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Tuesday, February 19, 2008

Characterizing Consciousness and Will in Terms of Hypersets

This is another uber-meaty blog post, which reports a train of thought I had while eating dinner with my wife last night, which appears to me to provide a new perspective on two of the thorniest issues in the philosophy of mind: consciousness and will.

(No, I wasn't eating any hallucinogenic mushrooms for dinner; just some grilled chicken with garlic and ginger and soy sauce, on garlic naan. Go figure.)

These are of course very old issues and it may seem every possible perspective on them has already been put forth, without anything fundamentally being resolved.

However, it seems to me that the perspectives on these topics explored so far constitute only a small percentage of the perspectives that may sensibly be taken.

What I'm going to do here is to outline a new approach to these issues, which is based on hyperset theory -- and which ties in with various things I've written on these topics before, inspired by neuropsychology and systems theory and probabilistic logic and so on and so forth.

(A brief digressive personal comment: I've been sooooo overwhelmingly busy with Novamente-related business stuff lately, it's really been a pleasure to take a couple hours to write down some thoughts on these more abstract topics! Of course, no matter what I'm doing with my time as I go through my days, my unconscious is constantly churning on conceptual issues like the ones I talk about in this blog post -- but time to write down my thoughts on such things is so damn scant lately.... One of the next things to get popped off the stack is the relation of the model of will given here with ethical decision-making, as related to the iterated prisoner's dilemma, the voting problem, and so forth. Well, maybe next week ... or next month.... I certainly feel like working toward making a thinking machine for real, is more critical than exploring concepts in the theory of mind; but on a minute-by-minute basis, I have to admit I find the latter more fun....)

Hypersets

One of the intuitions underlying the explorations presented here is that possibly it's worth considering hypersets as an important part of our mathematical and conceptual model of mind -- and consciousness and will in particular.

A useful analogy might be the way that differential equations are an important part of our mathematical and conceptual model of physical reality. Differential equations aren't in the world; and hypersets aren't in the mind; but these sorts of mathematical abstractions may be extremely useful for modeling and understanding what's going on.

In brief, hypersets are sets that allow circular membership structures, e.g. you can have

A = {A}

A = {B,{A}}

and so forth. It follows that you can have functions that take themselves as arguments, and lots of other stuff that doesn't work according to the standard axioms of set theory.

While exotic, hypersets are well-defined mathematical structures, and in fact simple hypersets have fewer conceptual conundrums associated with them than the real number system (which is assumed in nearly all our physics theories).

The best treatment of hypersets for non-mathematicians that I know of is the book The Liar, which I highly recommend.

Anyway, getting down to business, let's start with consciousness, and then after that we'll proceed to will.

Disambiguating Consciousness

Of course the natural language term "consciousness" is heavily polysemous, and I'm not going to try to grapple with every one of its meanings. Specifically, I'm going to focus on the meaning that might be specified as "reflective consciousness." Which is different from the "raw awareness" that, arguably, worms and bugs have, along with us bigger creatures.

Raw awareness is also an interesting topic, though I tend toward a kind of panpsychism, meaning that I tend to believe everything (even a rock or an electron) possesses some level of raw awareness. Which means that raw awareness is then just an aspect of being, rather than a separate quality that some entities possess and not others.

Beyond raw awareness, though, it's clear that different entities in the universe manifest different kinds of awareness. Worms are aware in a different way than rocks; and, I argue, dogs, pigs, pigeons and people are aware in a different way from worms. What I'll (try to) deal with here is the sense in which the latter beasts are conscious whereas worms are not -- i.e. what might be called "reflective consciousness." (Not a great term, but I don't know any great terms in this domain.)

Defining Reflective Consciousness

So, getting down to business.... My starting-point is the old cliche' that

Consciousness is consciousness of consciousness

This is very nice, but doesn't really serve as a definition or precise characterization.

In hyperset theory, one can write an equation

f = f(f)

with complete mathematical consistency. You feed f, as input, f; and you receive, as output, f.

