Re: Is the universe computable

[CMR]

> And what does it say about the physical properties which are necessary
> for computation?  We have energy; Life has "blinkiness" (the degree to
> which cells are blinking on and off within a structure); neither property
> has a good analog in the other universe.  Does the "real" universe win,
> in terms of deciding what properties are really needed for computation?
> I don't think so, because we could reverse the roles of the two universes
> and it wouldn't make any fundamental difference.
>

Yes! you've captured the gist and fleshed out the raw concept that "hit" me
whilst reading your post on "weightless" computation; that's potentially the
value of it as an avenue to explore, I think: that there is an
equivalence/symmetry/correspondence by which the universe's map to one
another but it's not direct(?) is it a form of information conveyance?
hmmm..

Reference time...

Re: Is the universe computable?

[CMR]

> Think of it this way, what is the cardinality of the equivalence class
> of representations R of, say, a 1972 Jaguar XKE, varying over *all
possible
> languages* and *symbol systems*? I think it is at least equal to the
Reals.
> Is this correct? If R has more than one member, how can we coherently
argue
> that "information is physical" in the material monist sense?
>

Assuming you mean R is countably infinite(?), then a solution would be a
finite universe of underlying discrete structure, ala Fredkin, I imagine.

>
>  What if the "informing" and "constraining" (?) is done, inter alia,
by
> the systems that "use up" the universal resources?
>
> What if, instead of thinking in terms of a priori existing solutions,
> ala Platonia, if we entertain the idea that the *solutions are being
> computation in an ongoing way* and that what we experience is just one (of
> many)stream(s) of this computation. Such a computation would require
> potentially infinite "physical resources"...
> Would it be to much to assume that all we need to assume is that the
> "resources" (for Qcomputations, these are Hilbert space dimensions) are
all
> that we have to assume exists a priori? Does not Quantum Mechanics already
> have such build in?

Yes, this would indeed follow. But what of a view of QM itself emerging form
qubits?
as, for instance, expressed in the so-called Bekenstein bound: the entropy
of any region
of space cannot exceed a fixed constant times the surface area of the
region. This suggests
that the complete state space of any spatially finite quantum system is
finite, so
that it would contain only a finite number of independent qubits.

Re: [issues] Re: Is the universe computable

[James N Rose]

Calm, Steve, calm.  :-)  Remember my comment the
other evening:  It is the appropriate moment in 
human thought to change the definitions of
'objective' and 'subjective'.

Implementation is the 'subjective'.  Relationship
need not be.  In fact, relationship is necessarily
-intangible-, but -is- the object of any search
for 'the objective'.

That 'relationship' is made explicit via implementation
does not detract from its purity of specification .. its
'objectivity'.

Nor is the objectivity of a 'relationship' diminished
by the fact that relationship can only be explore, examined,
or empirically specified, except via subjective 'instantiation'.

These simultaneous aspects of reality/being are superposed
with one another.  Both present even as they are mutually
distinguishable.

This takes 'objectivity' to an independent level of
identification, beyond any potential for anomaly, for
variation; immune to perturbation and noise.

It finally allows us to consiliently accomodate
'subjective' truths with objective basese.
Objectivity is the intangible and uncorruptable
'relations', rules, and laws, of being and performance.

Subjectivity is all the necessary examples and instantiations
-by which- we can and do 'know' the 'relations', rules, and
laws, of being and performance.

Jamie Rose
MetaScience Academy. Japan.
Ceptual Institute. USA.






Stephen Paul King wrote:
> 
> Dear Hal,
> 
> "A theorem doesn't weigh anything, and neither does a computation."
> 
> Nice try but that is a very smelly Red Herring. Even Conway's Life can
> not exist, even in the abstract sense, without some association with the
> possibility of "being implemented" and it is this "Implementation" that I am
> asking about.
> 
> Let us consider Bruno's beloved "Arithmetic Realism". Are we to believe
> that Arithmetic can be considered to "exist" without, even tacitly, assuming
> the possibility that numbers must be "symbolic representable"? If they can
> be, I strongly argue that we have merely found a very clever definition for
> the term "meaninglessness".
> 
> I beg you to go directly to Turing's original paper discussing what has
> become now know as a "Turing Machine". You will find discussions of things
> like "tape" and "read/write head". Even if these, obviously physical,
> entities are, as you say, "by definition within a universe" and that such
> "universes" can be rigorously proven to be "mathematical entities", this
> only strengthens my case: An abstract entity must have a possibility of
> being physically represented, even if in a "Harry Potter Universe", to be a
> meaningful entity. Otherwise what restrains us from endless Scholastic
> polemics about "how many Angels can dance on the head of a Pin" and other
> meaningless fantasies.
> 
> The fact that an Algorithm is "independent of any particular
> implementation" is not reducible to the idea that Algorithms (or Numbers, or
> White Rabbits, etc.) can exist without some "REAL" resources being used in
> their implementation (and maybe some kind of "thermodynamics").
> 
> BTW, have you read Julian Barbour's The End of Time? It is my opinion
> that Julian's argument falls flat on its face because he is making the very
> same mistake: Assuming that his "best-matching" scheme can exists without
> addressing the obvious status that it is an NP-Complete problem of
> uncountable infinite size. It is simply logically impossible to say that the
> mere postulation of a Platonia allows for the a priori existence of the
> solution to such a computationally intractable problem.
> 
> Kindest regards,
> 
> Stephen
> 
> - Original Message -
> From: "Hal Finney" <[EMAIL PROTECTED]>
> To: <[EMAIL PROTECTED]>
> Sent: Tuesday, January 20, 2004 1:39 PM
> Subject: Re: Is the universe computable
> 
> > At 13:19 19/01/04 -0500, Stephen Paul King wrote:
> >
> > >Where and when is the consideration of the "physical resources" required
> > >for the computation going to obtain? Is my question equivalent to the old
> > >"first cause" question?
> >
> > Anything "physical" is by definition within a universe (by my definition,
> > anyway!).  What are the physical properties of a system in our universe?
> > Mass, size, energy, electrical charge, partical composition, etc.  If we
> > at least hypothetically allow for the existence of other universes,
> > wouldn't you agree that they might have completely different physical
> > properties?  That they might not have mass, or charge, or size; or that
> > these properties would vary in some bizarre way much different from how
> > stable they are in our universe.
> >
> > Consider Conway's 2-dimensional Cellular Automota universe called Life.
> > Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing
> > implementation of a computer, a Turing Machine, in this universe.
> > I spent a couple of hours yesterday looking at this thing, seeing how
> > the parts work.  He did an incredible job in putting all the details
> > toget

RE: Is the universe computable

[David Barrett-Lennard]

Kory said...

> 
> At 1/21/04, David Barrett-Lennard wrote:
> >This allows us to say the probability that an integer is even is 0.5,
or
> >the probability that an integer is a perfect square is 0.
> 
> But can't you use this same logic to show that the cardinality of the
even
> integers is half that of the cardinality of the total set of integers?
Or
> to show that there are twice as many odd integers as there are
integers
> evenly divisible by four? In other words, how can we talk about
> probability
> without implicitly talking about the cardinality of a subset relative
to
> the cardinality of one of its supersets?

Saying that the probability that a given integer is even is 0.5 seems
intuitively to me and can be made precise (see my last post).  Clearly
there is a weak relationship between cardinality and probability
measures.  Why does that matter?

Why do you assume infinity / infinity = 1 , when the two infinities have
the same cardinality?   Division is only well defined on finite numbers.

> 
> I'm not denying that your procedure "works", in the sense of actually
> generating some number that a sequence of probabilities converges to.
The
> question is, what does this number actually mean? I'm suspicious of
the
> idea that the resulting number actually represents the probability
we're
> looking for. Indeed, what possible sense can it make to say that the
> probability that an integer is a perfect square is *zero*?
> 
> -- Kory

For me, there *is* an intuitive reason why the probability that an
integer is a perfect square is zero.  It simply relates to the fact that
the squares become ever more sparse, and in the limit they become so
sparse that the chance of finding a perfect square approaches zero.

