Re: [issues] Re: Is the universe computable?
Dear Russell, Don Page explored a similar idea to mine in: quant-ph/9506010 Kindest regards, Stephen - Original Message - From: "Stephen Paul King" <[EMAIL PROTECTED]> To: "Russell Standish" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Sunday, February 22, 2004 11:45 PM Subject: [issues] Re: Is the universe computable? > Dear Russell, > > Let me add that I do not think that it is sufficient to embed space-time > in Hilbert space, we also need some way of explaining how space-time > phenomena acts on the Hilbert space's vectors. The infamous "back-action"... > I have an idea but it is pure vapor at this point ... > > > Kindest regards, > > Stephen > > - Original Message - > From: "Stephen Paul King" <[EMAIL PROTECTED]> > To: "Russell Standish" <[EMAIL PROTECTED]> > Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > Sent: Sunday, February 22, 2004 11:39 PM > Subject: Re: Is the universe computable? > > > > Dear Russel, > > > > Does this "quantum theorist " have anything published on this that i > can > > find online? I do need to do better than "can"! I need a "must"! ;-) > > > > Stephen > > > > - Original Message - > > From: "Russell Standish" <[EMAIL PROTECTED]> > > To: "Stephen Paul King" <[EMAIL PROTECTED]> > > Cc: "Russell Standish" <[EMAIL PROTECTED]>; > > <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > > Sent: Sunday, February 22, 2004 11:22 PM > > Subject: Re: Is the universe computable? > > > > On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote: > > > Dear Russel, > > > > > > The reference page is about the necessary resources for quantum > > > computation in general. The "result" that "our space-time structure can > > > emerge from a computation on a Hilbert space" is not complicated, we > just > > > prove that the class of all possible evolutions of QM systems includes > QM > > > computations. > > > Then we take Deutsch's work showing how classical systems can be > > > simulated by quantum computations and identify the subset(class) of > > > simulations with the subset(class) of our experiences of "our world" > and > > > figure out how to switch from a 3rd person to a 1st person > representation > > > (something like what Bruno Marchal proposes) . > > > > Ahh, that little word "can". I was taking your previous statement as > > stating something much more profound - that 4D space-time must emerge > > from a Hilbert space computation. Still - perhaps it is possible. I > > was at dinner a couple of weeks ago with a quantum theorist who > > claimed exactly that, starting from a standard QED formulation, and > > taking the h->0 limit. Alas, they tend not to teach QED at > > undergraduate level, so my ability to evaluate this claim is > > impoverished. > > > > > The hard part is taking the idea that Hilbert space is a > > representation > > > of something that has ontological reality - not just a mental construct. > > > > > > > Its not so hard. If we accept ensembles of descriptions as having the > > ultimate ontological reality (similar, if not equivalent, to Bruno's > > arithmetic realism), then Hilbert spaces emerge as the highest measure > > structure under fairly mild assumptions about the nature of > > consciousness. (detailed in my "Why Occam's Razor paper). > > > > > Kindest regards, > > > > > > > > > Stephen > > > > > > - Original Message - > > > From: "Russell Standish" <[EMAIL PROTECTED]> > > > To: "Stephen Paul King" <[EMAIL PROTECTED]> > > > Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > > > Sent: Sunday, February 22, 2004 6:04 PM > > > Subject: Re: Is the universe computable? > > > > > > On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: > > > > > > > > Again, that does not work because we can not take space-time (ala > > GR) > > > to > > > > be "big enough" to allow us to fit QM into it. On the other hand, it > has > > > > been shown that a QM system, considered as a quantum computational > > system, > > > > can simulate, with arbitrary accurasy, any classic
Re: Is the universe computable?
Dear Russell, Let me add that I do not think that it is sufficient to embed space-time in Hilbert space, we also need some way of explaining how space-time phenomena acts on the Hilbert space's vectors. The infamous "back-action"... I have an idea but it is pure vapor at this point ... Kindest regards, Stephen - Original Message - From: "Stephen Paul King" <[EMAIL PROTECTED]> To: "Russell Standish" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Sunday, February 22, 2004 11:39 PM Subject: Re: Is the universe computable? > Dear Russel, > > Does this "quantum theorist " have anything published on this that i can > find online? I do need to do better than "can"! I need a "must"! ;-) > > Stephen > > - Original Message - > From: "Russell Standish" <[EMAIL PROTECTED]> > To: "Stephen Paul King" <[EMAIL PROTECTED]> > Cc: "Russell Standish" <[EMAIL PROTECTED]>; > <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > Sent: Sunday, February 22, 2004 11:22 PM > Subject: Re: Is the universe computable? > > On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote: > > Dear Russel, > > > > The reference page is about the necessary resources for quantum > > computation in general. The "result" that "our space-time structure can > > emerge from a computation on a Hilbert space" is not complicated, we just > > prove that the class of all possible evolutions of QM systems includes QM > > computations. > > Then we take Deutsch's work showing how classical systems can be > > simulated by quantum computations and identify the subset(class) of > > simulations with the subset(class) of our experiences of "our world" and > > figure out how to switch from a 3rd person to a 1st person representation > > (something like what Bruno Marchal proposes) . > > Ahh, that little word "can". I was taking your previous statement as > stating something much more profound - that 4D space-time must emerge > from a Hilbert space computation. Still - perhaps it is possible. I > was at dinner a couple of weeks ago with a quantum theorist who > claimed exactly that, starting from a standard QED formulation, and > taking the h->0 limit. Alas, they tend not to teach QED at > undergraduate level, so my ability to evaluate this claim is > impoverished. > > > The hard part is taking the idea that Hilbert space is a > representation > > of something that has ontological reality - not just a mental construct. > > > > Its not so hard. If we accept ensembles of descriptions as having the > ultimate ontological reality (similar, if not equivalent, to Bruno's > arithmetic realism), then Hilbert spaces emerge as the highest measure > structure under fairly mild assumptions about the nature of > consciousness. (detailed in my "Why Occam's Razor paper). > > > Kindest regards, > > > > > > Stephen > > > > - Original Message - > > From: "Russell Standish" <[EMAIL PROTECTED]> > > To: "Stephen Paul King" <[EMAIL PROTECTED]> > > Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > > Sent: Sunday, February 22, 2004 6:04 PM > > Subject: Re: Is the universe computable? > > > > On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: > > > > > > Again, that does not work because we can not take space-time (ala > GR) > > to > > > be "big enough" to allow us to fit QM into it. On the other hand, it has > > > been shown that a QM system, considered as a quantum computational > system, > > > can simulate, with arbitrary accurasy, any classical system, given > > > sufficient "Hilbert space" dimensions - which play the role of "physical > > > resources" for QM systems. > > > > > > See: http://arxiv.org/abs/quant-ph/0204157 > > > > > > > > > > > > This leads me to the idea that maybe space-time itself is something > > that > > > is secondary. It and all of its contents (including our physical bodies) > > > might just be a simulation being generated in some sufficiently large > > > Hilbert space. This idea, of course, requires us to give Hilbert space > > (and > > > L^2 spaces in general?) the same ontological status that we usually only > > > confer to space-time. ;-) > > > > > > > > > > Interesting speculation. I'm not s
Re: Is the universe computable?
Dear Russel,
Does this "quantum theorist " have anything published on this that i can
find online? I do need to do better than "can"! I need a "must"! ;-)
Stephen
- Original Message -
From: "Russell Standish" <[EMAIL PROTECTED]>
To: "Stephen Paul King" <[EMAIL PROTECTED]>
Cc: "Russell Standish" <[EMAIL PROTECTED]>;
<[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Sunday, February 22, 2004 11:22 PM
Subject: Re: Is the universe computable?
On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote:
> Dear Russel,
>
> The reference page is about the necessary resources for quantum
> computation in general. The "result" that "our space-time structure can
> emerge from a computation on a Hilbert space" is not complicated, we just
> prove that the class of all possible evolutions of QM systems includes QM
> computations.
> Then we take Deutsch's work showing how classical systems can be
> simulated by quantum computations and identify the subset(class) of
> simulations with the subset(class) of our experiences of "our world" and
> figure out how to switch from a 3rd person to a 1st person representation
> (something like what Bruno Marchal proposes) .
Ahh, that little word "can". I was taking your previous statement as
stating something much more profound - that 4D space-time must emerge
from a Hilbert space computation. Still - perhaps it is possible. I
was at dinner a couple of weeks ago with a quantum theorist who
claimed exactly that, starting from a standard QED formulation, and
taking the h->0 limit. Alas, they tend not to teach QED at
undergraduate level, so my ability to evaluate this claim is
impoverished.
> The hard part is taking the idea that Hilbert space is a
representation
> of something that has ontological reality - not just a mental construct.
>
Its not so hard. If we accept ensembles of descriptions as having the
ultimate ontological reality (similar, if not equivalent, to Bruno's
arithmetic realism), then Hilbert spaces emerge as the highest measure
structure under fairly mild assumptions about the nature of
consciousness. (detailed in my "Why Occam's Razor paper).
> Kindest regards,
>
>
> Stephen
>
> - Original Message -----
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: "Stephen Paul King" <[EMAIL PROTECTED]>
> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
> Sent: Sunday, February 22, 2004 6:04 PM
> Subject: Re: Is the universe computable?
>
> On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote:
> >
> > Again, that does not work because we can not take space-time (ala
GR)
> to
> > be "big enough" to allow us to fit QM into it. On the other hand, it has
> > been shown that a QM system, considered as a quantum computational
system,
> > can simulate, with arbitrary accurasy, any classical system, given
> > sufficient "Hilbert space" dimensions - which play the role of "physical
> > resources" for QM systems.
> >
> > See: http://arxiv.org/abs/quant-ph/0204157
> >
> >
> >
> > This leads me to the idea that maybe space-time itself is something
> that
> > is secondary. It and all of its contents (including our physical bodies)
> > might just be a simulation being generated in some sufficiently large
> > Hilbert space. This idea, of course, requires us to give Hilbert space
> (and
> > L^2 spaces in general?) the same ontological status that we usually only
> > confer to space-time. ;-)
> >
> >
>
> Interesting speculation. I'm not sure that it follows from the ref you
> give above, however if indeed our space-time structure can emerge from
> a computation on a Hilbert space as you suggest, then this would be a
> powerful result. I have already shown (viz my Occam's Razor paper)
> that the Hilbert space stucture follows from Anthropic arguments on
> ensemble theories. Getting the space time structure is the next big
> task to be solved.
>
> Cheers
>
> --
--
> A/Prof Russell Standish Director
> High Performance Computing Support Unit, Phone 9385 6967, 8308 3119
(mobile)
> UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
> Australia[EMAIL PROTECTED]
> Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
> International prefix +612, Interstate prefix 02
> --
--
>
Re: Is the universe computable?
On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote:
> Dear Russel,
>
> The reference page is about the necessary resources for quantum
> computation in general. The "result" that "our space-time structure can
> emerge from a computation on a Hilbert space" is not complicated, we just
> prove that the class of all possible evolutions of QM systems includes QM
> computations.
> Then we take Deutsch's work showing how classical systems can be
> simulated by quantum computations and identify the subset(class) of
> simulations with the subset(class) of our experiences of "our world" and
> figure out how to switch from a 3rd person to a 1st person representation
> (something like what Bruno Marchal proposes) .
Ahh, that little word "can". I was taking your previous statement as
stating something much more profound - that 4D space-time must emerge
from a Hilbert space computation. Still - perhaps it is possible. I
was at dinner a couple of weeks ago with a quantum theorist who
claimed exactly that, starting from a standard QED formulation, and
taking the h->0 limit. Alas, they tend not to teach QED at
undergraduate level, so my ability to evaluate this claim is
impoverished.
> The hard part is taking the idea that Hilbert space is a representation
> of something that has ontological reality - not just a mental construct.
>
Its not so hard. If we accept ensembles of descriptions as having the
ultimate ontological reality (similar, if not equivalent, to Bruno's
arithmetic realism), then Hilbert spaces emerge as the highest measure
structure under fairly mild assumptions about the nature of
consciousness. (detailed in my "Why Occam's Razor paper).
> Kindest regards,
>
>
> Stephen
>
> - Original Message -
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: "Stephen Paul King" <[EMAIL PROTECTED]>
> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
> Sent: Sunday, February 22, 2004 6:04 PM
> Subject: Re: Is the universe computable?
>
> On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote:
> >
> > Again, that does not work because we can not take space-time (ala GR)
> to
> > be "big enough" to allow us to fit QM into it. On the other hand, it has
> > been shown that a QM system, considered as a quantum computational system,
> > can simulate, with arbitrary accurasy, any classical system, given
> > sufficient "Hilbert space" dimensions - which play the role of "physical
> > resources" for QM systems.
> >
> > See: http://arxiv.org/abs/quant-ph/0204157
> >
> >
> >
> > This leads me to the idea that maybe space-time itself is something
> that
> > is secondary. It and all of its contents (including our physical bodies)
> > might just be a simulation being generated in some sufficiently large
> > Hilbert space. This idea, of course, requires us to give Hilbert space
> (and
> > L^2 spaces in general?) the same ontological status that we usually only
> > confer to space-time. ;-)
> >
> >
>
> Interesting speculation. I'm not sure that it follows from the ref you
> give above, however if indeed our space-time structure can emerge from
> a computation on a Hilbert space as you suggest, then this would be a
> powerful result. I have already shown (viz my Occam's Razor paper)
> that the Hilbert space stucture follows from Anthropic arguments on
> ensemble theories. Getting the space time structure is the next big
> task to be solved.