It seems evident, though, that while this sort of anti-foundational recursion may be closely associated with consciousness, this simple equation itself doesn't tell you much about consciousness. We don't really want to say

Consciousness = Consciousness(Consciousness)

I think it's probably more useful to say:

Consciousness is a hyperset, and consciousness is contained in its membership scope

Here by the "membership scope" of a hyperset S, what I mean is the members of S, plus the members of the members of S, etc.

This is no longer a definition of consciousness, merely a characterization.

What is says is that consciousness must be defined anti-foundationally as some sort of construct via which consciousness builds consciousness from consciousness -- but it doesn't specify exactly how.

Next, I want to introduce the observation, which I made in The Hidden Pattern (and in an earlier essay) that the subjective experience of being conscious of some entity X, is correlated with the presence of a very intense pattern in one's overall mind-state, corresponding to X. This idea is also the essence of neuroscientist Susan Greenfield's theory of consciousness (but in her theory, "overall mind-state" is replaced with "brain-state").

Putting these pieces together (hypersets, patterns and correlations), we arrive at the following working definition of consciousness:

"S is conscious of X" is defined as: The declarative content that {"S is conscious of X" correlates with "X is a pattern in S"}

In other words: Being conscious of a pig, means having in one's mind declarative knowledge of the form that one's consciousness of that pig is correlated with that pig being a pattern in one's overall mind-state.

Note that this declarative knowledge must be expressed in some language such as hyperset theory, in which anti-foundational inclusions are permitted. But of course, it doesn't have to be a well-formalized language -- just as pigeons, for instance, can carry out deductive reasoning without having a formalization of the rules of Boolean or probabilistic logic in their brains. All that is required is that the conscious mind has an internal informal language capable of expressing and manipulating simple hypersets.

To make this formal, one requires also a definition of pattern, which I've supplied in The Hidden Pattern.

OK, so much for consciousness. Now, on to our other old friend, will.

Defining Will

The same approach, I suggest, can be used to define the notion of "will," by which I mean the sort of willing process that we carry out in our minds when we subjectively feel like we are deciding to make one choice rather than another.

In brief:

"S wills X" is defined as: The declarative content that {"S wills X" causally implies "S does X"}

To fully explicate this is slightly more complicated than in the case of consciousness, due to the need to unravel what's meant by "causal implication." This is done in my forthcoming book Probabilistic Logic Networks in some detail, but I'll give the basic outline here.

Causal implication may be defined as: Predictive implication combined with the existence of a plausible causal mechanism.

More precisely, if A and B are two classes of events, then A "predictively implies B" if it's probabilistically true that in a situation where A occurs, B often occurs afterwards. (Yes, this is dependent on a model of what is a "situation", which is assumed to be part of the mind assessing the predictive implication.)

And, a "plausible causal mechanism" associated with the assertion "A predictively implies B" means that, if one removed from one's knowledge base all specific instances of situations providing direct evidence for "A predictively implies B", then the inferred evidence for "A predictively implies B" would still be reasonably strong. (In a certain logical lingo, this means there is strong intensional evidence for the predictive implication, along with extensional evidence.)

If X and Y are particular events, then the probability of "X causally implies Y" may be assessed by probabilistic inference based on the classes (A, B, etc.) of events that X and Y belong to.

In What Sense Is Will Free?

But what does this say about the philosophical issues traditionally associated with the notion of "free will"?

Well, it doesn't suggest any validity for the idea that will somehow adds a magical ingredient beyond the familiar ingredients of "rules" plus "randomness." In that sense, it's not a very radical approach. It fits in with the modern understanding that free will is to a certain extent an "illusion."

However, it also suggests that "illusion" is not quite the right word.

The notion that willed actions somehow avoid the apparently-deterministic/stochastic nature of the universe is not really part of the subjective experience of free will ... it's a conceptual add-on that comes from trying to integrate our subjective experience with the modern scientific understanding of the world, in an overly simplistic and partially erroneous way.

An act of will may have causal implication, according to the psychological definition of the latter, without this action of will violating the basic deterministic/stochastic equations of the universe. The key point is that causality is itself a psychological notion (where within "psychological" I include cultural as well as individual psychology). Causality is not a physical notion; there is no branch of science that contains the notion of causation within its formal language.