- David

Re: Modern Physical theory as a basis for Ethical and Existential Nihilism

[Norman Samish]

Your conclusion that "there is no scientific justification for morals of any
sort, only that in the Darwinistic sense" depends on the definition of
"scientific."  Without "morals" an argument could be made that mankind would
not exist - it would have self-destructed.  Perhaps that is "scientific
justification" for morals, at least as far as mankind is concerned.  And
perhaps our lack of morals will yet wipe us out through WMD, or other evil.
Norman
- Original Message - 
From: <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 6:04 PM
Subject: Modern Physical theory as a basis for Ethical and Existential
Nihilism


>
> I am writing my high school senior project term paper on defending ethical
and existential nihilism based on quantum and multiverse theory. I was
looking for any comments on the subject. Here I place my outline for said
paper:
>
> --- 
> A Scientific Basis for Ethical and Existential Nihilism
>
> I. Introduction
>  A. Societal habit of classification of moral disciplines
>  B. Difference of anyone to a possibly fitting classification makes
such divvying impossible
>  C. One must evaluate the individual sets of moral principles to
establish their validity
> II. What is ethical?-Establishing a Basis for Reference
>  A. Definition of ethic/moral
>   1. Participation/contribution
>   2. Action
>   3. Earning
>  B. Earning as an ethical point for reference
>   1. Earning governed by psychological history
>   2. Psychology influenced by the physical
>   3. The physical is governed by causality
>  C. Ethic is debunked by the causal nature of space-time and quantum
superpositioning
> III.   Space-Time and Quantum Physics form a basis for inevitability
>  A. The "So-Called Relativity Theory" Perspective
>   1. The space-time manifold is a substrate upon which things
exist
>   2. The future condition of events or anything can be determined
using equations to model energy and position over time
>   3. All things have a definite past, present, and future,
ontologically
>   4. Limited by information acquisition
>a) speed of light
>b) infinitesimal spaces governed by quantum theory
>  B. Quantum Physics Perspective
>   1. Heisenberg's Uncertainty Principle
>a) impossible to know one's future
>b) definite past
>   2. Schrödinger's wave function
>a) Schrödinger's Cat Paradox
>b) superposition of waves
>c) collapse of the wave function
>d) Copenhagen Interpretation (CHI)
>e) Hugh Everett III's theory that all possible resultant
collapses can be defined by a superposition in Hilbert Space
>  C. Multiverse Theory-Multiple Universes in which all possibilities
are played out
>   1. There is a total number of possible arrangements of matter
based on the limits of the entropy of space-time, where the total is equal
to the permutation of particles and energies and dependent on the total
number of particles
>   2. All these possibilities are superimposed upon one another to
form an infinite-dimensional Hilbert Space in which the wave function
resides, evolving over time
>a) Each universe is a subset, a space-time system in which
one arrangement of matter exists
>b) One space-time event sequence is merely the use of time
and physical law/rules to determine a valid progression of one universal
space to another
>c) This creates multiple space-time pathways, each of which
encompasses a version of the past, present, and future
>d) Each point has a past with possible futures to be
determined upon collapse of the wave function
>e) Our own physical, present reality, interpreted as a
resulting situation of the collapse, is one point in space-time with a
sequence of probability states with the same past configuration
>f) This course of action leading to each possible reality
yields multiple pathways from the beginning to the end of time
>g) Each point in time has nearly infinite future
possibilities, but each path contains only itself-one path with two
endpoints-essentially arriving from the restraints of causality on the
topological set
> IV. Philosophical Implications
>  A. Every person has a definite past
>   1. Every person is the result of the path of space-time upon
which its universe's energy has traveled
>   2. Because of causality and entropy bounds, one has no control
over the past
>   3. A future is simply the result of influences of the wave
function and its probabilities on space-time
>  B. A person's future is inevitable
>   1. No matter what decision one chooses, the psyche's action is
defined

Re: Modern Physical theory as a basis for Ethical and Existential Nihilism

[Eric Hawthorne]

Sorry. Can't help myself : Is there any point in completing that term 
paper really?

On a few points.

I don't believe in the point of view of "nihilism because everything 
will happen in the multiverse, anyway, regardless of what I do"..
My reasons are a little vague, but here's a stab at it:

1. I look at us group of human observer SAS's as results of and 
guardians of emerged complex order in our universe.
In fact I believe our universe (its temporal arrow etc) is only 
observable because it is the set of paths through the multiverse
that has all this emerged complex order in it.I believe these 
potentially observable sets of paths through the multiverse's general
disorder are rare (of small measure.)

2. Somehow, all of us human observers are clearly "in" or "observing" 
the SAME set of paths through the multiverse.
Now that is significant. It tells us that in the emergent-order paths of 
multiverse info-state evolution, that those paths
are observable consistently to ANY observer that emerges as part of the 
emerged complex order present in those paths.

3. I see humans (or other intelligent lifeforms) as in some strange ways 
the smart-lookahead "guardians" of the particular
piece of emergent-order their most a part of (their planet, their 
ecosystems, their societies, themselves).The reason
we emerged (or are still here) is because we have helped make our 
emergent complex system "successful" (robust).

4. For some strange reason, I value the most complex yet elegant and 
robust emergent order (for itself). This is why
for example, I'm an environmental activist in my spare (hah!) time.

5. I think if one values elegant, robust complex order, and if one is an 
active part of the elegant, robust, complex
order, who emerged precisely so that a SAS of the emerged system could 
sense and make sense of the surroundings,
and could model and influence the future, and guard the SAS's own 
existence and that of the whole emerged system of
which it is a part, then "guard away" I say, actively, not 
nihilistically. Model your world. Predict its different possible
futures, and use your emerged (and cultivated, same thing) wisdom to 
steer yourself, and your society, and your
ecosystem, and your planet, away from harm and too-soon reduction to 
entropy. In the very, very end, it is said,
entropy wins (like the house wins in Vegas.) But why not have as good a 
game as possible before it ends in a billion
or trillions of years.

6. Of course, it doesn't make sense to try to protect (and advance in 
elegance) an emergent order that is indeed truly
robust, does it? But my point back there was that we are supposed to be 
part of the emergent system's self-defense
mechanism, because we can think and plan, and change things in our universe.

7. So can we change the multiverse as a whole? Probably not. But all 
that observers can ever co-observe
is a single self-consistent universe in the multiverse. Look at earth 
and earthlife like a surfboard and surfer surfing
this big coherent wave of informationally self-consistent order that is 
our universe. What we as the surfer can
do is look ahead, and steer the board, and prolong the ride, and make it 
as amazing as possible before it
tumbles into the vortex. That's enough control to say let's delay 
nihilism til the very last possible moment at least,
shall we. Let's see where we might wash up if we keep riding well. 
Enough. Enough. This tortured analogy is
killing me.

8. You may say that there's all these other virtual doppelganger surfers 
and surfboards (even on our same order-wave universe)
so why bother steering anyway? One of us will make it. Yeah well I don't 
think so. I think all the emergent systems
kind of compete with each other to organize things, and there's winners 
and losers, and the losers are all just info-noise.

8. I guess the above is premised on the supposition that we CAN steer. 
That we have any say over when and how
our part of our universe degrades into entrop (info-noise.) This is 
really vague but I have some strange
sense that what observing AGENT (actor) systems such as ourselves are 
doing is choosing (or having a part
in choosing) the way in which their quantum world becomes their 
classical world. I think there's the possibility
of free will there. It's like their steering the NOW wavefront itself 
(in their shared universe). If the possibly ordered
paths through multiverse infospace near these observers are more than 
one possible path, maybe its the observers,
by the sum total of their collective actions, that micro-manage the 
choice of future info-paths that will still be
consistent with the path(s) their all on. Maybe the set of possible 
consistent and ordered paths is narrower and narrower as
time goes on for them, but I think there are still choices to be made. 
It's possible that that's an illusion, but choice being an illusion
is a concept for the theoretical meta-level, for OUTSIDE our universe 
path. Inside our path(s), our pa

RE: Is the universe computable

[Jesse Mazer]

Kory Heath wrote:
At 1/19/04, Hal Finney wrote:
However, here is an alternate formulation of my argument which seems to
be roughly equivalent and which avoids this objection: create a random
program tape by flipping a coin for each bit.  Now the probability that
you created the first program above is 1/2^100, and for the second,
1/2^120, so the first program is 2^20 times more probable than the second.
That's an interesting idea, but I don't know what to make of it. All it 
does is create a conflict of intuition which I don't know how to resolve. 
On the one hand, the following argument seems to make sense: consider an 
infinite sequence of random bits. The probability that the sequence begins 
with "1" is .5. The probability that it begins with "01" is .25. Therefore, 
in the uncountably infinite set of all possible infinite bit-strings, those 
that begin with "1" are twice as common as those that begin with "01". 
However, this is in direct conflict with the intuition which says that, 
since there are uncountably many infinite bit-strings that begin with "1", 
and uncountably many that begin with "01", the two types of strings are 
equally as common. How can we resolve this conflict?