>
> Cheers
>
>
> A/Prof Russell Standish Director
> High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
> UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
> Australia[EMAIL PROTECTED]
> Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
> International prefix +612, Interstate prefix 02
>
>
--
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
pgp0.pgp
Description: PGP signature
Re: Is the universe computable?
Dear Russel,
The reference page is about the necessary resources for quantum
computation in general. The "result" that "our space-time structure can
emerge from a computation on a Hilbert space" is not complicated, we just
prove that the class of all possible evolutions of QM systems includes QM
computations.
Then we take Deutsch's work showing how classical systems can be
simulated by quantum computations and identify the subset(class) of
simulations with the subset(class) of our experiences of "our world" and
figure out how to switch from a 3rd person to a 1st person representation
(something like what Bruno Marchal proposes) .
The hard part is taking the idea that Hilbert space is a representation
of something that has ontological reality - not just a mental construct.
Kindest regards,
Stephen
- Original Message -
From: "Russell Standish" <[EMAIL PROTECTED]>
To: "Stephen Paul King" <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Sunday, February 22, 2004 6:04 PM
Subject: Re: Is the universe computable?
On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote:
>
> Again, that does not work because we can not take space-time (ala GR)
to
> be "big enough" to allow us to fit QM into it. On the other hand, it has
> been shown that a QM system, considered as a quantum computational system,
> can simulate, with arbitrary accurasy, any classical system, given
> sufficient "Hilbert space" dimensions - which play the role of "physical
> resources" for QM systems.
>
> See: http://arxiv.org/abs/quant-ph/0204157
>
>
>
> This leads me to the idea that maybe space-time itself is something
that
> is secondary. It and all of its contents (including our physical bodies)
> might just be a simulation being generated in some sufficiently large
> Hilbert space. This idea, of course, requires us to give Hilbert space
(and
> L^2 spaces in general?) the same ontological status that we usually only
> confer to space-time. ;-)
>
>
Interesting speculation. I'm not sure that it follows from the ref you
give above, however if indeed our space-time structure can emerge from
a computation on a Hilbert space as you suggest, then this would be a
powerful result. I have already shown (viz my Occam's Razor paper)
that the Hilbert space stucture follows from Anthropic arguments on
ensemble theories. Getting the space time structure is the next big
task to be solved.
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
Re: Is the universe computable?
On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote:
>
> Again, that does not work because we can not take space-time (ala GR) to
> be "big enough" to allow us to fit QM into it. On the other hand, it has
> been shown that a QM system, considered as a quantum computational system,
> can simulate, with arbitrary accurasy, any classical system, given
> sufficient "Hilbert space" dimensions - which play the role of "physical
> resources" for QM systems.
>
> See: http://arxiv.org/abs/quant-ph/0204157
>
>
>
> This leads me to the idea that maybe space-time itself is something that
> is secondary. It and all of its contents (including our physical bodies)
> might just be a simulation being generated in some sufficiently large
> Hilbert space. This idea, of course, requires us to give Hilbert space (and
> L^2 spaces in general?) the same ontological status that we usually only
> confer to space-time. ;-)
>
>
Interesting speculation. I'm not sure that it follows from the ref you
give above, however if indeed our space-time structure can emerge from
a computation on a Hilbert space as you suggest, then this would be a
powerful result. I have already shown (viz my Occam's Razor paper)
that the Hilbert space stucture follows from Anthropic arguments on
ensemble theories. Getting the space time structure is the next big
task to be solved.
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia[EMAIL PROTECTED]
Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
pgp0.pgp
Description: PGP signature
Re: Is the universe computable
- Original Message - From: Bruno Marchal To: Stephen Paul King ; [EMAIL PROTECTED] ; [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Friday, January 30, 2004 6:48 AM Subject: Re: Is the universe computable Dear Stephen, [SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a support that was stronger than the one that you propose ...[BM] Where do I give a support to comp? I don't remember. No doubt that I am fascinated by its consequences, and that I appreciate the so deep modesty and silence of the Wise Machine.But the reason why I work on comp is just that it makes mathematical logic a tool to proceed some fundamental question I'm interested in. and that in addition to your 1 and 3-determinacy that there would be a way to shift from the Dovetailer view (the "from the outside" view) to the "inside" view such that some predictiveness would obtain when we are trying to predict, say the dynamics of some physical system. Otherwise, I claim, your theory is merely an excursion into computational Scholasticism.The whole point of my work consists to show (thanks to math) that comp is indeed popper falsifiable. It is just a matter of work and time to see if the logic of observable proposition which has been derived from comp gives a genuine quantum logic and ascribes the correct probability distribution to the verifiable facts.The weakness of the approach is that it leads to hard mathematical question. I am sanguine about QM's "weirdness"! I see it as implying that there is much more to "Existence" than what we can experience with our senses. ;-)I agree with you. Now comp shows much more easily that it *must* be so. You know Bohr saidthat someone pretending to understand QM really does not understand it. The same with comp, it can even be justified. If a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences until she realizes that indeed if (apology for this infinite sentence). [BM]> comp => 1) there is level of description of me such that I cannot be aware of functional digital > substitution made at that level. [SPK] Here we differ as I do not believe that "digital substitution" is possible, IF such is restricted to UTMs or equivalents.No consistent machine can really "believe" that indeed. But this does not mean a consistent machine will believe not-comp. The point is: are you willing to accept it for the sake of the reasoning. > 2) Church thesis [SPK] I have problems with Churches thesis because it, when taken to its logical conclusion, explicitly requires that all of the world to be enumerable and a priori specifiable. Peter Wegner, and others, have argued persuasively, at least for me, that this is simply is not the case.Church thesis entails that the partial (uncontrolable a priori) processes are mechanically enumerable.AND Church thesis entails that the total (controlable) processes are NOT mechanically enumerable.In each case we face either uncontrolability or non enumerability. It is Church thesis which reallyprotects comp from reductionnism. That was the subject of one thesis I propose in the seventies. Since then Judson Webb has written a deep book on that point. (Webb 1980, ref in my thesis, url below).See my everything-list posts "diagonalisation" for the proof of those facts. > 3) Arithmetical Realism)> makes the physical science eventually secondary with respect to number theory/computer science/machine > psychology/theology whatever we decide to call that fundamental field ... [SPK] I have no problem with AR, per say, but see it as insufficient, since it does not address the "act" of counting, it merely denotes the list of rules for doing so.Certainly not. AR is the doctrine that even in a case of absolute catastrophe killing all living form in the multiverse, the statement that there is no biggest prime will remain true. It has nothing to do with axioms and rules of formal system. Indeed by Godel's incompleteness theorem Arithmetical truth extends itself well beyond any set of theorem provable in any axiomatizable theory.Now, what do you mean by AR is insufficient? AR just say that arithmetical truth does not depend on us. It does not say that some other truth does not exist as well (although as a *conseque
Re: Is the universe computable
Dear Stephen, [SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a support that was stronger than the one that you propose ... [BM] Where do I give a support to comp? I don't remember. No doubt that I am fascinated by its consequences, and that I appreciate the so deep modesty and silence of the Wise Machine. But the reason why I work on comp is just that it makes mathematical logic a tool to proceed some fundamental question I'm interested in. and that in addition to your 1 and 3-determinacy that there would be a way to shift from the Dovetailer view (the "from the outside" view) to the "inside" view such that some predictiveness would obtain when we are trying to predict, say the dynamics of some physical system. Otherwise, I claim, your theory is merely an excursion into computational Scholasticism. The whole point of my work consists to show (thanks to math) that comp is indeed popper falsifiable. It is just a matter of work and time to see if the logic of observable proposition which has been derived from comp gives a genuine quantum logic and ascribes the correct probability distribution to the verifiable facts. The weakness of the approach is that it leads to hard mathematical question. I am sanguine about QM's "weirdness"! I see it as implying that there is much more to "Existence" than what we can experience with our senses. ;-) I agree with you. Now comp shows much more easily that it *must* be so. You know Bohr said that someone pretending to understand QM really does not understand it. The same with comp, it can even be justified. If a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences until she realizes that indeed if (apology for this infinite sentence). [BM] > comp = > 1) there is level of description of me such that I cannot be aware of functional digital substitution made at > that level. [SPK] Here we differ as I do not believe that "digital substitution" is possible, IF such is restricted to UTMs or equivalents. No consistent machine can really "believe" that indeed. But this does not mean a consistent machine will believe not-comp. The point is: are you willing to accept it for the sake of the reasoning. > 2) Church thesis [SPK] I have problems with Churches thesis because it, when taken to its logical conclusion, explicitly requires that all of the world to be enumerable and a priori specifiable. Peter Wegner, and others, have argued persuasively, at least for me, that this is simply is not the case. Church thesis entails that the partial (uncontrolable a priori) processes are mechanically enumerable. AND Church thesis entails that the total (controlable) processes are NOT mechanically enumerable. In each case we face either uncontrolability or non enumerability. It is Church thesis which really protects comp from reductionnism. That was the subject of one thesis I propose in the seventies. Since then Judson Webb has written a deep book on that point. (Webb 1980, ref in my thesis, url below). See my everything-list posts "diagonalisation" for the proof of those facts. > 3) Arithmetical Realism) > makes the physical science eventually secondary with respect to number theory/computer science/machine > psychology/theology whatever we decide to call that fundamental field ... [SPK] I have no problem with AR, per say, but see it as insufficient, since it does not address the "act" of counting, it merely denotes the list of rules for doing so. Certainly not. AR is the doctrine that even in a case of absolute catastrophe killing all living form in the multiverse, the statement that there is no biggest prime will remain true. It has nothing to do with axioms and rules of formal system. Indeed by Godel's incompleteness theorem Arithmetical truth extends itself well beyond any set of theorem provable in any axiomatizable theory. Now, what do you mean by AR is insufficient? AR just say that arithmetical truth does not depend on us. It does not say that some other truth does not exist as well (although as a *consequence* of comp plus occam they do indeed vanish). Don't confuse AR with "Pythagorean AR" which asserts explicitely "AR and no more". We got P.AR as a consequence of comp, but we do not postulate it in the comp hyp. I will go through your thesis step by step again and see if I can wrestle my prejudices down into some reasonableness. ;-) OK. Be sure to go to step n only if you manage to go to step n-1 before. Don't hesitate to ask question if something is unclear. Be sure you accept the hypotheses (if only for the sake of the argument). Best Regards, Bruno http://irid
Re: Is the universe computable
At 1/27/04, Hal Finney wrote: One way to approach an answer to the question is to ask, is there such a CA in which a universal computer can be constructed? That would be evidence for at least a major prerequisite for conscious observations. Do you have any examples like this? In my opinion, computation universality is the *only* prerequisite for the possibility of SASs, so I agree that the correct question to ask is "can a CA with bi-directional time be computation universal?" I think that the answer is almost certainly "yes". Let me explain why. First, lets get a really clear picture of what we're talking about. I want to consider a CA with only 2 spacial dimensions, because I find it easy to picture the resulting 3D block universe. (It's too hard for me to picture the 4D block universe that results from a 3+1D CA.) Lets imagine that the spacial planes of this CA are stacked on top of each other, so that the block universe looks like a tall tower, with the time dimension being the "up" and "down" directions. Now, the state of any particular cell of this block universe is determined by the 3x3 square of cells directly below it, as well as the 3x3 square of cells above it. For the rest of this discussion, lets refer to any particular chosen cell as the "center cell", and the 18 cells below and above it as the "neighborhood". For every possible combination of states of those 18 cells, the rules of the CA dictate what state the center cell must be in. Now, lets imagine that the cells in this particular CA have three possible states - lets call them "black" (empty), blue, and red. Lets set up the rules of the CA in the following way. First of all, lets consider a "center cell" whose neighborhood contains nothing but blue cells and empty cells. Lets define our CA rule so that, in such a case, the state of the center cell will either be blue or black, and this will be determined only by the 3x3 square of cells below it. In fact, lets go ahead and use Conway's life rule here. So, if the lower 9 cells are all blue and the upper 9 cells are any combination of blue and black, the center cell must be black. And so on. Now lets imagine the exact same thing for the red cells, except this time the state of the center cell is determined by the 9 cells *above* the center cell. For any 18-cell neighborhood that contains *only* red cells and black cells, the center cell will either be red or black, as determined by the upper 9 cells. Basically, what we have so far is a universe which contains blue "matter" which moves "forward" in time (i.e. upwards along the tower), and red "anti-matter" which moves backwards in time (downwards along the tower). Each kind of matter, in isolation, will follow the old familiar rules of Conway's life. If you were to "grow" an instance of the universe containing only red matter or only blue matter, it would be indistinguishable from Conway's life. And of course, we know that Conway's life is computation universal. So this universe is capable of containing SASs. Now, of course, we need to define what happens when matter and anti-matter interact. In other words, for every possible combination of 18 neighbors that contains both red and blue cells, we need to specify what the state of the center cell should be. It should be clear that there is a Vast number of possibilities here, each representing a unique universe. We can consider the simplest possible rule, which is that the center cell is always empty for any neighborhood which contains both red and blue cells. Perhaps under that rule, matter and anti-matter will tend to obliterate each other. I can imagine a whole range of other possible rules, some of which cause red and blue gliders to bounce off of each other, etc. Clearly we can imagine universes which contain large, isolated chunks of blue matter or red matter, and those portions of the universe would be capable of containing SASs. We can imagine stray red gliders occasionally wandering into realms of blue space, and vice-versa, causing subtle changes, but not necessarily destroying any of the SASs there. It seems to me that this is enough to show that it must be possible for CAs with bi-directional time to contain universal computation, and therefore, potentially, SASs. After saying all of this, I'm realizing that I don't really need to consider these bi-directional CAs to make the original points I was trying to make. I can just as easily consider a "normal" CA like Conway's life (or some other hypothetical CA that's more conducive to life). We can still do the trick of running through all the possible "block universes" of a given size, and discarding all of those that don't represent a valid evolution of the rule in question. If our universes are big enough, some of the remaining ones will contain patterns that look like SASs. Are these patterns really conscious? At what point in the testing process did they become cons
