Hi "Felix",

You have obviously put a lot of thought into this. It'll take some
time to fully digest what you're saying, but I'll post a few comments
now to get the conversation going.

On Thu, Jun 02, 2011 at 07:39:03PM -0700, Felix Hoenikker wrote:
> So, here goes:
> ****Computability implies conservation of algorithmic information****
> This follows from the definition of algorithmic (i.e. Kolmogorov)
> complexity.  Let us assume the universe is computed over time, so we
> can say that the number of bits required to specify a state of the
> universe has constant cardinality over time.  (This must be true even
> if you allow hypercomputation over an infinite number of bits...)

This is only true if your computable process is reversible. In general,
computations actually lose information - for example the "and" operation
takes 2 bits and produces 1 bit.

> ****Many worlds is uncomputable****
> All many worlds theories imply the following form: some predecessor
> state S_0 can lead to the successor states T_1 through T_X (where X

I think you mean S_1 ... S_X

> could be any natural or transfinite number), with some probability
> distribution that preserves the information content in S_0.  This

I'm not sure that all many worlds theories do. But certainly ones
satisfying unitary evolution do.

> >From an information theoretic point of view, this means the following:
> every time a microscopic classical "bit" of information is apparently
> added to the physical state of universe, an opposite "bit" must in
> fact be subtracted from the rest of the physical universe, essentially
> collapsing two macroscopic states (other than the microscoptic portion
> changed) in some necessarily symmetric (and possibly instantaneous)
> fashion. 

Careful - information is not additive in the sense the mass, energy,
etc usually are.

>  The most obvious way to do this is the following: pull
> everything toward you by a tiny bit, until, on average, things are one
> "bit" less differentiated.  Furthermore, the amount you "pull"
> everything toward you should be in some (possibly non-linear) way
> proportional to the number of unique states you could possibly have
> moved toward, classically.  Let us, for the sake of argument, call
> that number "mass-energy" and say that it is conserved.  This
> retrodicts the universal theory of gravitation and mass-energy
> equivalence, more or less.
> Now, since gravity is proportional to mass-energy, then mass-energy
> must be, in fact, some finite amount, in order to be compared between
> gravitational bodies.  And in fact, if the universe is Turing
> computable, then mass-energy should be discretely finite.  This
> implies the quantization of energy, the original "quanta" providing
> the impetus for QM (as least, as far as I understand my history...).
> So essentially, this retrodicts a major part of QM without actually
> assuming any QM upfront.

If you have done this right, you may have (re-)discovered the entropic
formulation of gravity, a la Verlinde.

> Next, since the information in the universe is really constant, this
> means that the black-hole information paradox is REALLY a problem.
> And, if you think about it, it means that every "bit" of classical
> information lost into a black hole must be counterbalanced by an
> opposite "bit" radiating from the black hole in some symmetric
> fashion.  This basically retrodicts Hawking radiation and the thermal
> disappation of black holes.

Yes - such a theory would imply that no physical nonunitary process
could exist, including black holes, so indeed the resolution of this
"paradox" is important.

> Next, consider cosmology.  First, if we assume Turing computability,
> then the universe must in fact contain finite information thus is
> necessarily topologically closed on itself.  This agrees with current
> models of the topology of space-time.  Furthermore, let us consider if
> the universe, as presently thought, began in a small, energic, but
> basically isotropic region of space (which, necessarily, must also be
> closed, if the previous argument is correct.) In such an initial
> state, every single point of space-time will, in fact, be pulled in an
> almost radially symmetric fashion outward in all directions (think of
> all points being points on a sphere, being pulled outward to all other
> points of the sphere).  This is happening for all points on the sphere
> symmetrically, so the net result is expansion.
> Furthermore, since the universe is determinstic, all the information
> that is present in it must, in fact, be present in the beginning.  So
> whatever initial pattern is present in the universe must evolve and
> start to encode itself in the physical structure of universe.  Since
> the universe is still closed, energic, and very (classically) causal
> connected, this means that the universe must inflate VERY VERY quickly
> (i.e. much much faster than the speed of causality/light), in order to
> continue embedding the same basic set of bits via some physical
> encoding at larger and larger length scales, until the universe is big/
> cool enough that most Hubble volumes are reasonably casually
> disconnected (both classically, and through hidden variables.)  