-- Kory
I haven't studied measure theory, but from reading definitions and seeing 
discussions my understanding is that it's about functions that assign real 
numbers to collections of subsets (defined by 'sigma algebras') of infinite 
sets. As applied to probability theory, it allows you to define a notion of 
probability on a set with an infinite number of members. Again, this would 
involve assigning probabilities to *subsets* of this infinite set, not to 
every member of the infinite set--for example, if you are dealing with the 
set of real numbers between 0 and 1, then although each individual real 
number could not have a finite probability (since this would not be 
compatible with the idea that the total probability must be 1), perhaps each 
finite nonzero interval (say, 0.5 - 0.8) would have a finite probability. In 
a similar way, if you were looking at the set of all possible infinite 
bit-strings, although each individual string might not get a probability, 
you might have a measure that can tell you the probability of getting a 
member of the subset "strings beginning with 1" vs. the probability of 
getting a member of the subset "strings beginning with 01". Some references 
on measure theory that may be helpful:

http://en2.wikipedia.org/wiki/Measure_theory
http://en2.wikipedia.org/wiki/Sigma_algebra
http://en2.wikipedia.org/wiki/Probability_axioms
http://mathworld.wolfram.com/Measure.html
http://mathworld.wolfram.com/ProbabilityMeasure.html
Jesse Mazer

_
Learn how to choose, serve, and enjoy wine at Wine @ MSN. 
http://wine.msn.com/

RE: Is the universe computable

[Kory Heath]

At 1/21/04, David Barrett-Lennard wrote:
This allows us to say the probability that an integer is even is 0.5, or
the probability that an integer is a perfect square is 0.
But can't you use this same logic to show that the cardinality of the even 
integers is half that of the cardinality of the total set of integers? Or 
to show that there are twice as many odd integers as there are integers 
evenly divisible by four? In other words, how can we talk about probability 
without implicitly talking about the cardinality of a subset relative to 
the cardinality of one of its supersets?

I'm not denying that your procedure "works", in the sense of actually 
generating some number that a sequence of probabilities converges to. The 
question is, what does this number actually mean? I'm suspicious of the 
idea that the resulting number actually represents the probability we're 
looking for. Indeed, what possible sense can it make to say that the 
probability that an integer is a perfect square is *zero*?

-- Kory

RE: Is the universe computable

[Kory Heath]

At 1/19/04, Hal Finney wrote:
However, here is an alternate formulation of my argument which seems to
be roughly equivalent and which avoids this objection: create a random
program tape by flipping a coin for each bit.  Now the probability that
you created the first program above is 1/2^100, and for the second,
1/2^120, so the first program is 2^20 times more probable than the second.
That's an interesting idea, but I don't know what to make of it. All it 
does is create a conflict of intuition which I don't know how to resolve. 
On the one hand, the following argument seems to make sense: consider an 
infinite sequence of random bits. The probability that the sequence begins 
with "1" is .5. The probability that it begins with "01" is .25. Therefore, 
in the uncountably infinite set of all possible infinite bit-strings, those 
that begin with "1" are twice as common as those that begin with "01". 
However, this is in direct conflict with the intuition which says that, 
since there are uncountably many infinite bit-strings that begin with "1", 
and uncountably many that begin with "01", the two types of strings are 
equally as common. How can we resolve this conflict?

-- Kory

Modern Physical theory as a basis for Ethical and Existential Nihilism

[[EMAIL PROTECTED]]

I am writing my high school senior project term paper on defending ethical and 
existential nihilism based on quantum and multiverse theory. I was looking for any 
comments on the subject. Here I place my outline for said paper:

--- 
A Scientific Basis for Ethical and Existential Nihilism

I. Introduction
 A. Societal habit of classification of moral disciplines
 B. Difference of anyone to a possibly fitting classification makes such divvying 
impossible
 C. One must evaluate the individual sets of moral principles to establish their 
validity
II. What is ethical?—Establishing a Basis for Reference
 A. Definition of ethic/moral
  1. Participation/contribution
  2. Action
  3. Earning
 B. Earning as an ethical point for reference
  1. Earning governed by psychological history
  2. Psychology influenced by the physical
  3. The physical is governed by causality
 C. Ethic is debunked by the causal nature of space-time and quantum 
superpositioning
III.   Space-Time and Quantum Physics form a basis for inevitability
 A. The “So-Called Relativity Theory” Perspective
  1. The space-time manifold is a substrate upon which things exist
  2. The future condition of events or anything can be determined using 
equations to model energy and position over time
  3. All things have a definite past, present, and future, ontologically
  4. Limited by information acquisition
   a) speed of light
   b) infinitesimal spaces governed by quantum theory
 B. Quantum Physics Perspective
  1. Heisenberg’s Uncertainty Principle
   a) impossible to know one’s future
   b) definite past
  2. Schrödinger’s wave function
   a) Schrödinger’s Cat Paradox
   b) superposition of waves
   c) collapse of the wave function
   d) Copenhagen Interpretation (CHI)
   e) Hugh Everett III’s theory that all possible resultant collapses can 
be defined by a superposition in Hilbert Space
 C. Multiverse Theory—Multiple Universes in which all possibilities are played out
  1. There is a total number of possible arrangements of matter based on the 
limits of the entropy of space-time, where the total is equal to the permutation of 
particles and energies and dependent on the total number of particles
  2. All these possibilities are superimposed upon one another to form an 
infinite-dimensional Hilbert Space in which the wave function resides, evolving over 
time
   a) Each universe is a subset, a space-time system in which one 
arrangement of matter exists
   b) One space-time event sequence is merely the use of time and physical 
law/rules to determine a valid progression of one universal space to another
   c) This creates multiple space-time pathways, each of which encompasses 
a version of the past, present, and future
   d) Each point has a past with possible futures to be determined upon 
collapse of the wave function
   e) Our own physical, present reality, interpreted as a resulting 
situation of the collapse, is one point in space-time with a sequence of probability 
states with the same past configuration
   f) This course of action leading to each possible reality yields 
multiple pathways from the beginning to the end of time
   g) Each point in time has nearly infinite future possibilities, but 
each path contains only itself—one path with two endpoints—essentially arriving from 
the restraints of causality on the topological set
IV. Philosophical Implications
 A. Every person has a definite past
  1. Every person is the result of the path of space-time upon which its 
universe’s energy has traveled
  2. Because of causality and entropy bounds, one has no control over the past
  3. A future is simply the result of influences of the wave function and its 
probabilities on space-time 
 B. A person’s future is inevitable
  1. No matter what decision one chooses, the psyche’s action is defined and 
controlled by the wave function in its space
  2. All decisions, choices, and outcomes are predefined, if only in a 
superposition of probabilities
  3. This leads to a lack of personal contribution on the part of the person.
 C. A person is not to be held accountable for what he/she cannot control
  1. If a person cannot control the set of probabilities of the outcome, then 
are they really making a decision?
   a) Yes, they do define a pathway,
   b) But, there is no preference of one over the other physically, except 
what is determined by the probabilities defined by the wave function
   c) No one outcome is more likely then another with respect to its 
pre

RE: Is the universe computable

[David Barrett-Lennard]

Does this help...

Let f(x) be a predicate on positive integer x.  

Let pn = |{ x <= n | f(x) }| / n

(ie the fraction of the first n positive integers that satisfy the
predicate)

I propose that we define the probability of f as P(f) = p if pn
converges to p.

This allows us to say the probability that an integer is even is 0.5, or
the probability that an integer is a perfect square is 0.

- David


> -Original Message-
> From: Hal Finney [mailto:[EMAIL PROTECTED]
> Sent: Tuesday, 20 January 2004 1:24 AM
> To: [EMAIL PROTECTED]
> Subject: RE: Is the universe computable
> 
> Kory Heath wrote:
> > At 1/18/04, Hal Finney wrote:
> > >Now consider all possible program tapes being run at the same time,
> > >perhaps on an infinite ensemble of (virtual? abstract?) machines.
> > >Of those, a fraction of 1 in 2^100 of those tapes will start with
that
> > >100 bit sequence for the program in question.
> > [snip]
> > >Now consider another program that is larger, 120 bits.  By the same
> > >reasoning, 1 in 2^120 of all possible program tapes will start with
> that
> > >particular 120-bit sequence.  And so 1/2^120 of all the executions
will
> > >be of that program.
> >
> > Yes, but if we're really talking about all possible finite bit
strings,
> > then the number of bit strings that begin with that 100 bit program
is
> > exactly the same as the number that begin with the 120 bit program -
> > countably infinite. You can put them into a 1 to 1 correspondence
with
> each
> > other, just like you can put the integers into a 1 to 1
correspondence
> with
> > the squares. The intuition that there must be more integers than
squares
> is
> > simply incorrect, as Galileo pointed out long ago. So shouldn't your
two
> > programs have the exact same measure?
> 
> Well, I'm not a mathematician either, so I can't say for sure.
> And actually it's worth than this, because I spoke of infinite program
> tapes, so the number of programs is uncountably infinite.
> 
> However, here is an alternate formulation of my argument which seems
to
> be roughly equivalent and which avoids this objection: create a random
> program tape by flipping a coin for each bit.  Now the probability
that
> you created the first program above is 1/2^100, and for the second,
> 1/2^120, so the first program is 2^20 times more probable than the
second.
> 
> That seems correct, doesn't it?  And it provides a similar way to
justify
> that the universe created by the first program has 2^20 times greater
> measure than the second.
> 
> Hal Finney

RE: Are conscious beings always fallible?