Re: Is the universe computable
Dear Bruno, Let me put to the most salient part of your reply: > My feeling Stephen is just that you don't like comp, and I have no problem with that. Some people takes my > work to be a beginning of refutation of comp, and perhaps they are right. I want just illustrate that this is not > obvious, and the tiny part of physics I have extracted from comp is for me just very weird (and no more so I > estimate we are still far from a real reductio ad absurde of comp). [SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a support that was stronger than the one that you propose and that in addition to your 1 and 3-determinacy that there would be a way to shift from the Dovetailer view (the "from the outside" view) to the "inside" view such that some predictiveness would obtain when we are trying to predict, say the dynamics of some physical system. Otherwise, I claim, your theory is merely an excursion into computational Scholasticism. > The weirdness is the many world like feature of any comp reality, the non computability of the physical > processes in any reality compatible with comp, and a sort of quantum logic weaker than usual quantum logic. Is > that so weird? Certainly no more weird than quantum weirdness. [SPK] I am sanguine about QM's "weirdness"! I see it as implying that there is much more to "Existence" than what we can experience with our senses. ;-) > If you are really interested in my reasoning, I would dare to insist going from step to step. If you prefer not > studying the consequences of comp because you don't have the taste for it, I will not insist at all. My point is > just that comp (that is > 1) there is level of description of me such that I cannot be aware of functional digital substitution made at > that level. [SPK] Here we differ as I do not believe that "digital substitution" is possible, IF such is restricted to UTMs or equivalents. > 2) Church thesis [SPK] I have problems with Churches thesis because it, when taken to its logical conclusion, explicitly requires that all of the world to be enumerable and a priori specifiable. Peter Wegner, and others, have argued persuasively, at least for me, that this is simply is not the case. > 3) Arithmetical Realism)> makes the physical science eventually secondary with respect to number theory/computer science/machine > psychology/theology whatever we decide to call that fundamental field ... [SPK] I have no problem with AR, per say, but see it as insufficient, since it does not address the "act" of counting, it merely denotes the list of rules for doing so. I will go through your thesis step by step again and see if I can wrestle my prejudices down into some reasonableness. ;-) Kindest regards, Stephen Bruno - Original Message - From: Bruno Marchal To: [EMAIL PROTECTED] ; [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Wednesday, January 28, 2004 9:27 AM Subject: Re: Is the universe computable At 11:57 27/01/04 -0500, Stephen Paul King wrote: Thank you for this post. It gives me a chance to reintroduce one problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis. You wrote: "... remembering the comp 1-indeterminacy, that is that if you are duplicateinto an exemplary at Sidney and another at Pekin, your actualexpectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the timechosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person))." Now my problem is that IF there is any aspect of perception and/or "observers" that involves a quantum mechanical state there will be the need to take the "no-cloning" theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation: http://arxiv.org/abs/quant-ph/0012121This is a question people ask me often. But not only the cloning theorem is not a problem with the comp hyp, but actually it is highly plausible the non-cloning theorem is a direct consequence of comp. Remember that, with comp, physicalities emerges from an average of an infinity of computationnal histories: it is a priori hard to imagine how we could clone that. This is no more amazing than the fact the white rabbit. remember that with comp, from inside things look a priori not computable. The apparant computability of the laws of physics is what
Re: Is the universe computable
At 11:57 27/01/04 -0500, Stephen Paul King wrote: Thank you for this post. It gives me a chance to reintroduce one problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis. You wrote: "... remembering the comp 1-indeterminacy, that is that if you are duplicate into an exemplary at Sidney and another at Pekin, your actual expectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the time chosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person))." Now my problem is that IF there is any aspect of perception and/or "observers" that involves a quantum mechanical state there will be the need to take the "no-cloning" theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation: http://arxiv.org/abs/quant-ph/0012121 This is a question people ask me often. But not only the cloning theorem is not a problem with the comp hyp, but actually it is highly plausible the non-cloning theorem is a direct consequence of comp. Remember that, with comp, physicalities emerges from an average of an infinity of computationnal histories: it is a priori hard to imagine how we could clone that. This is no more amazing than the fact the white rabbit. remember that with comp, from inside things look a priori not computable. The apparant computability of the laws of physics is what is in need to be explain with comp. We should perhaps come back when you have accept all the steps in uda step by step. As a possible way to exploit a potential loop hole in this, I point you to the following: http://www.fi.muni.cz/usr/buzek/mypapers/96pra1844.pdf My main question boils down to this: Does Comp 1-determinacy require this duplication to be exact? Is it sufficient that approximately similar copies could be generated and not exact duplicates? It must be exact if the duplication is done exactly at the right level of substitution (which exits by hypothesis), and can be approximate if some lower level of duplication is chosen instead. How would this affect your ideas about measures, if at all? I understand that you are trying to derive QM from Comp and thus might not see the applicability of my question, but as a reply to this I will again point your to the various papers that have been written showing that it is impossible to embed or describe completely a QM system (and its logics) using only a classical system (and its logics), if that QM system has more that two Hilbert space dimensions associated. Start with the Kochen-Specker theorem... http://plato.stanford.edu/entries/kochen-specker/ I'm afraid you make a confusion of level here. What KS showed is that you cannot put a boolean algebra of values to quantum observable pertaining to some systems. But this is exactly what comp predict for matter and time notion. That is why we get quantum logics for the first person verifiable proposition. Nowhere I pretend to recover a classical logic in which quantum measurement value can be embedded, quite the contrary with comp classical logic is plainly false for all verifiable 1-notion right at the beginning. BTW, even if KS was a threat, your argument does not follow because KS is a theorem in quantum mechanics, and as you say, I just show that the physics is derivable from comp; if KS is false in the physics derived from comp then KS would indeed be a problem, but I insist it is not. It is only the apparent computability of the universe which still remains the miracle. My feeling Stephen is just that you don't like comp, and I have no problem with that. Some people takes my work to be a beginning of refutation of comp, and perhaps they are right. I want just illustrate that this is not obvious, and the tiny part of physics I have extracted from comp is for me just very weird (and no more so I estimate we are still far from a real reductio ad absurde of comp). The weirdness is the many world like feature of any comp reality, the non computability of the physical processes in any reality compatible with comp, and a sort of quantum logic weaker than usual quantum logic. Is that so weird? Certainly no more weird than quantum weirdness. If you are really interested in my reasoning, I would dare to insist going from step to step. If you prefer not studying the consequences of comp because you don't have the taste for it, I will not insist at all. My point is just that comp (that is 1) there is level of description of me such that I cannot be aware of functional digital substitution made at that level. 2) Church thesis 3) Arithmetical Realism) makes the physical science eventually secondary with respect to number
Re: Is the universe computable
At 17:12 27/01/04 -0500, Stephen Paul King wrote: Dear Kory and Hal, Kory's idea strongly reminds me of the basic idea explored by John Cramer in his "Interactional" interpretation in that it takes into account both past and future states. Please see: http://www.lns.cornell.edu/spr/2000-03/msg0023110.html http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html One thing you might wish to bear in mind is that David Deutsch has pointed out that Cramer's idea is equivalent to the Many worlds interpretation, but I can not find the exact quote at this time. ;-) The main problem that I have with any CA based model is that it explicity requires some from of absolute synchronicity of the shift functions of the cells. I see this as a disallowance of CA based models to guide us into our questions about the appearence of a "flow of time", it assumes a form of Newton's "Absolute time" from the onset! Only if you think of a physical implementation of a CA, which is what people here try to avoid (I think). In addition, it has been pointed out be several CA experts that CAs are equivalent to universal Turing Machines and if UTMs are incapable of deriving QM and its phenomena then neither can CAs. Just to be clear (because your term "deriving" is a little ambiguous), but UTM can emulate (perfectly simulate) any quantum piece of matter including quantum computer (just dovetail on the superpositions). This entails an exponential slow down, but as we search to define time from inside this is not a problem. As I say in my other post, the real problem is the apparent computability of matter/physical processes. Newton physics would not have been falsified I would have pretend having find a refutation of comp, for comp makes reality much weirder than classical physics. bruno
Re: Is the universe computable
Dear Kory and Hal, Kory's idea strongly reminds me of the basic idea explored by John Cramer in his "Interactional" interpretation in that it takes into account both past and future states. Please see: http://www.lns.cornell.edu/spr/2000-03/msg0023110.html http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html One thing you might wish to bear in mind is that David Deutsch has pointed out that Cramer's idea is equivalent to the Many worlds interpretation, but I can not find the exact quote at this time. ;-) The main problem that I have with any CA based model is that it explicity requires some from of absolute synchronicity of the shift functions of the cells. I see this as a disallowance of CA based models to guide us into our questions about the appearence of a "flow of time", it assumes a form of Newton's "Absolute time" from the onset! In addition, it has been pointed out be several CA experts that CAs are equivalent to universal Turing Machines and if UTMs are incapable of deriving QM and its phenomena then neither can CAs. Kindest regards, Stephen - Original Message - From: "Hal Finney" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, January 27, 2004 1:33 PM Subject: Re: Is the universe computable > Kory Heath writes: > > Forget about our own (potentially non-computable) universe for a second. > > Surely you agree that we can imagine some large-but-finite 3+1D CA (it > > doesn't have to be anything like our own universe) in which the state of > > each bit is dependent on the states of neighboring bits one tick in the > > "future" as well as one tick in the "past". Surely you agree that we could > > search through all the possible 4D cube bit-strings, discarding those that > > don't follow our rule. (This would take a Vast amount of computation, but > > that's irrelevant to the particular questions I'm interested in.) Some of > > the 4D cubes that we're left with will (assuming we've chosen a good rule > > for our CA) contain patterns that look all the world like SASs, moving > > through their world, reacting to their environment, having a sense of > > passing time, etc. > > That is indeed a fascinating thought experiment, and I agree with > everything up to the last part. Are you sure that a CA whose state > depends on the future as well as the past can have self aware subsystems? > This seems different enough from our own physics that I'm not sure that we > can assume that it will work like that. I'm not saying it can't happen, > but I'm curious to see evidence that it can. > > Our own universe's microphysics appears to be basically reversible, and > I remember that Wolfram's book had some CAs, I think universal ones, > which could be expressed in reversible terms. A reversible CA is one > where the present state can be deduced either from the future or the > past. > > But I think you're talking about something stronger and stranger, where > you'd need to know both the future and the past in order to compute > the present. This puts your questions about "when" the consciousness > exists in a much sharper light. (I do have answers to those questions > which I have somewhat explained in recent postings.) > > One way to approach an answer to the question is to ask, is there such > a CA in which a universal computer can be constructed? That would be > evidence for at least a major prerequisite for conscious observations. > Do you have any examples like this? > > Hal Finney > >
Re: Is the universe computable
Kory Heath writes: > Forget about our own (potentially non-computable) universe for a second. > Surely you agree that we can imagine some large-but-finite 3+1D CA (it > doesn't have to be anything like our own universe) in which the state of > each bit is dependent on the states of neighboring bits one tick in the > "future" as well as one tick in the "past". Surely you agree that we could > search through all the possible 4D cube bit-strings, discarding those that > don't follow our rule. (This would take a Vast amount of computation, but > that's irrelevant to the particular questions I'm interested in.) Some of > the 4D cubes that we're left with will (assuming we've chosen a good rule > for our CA) contain patterns that look all the world like SASs, moving > through their world, reacting to their environment, having a sense of > passing time, etc. That is indeed a fascinating thought experiment, and I agree with everything up to the last part. Are you sure that a CA whose state depends on the future as well as the past can have self aware subsystems? This seems different enough from our own physics that I'm not sure that we can assume that it will work like that. I'm not saying it can't happen, but I'm curious to see evidence that it can. Our own universe's microphysics appears to be basically reversible, and I remember that Wolfram's book had some CAs, I think universal ones, which could be expressed in reversible terms. A reversible CA is one where the present state can be deduced either from the future or the past. But I think you're talking about something stronger and stranger, where you'd need to know both the future and the past in order to compute the present. This puts your questions about "when" the consciousness exists in a much sharper light. (I do have answers to those questions which I have somewhat explained in recent postings.) One way to approach an answer to the question is to ask, is there such a CA in which a universal computer can be constructed? That would be evidence for at least a major prerequisite for conscious observations. Do you have any examples like this? Hal Finney
Re: Is the universe computable