In the internal language of mind, acts of will have causal impacts -- and this is consistent with the hypothesis that mental actions may potentially be ultimately determined via determistic/stochastic lower-level dynamics. Acts of will exist on a different level of description than these lower-level dynamics.

The lower-level dynamics are part of a theory that compactly explains the behavior of cells, molecules and particles; and some aspects of complex higher-level systems like brains, bodies and societies. Will is part of a theory that compactly explains the decisions of a mind to itself.

My own perspective is that neither the lower-level dynamics (e.g. physics equations) nor will should be considered as "absolutely real" -- there is no such thing as absolute reality. The equations of physics, glorious as they are, are abstractions we've created, and that we accept due to their utility for helping us carry out various goals and recognize various regularities in our own subjective experience.


Connecting Will and Consciousness


Connecting back to our first topic, consciousness, we may say that:


In the domain of reflective conscious experiences, acts of will are experienced as causal.

This of course looks like a perfectly obvious assertion. What's nice is that it seems to fall out of a precise, abstract characterization of consciousness and will.

Free Will and Virtual Multiverse Modeling

In a previous essay, written a few years back and ultimately incorporated into The Hidden Pattern, I gave an analysis of the psychological dynamics underlying free will, the essence of which may be grokked from the following excerpt:

For example, suppose I am trying to decide whether to kiss my beautiful neighbor. One part of my brain is involved in a dynamic which will actually determine whether I kiss her or not. Another part of my brain is modeling that first part, and doesn’t know what’s going to happen. A virtual multiverse occurs in this second part of the brain, one branch in which I kiss her, the other in which I don’t. Finally, the first part comes to a conclusion; and the second part collapses its virtual multiverse model almost instantly thereafter.

The brain uses these virtual multiverse models to plan for multiple contingencies, so that it is prepared in advance, no matter what may happen. In the case that one part of the brain is modeling another part of the brain, sometimes the model produced by the second part may affect the actions taken by the first part. For instance, the part (call it B) modeling the action of kissing my neighbor may come to the conclusion that the branch in which I carry out the action is a bad one. This may affect the part (call it A) actually determining whether to carry out the kiss, causing the kiss not to occur. The dynamic in A which causes the kiss not to occur, is then reflected in B as a collapse in its virtual multiverse model of A.


Now, suppose that the timing of these two causal effects (from B to A and from A to B) is different. Suppose that the effect of B on A (of the model on the action) takes a while to happen (spanning several subjective moments), whereas the effect of A and B (of the action on the model) is nearly instantaneous (occurring within a single subjective moment). Then, another part of the brain, C, may record the fact that a collapse to definiteness in B’s virtual multiverse model of A, preceded an action in A. On the other hand, the other direction of causality, in which the action in A caused a collapse in B’s model of A, may be so fast that no other part of the brain notices that this was anything but simultaneous. In this case, various parts of the brain may gather the mistaken impression that virtual multiverse collapse causes actions; when in fact it’s the other way around. This, I conjecture, is the origin of our mistaken impression that we make “decisions” that cause our actions.



How does this relate to the current analysis in terms of hypersets?

The current analysis adds an extra dimension to the prior one, which has to do with what in the above quote is called the "second part" of the brain involved with the experience of will -- the "virtual multiverse modeler" component.

The extra dimension has to do with the ability of the virtual multiverse modeler to model itself and its own activity.

My previous theory discusses perceived causal implications between actions taken by one part of the brain, and models of the consequences of these actions occurring in another part (the virtual multiverse modeler). It notes that sometimes the mind makes mistakes in perceiving a causal implication between a collapse in the virtual multiverse model and an action, when a more careful understanding of the mental dynamics would reveal a more powerful causal implication in the other direction. There is much evidence for this in the neuropsychology literature, some of which is reviewed in my previous article.

The new ingredient added by the present discussion is an understanding that the virtual multiverse modeler can model its own activity and its relationship with the execution of actions. Specifically, the virtual multiverse modeler can carry out modeling in terms of an intuitive notion of "will" that may be formalized as I described above;


"S wills X" is defined as: The declarative content that {"S wills X" causally implies "S does X"}



where "S" refers specifically to the virtual multiverse modeler component, the nexus of the feeling of will.

And, as noted in my prior essay, it may do so whether or not this causal implication would hold up when the dynamics involved were examined at a finer level of granularity.