[David Barrett-Lennard]

Even if we utilize a language with reflection capability, do we still
have an underlying problem with different levels of "mathematical truth"
as indicated by the question of whether 3+4 equals 7?

When an expression contains a sub-expression, don't we expect to be able
to replace that sub-expression by an equivalent one?  But deciding
whether two expressions are equivalent depends on a particular
perspective of mathematical truth.

Btw I thought Smalltalk was weakly typed (can throw a message at any
object regardless of type)

- David


> -Original Message-
> From: Bruno Marchal [mailto:[EMAIL PROTECTED]
> Sent: Tuesday, 20 January 2004 6:44 PM
> To: [EMAIL PROTECTED]
> Subject: Re: Are conscious beings always fallible?
> 
> I agree with you. Actually you can use the second recursion theorem
> of Kleene to collapse all the orders. This is easier in an untyped
> programming language like (pure) LISP than in a typed language,
> although some typed language have a primitive for handling untyped
> self-reference, like the primitive SELF in Smalltalk ...
> 
> Bruno
> 
> 
> 
> At 23:29 19/01/04 -0800, Eric Hawthorne wrote:
> >How would they ever know that I wonder?
> >"Well let's see. I'm conscious and I'm not fallible. Therefore"
;-)
> >
> >David Barrett-Lennard wrote:
> >
> >>I'm wondering whether the following demonstrates that a computer
that
> can
> >>only generate "thoughts" which are sentences derivable from some
> underlying
> >>axioms (and therefore can only generate "true" thoughts) is unable
to
> think.
> >>
> >>This is based on the fact that a formal system can't understand
> sentences
> >>written down within that formal system (forgive me if I've worded
this
> >>badly).
> >>
> >>Somehow we would need to support free parameters within quoted
> expressions.
> >>Eg to specify the rule
> >>
> >> It is a good idea to simplify "x+0" to "x"
> >>
> >>It is not clear that language reflection can be supported in a
> completely
> >>general way.  If it can, does this eliminate the need for a meta-
> language?
> >>How does this relate to the claim above?
> >>
> >>- David
> >>
> >I  don't see the problem with representing logical meta-language, and
> >meta-metalanguage... etc if necessary
> >in a computer. It's a bit tricky to get the semantics to work out
> >correctly, I think, but there's nothing
> >"extra-computational" about doing higher-order theorem proving.
> >
> >http://www.cl.cam.ac.uk/Research/HVG/HOL/
> >
> >This is an example of an interactive (i.e. partly human-steered)
> >higher-order thereom prover.
> >I think with enough work someone could get one of these kind of
systems
> >doing some useful higher-order
> >logic reasoning on its own, for certain kinds of problem domains
anyway.
> >
> >Eric

Re: Is the universe computable

[Stephen Paul King]

Dear Hal,

Consider the last two paragraphs from one of Stephen Wolfram's papers:

http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html

***
"Quantum and statistical mechanics involve sums over possibly infinite sets
of configurations in systems. To derive finite formulas one must use finite
specifications for these sets. But it may be undecidable whether two finite
specifications yield equivalent configurations. So, for example, it is
undecidable whether two finitely specified four-manifolds or solutions to
the Einstein equations are equivalent (under coordinate
reparametrization).[24] A theoretical model may be considered as a finite
specification of the possible behavior of a system. One may ask for example
whether the consequences of two models are identical in all circumstances,
so that the models are equivalent. If the models involve computations more
complicated than those that can be carried out by a computer with a fixed
finite number of states (regular language), this question is in general
undecidable. Similarly, it is undecidable what is the simplest such model
that describes a given set of empirical data.[25]
This paper has suggested that many physical systems are computationally
irreducible, so that their own evolution is effectively the most efficient
procedure for determining their future. As a consequence, many questions
about these systems can be answered only by very lengthy or potentially
infinite computations. But some questions answerable by simpler computations
may still be formulated."

***

It has been pointed out, by Roger Penrose himself (!), that the
decidability problem for Einstein's equations is equivalent to Halting
Problem of Turing Machines (pg. 337 of "Shadows of the Mind"). When we put
these two arguments together, what do we get?

See: http://arxiv.org/abs/quant-ph/0304128   ;-)

Stephen



- Original Message - 
From: "Hal Finney" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 7:18 PM
Subject: Re: Is the universe computable


> CMR writes:
> > Then question then becomes, I suppose, if in fact our universe is a
digital
> > one (if not strictly a CA) havng self-consistent emergent physics, then
> > might it not follow that it is "implemented" (run?) via some
extra-universal
> > physical processes that only indirectly correspond to ours?
>
> This is a good point, and in fact we could sharpen the situation as
> follows.
>
> Suppose multiverse theory is bunk and none of Tegmark's four levels work.
> The universe isn't infinite in size; there is no inflation; the MWI is
> false; and all that stuff about Platonic existence is so much hot air.
> There is, in fact, only one universe.
>
> However, that universe isn't ours.  It's a specific version of Conway's
> 2D Life universe, large but finite in size, with periodic edge conditions.
>
> Against all odds, life has evolved in Life and produced Self
> Aware Subsystems, i.e. observers.  These beings have developed a
> civilization and built computers.  See the link I supplied earlier,
> http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer.
>
> On their computers they run simulations of other universes, and one
> of the universes they have simulated is our own.  Due to a triumph
> of advanced mathematics, they have invented a set of physical laws of
> tremendous complexity compared to their own, and these laws allow for
> atoms, chemistry, biology and life of a form very different from theirs.
> They follow our universe's evolution from Big Bang to Heat Death with
> fascination.
>
> Unbeknown to us, this is the basis for our existence.  We are a simulation
> being run in a 2D CA universe with Conway's Life rules.
>
> Now, is this story inconceivable?  Logically contradictory?  I don't
> see how.  The idea that only one "real" universe might exist, but that it
> could create any number of "simulated" ones, is pretty common.  Of course
> it's more common to suppose that it's our universe which is the "real"
> one, but that's just parochialism.
>
> And what does it say about the physical properties which are necessary
> for computation?  We have energy; Life has "blinkiness" (the degree to
> which cells are blinking on and off within a structure); neither property
> has a good analog in the other universe.  Does the "real" universe win,
> in terms of deciding what properties are really needed for computation?
> I don't think so, because we could reverse the roles of the two universes
> and it wouldn't make any fundamental difference.
>
> Hal
>
>

Re: Is the universe computable?

[Stephen Paul King]

Dear CMR,

- Original Message - 
From: "CMR" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 6:46 PM
Subject: Re: Is the universe computable?


> Greetings Stephen,
>
> >BTW, have you ever read about the Maxwell Demon?
>
> Being partial to the information physical view; not only have I read it, I
> also account for it by viewing a system's information as physical.
>
[SPK]

Ok, but what about the fact that there does not exist a unique
representation for a given physical object, unless one is going to restrict
oneself to a Turing computable world and use the Kolmogorov notion. Doing
this is problematic because it requires that all of a given object's
properties be both enumerable and pre-specifiable. QM, as I understand it,
disallows this in most cases. Consider the problem of computing the Unitary
evolution of a DNA molecule's wave function.
Think of it this way, what is the cardinality of the equivalence class
of representations R of, say, a 1972 Jaguar XKE, varying over *all possible
languages* and *symbol systems*? I think it is at least equal to the Reals.
Is this correct? If R has more than one member, how can we coherently argue
that "information is physical" in the material monist sense?


> So by inference should then I be viewing the mapping of the intra and
extra
> universal resources as informational in "nature"? In that the
implementation
> "informs" (and thus constrins?) the evolution of our toy universe?
>

[SPK]

 What if the "informing" and "constraining" (?) is done, inter alia, by
the systems that "use up" the universal resources?