Dear Bruno, Thank you for this post. It gives me a chance to reintroduce one problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis. You wrote: "... remembering the comp 1-indeterminacy, that is that if you are duplicateinto an exemplary at Sidney and another at Pekin, your actualexpectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the timechosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person))." Now my problem is that IF there is any aspect of perception and/or "observers" that involves a quantum mechanical state there will be the need to take the "no-cloning" theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation: http://arxiv.org/abs/quant-ph/0012121 As a possible way to exploit a potential loop hole in this, I point you to the following: http://www.fi.muni.cz/usr/buzek/mypapers/96pra1844.pdf My main question boils down to this: Does Comp 1-determinacy require this duplication to be exact? Is it sufficient that approximately similar copies could be generated and not exact duplicates? How would this affect your ideas about measures, if at all? I understand that you are trying to derive QM from Comp and thus might not see the applicability of my question, but as a reply to this I will again point your to the various papers that have been written showing that it is impossible to embed or describe completely a QM system (and its logics) using only a classical system (and its logics), if that QM system has more that two Hilbert space dimensions associated. Start with the Kochen-Specker theorem... http://plato.stanford.edu/entries/kochen-specker/ I will address Kory's post latter. Kindest regards, Stephen - Original Message - From: Bruno Marchal To: [EMAIL PROTECTED] Sent: Tuesday, January 27, 2004 10:46 AM Subject: Re: Is the universe computable Hi Kory, Hi Stephen, Hi All, I understand Kory very well and believe he argues correctly in this post with respect to Stephen.But at the same time, I pretend that if we follow Kory's form of reasoning we are lead to expect a relation with (quantum) physics.This can seem a total miracle, ... but only for someone being both computationnalist and physicalist, and that has been showedimpossible (marchal 88, Maudlin 89, ref in my thesis).Let me try to explain shortly.The reason is that if the initial CA is universal enough the (and thatfollows for theoretical computer science) "universal CA" willdovetail on an infinite number of similar computations passing througheach possible SAS computational state, and then .. remembering the comp 1-indeterminacy, that is that if you are duplicateinto an exemplary at Sidney and another at Pekin, your actualexpectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the timechosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person)).So if we run an universal dovetailer (implemented in CA, or FORTRAN,or even just arithmetical truth), each SAS will have an indeterminate futurand his/her/its expectation (from his 1-person pov) will be given bya measure on all its computational continuation, runned, or even just defined,in the complete procession of the universal CA.Now, that measure on those computations must fit the SAS's physical law,if not the SAS will correctly infer that comp is false, which, we know,must be true (we runned the CA, for exemple).So the physical laws must result from a relative (conditional to a state S) measureon all computations continuing S. (and actually this looks like Feynman formulationof QM).OK, I was short, please look at (where UDA = Universal Dovetailer Argument)UDA step 1 http://www.escribe.com/science/theory/m2971.html UDA step 2-6 http://www.escribe.com/science/theory/m2978.html UDA step 7 8 http://www.escribe.com/science/theory/m2992.html UDA step 9 10 http://www.escribe.com/science/theory/m2998.html UDA last question http://www.escribe.com/science/theory/m3005.html Joel 1-2-3 http://www.escribe.com/science/theory/m3013.html Re: UDA... http://www.escribe.com/science/theory/m3019.html George'sigh http://www.escribe.com/science/theory/m3026.html Re:UDA... http://www.escribe.com/science/theory/m3035.html Joel's nagging question http://www.escribe.com/science/the
Re: Is the universe computable
Hi Kory, Hi Stephen, Hi All, At 01:19 27/01/04 -0500, Kory Heath wrote: At 1/26/04, Stephen Paul King wrote: The modern incarnation of this is the so-called 4D cube model of the universe. Again, these ideas only work for those who are willing to completely ignore the facts of computational complexity and the Heisenberg Uncertainty principle. I think you and I are living in two completely different argument-universes here. :) I'm not arguing that our universe is computable. I'm not arguing that our universe can definitely be modeled as a 4D cube. I'm not arguing that only integers exist. The only reason why I keep using CA models is that they're extraordinarily easy to picture and understand, *and*, since I believe that SASs can exist even in very simple computable universes like CAs, it makes sense to use CA models when trying to probe certain philosophical questions about SASs, physical existence, and instantiation. Quantum physics and the Heisenberg Uncertainty principle are simply irrelevant to the particular philosophical questions that I'm concerned with. Forget about our own (potentially non-computable) universe for a second. Surely you agree that we can imagine some large-but-finite 3+1D CA (it doesn't have to be anything like our own universe) in which the state of each bit is dependent on the states of neighboring bits one tick in the "future" as well as one tick in the "past". Surely you agree that we could search through all the possible 4D cube bit-strings, discarding those that don't follow our rule. (This would take a Vast amount of computation, but that's irrelevant to the particular questions I'm interested in.) Some of the 4D cubes that we're left with will (assuming we've chosen a good rule for our CA) contain patterns that look all the world like SASs, moving through their world, reacting to their environment, having a sense of passing time, etc. This simple thought experiment generates some fascinating philosophical questions. Are those SASs actually conscious? If so, at what point did they become conscious? Was it at the moment that our testing algorithm decided that that particular 4D block followed our specified CA rule? Or is it later, when we "animate" portions of the 4D block so that we can watch events unfold in "realtime"? These are not rhetorical questions - I'd really like to hear your answers, because it might help me get a handle on your position. (I'd like to hear other people's answers as well, because I think it's a fascinating problem.) Anyway, the point that I'm really trying to make is that, while these thought experiments have a lot of bearing on the question of mathematical existence vs. physical existence, they have nothing at all to do with quantum physics or Heisenberg uncertainty. The fact it seems so to you makes me think that we're not even talking about the same problem. -- Kory I understand Kory very well and believe he argues correctly in this post with respect to Stephen. But at the same time, I pretend that if we follow Kory's form of reasoning we are lead to expect a relation with (quantum) physics. This can seem a total miracle, ... but only for someone being both computationnalist and physicalist, and that has been showed impossible (marchal 88, Maudlin 89, ref in my thesis). Let me try to explain shortly. The reason is that if the initial CA is universal enough the (and that follows for theoretical computer science) "universal CA" will dovetail on an infinite number of similar computations passing through each possible SAS computational state, and then ... ... remembering the comp 1-indeterminacy, that is that if you are duplicate into an exemplary at Sidney and another at Pekin, your actual expectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the time chosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person)). So if we run an universal dovetailer (implemented in CA, or FORTRAN, or even just arithmetical truth), each SAS will have an indeterminate futur and his/her/its expectation (from his 1-person pov) will be given by a measure on all its computational continuation, runned, or even just defined, in the complete procession of the universal CA. Now, that measure on those computations must fit the SAS's physical law, if not the SAS will correctly infer that comp is false, which, we know, must be true (we runned the CA, for exemple). So the physical laws must result from a relative (conditional to a state S) measure on all computations continuing S. (and actually this looks like Feynman formulation of QM). OK, I was short, please look at (where UDA = Universal Dovetailer Argument) UDA step 1 http://www.escribe.com/science/theory/m2971.html UDA step 2-6 http://www.escribe.com/science/theory/m2978.html UDA step 7 8 http://www.escribe.com/science/theory/m2992.html UDA
Re: Is the universe computable
At 1/26/04, Stephen Paul King wrote: The modern incarnation of this is the so-called 4D cube model of the universe. Again, these ideas only work for those who are willing to completely ignore the facts of computational complexity and the Heisenberg Uncertainty principle. I think you and I are living in two completely different argument-universes here. :) I'm not arguing that our universe is computable. I'm not arguing that our universe can definitely be modeled as a 4D cube. I'm not arguing that only integers exist. The only reason why I keep using CA models is that they're extraordinarily easy to picture and understand, *and*, since I believe that SASs can exist even in very simple computable universes like CAs, it makes sense to use CA models when trying to probe certain philosophical questions about SASs, physical existence, and instantiation. Quantum physics and the Heisenberg Uncertainty principle are simply irrelevant to the particular philosophical questions that I'm concerned with. Forget about our own (potentially non-computable) universe for a second. Surely you agree that we can imagine some large-but-finite 3+1D CA (it doesn't have to be anything like our own universe) in which the state of each bit is dependent on the states of neighboring bits one tick in the "future" as well as one tick in the "past". Surely you agree that we could search through all the possible 4D cube bit-strings, discarding those that don't follow our rule. (This would take a Vast amount of computation, but that's irrelevant to the particular questions I'm interested in.) Some of the 4D cubes that we're left with will (assuming we've chosen a good rule for our CA) contain patterns that look all the world like SASs, moving through their world, reacting to their environment, having a sense of passing time, etc. This simple thought experiment generates some fascinating philosophical questions. Are those SASs actually conscious? If so, at what point did they become conscious? Was it at the moment that our testing algorithm decided that that particular 4D block followed our specified CA rule? Or is it later, when we "animate" portions of the 4D block so that we can watch events unfold in "realtime"? These are not rhetorical questions - I'd really like to hear your answers, because it might help me get a handle on your position. (I'd like to hear other people's answers as well, because I think it's a fascinating problem.) Anyway, the point that I'm really trying to make is that, while these thought experiments have a lot of bearing on the question of mathematical existence vs. physical existence, they have nothing at all to do with quantum physics or Heisenberg uncertainty. The fact it seems so to you makes me think that we're not even talking about the same problem. -- Kory
Re: Is the universe computable
> The problem is that there is a large class of physical systems that are > not "computable" by TMs, i.e., they are "intractable". Did you read the > Wolfram quote that I included in one of my posts? Please read the entire > article found here: > Another way of thinking of this is to concider the Laplacean notion > where given the specification of the "initial conditions" and/or "final > conditions" of the universe that all of the kinematics and dynamics of the > universe would be laid out. The modern incarnation of this is the so-called > 4D cube model of the universe. Again, these ideas only work for those who > are willing to completely ignore the facts of computational complexity and > the Heisenberg Uncertainty principle. > Stephen, Am I correct that you're essentially saying that our universe is algorithmically incompressible? If so I would agree and, interestingly, so does my friend Jim in a parallel thread I sparked from this very thread on the infophysics list a week or so back; thought I'd post it because he represents the "hard" info physical view on this subject much better than I could: From: "Jim Whitescarver" <[EMAIL PROTECTED]> Subject: Re: [InfoPhysics] Fw: Is the universe computable In so far as the universe is logical it can be modeled as a logical information system. The information nature of the quantum makes such a model convenient. It seems surprising how closely nature obeys logic granting validity to science. If we suppose that it is indeed logical and has no other constraints outside that logic, we then find it is an incompressible computation, that cannot be represented with fewer states. The universe is computably as it is a computer, but only a computer larger than the universe itself could model it. In this sense, the universe is not technically computable in practical terms. Intractability, however, is not exclusive of there existing good solutions. Unknowability is inherent in complex systems and we can capitalize on the the uniformity of the unknowable in the world of the known. Consider a pure entropy source, e.g. a stationary uncharged black hole. It effective eats all the information that falls in irretrievably randomizing it into the distant future. It is not that systems falling in stop behaving determistically, it is that we no longer care what their state is effectively randomized and outside our window of observation. Nothing in our world covaries with what happens inside the black hole but we know that there would be correlations due to the determinism that exists independently on the inside and the outside. I am not saying we can compute all of this. What happens at any point is the result of the entire universe acting at that point at this instant. Clearly this is not knowable. Causes are clearly not locally deterministic. But we can represent the black hole as a single integer, its mass in Plank action equivalents. From this all it's relevant properties to our perspective are known in spite of however complex it is internally. All participants, modeled as information systems, are entropy sources like black holes, but we get samplings of their internal state suggesting a finite state nature and deterministic behavior. The distinction is whether we can determine what that deterministic systems is or not. We cannot without communicating with all the participants and that is not always possible. But given a set of perspectives, there is no limit to how closely we can model them. Where no model works randomness may be substituted and often we will get good, if not perfect, results. Even legacy quantum mechanics, misguidedly based on randomness, yields deterministic results for quantum interactions shown accurate to many dozens of decimal places. This suggests that simple deterministic models will most likely be found. Jim
Re: Is the universe computable