Who Cares?

Well, now, that's a whole other question, isn't it....

Personally, I find it interesting to progressively move toward a greater and greater understanding of the processes that occur in my own mind everyday. Since understanding (long ago) that the classical notion of "free will" is full of confusions, I've struggled to figure out the right attitude to take in my own mind, toward decisions that come up in my own life.

Day after day, hour after hour, minute after minute, I'm faced with deciding between option A and option B -- yet how seriously can I take this decision process if I know I have no real will anyway?

But the way I try to think about it is as follows: Within the descriptive language in which my reflective consciousness exists, my will does exist. It may not exist within the descriptive language of physics, but that's OK. None of these descriptive languages has an absolute reality. But, each of these descriptive languages can usefully help us understand the others (as well as helping us to understand the world directly); and having an understanding of the systematic biases made by the virtual multiverse modeler in my brain has certainly been useful to me. It has given me a lot more respect for the underlying unconscious dynamics governing my decisions, and this I believe has helped me to learn to make better decisions.

In terms of my AI work, the main implication of the train of thought reported here is that in order to experience reflective consciousness and will, an AI system needs to possess an informal internal language allowing the expression of basic hyperset constructs. Of course, in different AI designs this could be achieved in different ways, for instance it could be explicitly wired into the formalism of a logic-based AI system, or it could emerge spontaneously from the dynamics of a neural net based AI system. In a recent paper I explored some hypothetical means via which a neural system could give rise to a neural module F that acts as a function taking F as an input; this sort of phenomenon could potentially serve as a substrate for an internal hyperset language in the brain.

There is lots left to explore and understand, of course. But my feeling is that reflective consciousness and will, as described here, are not really so much trickier than other mental phenomena like logical reasoning, language understanding and long-term memory organization. Hypersets are a different formalism than the ones typically used to model these other aspects of cognition, but ultimately they're not so complex or problematic.

Onward!

Thursday, February 14, 2008

Psi, Closed-Mindedness and Fear

Some of the followup (private) emails I've gotten in regard to my just-prior blog post on Damien Broderick's book on psi, have really boggled my mind.

These emails basically present arguments of two forms:

  1. You're nuts, don't you know all the psi experiments are fraud and experimental error, everyone knows that...
  2. Look, even if there's a tiny chance that some psi phenomena are real, you're a fool to damage your reputation by aligning yourself with the kooks who believe in it

What shocks me (though it shouldn't, as I've been around 41 years and seen a lot of human nature already) about arguments of the first form is the irrational degree of skepticism toward this subject, displayed by otherwise highly rational and reflective individuals.

It's not as though these people have read Damien's book or carefully studied the relevant literature. I would welcome debate with suitably informed skeptics. Rather, these people dismiss the experimental literature on psi based on hearsay, and don't consider it worth their while to spend the 3-10 hours (depending on individual reading speed) required to absorb a fairly straightforward nontechnical book on the subject, like Damien's.

What shocks me about arguments of the second form is how often they come from individuals who are publicly aligned with other extremely radical ideas. For instance a few Singularitarians have emailed me and warned me that me talking about psi is bad, because then people will think Singularitarians are kooks.

(Amusingly, one Singularitarian pointed out in their conversation with me that, to them, the best argument for the possibility of psi that they know of is the Simulation Argument, which contends that we probably live in a computer simulation. This is I suppose based on the idea that the laws of physics somehow rule out psi, which they don't; but anyway it's an odd argument because whether we live in a simulation or not, the laws of physics are merely a compact summary of our empirical observations of the world we see, and so if psi data are real, they need to be incorporated into our observation-set and accounted for in our theories, regardless of whether we interpret these theories as being about a "real" world or a "simulated" one.)

Whoa!! So psi is so far out there that people who believe the universe is a simulation and the Singularity is near don't want their reputations poisoned by association with it?

This really baffles me.

I have no personal axe to grind regarding psi.

I have never had any unambiguous, personally convincing psi experiences (except when under the influence of various psychotropic compounds, but that's a whole other story ;-)....

I don't actually care much whether psi is real or not.