What if, instead of thinking in terms of a priori existing solutions,
ala Platonia, if we entertain the idea that the *solutions are being
computation in an ongoing way* and that what we experience is just one (of
many)stream(s) of this computation. Such a computation would require
potentially infinite "physical resources"...
Would it be to much to assume that all we need to assume is that the
"resources" (for Qcomputations, these are Hilbert space dimensions) are all
that we have to assume exists a priori? Does not Quantum Mechanics already
have such build in?

Stephen

Re: Is the universe computable

[Hal Finney]

CMR writes:
> Then question then becomes, I suppose, if in fact our universe is a digital
> one (if not strictly a CA) havng self-consistent emergent physics, then
> might it not follow that it is "implemented" (run?) via some extra-universal
> physical processes that only indirectly correspond to ours?

This is a good point, and in fact we could sharpen the situation as
follows.

Suppose multiverse theory is bunk and none of Tegmark's four levels work.
The universe isn't infinite in size; there is no inflation; the MWI is
false; and all that stuff about Platonic existence is so much hot air.
There is, in fact, only one universe.

However, that universe isn't ours.  It's a specific version of Conway's
2D Life universe, large but finite in size, with periodic edge conditions.

Against all odds, life has evolved in Life and produced Self
Aware Subsystems, i.e. observers.  These beings have developed a
civilization and built computers.  See the link I supplied earlier,
http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer.

On their computers they run simulations of other universes, and one
of the universes they have simulated is our own.  Due to a triumph
of advanced mathematics, they have invented a set of physical laws of
tremendous complexity compared to their own, and these laws allow for
atoms, chemistry, biology and life of a form very different from theirs.
They follow our universe's evolution from Big Bang to Heat Death with
fascination.

Unbeknown to us, this is the basis for our existence.  We are a simulation
being run in a 2D CA universe with Conway's Life rules.

Now, is this story inconceivable?  Logically contradictory?  I don't
see how.  The idea that only one "real" universe might exist, but that it
could create any number of "simulated" ones, is pretty common.  Of course
it's more common to suppose that it's our universe which is the "real"
one, but that's just parochialism.

And what does it say about the physical properties which are necessary
for computation?  We have energy; Life has "blinkiness" (the degree to
which cells are blinking on and off within a structure); neither property
has a good analog in the other universe.  Does the "real" universe win,
in terms of deciding what properties are really needed for computation?
I don't think so, because we could reverse the roles of the two universes
and it wouldn't make any fundamental difference.

Hal

Re: Is the universe computable

[CMR]

Greetings Pete,

> If not, then can you say what it is about the active process of
> flipping or laying down that "counts" as computation but does not count
> when the stack is a static block?
>

I suppose I'm ultimately in the "hard" info physics camp, in that the
pattern's the thing; given the 2ds and the binary content, then the stacks
would map to a time dimension I suppose; were they to be unstacked and
recorded we'd have a history (were they unstacked , some flipped then read..
revisionist history?)


> If you think the static block "counts" as the implementation of a
> universe, then I think you can go all the way to abstract Platonism.
> Because since the stack's just sitting there, why not knock it down?
> Or melt it into a big ball?  Or throw it into a black hole...the two
> SASes won't care (will they?)
>

No, in this scenario I see the unverse as a function of the coins (or
computer, or space-time, or matter energy and information). Toss a stack
into a black whole (whether of not we get it back via hawkings radiation)
and the information capacity of the universe is affected. But note here I
say "this scenario".

> So I think the anti-Platonist must answer why exactly the coins need to
> be actively flipped or laid down to "really" implement a Life universe
> -- and by extension, why any universe needs to be "actively"
> implemented.

Because it's not there? Kidding. To elaborate on my statement above. I
definitely see time, energy, matter.. as emergent phenomena of an underlying
informational  and probably discrete process. But they emerged from a
pattern(order? information? logos?) and that pattern was informed upon( the,
a, some?) "void" (noise, chaos, "the one"? "the one of many?").  Per my just
prior post, I may in fact now see the extra-universal "implementation" as
informational.  So am I not a Platonist (or not? or am?)

Re: Is the universe computable?

[CMR]

Greetings Stephen,

>BTW, have you ever read about the Maxwell Demon?

Being partial to the information physical view; not only have I read it, I
also account for it by viewing a system's information as physical.

So by inference should then I be viewing the mapping of the intra and extra
universal resources as informational in "nature"? In that the implementation
"informs" (and thus constrins?) the evolution of our toy universe?

Re: Is the universe computable

[Hal Finney]

Pete Carlton writes:
> Imagine a Life universe that contains, among other things, two SASes 
> talking to each other (and showing each other pictures, and in general 
> having a very lucid, conscious, conversation.)  Imagine that instead of 
> being implemented on a computer, it's implemented by a large 2d array 
> of coins:  heads represents "live", and tails represents "dead".  Each 
> timestep, the coins are flipped over in concordance with the Life 
> rules.
> Does this setup implement a universe?

Let's say it does.

>   If you say it does, how about the next step:
> Instead of doing flipping operations on one set of coins, each new 
> generation is laid down in the proper configuration on top of the 
> preceding one with a new set of coins.  Does this >process< of laying 
> down coins also implement a universe?

Yes, it would seem that laying down coins isn't conceptually different
from flipping them, from the point of view of performing a calculation.

> If you say it does, then what about the stack itself?  (One can imagine 
> pointing to each layer in succession, saying "This is the current 
> step", "Now this is the current step", etc..) Does the stack's bare 
> existence suffice for the implementation of a universe?

The problem with this example is that you can't create the stacks without
laying them down first.  So there has definitely been an implementation
during the lay-down phase.  What you have to be asking is, in some sense,
is the implementation still going on?

This assumes a certain time-bound nature to the concept of implementation
which may not be valid.  You are assuming that the region of our universe
where the implementation occurs can be bounded in time, and asking if
the boundary only encloses the active lay-down phase, or also encloses
the passive stack phase.

You get the same problems if you try to describe the exact physical
boundaries of the implementation in space.  Does the implementation
encompass the spaces between the coins, for example?  Assuming you also
need some small calculator to compute how to flip each coin (a simple
lookup table for the 512 possibilities of 9 coins in a square), is that
part of the implementation?  What about the space between the coins and
the calculator?  Or perhaps the coins themselves don't have well-defined
boundaries, etc.

These questions suggest that it is difficult to consider "whether
a particular implementation is going on" to be a yes-or-no question
that can be asked at each point-event in space-time.  So it may not be
meaningful to ask whether the stack is also an implementation.

Having said that, I'll give two contradictory answers:

> If not, then can you say what it is about the active process of 
> flipping or laying down that "counts" as computation but does not count 
> when the stack is a static block?

In the philosophical literature on implementation (a good jumping-off
point is David Chalmers paper at
http://www.u.arizona.edu/~chalmers/papers/rock.html) it is considered that
a mere "trace" of a program execution does not count as an implementation,
for two reasons: first, there are no causal connections between the
layers, they're just sitting there; and second, the trace does not
represent counterfactuals, i.e. if you were to change a cell's value,
what would happen is not clear from the trace.

> If you think the static block "counts" as the implementation of a 
> universe, then I think you can go all the way to abstract Platonism.  
> Because since the stack's just sitting there, why not knock it down?  
> Or melt it into a big ball?  Or throw it into a black hole...the two 
> SASes won't care (will they?)

On the other hand, if I apply what I have been calling the Wei Dai
heuristic (about which I wrote a few messages in the past few days; BTW
Wei suggested the idea but it's not necessarily something he advocates),
I'd say that the presence of the stack does increase the measure of
the simulated universe, because it increases the percentage of our
universe's resources which are used by the simulation.  More precisely,
its presence would allow a shorter program to locate the implementation
among all the vastness of our universe.

However, in that case, knocking down or destroying the stack would
eliminate this property; the stack would no longer contain the
information which would allow shortening the program which would localize
the implementation.

Hal Finney

Re: Is the universe computable?

[Stephen Paul King]

Dear CMR,

- Original Message - 
From: "CMR" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 5:19 PM
Subject: Re: Is the universe computable


> [SPK previous]
> > The fact that an Algorithm is "independent of any particular
> > implementation" is not reducible to the idea that Algorithms (or
Numbers,
> > or
> > White Rabbits, etc.) can exist without some "REAL" resources being used
in
> > their implementation (and maybe some kind of "thermodynamics").
> >
> [CMR]
> To paraphrase Bill, that depends on what the meaning of the word "real"
is.
>
[SPK]

Ok, how about: Reality is that which is "unimpeachable". ;-)

> [CMR]
> My point being that, if one accepts, even if only hypothetically (humor
me),
> that a (toy) universe can be modeled by a CA, then would not the
> self-consistent "physics" of the universe emerge from "following" the
rule?