Dear Kory, Interleaving below. - Original Message - From: "Kory Heath" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, January 26, 2004 2:54 AM Subject: Re: Is the universe computable > At 1/24/04, Stephen Paul King wrote: > > I should respond to Kory's ME == PE idea. In PE we find such things as > >"thermodynamic entropy" and "temporality". If we are to take Kory's idea > >(that Mathspace doesn't require resources) seriously, ME does not. This > >seems a direct contradiction! > > Perhaps Kory has a paper on-line that lays out his thesis of > >"Instantiationism". > > No, I wish had the energy to write such an online paper. :) Anyway, please > note that my own position is not "Instantiationism". This was the word I > used to describe the position that I *don't* accept - i.e., the idea that > computations need to somehow be physically instantiated in order for them > (or more importantly, the SASs within them) to be "real" or "conscious". If > I had to come up with a name for my position, I might call it "Mathematical > Physicalism". [SPK] I am not arguing for the necessity of physical instatiation, in the sense of a "prior". I am claiming that the notion of computation itself, however one wants to represent it, implicitly requires some form of implementation, even if such is merely "possible" if one is going to try to build a theoretical model of the world we experience, a world where we can not predict to arbitrary accurasy "what is going to happen next". The idea I have is that the computations that render our worlds of experience are implemented by the unitary evolution of quantum mechanical systems and that these computations are not reducible to Turing Machines. Notice that this idea involves a form of realism for quantum wavefunctions similar to that proposed by Bohm and others. > I have to confess that I'm not sure I'm following your argument. Are you > referring to the tension between the static view of Mathspace, in which > there is no concept of "resources" and computational structures exist "all > at once", and the dynamic, 1st-person view that we have as creatures, where > time exists and resources are limited? I'm willing to admit that there's > tension there, but it seems to me that the tension exists for the > Instantiationist as well as the Mathematical Physicalist. > [SPK] Yes, that "tension" is part of what I am trying to address. There is a similar situation involved in the "problem of Time". One solution has been proposed by Julian Barbour with his idea of a "time capsule". I hope that you get a chance to read his book "The End of Time" which discusses this idea. I have serious problems with Barbour's proposal and have found that it is the same problem that I trying to point out as existing in the various computalionalist theories. His "best matching" scheme involves the same kind of computational intractibility that disallows it to be taken as "preexisting". > All I can do is trundle out the same old thought experiments that we're all > familiar with. Imagine a 2D CA in which the state of each cell is > determined by the state of its neighbors one tick in the "future" as well > as one tick in the "past". Such CA cannot be computed "one tick of the > clock at a time" like a regular CA. Instead you'd have to consider the > whole structure as a 3D block of bits (one of the dimensions representing > time) and somehow "accrete" the patterns within it. Or you could do a > brute-force search through every possible block of bits, discarding all > those that don't follow the rules. Some of the universes that you're left > with may exhibit "thermodynamic entropy" and "temporality" - we can imagine > a particular block universe that contains patterns which represent > observers moving around, interacting with their environment, etc. - and yet > from our perspective the whole structure is entirely static. [SPK] Your 3D CA will only work IF and only IF the computational content is Turing Machine emulable and this requires that the TM is specifiable with integers (enumerable). This, to me, explains why Comp proponents only seen to want the Intergers to exist and will go to great and clever lengths to "explain" why only they are needed. The problem is that there is a large class of physical systems that are not "computable" by TMs, i.e., they are "intractable". Did you read the Wolfram quote that I included in one of my posts? Please read the entire ar
Re: Is the universe computable
At 1/24/04, Stephen Paul King wrote: I should respond to Kory's ME == PE idea. In PE we find such things as "thermodynamic entropy" and "temporality". If we are to take Kory's idea (that Mathspace doesn't require resources) seriously, ME does not. This seems a direct contradiction! Perhaps Kory has a paper on-line that lays out his thesis of "Instantiationism". No, I wish had the energy to write such an online paper. :) Anyway, please note that my own position is not "Instantiationism". This was the word I used to describe the position that I *don't* accept - i.e., the idea that computations need to somehow be physically instantiated in order for them (or more importantly, the SASs within them) to be "real" or "conscious". If I had to come up with a name for my position, I might call it "Mathematical Physicalism". I have to confess that I'm not sure I'm following your argument. Are you referring to the tension between the static view of Mathspace, in which there is no concept of "resources" and computational structures exist "all at once", and the dynamic, 1st-person view that we have as creatures, where time exists and resources are limited? I'm willing to admit that there's tension there, but it seems to me that the tension exists for the Instantiationist as well as the Mathematical Physicalist. All I can do is trundle out the same old thought experiments that we're all familiar with. Imagine a 2D CA in which the state of each cell is determined by the state of its neighbors one tick in the "future" as well as one tick in the "past". Such CA cannot be computed "one tick of the clock at a time" like a regular CA. Instead you'd have to consider the whole structure as a 3D block of bits (one of the dimensions representing time) and somehow "accrete" the patterns within it. Or you could do a brute-force search through every possible block of bits, discarding all those that don't follow the rules. Some of the universes that you're left with may exhibit "thermodynamic entropy" and "temporality" - we can imagine a particular block universe that contains patterns which represent observers moving around, interacting with their environment, etc. - and yet from our perspective the whole structure is entirely static. There certainly seems to be a kind of mystery when we think about "temporality" within this static structure. We can "follow along with our finger" and "watch" some creature - some pattern of bits in the block universe - struggling valiantly against some obstacle in its environment. Yet clearly our act of following along with our finger is not suddenly making that creature conscious. The computations have already been performed - the entire block universe has already been physically instantiated. All we're doing now is observing it, like looking at the frames of a film. So at what point in time was that creature actually conscious? Did it happen "all at once" when our computation "found" that block universe? These are deep and murky questions, and I don't see how the idea of "physical instantiation" makes them go away. Indeed, it's precisely these "block universe" scenarios that suggest that it *does* make sense to view our universe as existing "all at once" out there in Mathspace, even though I'm in here perceiving it in this temporal fashion. -- Kory
Re: Is the universe computable?
Dear Jesse,
- Original Message -
From: "Jesse Mazer" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, January 07, 2004 9:45 PM
Subject: RE: Is the universe computable?
> David Barrett-Lennard wrote:
> >
> >Georges Quenot wrote:
> >
> > > Also I feel some confusion between the questions "Is the universe
> > > computable ?" and "Is the universe actually 'being' computed ?".
> > > What links do the participants see between them ?
> >
> >An important tool in mathematics is the idea of an isomorphism between
> >two sets, which allows us to say *the* integers or *the* Mandelbrot set.
> >This allows us to say *the* computation, and the device (if any) on
> >which it is run is irrelevant to the existence of the computation. This
> >relates to the idea of the Platonic existence of mathematical objects.
> >
> >This makes the "confusion" between the above questions irrelevant.
> >
> >I think it was John Searle (who argues that computers can't be aware)
> >who said "A simulation of a hurricane is not a hurricane, therefore a
> >simulation of mind is not mind". His argument breaks down if
> >*everything* is a computation - because we can define an isomorphism
> >between a computation and the simulation of that computation.
> >
> >- David
>
> Isn't there a fundamental problem deciding what it means for a given
> simulated object to implement some other computation? Philosopher David
> Chalmers discusses the similar question of how to decide whether a given
> physical object is implementing a particular computation in his paper
"Does
> a Rock Implement Every Finite-State Automaton?", available here:
>
> http://www.u.arizona.edu/~chalmers/papers/rock.html
>
> --Jesse Mazer
I am VERY interested in this question because it is part of a hypothesis
that I am working on as a model of interactions within Prof. Hitoshi
Kitada's theory of Local Time.
In the Chalmer's paper that you reference we find:
begin quote
***
For a Putnam-style counterexample to be possible, every component state must
be sensitive to every previous component state. The most straightforward way
to do this is as follows: build an implementation in which state [a,b,c]
with input I transits into state [abcI,abcI,abcI] (where abcI is a
concatenation of a, b, c, and I). Now, we are assured that for every
resultant component state, there is a unique candidate for the preceding
state and input. Then we can construct the natural mapping from strings abcI
(in various positions) onto substates of the CSA, without fear of troubles
with recombination. A recombined state such as [a,b',c'] will transit into a
new state with unique component states in every position, each of which can
be mapped to the appropriate CSA substate.
But this sensitivity comes at a price. A system like this will suffer from
an enormous combinatorial explosion, getting three times bigger at every
time-step. If the strings that make up each component have length L at one
point, within 100 time-steps they will have length 3^{100}L, which is about
5.10^{47} times larger. In a very short time, the system will be larger than
the known universe! CSAs that are candidates to be bases for cognition will
have many more than three components, so the situation there will only be
worse. Here, the "implementing" system will reach the boundaries of the
universe in number of steps corresponding to a fraction of a second in the
life of a brain. So there is no chance that any realistic system could ever
qualify as an implementation in this manner.
***
end quote
It is this "combinatorial explosion" that I have been addressing in
terms of NP-Completeness and has proposed that we consider the possibility
that the necessary "computational power" is available to QM systems and not
to classical ("realistic") systems. As an example please read:
http://arxiv.org/abs/quant-ph/0304128
It has been pointed out by Feynman and Deutsch that classical systems
can be simulated with arbitrary precision by a quantum computation that has
"sufficient resources", and these "resources" are the Hilbert space
dimensions of the QM system that is doing (via its unitary evolution?) the
computing.
http://citeseer.nj.nec.com/gramss94speed.html
http://beige.ucs.indiana.edu/B679/
My conjecture is that the Unitary evolution of an arbitrary QM system is
equivalent to the computational behavior of an quantum computer.
One idea that I have proposed informally is that "an experienced object
is indistinguishable from the *best possible* simulation of the object".
The reasoning that I am using here follows a similar line as that w
Re: Is the universe computable
Dear John, If we grant your point that: > So while the natural numbers and the integers have a rich internal structure > (rich enough to contain the whole universe and more, according to most > subscribers on this list, I suspect), the reals can be encoded in the single > 'program' of tossing a coin. How do you distinguish the generation of the Reals from the "'program' of tossing a coin"? Are they one and the same? If so, I can go along with that, but what about "complex numbers"? The main problem that I have with your reasoning is that it seems to conflate objective existence (independent of implementation or representation) with representable existence, the latter being those that can be known by finite entities, such as us humans (or Machines pretending to be humans). Your reasoning also neglects the "meaningfulness" of the NP-Complete problem. Kindest regards, Stephen - Original Message - From: "John Collins" <[EMAIL PROTECTED]> To: "Stephen Paul King" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Thursday, January 22, 2004 6:02 AM Subject: Re: Is the universe computable > > - Original Message - > From: "Stephen Paul King" <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> > Sent: Wednesday, January 21, 2004 5:39 PM > Subject: Re: Is the universe computable > > SPK wrote: > > > You are confussing the postential existence > of a computation with its "meaningfulness". But in the last time you are > getting close to my thesis. We should not take the a priori existence of, > for example, answers to NP-Complete problems to have more "ontological > weight" than those that enter into what it takes for "creatures like us" to > "view" the answers. This is more the realm of theology than mathematics. ;-) > > > > ..This is rather like an argument I like to put forward when I'm feeling > outrageous, and one which I've eventually come to believe: That the real > number line 'does not exist.' There are only countably many numbers you > could give a finite description of, even with a universal computer (which > the human mathematical community probably constitutes, assuming we don't die > out), and in the end the rest of the real numbers result from randomly > choosing binary digits to be zero or one (see eg. anything by G. Chaitin). > So while the natural numbers and the integers have a rich internal structure > (rich enough to contain the whole universe and more, according to most > subscribers on this list, I suspect), the reals can be encoded in the single > 'program' of tossing a coin. By this I mean that the only 'use' or 'meaning' > you could extract from some part of the binary representation would be of > the form 'is this list of 0s and 1s the same as some pre-chosen lis of 0s > and 1s?', which just takes you back to the random number choosing program > you used to create the reals in the first place. > -- Chris Collins
Re: Is the universe computable
Dear Bruno, Interleaving. - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Friday, January 23, 2004 9:42 AM Subject: Re: Is the universe computable > Dear Stephen, > > At 12:39 21/01/04 -0500, Stephen Paul King wrote: > >Dear Bruno and Kory, > > > > Interleaving. > > > >- Original Message - > >From: "Bruno Marchal" <[EMAIL PROTECTED]> > >To: <[EMAIL PROTECTED]> > >Sent: Wednesday, January 21, 2004 9:21 AM > >Subject: Re: Is the universe computable > > > > > > > At 02:50 21/01/04 -0500, Kory Heath wrote: > > > >At 1/19/04, Stephen Paul King wrote: > > > > > 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? > > > >[KH] > > > >The view that Mathematical Existence == Physical Existence implies that > > > >"physical resources" is a secondary concept, and that the ultimate ground > > > >of any physical universe is Mathspace, which doesn't require resources of > > > >any kind. Clearly, you don't think the idea that ME == PE makes sense. > > > >That's understandable, but here's a brief sketch of why I think it makes > > > >more sense than the alternative view (which I'll call > > > > "Instantiationism"): > > > > > > [SPK] I should respond to Kory's ME == PE idea. In PE we find such things as "thermodynamic entropy" and "temporality". If we are to take Kory's idea (that Mathspace doesn't require resources) seriously, ME does not. This seems a direct contradiction! Perhaps Kory has a paper on-line that lays out his thesis of "Instantiationism". > >[SPK] > > > > Again, the mere postulation of existence is insufficient: it does not > >thing to inform us of how it is that it is even possible for us, as mere > >finite humans, to have experiences that "change". We have to address why it > >is that Time, even if it is ultimately an "illusion", and the distingtion > >between past and future is so intimately intetwined in our world of > >experience. > >[BM] > Good question. But you know I do address this question in my thesis > (see url below). I cannot give you too much technical details, but here is a > the main line. As you know, I showed that if we postulate the comp hyp > then time, space, energy and, in fact, all physicalities---including the > communicable (like 3-person results of experiments) as the uncommunicable > one (like qualie or results of 1-person experiment) appears as modalities > which are > variant of the Godelian self-referential provability predicates. As you know > Godel did succeed in defining "formal provability" in the language of a > consistent machine and many years later Solovay succeeds in formalising > all theorems of provability logic in a couple of modal logics G and G*. > G formalizes the provable (by the machine) statements about its own > provability ability; and G* extends G with all true statements about the > machine's ability (including those the machine cannot prove). [SPK] In my thinking all 1st person experiences are "best possible simulations". The problem I find is that we can not use the modern equivalent to Leibniz' "preordained harmony", whether in the form of a "universal prior" or "modelization" of some modal logic, since the "list" of all possible interactions is not enumerable. This is the aspect that I have tried to address by referencing Wolfram on the computational intractibility of some key aspects of "physicality". There is also the seperate issue of how does one aspect of a logic "address" some other? We have the example of a Turing Machine that considers a "tape" and a "head": there are separate in that one can "move" relative to the other all the while the transitions of the state of the head and the "spot" on the tape change. I do not see how some form of Monism can explain this. Additionally, there is the problem of "simulating" QM using formal logics. I have reference the Calude et al paper on this and you have said that it is good, but you seem to not have actually read it and let its implications "set in". ;-) > [BM] > Now, independently, temporal logicians