About psi and physics ... I am skeptical of attempts to explain psi based on quantum theory, due to not understanding how decoherence would be avoided in the hypothesized long-range quantum nonlocal binding between brains and other systems; but I recognize that quantum theory as such does not actually rule out psi. And, I am acutely aware that modern physics theories are incomplete, even leaving out psi data -- just taking into account well-accepted physics data. Modern physics does not provide a complete, conceptually consistent accounting of all well-accepted physics data. So all in all, our incomplete physics model doesn't rule out psi but makes it hard to explain. This does not seem a strong enough reason to ignore the available psi data on theoretical-physics grounds.

My observation is merely that, after spending a few dozen hours perusing the available data, it seems fascinating and compelling. Ed May's data is not the only good data out there by any means, but it's a great place to start if you want to dig into it.

I do not think we, as a community of thinking and understanding minds, should be ignoring all this high-quality data collected by serious, intelligent, careful scientists.

What is the reason for ignoring it? Presumably the reason is that a bunch of bullshit about psi has been promoted by a bunch of flakes and kooks. It's true. I admit it, Damien admits it, it's obvious. Let's get over that historical and cultural reality and look at the actual data -- quite possibly there's something to be learned from it. I don't know exactly what, but that's how science works -- you investigate and then you find out. What's frustrating is that in this extremely fascinating, important, potentially highly impactful area, research is proceeding so slowly because of excesses of skepticism and fear in the scientific community.

Scientists want to preserve their careers and reputations, so going out on a limb for something perceived as wacky is something very few of them are willing to do. As a consequence our understanding of the universe advances much more slowly than it otherwise could.

Finally, a brief aside.... For those who believe a Singularity is likely but who are highly skeptical of psi (a small percentage of the world, but disproportionately represented in the readership of this blog, I would imagine), I ask you this: Wouldn't it be nice to understand the universe a little better before launching a Singularity? If psi is real that would seem to have various serious implications for what superhuman AI's may be like post-Singularity, for example.

Well, anyway. I'm going to drop this topic for now as I have other stuff to focus on, like building AGI.... And I've been (finally) mixing down some of my music from MIDI to MP3; I'll post some on my website within the next month or so.... I don't have time to push ahead psi research myself nor to actively advocate for funding for those doing the research; but by writing these blog posts and reviewing Damien's book on Amazon.com, I've tried to do what I can (within my limited available time) to nudge the world toward being less closed-minded and less fearful in this regard.

Come on, people! Really! Have some guts and some mental-openness -- it's a big, weird, mysterious world out there, and I'm damn sure we understand only a teensy weensy bit of it. Experience gives us clues, empirical science gives us clues -- and the extent to which we manage to ignore some of the most interesting clues the world provides us, is pretty disappointing...

Saturday, February 02, 2008

The Scientific Evidence for Psi (is most likely stronger than you think)

My goal in this blog is to convince you to read Damien Broderick's book Outside the Gates of Science: Why It's Time for the Paranormal to Come in From the Cold.

Reviewing a host of research done by others over many decades, the book makes a remarkably and excitingly strong case that psi phenomena are worthy of intensive further investigation....

Let me explain why I'm so excited by Broderick's work.

Having grown up on SF, and being a generally open-minded person but also mathematician/scientist with a strong rationalist and empiricist bent, I've never quite known what to make of psi. (Following Broderick, I'm using "psi" as an umbrella term for ESP, precognition, psychokinesis, and the familiar array of suspects...).

Broderick's book is the first I've read that rationally, scientifically, even-handedly and maturely, reviews what it makes sense to think about psi given the available evidence.

(A quick word on my science background, for those who don't know me and may be new to this blog: I have a math PhD and although my main research areas are AI and cognitive science, I've also spent a lot of time working on empirical biological science as a data analyst. I was a professor for a 8 years but have been doing research in the software industry for the last decade.)

My basic attitude on psi has always been curious but ambivalent. One way to summarize it would be via the following three points....

First: Psi seems, on the face of it, is not wildly scientifically implausible after the fashion of, say, perpetual motion machines built out of wheels and pulleys and spinning chanbers filled with ball bearings. Science, at this point, understands the world only very approximately, and there is plenty of room in our current understanding of the physical universe for psi. Quantum theory's notions of nonlocality and resonance are conceptually somewhat harmonious with some aspects of psi, but that's not the main point. The main point is that science does not rule out psi, in the sense that it rules out various sorts of crackpottery.