[SPK]

Ok, I will bite. ;-)

> [CMR]
> Given this, then, would not the "resources" be mapped directly only to
those
> physics and not directly to ours, even though the CA is "implemented"
> according to and via our physics. What I'm getting at here is that
"weight"
> as a function of mass and gravitation may well have no direct
correspondence
> in the CA's physics. If not, then it could be argued that the computation
> within the context of it's own universe has no "weight" (i.e: consumes no
> EXTRA-universal resources) even though the implemention of same does.
>
> Then question then becomes, I suppose, if in fact our universe is a
digital
> one (if not strictly a CA) havng self-consistent emergent physics, then
> might it not follow that it is "implemented" (run?) via some
extra-universal
> physical processes that only indirectly correspond to ours?

[SPK]

Again, shifting the "resources problem" via a mapping to alternative
worlds is the logical equivalent of "sweeping the dirt under the rug". It
still exists!
This reminds me of how an ameoba (the twin of Bruno's) that lives in the
bottom drawer of my refrigerator has the belief that his universe (the
inside of the refrigerator) has a "thermodynamic arrow" that is
anti-parallel (goes in the opposite direction) to the one "outside" when
ever the light goes out...
BTW, have you ever read about the Maxwell Demon?

> [CMR]
> (if the above is too painfully obvious (or goofy?) and/or old news then,
> again, do humor me..)
>

[SPK]

It was a good try! ;-)

Stephen

Re: Is the universe computable

[Pete Carlton]

The following thought experiment might provoke some intuitions on this 
question..

Imagine a Life universe that contains, among other things, two SASes 
talking to each other (and showing each other pictures, and in general 
having a very lucid, conscious, conversation.)  Imagine that instead of 
being implemented on a computer, it's implemented by a large 2d array 
of coins:  heads represents "live", and tails represents "dead".  Each 
timestep, the coins are flipped over in concordance with the Life 
rules.
Does this setup implement a universe?
 If you say it does, how about the next step:
Instead of doing flipping operations on one set of coins, each new 
generation is laid down in the proper configuration on top of the 
preceding one with a new set of coins.  Does this >process< of laying 
down coins also implement a universe?
If you say it does, then what about the stack itself?  (One can imagine 
pointing to each layer in succession, saying "This is the current 
step", "Now this is the current step", etc..) Does the stack's bare 
existence suffice for the implementation of a universe?

If not, then can you say what it is about the active process of 
flipping or laying down that "counts" as computation but does not count 
when the stack is a static block?

If you think the static block "counts" as the implementation of a 
universe, then I think you can go all the way to abstract Platonism.  
Because since the stack's just sitting there, why not knock it down?  
Or melt it into a big ball?  Or throw it into a black hole...the two 
SASes won't care (will they?)

So I think the anti-Platonist must answer why exactly the coins need to 
be actively flipped or laid down to "really" implement a Life universe 
-- and by extension, why any universe needs to be "actively" 
implemented.

Then question then becomes, I suppose, if in fact our universe is a 
digital
one (if not strictly a CA) havng self-consistent emergent physics, then
might it not follow that it is "implemented" (run?) via some 
extra-universal
physical processes that only indirectly correspond to ours?

(if the above is too painfully obvious (or goofy?) and/or old news 
then,
again, do humor me..)

Re: Is the universe computable

[CMR]

> The fact that an Algorithm is "independent of any particular
> implementation" is not reducible to the idea that Algorithms (or Numbers,
or
> White Rabbits, etc.) can exist without some "REAL" resources being used in
> their implementation (and maybe some kind of "thermodynamics").
>

To paraphrase Bill, that depends on what the meaning of the word "real" is.

My point being that, if one accepts, even if only hypothetically (humor me),
that a (toy) universe can be modeled by a CA, then would not the
self-consistent "physics" of the universe emerge from "following" the rule?
Given this, then, would not the "resources" be mapped directly only to those
physics and not directly to ours, even though the CA is "implemented"
according to and via our physics. What I'm getting at here is that "weight"
as a function of mass and gravitation may well have no direct correspondence
in the CA's physics. If not, then it could be argued that the computation
within the context of it's own universe has no "weight" (i.e: consumes no
EXTRA-universal resources) even though the implemention of same does.

Then question then becomes, I suppose, if in fact our universe is a digital
one (if not strictly a CA) havng self-consistent emergent physics, then
might it not follow that it is "implemented" (run?) via some extra-universal
physical processes that only indirectly correspond to ours?

(if the above is too painfully obvious (or goofy?) and/or old news then,
again, do humor me..)

Re: Is the universe computable

[Stephen Paul King]

Dear Hal,

"A theorem doesn't weigh anything, and neither does a computation."

Nice try but that is a very smelly Red Herring. Even Conway's Life can
not exist, even in the abstract sense, without some association with the
possibility of "being implemented" and it is this "Implementation" that I am
asking about.

Let us consider Bruno's beloved "Arithmetic Realism". Are we to believe
that Arithmetic can be considered to "exist" without, even tacitly, assuming
the possibility that numbers must be "symbolic representable"? If they can
be, I strongly argue that we have merely found a very clever definition for
the term "meaninglessness".

I beg you to go directly to Turing's original paper discussing what has
become now know as a "Turing Machine". You will find discussions of things
like "tape" and "read/write head". Even if these, obviously physical,
entities are, as you say, "by definition within a universe" and that such
"universes" can be rigorously proven to be "mathematical entities", this
only strengthens my case: An abstract entity must have a possibility of
being physically represented, even if in a "Harry Potter Universe", to be a
meaningful entity. Otherwise what restrains us from endless Scholastic
polemics about "how many Angels can dance on the head of a Pin" and other
meaningless fantasies.

The fact that an Algorithm is "independent of any particular
implementation" is not reducible to the idea that Algorithms (or Numbers, or
White Rabbits, etc.) can exist without some "REAL" resources being used in
their implementation (and maybe some kind of "thermodynamics").

BTW, have you read Julian Barbour's The End of Time? It is my opinion
that Julian's argument falls flat on its face because he is making the very
same mistake: Assuming that his "best-matching" scheme can exists without
addressing the obvious status that it is an NP-Complete problem of
uncountable infinite size. It is simply logically impossible to say that the
mere postulation of a Platonia allows for the a priori existence of the
solution to such a computationally intractable problem.

Kindest regards,

Stephen



- Original Message - 
From: "Hal Finney" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 1:39 PM
Subject: Re: Is the universe computable


> At 13:19 19/01/04 -0500, Stephen Paul King wrote:
>
> >Where and when is the consideration of the "physical resources" required
> >for the computation going to obtain? Is my question equivalent to the old
> >"first cause" question?
>
> Anything "physical" is by definition within a universe (by my definition,
> anyway!).  What are the physical properties of a system in our universe?
> Mass, size, energy, electrical charge, partical composition, etc.  If we
> at least hypothetically allow for the existence of other universes,
> wouldn't you agree that they might have completely different physical
> properties?  That they might not have mass, or charge, or size; or that
> these properties would vary in some bizarre way much different from how
> stable they are in our universe.
>
> Consider Conway's 2-dimensional Cellular Automota universe called Life.
> Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing
> implementation of a computer, a Turing Machine, in this universe.
> I spent a couple of hours yesterday looking at this thing, seeing how
> the parts work.  He did an incredible job in putting all the details
> together to make this contraption work.
>
> So we can have computers in the Life universe.  Now consider this: what
> is the mass of this computer?  There is no such thing as mass in Life.
> There are cells, so you could count the number of "on" cells in the system
> (although that varies quite a bit as it runs).  There is a universal
> clock, so you could count the time it takes to run.  Some of our familiar
> properties exist, and others are absent.
>
> So in general, I don't think it makes sense to assume literally that
> computers require physical resources.  Considered as an abstraction,
> computation is no more physical than is mathematics or logic.  A theorem
> doesn't weigh anything, and neither does a computation.
>
> Hal Finney
>
>

Re: Is the universe computable

[Hal Finney]

At 13:19 19/01/04 -0500, Stephen Paul King wrote:

>Where and when is the consideration of the "physical resources" required
>for the computation going to obtain? Is my question equivalent to the old
>"first cause" question?

Anything "physical" is by definition within a universe (by my definition,
anyway!).  What are the physical properties of a system in our universe?
Mass, size, energy, electrical charge, partical composition, etc.  If we
at least hypothetically allow for the existence of other universes,
wouldn't you agree that they might have completely different physical
properties?  That they might not have mass, or charge, or size; or that
these properties would vary in some bizarre way much different from how
stable they are in our universe.