Re: Is the universe computable
Dear Stephen, At 12:39 21/01/04 -0500, Stephen Paul King wrote: Dear Bruno and Kory, Interleaving. - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, January 21, 2004 9:21 AM Subject: Re: Is the universe computable > At 02:50 21/01/04 -0500, Kory Heath wrote: > >At 1/19/04, Stephen Paul King wrote: > >> 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? > >[KH] > >The view that Mathematical Existence == Physical Existence implies that > >"physical resources" is a secondary concept, and that the ultimate ground > >of any physical universe is Mathspace, which doesn't require resources of > >any kind. Clearly, you don't think the idea that ME == PE makes sense. > >That's understandable, but here's a brief sketch of why I think it makes > >more sense than the alternative view (which I'll call "Instantiationism"): > > [SPK] Again, the mere postulation of existence is insufficient: it does not thing to inform us of how it is that it is even possible for us, as mere finite humans, to have experiences that "change". We have to address why it is that Time, even if it is ultimately an "illusion", and the distingtion between past and future is so intimately intetwined in our world of experience. Good question. But you know I do address this question in my thesis (see url below). I cannot give you too much technical details, but here is a the main line. As you know, I showed that if we postulate the comp hyp then time, space, energy and, in fact, all physicalities---including the communicable (like 3-person results of experiments) as the uncommunicable one (like qualie or results of 1-person experiment) appears as modalities which are variant of the Godelian self-referential provability predicates. As you know Godel did succeed in defining "formal provability" in the language of a consistent machine and many years later Solovay succeeds in formalising all theorems of provability logic in a couple of modal logics G and G*. G formalizes the provable (by the machine) statements about its own provability ability; and G* extends G with all true statements about the machine's ability (including those the machine cannot prove). Now, independently, temporal logicians have defined some modal systems capable of formalizing temporal statements. Also, Brouwer developed a logic of the conscious subject, which has given rise to a whole constructive philosophy of mathematics, which has been formalize by a logic known as "intuitionist logic", and later, like the temporal logic, the intuitionist logic has been captured formally by an modal extension of a classical modal logic. Actually it is Godel who has seen the first that Intuitionist logic can be formalised by the modal logic S4, and Grzegorczyk makes it more precise with the extended system S4Grz. And it happens that S4Grz is by itself a very nice logic of subjective, irreversible (anti-symmetric) time, and this gives a nice account too of the relationship Brouwer described between time and consciousness. Now, if you remember, I use the thaetetus trick of defining (machine) "knowledge of p" by "provability of p and p". Independently Boolos, Goldblatt, but also Kusnetsov and Muravitski in Russia, showed that the formalization of that form of knowledge (i.e. "provability of p and p") gives exactly the system of S4Grz. That's the way subjective time arises in the discourse of the self-referentially correct machine. Physical discourses come from the modal variant of provability given by "provable p and consistent p" (where consistent p = not provable p): this is justified by the thought experiment and this gives the arithmetical quantum logics which capture the "probability one" for the probability measure on the computational histories as seen by the average consistent machine. Physical time is then captured by "provable p and consistant p and p". Obviously people could think that for a consistent machine the three modal variants, i.e: provable p provable p and p provable p and consistent p and p are equivalent. Well, they are half right, in the sense that for G*, they are indeed equivalent (they all prove the same p), but G, that is the self-referential machine cannot prove those equivalences, and that's explain why, from the point of view of the machine, they give rise to so different logics. To translate the comp hyp into the language of the machine, it is necessary to restrict p to the \Sigma_1 arithmetical sentences (that is those who are accessible by the Universal Dovet
RE: Is the universe computable
Yes, I agree that my definition (although well defined) doesn't have a useful interpretation given your example of perfect squares interleaved with the non perfect-squares. - David > -Original Message- > From: Kory Heath [mailto:[EMAIL PROTECTED] > Sent: Wednesday, 21 January 2004 8:30 PM > To: [EMAIL PROTECTED] > Subject: RE: Is the universe computable > > At 1/21/04, David Barrett-Lennard wrote: > >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). > > We can say with precision that a certain sequence of rational numbers > (generated by looking at larger and larger finite sets of integers from 0 > - > n) converges to 0.5. What we can't say with precision is that this result > means that "the probability that a given integer is even is 0.5". I don't > think it's even coherent to talk about "the probability of a given > integer". What could that mean? "Pick a random integer between 0 and > infinity"? As Jesse recently pointed out, it's not clear that this idea is > even coherent. > > >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. > > Once again, I fully agree that, given the natural ordering of the > integers, > the perfect squares become ever more sparse. What isn't clear to me is > that > this sparseness has any affect on "the probability that a given integer is > a perfect square". Your conclusion implies: "Pick a random integer between > 0 and infinity. The probability that it's a perfect square is zero." That > seems flatly paradoxical to me. If the probability of choosing "25" is > zero, then surely the probability of choosing "24", or any other specified > integer, is also zero. A more intuitive answer would be that the > probability of choosing any pre-specified integer is "infinitesimal" (also > a notoriously knotty concept), but that's not the result your method is > providing. Your method is saying that the chances of choosing *any* > perfect > square is exactly zero. Maybe there are other possible diagnoses for this > problem, but my diagnosis is that there's something wrong with the idea of > picking a random integer from the set of all possible integers. > > Here's another angle on it. Consider the following sequence of integers: > > 0, 1, 2, 4, 3, 9, 5, 16, 6, 25 ... > > Here we have the perfect squares interleaved with the non perfect-squares. > In the limit, this represents the exact same set of integers that we've > been talking about all along - every integer appears once and only once in > this sequence. Yet, following your logic, we can prove that the > probability > that a given integer from this set is a perfect square is 0.5. Can't we? > > -- Kory
Re: Is the universe computable
- Original Message - From: "Stephen Paul King" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Wednesday, January 21, 2004 5:39 PM Subject: Re: Is the universe computable SPK wrote: > You are confussing the postential existence of a computation with its "meaningfulness". But in the last time you are getting close to my thesis. We should not take the a priori existence of, for example, answers to NP-Complete problems to have more "ontological weight" than those that enter into what it takes for "creatures like us" to "view" the answers. This is more the realm of theology than mathematics. ;-) > ..This is rather like an argument I like to put forward when I'm feeling outrageous, and one which I've eventually come to believe: That the real number line 'does not exist.' There are only countably many numbers you could give a finite description of, even with a universal computer (which the human mathematical community probably constitutes, assuming we don't die out), and in the end the rest of the real numbers result from randomly choosing binary digits to be zero or one (see eg. anything by G. Chaitin). So while the natural numbers and the integers have a rich internal structure (rich enough to contain the whole universe and more, according to most subscribers on this list, I suspect), the reals can be encoded in the single 'program' of tossing a coin. By this I mean that the only 'use' or 'meaning' you could extract from some part of the binary representation would be of the form 'is this list of 0s and 1s the same as some pre-chosen lis of 0s and 1s?', which just takes you back to the random number choosing program you used to create the reals in the first place. -- Chris Collins --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.561 / Virus Database: 353 - Release Date: 1/13/04
Re: Is the universe computable
On Wed, Jan 21, 2004 at 09:34:50AM -0800, CMR wrote: > I'm familiar with the concept of a metalayer in software dev as a > compatibility interface between apps etc.. So, in this case the > "meta-layer" being I assume the "interface" between the universes abstractly > and between the simulation and the platform concretely, or is it referring > to the computational device itself that the simulation is running on (per > your bit "storage" reference below)? The latter. Just ab abstraction of the physical layer embedding the simulation. > The "visible" universe meaning ours(?) I assume, and the the bit storage Yes. > accounting for our 4th Dimensional progression? That depends whether we're an object, or a process in the metalayer. > matrioshka = nested I assume as in the dolls; I interpret this to mean that Yes, e.g. us implementing a virtual universe large enough to include observers. The limitations of the host substrate (relativistic universe of limited duration, constraints of computational physics --> upper limit to the bits and number of operations on these bits). > "selection" would favor a universal resource economy of high efficiency and > so the "cost" of simulating a universe of at least our's complexity would be > deleterious to the "survival" of the "host" universe and thus lower it's > relative fitness? Or am I full of it here? No, this is not selection of universes, just motivations of systems occupying an universe. Matter and energy is a scarce commodity in the current universe, so assuming an universe we're currently observing is not doesn't require trivial resources to run there's a negative pressure on the motivations to run it. -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable
Dear Bruno and Kory, Interleaving. - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, January 21, 2004 9:21 AM Subject: Re: Is the universe computable > At 02:50 21/01/04 -0500, Kory Heath wrote: > >At 1/19/04, Stephen Paul King wrote: > >> 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? > >[KH] > >The view that Mathematical Existence == Physical Existence implies that > >"physical resources" is a secondary concept, and that the ultimate ground > >of any physical universe is Mathspace, which doesn't require resources of > >any kind. Clearly, you don't think the idea that ME == PE makes sense. > >That's understandable, but here's a brief sketch of why I think it makes > >more sense than the alternative view (which I'll call "Instantiationism"): > > [SPK] Again, the mere postulation of existence is insufficient: it does not thing to inform us of how it is that it is even possible for us, as mere finite humans, to have experiences that "change". We have to address why it is that Time, even if it is ultimately an "illusion", and the distingtion between past and future is so intimately intetwined in our world of experience. How is it that we can think that it is reasonable to expect the physically impossible to become possible by just postulating that it be so? "There ain't no such thing as a free lunch!" - Robert Heinleim > >Here's my definition of "Computational Realism", which is sort of a > >restricted version of Mathematical Realism. (I'm not sure if my definition > >is equivalent to what others call "Arithmetic Realism", so I'm using a > >different term.) > > [BM] > OK. Just to cut the hair a little bit: with Church thesis "computational > realism" is equivalent to > a restricted form of arithmetical realism. Comp. realism is equivalent to > Arith. realism restricted > to the Sigma_1 sentences, i.e. those sentence which are provably equivalent > (in Peano arithmetic, say) to sentences of the form "it exists x such that > p(x)" with p(x) a decidable (recursive) predicate. > This is equivalent to say that either a machine (on any argument) will stop > or will not stop, and this > independently of any actual running. Indeed, sometimes I say that > (Sigma_1) arithmetical realism > is equivalent to the belief in the excluded middle principe (that is "A or > not A) applied to > (Sigma_1) arithmetical sentences. (Sigma_1 sentences plays a prominant role > in the derivation > of the logic of the physical propositions from the logic of the > self-referential propositions). Actually > the Universal Dovetailing is arithmetically equivalent with an enumeration > of all true Sigma_1 sentences. The key feature of those sentences is that > their truth entails their provability (unlike > arbitrary sentences which can be true and not provable (by Peano > arithmetic, for exemple). > [SPK] Bruno, I do not understand why you use so weak a support for your very clever theory! If we are to take the collection of a "true Sigma_1 sentenses" to have "independent of implementation" existence, why not all of the endless hierarchy of Cantor's Cardinals? I have never understood this Kroneckerian attitute. > > [KH] > >Let's say that you're about to physically implement some computation, and > >lets say that there are only three possible things that this computation > >can do: return 0, return 1, or never halt. Computational Realism is simply > >the belief that *there is a fact of the matter* about what this > >computation will do when you implement it, and that this fact is true > >*right now*, before you even begin the implementation. Furthermore, CR is > >the belief that there is fact of the matter about what the result of the > >computation *would be*, even if it's never actually implemented. CR > >implies that there is such a fact of the matter about every conceivable > >computation. [SPK] That seems to me to be equivalent to postulating the existence of a List of all possible algorithms and claiming that the postulation is sufficient to prove that the output of an arbitrary computation *exists*. This reminds me of the joke about Money growing on trees: We would still have to pay people to do the "picking". My point is that while it ok to assume that "what the result of the computation *would be*, even if it's
Re: Is the universe computable
Greetings Eugen >While it is not possible to infer physics of the metalayer, it is possible to >infer the number of bits necessary to encode this universe. I'm familiar with the concept of a metalayer in software dev as a compatibility interface between apps etc.. So, in this case the "meta-layer" being I assume the "interface" between the universes abstractly and between the simulation and the platform concretely, or is it referring to the computational device itself that the simulation is running on (per your bit "storage" reference below)? >Give the visible universe's timespace complexity (assuming, it's not just >an elaborate fake rendered for a few observers, which is synononymous to >postulating gods or a God), the metalayer needs to store an awful lot of >bits, and track them over an awful lot of iterations (or represent time >implicitly). The "visible" universe meaning ours(?) I assume, and the the bit storage accounting for our 4th Dimensional progression? >It is very, very big, judged by our standards of computational physics. Indeed >As such postulating matrioshka universes implies running very large >simulations is essentially free, this is not true in a darwinian context >(which applies for all places supporting imperfect replication and limited >amount of dimensions). matrioshka = nested I assume as in the dolls; I interpret this to mean that "selection" would favor a universal resource economy of high efficiency and so the "cost" of simulating a universe of at least our's complexity would be deleterious to the "survival" of the "host" universe and thus lower it's relative fitness? Or am I full of it here? Ever fearing the latter, CMR <-- insert gratuitous quotation that implies my profundity here -->
Re: Is the universe computable?