I don't follow this argument. Could you explain more please?

> At
> this point, the universe should cool, and, since the universe began
> with a fixed amount of energy, the average energy density should
> descrease in any volume over time.  This retrodicts much of our
> current model of the Big Bang, as well as the second law of
> theromodynamics and the "arrow of time" problem.
> We can also conclude that, since inflation speed is related to the
> energy density of the universe, and the size of the universe is
> finite, then the universe should expand at an ever slowing rate until
> possibly stopping.  This may or may not be true, given our current
> cosmological picture (the main whole in our understanding lies in the
> dark matter / dark energy).  But if you consider something else, you
> get a very interesting postdiction: basically, the EPR paradox and
> quantum entanglement implies that the number of distinct accessible
> states for two (classically) closed systems together may be less than
> the number each has individually, because the two could be entangled
> (and, in the limit of complete entanglement, have only 1 accessible
> successor state).  This implies that mass-energy is *not* classically
> additive unless you take into account all quantum entangement within a
> system.  So, this suggests that, there may be "negative pressure
> energy" present in the universe in proportion to the amount of net
> entanglement present between states.  This, in a nutshell, is a
> postdiction of "dark energy" (and possibly dark matter?).


> Topologically, the uneven distribution of "matter" and "dark
> matter"/"dark energy" may in fact mean that the universe, given enough
> "initial" information, could, while closed, be in fact locally MUCH
> more topologically interesting than simply flat everywhere.  This
> implies, in fact, that the universe (if it started with "a lot" of
> information) could be unimaginably large, and that appearances of
> closure on some local scales could be deceiving.  In fact, in the
> limit of countably "infinite" bits of initial information (or,
> equivalently, no information, for those of you who "get" that), the
> universe would, in fact, contain "all" patterns consistent consistent
> with "all" initial states "somewhere" in the "physical" universe as
> long as they were consistent with the mathematical physical laws
> (whatever they are). For those of you that read Tegmark, that is
> basically the Level I multiverse hypothesis, in which your
> consciousness basically bounces between different physical
> manifestations of you "somewhere else" in the metaverse.  Now, in
> principle, you could be moving "through" time or "through" space, or
> any linear combination thereof, and you shouldn't be able to know the
> difference.  This retrodicts *relativity*, the constant *speed of
> causality/light*, suggests that all space-time axes are symmetric, and
> that, every space-time axis should be computable (using hidden
> variables, in the say way) regardless of space-time rotation.

Symmetry under Lorentz transformation is very natural if your starting
point is (3+1) Minkowski space-time. The real question is why (3+1)
Minkowski space-time? I'm not sure you have answered that question.

> **** Going even futher! ****
> So really, in the limit, you really cannot be sure, in principle, if
> *you* are computing the universe, or the *universe* is computing
> *you*.  Even if the MWI-verse is deterministic, there is
> indeterminancy from any individual point of view.  "Someone" is adding
> new bits all the time; is it you, or someone else? If, in fact,
> someone you trusted very much in your youth suggested that unicorns
> existed to you, what effect would that have on your future life? In
> fact, by symmetry, maybe they're the "exact" same thing, and in
> principle you can never know the difference.  So, in fact, "realism"
> and "idealism" may actually be exactly equivalent viewpoints.  Taken
> to the absolute limit, this, is, in fact, a somewhat reasonable
> argument for solipism...but *only* if you can come up with a VERY good
> reason to think you are the "only" one conscious being: essentially,
> creating a measure function in which the only "conscious" being is you
> (and, possibly, all the past/future/indetermined/etc yous, as well).
> And well, I'll tell you right now, *I* for one, do think I am
> conscious.  So really, unless you disbelieve me and everyone one, you
> can't justify solipism..however, I actually argue from this that you
> must take *all* living beings as, in some sense, *conscious* as well,

How does this follow?