Consider Conway's 2-dimensional Cellular Automota universe called Life.
Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing
implementation of a computer, a Turing Machine, in this universe.
I spent a couple of hours yesterday looking at this thing, seeing how
the parts work.  He did an incredible job in putting all the details
together to make this contraption work.

So we can have computers in the Life universe.  Now consider this: what
is the mass of this computer?  There is no such thing as mass in Life.
There are cells, so you could count the number of "on" cells in the system
(although that varies quite a bit as it runs).  There is a universal
clock, so you could count the time it takes to run.  Some of our familiar
properties exist, and others are absent.

So in general, I don't think it makes sense to assume literally that
computers require physical resources.  Considered as an abstraction,
computation is no more physical than is mathematics or logic.  A theorem
doesn't weigh anything, and neither does a computation.

Hal Finney

Re: Determinism - Mind and Brain

[CMR]

> > This would appear to assume that self-awareness equates to being human
(as
> > in homo sapien?); I don't see that as the being the case. I certainly
> don't
> > believe the infinite time/memory device is required; maybe a Linux
Beowulf
> > cluster running on some g5s?
> [JM]: We did not settle the self-awareness puzzle. I believe thath HUMAN
> self-awareness is homo sapientist, as we know it (do we indeed?). I don't
> argue your Linux, just show me. In non-conditional terms. No 'maybe'.
> What I started out with was the mind > brain inequality. Brain as the
> bio-machine-component in the human complexity of a 'more'  (consider
> Aristotle's  -  Aris-Total).

Can't argue with that. Fortunately, "prove" was your word not mine. This
being a discussion list I was acting accordingly. (I tend towards a
Popperian view of "proof" in any case, and don't expend the energy) By the
way, are you by any chance from Missouri?

Obviously, I once again should have followed my own advice and stood pat a
couple of  posts back where I pointed to the futility of these circular
"head of a pin" debates (no, not pin-head debates). It's seems it's that old
"human 'consciousness' as a special case" vs same as pattern along a
continuum (with discrete underlying structure?). I just happen to view this
as a difference of degree, not of kind. I can't prove it; you can't
disprove; there it is. So, again, I'll let things take their own course and
if in some universe a "me" survives long enough to behold the birth of our
inheritor (a good bet given sufficient # of possible worlds), and if that
universe also happens to be one where we co-exist, I'll get back to you. (If
I already have done so in that universe, and you already graciously
conceded, then apologies up front and kindly disregard this message..)

Till then
Cheers

Re: Determinism - Mind and Brain

[John M]

Let me interleave - although I don't like to continue an exchange beyond 3:
from the 4th arguments go astray and fall into 'in other words' rather than
saying sthg. I will use [JM]: insert lines.

- Original Message -
From: "CMR" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Monday, January 19, 2004 5:58 PM
Subject: Re: Determinism - Mind and Brain


> According to the dictionary of Philo of Mind Self awareness id synonymous
> with consciousness.
[JM]: a fine definition, others define it differently, eg during the series
of the
Consciousness Worldwide Symposia since 1991 in Tucson (yearly?) with
thousands of concerned professionals from all the world. They could not
agree so far. My take is rather 'abiotic' and consider it an "acknowledgment
of and response to information" (with some details on the details) which
leaves open
the way to 'conscious' particles as well.
Yet... this is a sidetrack (3rd response?) because I mentioned only a def.
of "mind":
>
> > > Would a artificial self-aware entity emerging from human technology
> > > represent "mind"?
> > (depends on YOUR definition of mind, of course) - but
> > self-aware? does that mean that if the program calls for some
> math-churning,
> > the computer will say "I rather play some Bach music now" and does so?
>
> I 'm not convinced that being conscious, it necessarily follows that you
are
> contrarian as well.
[JM]: to have a mind on one's own does not mean contrarian IMO, just having
ideas, (dis?)likes, emotional responses, putting logic aside sometimes,
dicisions
to refrain from the 'best' solution, etc. etc: a "human" behavior
(imperfect),
as contrasted to the machine-reliability. Politicians know that.
>
> But, one can imagine a "program" that monitors various inputs, external
and
> internal, that are reinforcing to varying degrees and prioritized via a
some
> "value"  hierarchy most likely pre-supplied by the "masters". Of course,
> where I'm going with this is "training the baby" and, of course, such
> projects are currently underway at various locations and with varying
> results(!). But it's early days. In any case, as I've alluded to in prior
> posts, something that could "spot the dot" (manage convince a sufficient
set
> humans of it's self-awreness: see below) may emerge unannounced from the
> collective tinkering underway. Only the Shadow knows.
[JM]: Ignorantia non est argumentum. To say: we don't know that, but it
proves... - is not very convincing, just as well as: There is a possibility
and I
base my argument on that, however not yet discovered/realized.
This is why I call "MY" MWI-BigBang-cosmological version a "narrative" and
just "tell it", don't argue it. I like it, because it fits my human logical
mind
(with all its non-machine illogicalities) and 'explains' some paradoxes
which
are left open in 'science'. So I don't take the "conditionals" at face
value.
Could be is fine, but only as that. We don't have those computers and I
think
you do not assign to "them" really every aspect/facet of the human "mind(!)"
not even in spe. If they 'will' realize, will they be sexy?
>
> > or would you assume in that (hard) AI to program EVERYTHING what a
> > human (callable normal or derailed) might react by? We are back to the
> > infinite time comp with unlimited memory.
> > My limited little 'mind' does not go that far.
> >
>
> This would appear to assume that self-awareness equates to being human (as
> in homo sapien?); I don't see that as the being the case. I certainly
don't
> believe the infinite time/memory device is required; maybe a Linux Beowulf
> cluster running on some g5s?
[JM]: We did not settle the self-awareness puzzle. I believe thath HUMAN
self-awareness is homo sapientist, as we know it (do we indeed?). I don't
argue your Linux, just show me. In non-conditional terms. No 'maybe'.
What I started out with was the mind > brain inequality. Brain as the
bio-machine-component in the human complexity of a 'more'  (consider
Aristotle's  -  Aris-Total).
>
> Ultimately, I believe I'm self aware (although, decidedly not
> self-actualized); I assume you are but can't prove it beyond doubt. For
that
> matter, given our mode of communication, you might indeed be a machine
and,
> in this case, just passing the Turing test. If you we here in person I
might
> sneak a red dot on your forehead (during a blink?), hold up a mirror and
> watch your reaction (apparently passes muster regarding self-awareness in
> our relatives). If some such procedure that meets at least that level of
> acceptable evidence suffices for a chimp, then it  should as well for an
AI,
> I should think.
>
> Cheers
> CMR
[JM]: thanks for your benevolence.
re-Cheers
John, the self-aware AI-chimp

Re: Is the universe computable

[Stephen Paul King]

Dear Bruno,

Interleaving.
- Original Message - 
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 5:55 AM
Subject: Re: Is the universe computable


> Dear Stephen,
>
> At 13:19 19/01/04 -0500, Stephen Paul King wrote:
> >Dear Hal, and Friends,
> >
> > Were and when is the consideration of the "physical resources"
required
> >for the computation going to obtain? Is my question equivalent to the old
> >"first cause" question?
>
>
> This is a good question for a physicalist. But if you accept the idea that
> the very notion of time, energy, space are secondary and "logically
emerges"
> as a modality in the average memory of an average universal machine, then
> that question is solved (once we get the right measure of course).

[SPK]

I do not accept that the "very notion of time, energy, space are
secondary" nor do I elevate "logicality" above physicality; I take them as
having the same ontological status, this follows from the proposed dualism
of Pratt that we have discussed previously. While we can argue coherently
that all of the content of experience is that which is simulated by our
"universal machine", we still must give some accounting for these. This is
why I asked the question.

> Now, about the measure, I am not convinced by Hal Finney's attempt
> to define or compute it for reason we have already discussed a lot,
> and which has just been recalled by George Levy in his last post.

[SPK]

Could it be that the sought after measure is only a meaningful notion
when given from "within" a world? For example, when we consider the "White
Rabbit" problem we are taking as a base line our mutal non-experience of
White Rabbits and other "Harry Potter-ish" phenomena. This argues along a
similar line as what we find in Tipler et al's "Anthropic principle", a way
of thinking going back to Descartes: What I experience here and now must be
given a probability of 1 since I can not question that it is being
experienced.
The skeptic would say: "But what if it is just an illusion or the
machinations of an "evil demon"?" (See the Bennaceraf, Lucas, Searle, etc.
debate...) In reply I would say: "Even if it is just an illusion, simulation
or whatever, the fact that it is experienced and not some thing else demands
that it be taken as probability one when we start considering "possible
worlds" and other modal ideas. You have to start somewhere and the most
obvious place is right where one is stating.