Second
: Anecdotal evidence for psi is so strong and so prevalent that it's hard to ignore. Yes, people can lie, and they can also be very good at fooling themselves. But the number of serious, self-reflective intelligent people to report various sorts of psi experiences is not something that should be glibly ignored.

Third: There is by now a long history of empirical laboratory work on psi, with results that are complex, perplexing, but in many ways so apparently statistically significant as to indicate that SOMETHING important is almost surely going on in these psi experiments...

Broderick, also being an open-minded rationalist/empiricist, seems to have started out his investigation of psi, as reported in his book, with the same basic intuition as I've described in the above three points. And he covers all three of these points in the book, but the main service he provides is to very carefully address my third point above: the scientific evidence.

His discussion of possible physical mechanisms of psi is competent but not all that complete or imaginative; and he wisely shies away from an extensive treatment of anecdotal evidence (this stuff has been discussed ad nauseum elsewhere). But his treatment of the scientific literature regarding psi is careful, masterful and compellingly presented. And this is no small achievement.

The scientific psi literature is large, complex, multifaceted and subtle -- and in spite of a lifelong peripheral fascination with psi, I have never taken the time to go through all that much it myself. I'm too busy doing other sorts of scientific, mathematical and engineering work. Broderick has read the literature, sifted out the good from the bad, summarized the most important statistical and conceptual results, and presented his conclusions in ordinary English that anyone with a strong high school education should be able to understand.

His reviews of the work on remote viewing and precognition I found particularly fascinating, and convincing. It is hard to see how any fair-minded reader could come away from his treatments of these topics without at least a sharp pang of curiousity regarding what might actually be going on.

Perhaps my most valued discovery, based on Broderick's book, was Edwin May's work on precognition and related phenomena. Anyone with a science background is strongly encouraged to inspect the website of May's Cognitive Sciences Laboratory, which hosts an impressive collection of papers on his team's government-funded psi research.

What is my conclusion about psi after reading Damien's book, and exploring in more depth the work of May's team and others?

Still not definitive -- and indeed, Broderick's own attitude as expressed in the book is not definitive.

I still can't feel absolutely certain whether psi is a real phenomenon; or whether the clearly statistically significant patterns observed across the body of psi experiments bespeak some deep oddities in the scientific method and the statistical paradigm that we don't currently understand.

But after reading Broderick's book, I am much more firmly convinced than before that psi phenomena are worthy of intensive, amply-funded scientific exploration. Psi should not be a fringe topic, it should be a core area of scientific investigation, up there with, say, unified physics, molecular biology, AI and so on and so forth.

Read the book for yourself, and if you're not hopelessly biased in your thinking, I suspect you'll come to a conclusion somewhat similar to mine.

As a bonus, as well as providing a profound intellectual and cultural service, the book is a lot of fun to read, due to Broderick's erudite literary writing style and ironic sense of humor.

My worry -- and I hope it doesn't eventuate -- is that the book is just too far ahead of its time. I wonder if the world is ready for a rational, scientific, even-handed treatment of psi phenomena.

Clearly, Broderick's book is too scientific and even-handed for die-hard psi believers; and too psi-friendly (though in a level-headed, evidence-based way) for the skeptical crowd. My hope is that it will find a market among those who are committed to really understanding the world, apart from the psychological pathologies of dogmatism or excessive skepticism.

I note that Broderick has a history of being ahead of his time as a nonfiction writer. His 1997 book "The Spike" put forth basically the same ideas that Ray Kurzweil later promulgated in his 2005 book "The Singularity Is near." Kurzweil's book is a very good one, but so was Broderick's; yet Kurzweil's got copious media attention whereas Broderick's did not ... for multiple reasons, one of which, however, was simply timing. The world in 1997 wasn't ready to hear about the Singularity. The world in 2006 is.

The question is: is the world in 2008 ready to absorb the complex, fascinating reality of psi research? If so, Broderick's book should strike a powerful chord. It certainly did for me.

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.