Dear CMR, Interleaving. - Original Message - From: "CMR" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, January 21, 2004 1:07 AM Subject: Re: Is the universe computable? > > > 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? > > > [CMR] > Assuming you mean R is countably infinite(?), then a solution would be a > finite universe of underlying discrete structure, ala Fredkin, I imagine. > [SPK] If Fredkin is proposing a Cellular Automata based model that would be the case, but CA based models have a problem of their own: how to show that the global synchrony of the shift function can obtain. It is puzzleling to me why it is hard to find a discussion of this in the literature. > >[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? > [CMR] > 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. [SPK] Maybe I am mistaken but does not QM enter into the very definition of a qubit? As the to idea of Bekenstein's bound, that is, IMHO, more of a problem than a solution and leads in the wrong direction. It has been shown (http://tph.tuwien.ac.at/~svozil/publ/embed.htm) that it is impossible to completely "embed" the logical equivalent of a QM system (with Hilbert space dimensions greater than 2) into the logical equivalent of a classical system. I take this to explicitly rule out considerations that space-time can be treated as just a Minkowskian (or, more generally, one would consider the Poincare' group) space and expect to be able to treat it as the background or "support" for the necessary machinery of a QM system. >[CMR] > 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. > [SPK] Again, that does not work because we can not take space-time (ala GR) to be "big enough" to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient "Hilbert space" dimensions - which play the role of "physical resources" for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Kindest regards, Stephen
Re: Is the universe computable
I think, Hal, you still used your "human" (anthropocentric) imagination when you wanted to show a 'free' thinking: cince they were missing from your 'eliminated' concepts: do you take space and time for granted in the 'universes' of different (physical?) principles? How about 'our' logic? causality (without time)? "WHEN" does such a universe exist (in our terms)? We have a hint to such "impossibilities": I call it 'idation', pure thought (since we have nothing to assign instead). We muster thought beyond the restrictions of space and time, dreams etc. surpass our physical system. Such ideas are not esoteric just unusual, especially in our physical natural science - brainwashed brains. When I speculated how to arrive at a Big Bang from a "plenitude" that has no info for us - including 'everything' (knowable and not), in some perfect invariant symmetry of an overall exchange, I found that the symmetry-brake may be a motor. Not spatial, not timely, the "total" infinite symmetry of the unlimited change, of unlimited identities which break just by the unlimitedness: it must lead to asymmetical elements as well in its infinity. So there we were at Big Bangs in unlimited qualities. One of them is ours, where an INSIDE 'system' of space-time evolved in causality and which, from the inside. played off the evolutional process of complexities, all the way to the final dissipation - back into the plenitude's infinite invariant symmetry. Other "universes" (I did not find a better word) may be completely different, based on the participant elements constituting the occurring fulgurations of occurring asymmetrical knots . In the timeless system all occur and dissipate (immediately? it has no sense) and may or may not have any impact on each other. I was careful NOT to imply on other such occurrences 'our' inside data about our system which we don't even know well ourselves. I don't believe we may have the imagination to dream up different ones. All (sci-fi, white rabbit, comp, etc.) are variations upon our universe. I try to be consequent in my "scientific agnosticism". Just FYI, I do not request acceptance. My 'narrative'. John Mikes - 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
At 02:50 21/01/04 -0500, Kory Heath wrote: At 1/19/04, Stephen Paul King wrote: 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? The view that Mathematical Existence == Physical Existence implies that "physical resources" is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call "Instantiationism"): Here's my definition of "Computational Realism", which is sort of a restricted version of Mathematical Realism. (I'm not sure if my definition is equivalent to what others call "Arithmetic Realism", so I'm using a different term.) OK. Just to cut the hair a little bit: with Church thesis "computational realism" is equivalent to a restricted form of arithmetical realism. Comp. realism is equivalent to Arith. realism restricted to the Sigma_1 sentences, i.e. those sentence which are provably equivalent (in Peano arithmetic, say) to sentences of the form "it exists x such that p(x)" with p(x) a decidable (recursive) predicate. This is equivalent to say that either a machine (on any argument) will stop or will not stop, and this independently of any actual running. Indeed, sometimes I say that (Sigma_1) arithmetical realism is equivalent to the belief in the excluded middle principe (that is "A or not A) applied to (Sigma_1) arithmetical sentences. (Sigma_1 sentences plays a prominant role in the derivation of the logic of the physical propositions from the logic of the self-referential propositions). Actually the Universal Dovetailing is arithmetically equivalent with an enumeration of all true Sigma_1 sentences. The key feature of those sentences is that their truth entails their provability (unlike arbitrary sentences which can be true and not provable (by Peano arithmetic, for exemple). Let's say that you're about to physically implement some computation, and lets say that there are only three possible things that this computation can do: return 0, return 1, or never halt. Computational Realism is simply the belief that *there is a fact of the matter* about what this computation will do when you implement it, and that this fact is true *right now*, before you even begin the implementation. Furthermore, CR is the belief that there is fact of the matter about what the result of the computation *would be*, even if it's never actually implemented. CR implies that there is such a fact of the matter about every conceivable computation. It's from this perspective that I can begin to explain why I feel that implementation is not a fundamental concept. In my view, implementing a computation is a way of "viewing" a structure that already exists in Mathspace (or Platonia, or whatever you want to call it). Implementation is clearly something that occurs within computational structures - for instance, we can imagine creatures in a cellular automata implementing computations on their computers, and they will have all the same concerns about "physical resources" that we do - computational complexity, NP-complete problems, etc. However, the entire infinite structure of their CA world exists *right now*, in Mathspace. If we consider the rules to their CA, and consider an initial state (even an infinite one - say, the digits of pi), then there is *a fact of the matter* about what the state of the infinite lattice would be in ten ticks of the clock - or ten thousand, or ten million. And the key point is that the existence of these facts doesn't require "resources" - there's really no concept of resources at all at that level. Every single fact about every single possible computation is simply a fact, right now. Every conceivable NP-complete problem has an answer, and it doesn't require any "computational resources" for these answers to exist. But of course, computational creatures like us require computational resources to "view" these answers. Since our resources are severely limited, we don't have access to most of the truths in Mathspace. I don't think that this form of realism automatically leads to the conclusion that ME == PE, but it certainly points in that direction. ME == PE becomes especially appealing when we consider the infinite regress problem that the alternative position generates. You ask if your question is equivalent to the old "first cause" question. I propose that it is exactly equivalent, and brings with it all of the attendant paradoxes and problems. If you believe that implementation is a fundamental concept - if you believe that, somehow, our universe must be "instantiated", or must have some other special quality that gives it its true reality - then y
RE: Is the universe computable
At 1/21/04, David Barrett-Lennard wrote: 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). We can say with precision that a certain sequence of rational numbers (generated by looking at larger and larger finite sets of integers from 0 - n) converges to 0.5. What we can't say with precision is that this result means that "the probability that a given integer is even is 0.5". I don't think it's even coherent to talk about "the probability of a given integer". What could that mean? "Pick a random integer between 0 and infinity"? As Jesse recently pointed out, it's not clear that this idea is even coherent. 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. Once again, I fully agree that, given the natural ordering of the integers, the perfect squares become ever more sparse. What isn't clear to me is that this sparseness has any affect on "the probability that a given integer is a perfect square". Your conclusion implies: "Pick a random integer between 0 and infinity. The probability that it's a perfect square is zero." That seems flatly paradoxical to me. If the probability of choosing "25" is zero, then surely the probability of choosing "24", or any other specified integer, is also zero. A more intuitive answer would be that the probability of choosing any pre-specified integer is "infinitesimal" (also a notoriously knotty concept), but that's not the result your method is providing. Your method is saying that the chances of choosing *any* perfect square is exactly zero. Maybe there are other possible diagnoses for this problem, but my diagnosis is that there's something wrong with the idea of picking a random integer from the set of all possible integers. Here's another angle on it. Consider the following sequence of integers: 0, 1, 2, 4, 3, 9, 5, 16, 6, 25 ... Here we have the perfect squares interleaved with the non perfect-squares. In the limit, this represents the exact same set of integers that we've been talking about all along - every integer appears once and only once in this sequence. Yet, following your logic, we can prove that the probability that a given integer from this set is a perfect square is 0.5. Can't we? -- Kory
Re: Is the universe computable
On Tue, Jan 20, 2004 at 10:33:57PM -0800, CMR wrote: > 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.. While it is not possible to infer physics of the metalayer, it is possible to infer the number of bits necessary to encode this universe. Give the visible universe's timespace complexity (assuming, it's not just an elaborate fake rendered for a few observers, which is synononymous to postulating gods or a God), the metalayer needs to store an awful lot of bits, and track them over an awful lot of iterations (or represent time implicitly). It is very, very big, judged by our standards of computational physics. As such postulating matrioshka universes implies running very large simulations is essentially free, this is not true in a darwinian context (which applies for all places supporting imperfect replication and limited amount of dimensions). > Reference time... -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable
At 1/19/04, Stephen Paul King wrote: 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? The view that Mathematical Existence == Physical Existence implies that "physical resources" is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call "Instantiationism"): Here's my definition of "Computational Realism", which is sort of a restricted version of Mathematical Realism. (I'm not sure if my definition is equivalent to what others call "Arithmetic Realism", so I'm using a different term.) Let's say that you're about to physically implement some computation, and lets say that there are only three possible things that this computation can do: return 0, return 1, or never halt. Computational Realism is simply the belief that *there is a fact of the matter* about what this computation will do when you implement it, and that this fact is true *right now*, before you even begin the implementation. Furthermore, CR is the belief that there is fact of the matter about what the result of the computation *would be*, even if it's never actually implemented. CR implies that there is such a fact of the matter about every conceivable computation. It's from this perspective that I can begin to explain why I feel that implementation is not a fundamental concept. In my view, implementing a computation is a way of "viewing" a structure that already exists in Mathspace (or Platonia, or whatever you want to call it). Implementation is clearly something that occurs within computational structures - for instance, we can imagine creatures in a cellular automata implementing computations on their computers, and they will have all the same concerns about "physical resources" that we do - computational complexity, NP-complete problems, etc. However, the entire infinite structure of their CA world exists *right now*, in Mathspace. If we consider the rules to their CA, and consider an initial state (even an infinite one - say, the digits of pi), then there is *a fact of the matter* about what the state of the infinite lattice would be in ten ticks of the clock - or ten thousand, or ten million. And the key point is that the existence of these facts doesn't require "resources" - there's really no concept of resources at all at that level. Every single fact about every single possible computation is simply a fact, right now. Every conceivable NP-complete problem has an answer, and it doesn't require any "computational resources" for these answers to exist. But of course, computational creatures like us require computational resources to "view" these answers. Since our resources are severely limited, we don't have access to most of the truths in Mathspace. I don't think that this form of realism automatically leads to the conclusion that ME == PE, but it certainly points in that direction. ME == PE becomes especially appealing when we consider the infinite regress problem that the alternative position generates. You ask if your question is equivalent to the old "first cause" question. I propose that it is exactly equivalent, and brings with it all of the attendant paradoxes and problems. If you believe that implementation is a fundamental concept - if you believe that, somehow, our universe must be "instantiated", or must have some other special quality that gives it its true reality - then you've got an infinite regress problem. Certainly, I can imagine that our universe is instantiated in some larger computation, but then that computation will have to be instantiated in something else to make *it* real... and where does it all end? Or is it turtles all the way down? Or does our universe simply have the elusive quality of "physical existence", while other mathematical structures lack it? In my opinion, the idea that ME == PE points to a solution to these problems. -- Kory
Re: Is the universe computable
> 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?
> 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
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, > >
RE: Is the universe computable
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: Is the universe computable
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
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
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
RE: Is the universe computable
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: Is the universe computable
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?
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
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
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?
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
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?
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
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
> 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
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
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
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
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). 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: Is the universe computable
I find it hard to believe that the measure of a
program/book/movie/experience is proportional to the number it is
executed/read/seen/lived, independently of everything else.
I have an alternative proposition:
Measure is a function of how accessible a particular
program/book/movie/experience is from a given observer moment.
More formally we can say that the measure of observer-moment B with
respect observer-moment A is the probability that observer moment B
occurs following observer moment A. Measure is simply a conditional
probability.
Thus, it is the probability of transition to the
program/book/movie that defines the measure. The actual number of
copies is meaningless.