> I could add this: if you take the Universal Dovetailer (UD), you must take
into
> account the fact that he generates all version of all programs an infinite
> number of times. For computer science reasons it is not possible to cut
out
> the vast redundancy of the codes in the production of the UD.
> Now, this does not mean that some other reasons could not be invoked
> for justifying the importance of "little" programs, though.
>

[SPK]

UD, UTM, QComp or whatever, all of these depend existentially on some
kind of "physical resource", be it some portion of Platonia, infinite tape
and read/write head, Hilbert space or whatever; you can not even define your
precious AR without representing it somehow. It is this necessity of
representation that you seem to dismiss so easily.

Again: When will a consideration of "physical resources" obtain?

Kindest regards,

Stephen

> Regards,
>
> Bruno
>
>
> >Stephen
> >
> >- Original Message -
> >From: "Hal Finney" <[EMAIL PROTECTED]>
> >To: <[EMAIL PROTECTED]>
> >Sent: Monday, January 19, 2004 12:23 PM
> >Subject: RE: Is the universe computable
> >
> >
> > > Kory Heath wrote:
> > > > At 1/18/04, Hal Finney wrote:
> > > > >Now consider all possible program tapes being run at the same time,
> > > > >perhaps on an infinite ensemble of (virtual? abstract?) machines.
> > > > >Of those, a fraction of 1 in 2^100 of those tapes will start with
that
> > > > >100 bit sequence for the program in question.
> > > > [snip]
> > > > >Now consider another program that is larger, 120 bits.  By the same
> > > > >reasoning, 1 in 2^120 of all possible program tapes will start with
> >that
> > > > >particular 120-bit sequence.  And so 1/2^120 of all the executions
will
> > > > >be of that program.
> > > >
> > > > Yes, but if we're really talking about all possible finite bit
strings,
> > > > then the number of bit strings that begin with that 100 bit program
is
> > > > exactly the same as the number that begin with the 120 bit program -
> > > > countably infinite. You can put them into a 1 to 1 correspondence
with
> >each
> > > > other, just like you can put the integers into a 1 to 1
correspondence
> >with
> > > > the squares. The intuition that there must be more integers than
squares
> >is
> > > > simply incorrect, as Galileo pointed out long ago. So shouldn't your
two
> > > > programs have the exact same measure?
> > >
> > > Well, I'm not a mathematician either, so I can't say for sure.
> > > And actually it's wor

Re: Is the universe computable

[Bruno Marchal]

Dear Stephen,

At 13:19 19/01/04 -0500, Stephen Paul King wrote:
Dear Hal, and Friends,

Were and when is the consideration of the "physical resources" required
for the computation going to obtain? Is my question equivalent to the old
"first cause" question?


This is a good question for a physicalist. But if you accept the idea that
the very notion of time, energy, space are secondary and "logically emerges"
as a modality in the average memory of an average universal machine, then
that question is solved (once we get the right measure of course).
Now, about the measure, I am not convinced by Hal Finney's attempt
to define or compute it for reason we have already discussed a lot,
and which has just been recalled by George Levy in his last post.
I could add this: if you take the Universal Dovetailer (UD), you must take into
account the fact that he generates all version of all programs an infinite
number of times. For computer science reasons it is not possible to cut out
the vast redundancy of the codes in the production of the UD.
Now, this does not mean that some other reasons could not be invoked
for justifying the importance of "little" programs, though.
Regards,

Bruno


Stephen

- Original Message -
From: "Hal Finney" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Monday, January 19, 2004 12:23 PM
Subject: RE: Is the universe computable
> Kory Heath wrote:
> > At 1/18/04, Hal Finney wrote:
> > >Now consider all possible program tapes being run at the same time,
> > >perhaps on an infinite ensemble of (virtual? abstract?) machines.
> > >Of those, a fraction of 1 in 2^100 of those tapes will start with that
> > >100 bit sequence for the program in question.
> > [snip]
> > >Now consider another program that is larger, 120 bits.  By the same
> > >reasoning, 1 in 2^120 of all possible program tapes will start with
that
> > >particular 120-bit sequence.  And so 1/2^120 of all the executions will
> > >be of that program.
> >
> > Yes, but if we're really talking about all possible finite bit strings,
> > then the number of bit strings that begin with that 100 bit program is
> > exactly the same as the number that begin with the 120 bit program -
> > countably infinite. You can put them into a 1 to 1 correspondence with
each
> > other, just like you can put the integers into a 1 to 1 correspondence
with
> > the squares. The intuition that there must be more integers than squares
is
> > simply incorrect, as Galileo pointed out long ago. So shouldn't your two
> > programs have the exact same measure?
>
> Well, I'm not a mathematician either, so I can't say for sure.
> And actually it's worth than this, because I spoke of infinite program
> tapes, so the number of programs is uncountably infinite.
>
> However, here is an alternate formulation of my argument which seems to
> be roughly equivalent and which avoids this objection: create a random
> program tape by flipping a coin for each bit.  Now the probability that
> you created the first program above is 1/2^100, and for the second,
> 1/2^120, so the first program is 2^20 times more probable than the second.
>
> That seems correct, doesn't it?  And it provides a similar way to justify
> that the universe created by the first program has 2^20 times greater
> measure than the second.
>
> Hal Finney
>
>

Re: Are conscious beings always fallible?

[Bruno Marchal]

I agree with you. Actually you can use the second recursion theorem
of Kleene to collapse all the orders. This is easier in an untyped
programming language like (pure) LISP than in a typed language,
although some typed language have a primitive for handling untyped
self-reference, like the primitive SELF in Smalltalk ...
Bruno



At 23:29 19/01/04 -0800, Eric Hawthorne wrote:
How would they ever know that I wonder?
"Well let's see. I'm conscious and I'm not fallible. Therefore" ;-)
David Barrett-Lennard wrote:

I'm wondering whether the following demonstrates that a computer that can
only generate "thoughts" which are sentences derivable from some underlying
axioms (and therefore can only generate "true" thoughts) is unable to think.
This is based on the fact that a formal system can't understand sentences
written down within that formal system (forgive me if I've worded this
badly).
Somehow we would need to support free parameters within quoted expressions.
Eg to specify the rule
It is a good idea to simplify "x+0" to "x"

It is not clear that language reflection can be supported in a completely
general way.  If it can, does this eliminate the need for a meta-language?
How does this relate to the claim above?
- David

I  don't see the problem with representing logical meta-language, and 
meta-metalanguage... etc if necessary
in a computer. It's a bit tricky to get the semantics to work out 
correctly, I think, but there's nothing
"extra-computational" about doing higher-order theorem proving.

http://www.cl.cam.ac.uk/Research/HVG/HOL/

This is an example of an interactive (i.e. partly human-steered) 
higher-order thereom prover.
I think with enough work someone could get one of these kind of systems 
doing some useful higher-order
logic reasoning on its own, for certain kinds of problem domains anyway.

Eric

Re: Are conscious beings always fallible?

[Eric Hawthorne]

How would they ever know that I wonder?
"Well let's see. I'm conscious and I'm not fallible. Therefore" ;-)
David Barrett-Lennard wrote:

I'm wondering whether the following demonstrates that a computer that can
only generate "thoughts" which are sentences derivable from some 
underlying
axioms (and therefore can only generate "true" thoughts) is unable to 
think.

This is based on the fact that a formal system can't understand sentences
written down within that formal system (forgive me if I've worded this
badly).
Somehow we would need to support free parameters within quoted 
expressions.
Eg to specify the rule

It is a good idea to simplify "x+0" to "x"

It is not clear that language reflection can be supported in a completely
general way.  If it can, does this eliminate the need for a 
meta-language?
How does this relate to the claim above?

- David
 

I  don't see the problem with representing logical meta-language, and 
meta-metalanguage... etc if necessary
in a computer. It's a bit tricky to get the semantics to work out 
correctly, I think, but there's nothing
"extra-computational" about doing higher-order theorem proving.

http://www.cl.cam.ac.uk/Research/HVG/HOL/

This is an example of an interactive (i.e. partly human-steered) 
higher-order thereom prover.
I think with enough work someone could get one of these kind of systems 
doing some useful higher-order
logic reasoning on its own, for certain kinds of problem domains anyway.

Eric