these things have no observable influence on anything in this universe, they are nonexistent for all practical purposes. Yet they may exist.

But if they do exist and can't influence this universe, does it matter?

Some smart aliens create a universe simulator, US 1. They can change its code and affect it directly. Then they settle for version 7.1 Service Pack 3, that seems to run smoothly. Some time later, another universe simulator starts running inside it, US 2 (though the guys inside call it US 1).. That's our universe. Even if they wanted to, they can't change US 1 anymore without affecting US 2 and more importantly they can't affect US 2 without changing US 1. They have to work through their own simulation. So they can't really have a say in our universe if they wish to keep their universe running like it is. For us, for all practical purposes those smart aliens are nonexistent, they're completely unfalsifiable, yet without their existence we wouldn't exist.

The Irrefutable Fool said...

So do we live universe Aleph naught then, or are we just one of the uncountables?