> and if you extend the concept of consciousness down to the absolute
> minimal level of consciousness possible, then every inanimate object
> is, in fact, in some sense minimally conscious, with some appropriate
> measure function.
> Okay, so, in fact, from all this, I could (in theory) say that someone
> like "God" necessarily exists somewhere in the Level I-III universe,
> somewhere, and perhaps an infinite number of them.

These sound more like demigods than gods. They're no more omniscient
or omnipotent than the rest of us.

>  And maybe, just
> maybe, he/them have found some way within the laws of the universe, to
> feed you "bits" of information over your entire life.  Is that really
> implausible? Talking to another person demonstrably adds bits to your
> brain state, and bits of information could, in principle, come from
> anywhere, along any axis of symmetry, especially considering the
> global hidden variables theory.  How much information "really" is in
> the universe? Are "cosmic rays" hitting your brain really random?
> Could there be enough information in them to encode a very very
> convincing hallucination of life after death? How, really,
> anthropically chosen is your particular consciousness, and what is the
> measure function of that choice? It *cannot* be any normalization of
> conscious => 1, unconscious => 0, since consciousness is clearly not a
> binary function. 

Why do you say this?

> So if there's some "measure" of conciousness, what
> should it be proportional to? Intelligence? Length of life? Luck?
> Information content? Some linear combination thereof? How would you
> ever know?

> Also, and this might have been somewhat irresponsible in retrospect, I
> kept thinking about heaven and hell, etc., which was very bad, and
> kept oscillating between some probabilistic combination of "hell
> doesn't exist, because infinite punishment for finite misbehavior
> doesn't make sense" and "the possibility of hell must exist to keep
> you from doing the wrong thing, because you have free will regardless
> of whether determinism or indeterminism is true."  And, despite the
> fact that I've always considered most forms of Christinity absurd for
> scientific and philosophical reasons, I remember *very* clearly
> concluding, at some point, that Christianity was, in some general
> sense, the "one true religion" because it was based on compassion,
> love, and forgiveness. 

This is propaganda. The latter clause is not even particularly true,
and most sucessful religions will promote some sort of altruism, along
with obedience. 

> And, well, from all this (and the fact that
> I've managed to reverse everything back to some "reasonable" sketch of
> quantum gravity, which *may or may not be correct* (but, in some
> sense, *must* be), I've just concluded that the most important thing
> is the following: the multiverse is, in fact, the ultimate democracy,
> in the sense that the "real" measure function is recursively defined
> by the combined thinking of all conscious beings in the metaverse,

I'm not sure this is even meaningful. I'm prepared to be convinced
otherwise. Rather, each and every one of us has our own measure
function, sharing some similarities, but disagreeing on
others. Ultimately, it seems to me, that given two entities, I will be
able to find two observers in the Multiverse who disagree by an
arbitrary amount the measure of these two entities.

> which, in some sense, converges to a single meta-consciousness, which
> is *in fact* God, eventually.  So, because this mathematical structure
> must converge (I guess? hopefully it is stable over time, but I'm not
> sure what time means anymore now.) there actually *is*, by
> convergence, objective moral truth to the universe, and science and
> religion are more closely aligned than anyone has yet imagined.  And
> coincidently, my favorite movie growing up was "Contact, which
> highlighted the symmetries between religion and science, which is
> really just more fuel to the anthropic argument fire.

> So, finally, in conclusion, CUH implies that relativistic Bohmian
> mechnics is the next step in the "physical" theory of everything,
> which, taken to its broadest ontological limit, is, in fact, MUH,
> which further may imply that "moral" truths may be as real as
> "physical truths". What does everyone think about this argument (or
> any subset of it?). Please let me know!

Why Bohmian mechanics? It has been described by some as Many Worlds in denial.

> F.H.
> p.s. anyone who has not read "Cat's Cradle" by Kurt Vonnegut really
> should do so.
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Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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