This definition of measure has the advantage of conforming with
everyday experience. In addition, it is a relative quantity
because it requires the specification of an observer moment from which
the transition can be accomplished.
For example the measure of the book Digital Fortress is much
higher for someone who has read The Da Vinci Code than for
someone who hasn't, independently of how many copies of Digital
Fortress has actually been printed, or read and not understood, or
read and understood. (These books have the same author).
If one insists in using the context of program to define measure, than
one could define measure as the probability that program B be called as
a subroutine from another given program A, or more generally, from a
set of program A{}. The actual number of copies of the subroutine B is
meaningless. It is the number of calls to B from A{}that matters.
George Levy
Hal Finney wrote:
David Barrett-Lennard writes:
Why is it assumed that a multiple "runs" makes any difference to the
measure?
One reason I like this assumption is that it provides a natural reason
for simpler universes to have greater measure than more complex ones.
Imagine a Turing machine with an infinite program tape. But suppose the
actual program we are running is finite size, say 100 bits. The program
head will move back and forth over the tape but never go beyond the
first 100 bits.
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. And since the TM never
goes beyond those 100 bits, all such tapes will run the same program.
Therefore, 1/2^100 of all the executions of all possible program tapes
will be of that program.
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.
Therefore runs of the first program will be 2^20 times more numerous
than runs of the second.
Re: Is the universe computable
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? 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: 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: Is the universe computable?
Eugen Leitl : > > On Tue, Jan 13, 2004 at 05:30:10PM +0100, Georges Quenot wrote: > > > No. They actually came to me while I was figuring some other > > ways of simulating a universe than the sequential one that seemed > > to give rise to many problems to me. The second one is influenced > > What's your take on how subjective timeflow looks like in a HashLife > universe? > > http://www.ericweisstein.com/encyclopedias/life/HashLife.html I am quite puzzled by the idea that the way in which the computation is carried out has no effect at all on the way the simulated perception is subjectively perceived. Max Tegmark goes much farther than what you suggest above in his paper, considering that a simple set of axioms would/should suffice to produce the same subjective perceptions as would a "full development" of them. We have a kind of paradox here. We have no way to figure how the way in which the computation is carried can have any effect on the way the simulated perception is subjectively perceived but have we any pro or con argument to claim that it *actually* doesn't matter ? Georges Quénot.
Re: Is the universe computable?
At 15:05 16/01/04 +0100, Georges Quenot wrote: Possibly making you not better than them. But this not that simple. They do not disagree with dialog and argumentation. Rather they argue in different ways and/or with different premises. OK, so I perhaps did not understand you fully. I thought they did not even accept AR, or "2+2=4" for the sake of the argument. > >If they finally have to abandon these positions due to the amount > >of evidence in favor of it, the last line of defence for their > >conception of a personal God and for a significant role for Him > >could be at the level of artihmetical realism. Artihmetical > >realism by itself (not from a distinct personal God) is therefore > >seen as evil by them. As I mentionned, they usually do not put it > >that way. Rather they argue that such a view would prevent the > >foundation of human dignity and the like. > > They make probably the same confusion of those who believe > that determinism is in contradiction with free will. I would say that one of the concern they have behind this is the question of free will versus determinism (and/or randomness). You and others might see this as making "the same confusion of those who believe that determinism is in contradiction with free will". But there might also be more than one conception of free will and we could also consider that what they are doing is trying to defend another conception of free will that the one which is not in contradiction with determinism (and/or randomness). Look, I have no problem at all with any people open to defend they point, I am always prepared to make evolve my own position. But I really don't appreciate those who wants to impose any position (even mine). By its very nature free-will is hard to define and I quite believe there is as many conception of free-will than there are free-person. Though we may or may not share this conception, I don't think that we can dismiss it. The only thing we can say is that they cannot convince us of it or possibly even of its meaningfulness but in the same way we have no ground to prove them they are wrong. No problem as long as they don't use authoritative argument. Basically, they want to believe that we humans are not reducible to numbers and I think that such a reductibility cannot be proved either way. Er... No scientific proposition can *ever* be proved. Only refuted, or confirm. Except perhaps a tiny part of intuistionist mathematics. Also I understand that one could feel offended by the idea that he could be reduced to mere numbers (not more but not less he would feel offended by the idea it could be reduced to a set of interacting molecules) even if these ideas are considered as just hypotheses. They want to believe (and they want to be generally believed) that there is (much) more than this in human beings (and incidently in themselves). It is ok, in principle. It all depend on the way they will make us to believe their proposition. I am used to met people who are shocked by the idea of being a machine. I think those people ahave just a lack of trust in themselves. If I like myself and if I learn that I am a machine, then I will say "formidable, some machine can be nice like me". If I dislike myself, and I learn that I am a machine, then I will say "I knew I was just a stupid machine". Just to say that if someone has the faith (or some deep faith) he/she will not be afraid by *and* hypothesis. Those who are afraid by hypotheses are really afraid of the fragility of their own ideas or of their own faith. > Actually I tend to think that Godel's and other incompleteness > result makes comp a sort of vaccine against reductionist view of > self and reality (and arithmetic). This is not obvious to me. Maybe what "reductionist" actually means needs to be clarified. Sure. It is a very big thread by itself. > You know "reason" works only through doubt, and through the ability > to listen to different opinions. I tend to agree but it does not seem enough just to say it. I guess it is not enough. As I said it is linked to "trusting oneself". This trust is given, I think, by appropriate love and education from generation through generation. That is, a very long work. may be some shortcut exists, but there is probably no universal simple recipe. > Now with Godel we can say more, > which is that "good faith" never fears "reason" and rationality. > Sincere Faith can only extend Ratio, and is always open to dialog. It seems that there exists other conceptions of what "good faith" and/or "Sincere Faith" should be. Idem for "Ratio". Which one? Bruno
Re: Is the universe computable
At 17:36 16/01/04 +0100, Eugen Leitl wrote: On Fri, Jan 16, 2004 at 02:28:27PM +0100, Bruno Marchal wrote: > of brain and the like. I of course respect completely that opinion; but I > point on the fact > that once you make the computationnalist hypothesis then it is the reverse > which becomes > true: even if locally pi is a production of the human brain, globally the > laws of physics logically > develop on the set of all possible beliefs of all possible universal and > immaterial (mathematical) > machines embedded in all possible computations (computationnal histories). I respect that opinion, Actually it is more a theorem than an opinion. But I don't want to insist on this at this stage, I guess it would be premature. I'm just interested in theories which are instrumental in solving this universe's problems. You know, trivial stuff: wars, famines and death. A TOE which says: universe is information, every possible pattern exists, observers which can observe themselves will, is a bit sterile in that respect. That's my point: the comp hyp is popper falsifiable, because it put very strong constraint on any possible measure on the set of all computational histories (as seen from any possible sound first person). Unfortunately the notion of first person is hard to make precise without going into the modal logics. There's a little problem with some practical relevance I don't have an answer, though, which I'd like to have your opinion on. We have a finite system, iteratively evolving along a trajectory in state space. We have observers within that system, subjectively experiencing a flow of time. I have trouble alternating between the internal and the external observer view. So we have a machine crunching bits, sequentially falling from state to state. This spans a continous trajectory. We can make a full record of that trajectory, eliminating a time axis. When does the subjective observation of existence assemble into place? The first time the computation was made? The type of approach advocated in this list makes indeed possible to answer such a question. Of course I will ask you, if only for the sake of the argument, to accept that idea that all arithmetical true propositions are true in a atemporal way (and a-spatial way too btw). Now a computation can be described as a purely arithmetical object (to make this precise you need Church thesis aswell). Such computation are never run, they exist like the decimals of PI once and forall (by Arithmetical realism of course). The subjective observation as such will then also exists out of space and time, and will be felt as a time ordered, or as a space-time structured scenario only from the point of view of the observer which is related to that computation. If you want, from each instant an observer can think, that instant is now. In philosophy such a treatment of subjective time is called an indexical. This is counterintuitive because people (including many defender of comp) are used to believe in the following psycho-physical relation: (the sensation of pain/pleasure) at space-time point (x,t) is associated with the physical state of some device at space-time (x,t) But comp precludes this and forces instead: the sensation of (pain/pleasure at space-time point (x,t)) is associated with a (infinite set of equivalent) relative computational state(s). That is the space-time qualia is completely part of the sensation. I have trouble seeing my subjective observer experience as a sequence of frames, already computed. No problem. It is totally unbelievable. As it should be in case it is true. *that* can be proved. Such unbelievable but true proposition belongs to the family of undecidable but true arithmetical propositions. Is the first run magical, and the static record dead meat? I'm confused. The static record (here it is the set of all true arithmetical proposition) is similar to any "block universe" view in which time is internal. Note that this is the case for quantum cosmology where time disappears from the fundamental equation without precluding internal time to be defined. Remember the DeWitt Wheeler equation H = 0. With comp, space itself is "illusion", although that word is misleading in the sense that comp justify the solidity and stability of such illusion. Actually this has not yet be shown, but It has been shown how to translate that problem into a mathematical question. In case the math leads to not enough stability, that will give a falsification of comp. Let's bring a little dust into the run. Let's say we use a HashLife approach, which assembles the flow from lightcone hashes. Does this screw up the subjective experience? If yes, how? I don't think this will screw up the subjective experience. The illusion of time makes part of the relativeness of the computational states. What about computing a record of all possible trajectories? Is enumerating all possible states sufficient to create an obse
RE: Is the universe computable
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? I don't mean to sound so critical - I'm genuinely asking for information. I know virtually nothing about measure theory. Is there some well-defined way of getting different measures for countably infinite sub-sets of a countably infinite ensemble? -- Kory
RE: Is the universe computable
David Barrett-Lennard writes: > Why is it assumed that a multiple "runs" makes any difference to the > measure? One reason I like this assumption is that it provides a natural reason for simpler universes to have greater measure than more complex ones. Imagine a Turing machine with an infinite program tape. But suppose the actual program we are running is finite size, say 100 bits. The program head will move back and forth over the tape but never go beyond the first 100 bits. 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. And since the TM never goes beyond those 100 bits, all such tapes will run the same program. Therefore, 1/2^100 of all the executions of all possible program tapes will be of that program. 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. Therefore runs of the first program will be 2^20 times more numerous than runs of the second. If we use the assumption that each of these multiple executions or runs contributes to the measure, we therefore can conclude that the measure of the universe generated by the first program is 2^20 times greater than the measure of the universe generated by the second. And more generally, the measure of a universe is inversely related to the size of the program which creates it. Therefore, QED, universes with simple programs have a higher measure than universes with more complex programs. This conclusion then allows us to further conclude that observers are likely to evolve in lawful universes, that is, universes without "flying rabbits", i.e. rare, magical exceptions to otherwise universal laws. And we can conclude that the physical laws are likely to be stable or at least predictable over time. All of these are very properties of the universe which are otherwise difficult or impossible to explain. The fact that the multiverse hypothesis can provide some grounds for explaining them is one of the main sources of its attractiveness, at least for me. However, all this is predicated on the assumption that multiple runs of the same program all contribute to the measure. If that is not true, then it would be harder to explain why simple programs are of higher measure than more complex ones. > If the computation is reversible we could run the simulation backwards - > even though the initial state make seem contrived because it leads to a > low entropy at the end of the computation. Given that the simulated > beings don't know the difference (their subjective time runs in the > direction of increasing entropy) the fact that the simulation is done in > reverse is irrelevant to them. > > Would a simulation done in reverse contribute to the measure? When I think of the abstract notion of a universal TM that runs all possible programs at once, I don't necessarily picture an explict time element being present. I think of it more as a mapping: TM + program ==> universe. The more programs which create a given universe, the higher the measure of that universe. However, I don't think I can escape from your question so easily. We could alternately imagine an actual, physical computer, sitting in our universe somewhere, simulating another universe. And that should contribute to that other universe's measure. In that case we should have some rule that would answer questions about how much reversible and reversed simulations contribute. I would consider applying Wei Dai's heuristic, which I discussed the other day. It says that the measure of an object is larger if the object is easier to find in the universe that holds it. I gave some rough justifications for this, such as the fact that a simple counting program eventually outputs every million bit number, but no one would say that this means that the complexity of a given million bit number is as small as the size of that program. In this context, the heuristic would say that the contribution of a physical computer simulating another universe to the measure of that simulated universe should be based on how easy it is to find the computation occuring in our own universe. Computations which occur multiple times would be easier to find, so by Wei's heuristic would have higher measure. This is another path to justify the assumption that multiple simulations should contribute more to measure. I'd say that a computation running backwards contributes as well, by making it easier to locate. Now take a complex case, where a computation ran forwards for a while, then backwards, then forwards. I'd say that this heuristic suggests that the portion of the simulated universe which was repeated 3 times (forwards, backwards, forwards
RE: Is the universe computable
Why is it assumed that a multiple "runs" makes any difference to the measure? If the computation is reversible we could run the simulation backwards - even though the initial state make seem contrived because it leads to a low entropy at the end of the computation. Given that the simulated beings don't know the difference (their subjective time runs in the direction of increasing entropy) the fact that the simulation is done in reverse is irrelevant to them. Would a simulation done in reverse contribute to the measure? Once we say that all possible computations exist in the Platonic sense, it seems to me that running them is irrelevant. Of course it is agreed that the existence hypothesis tells us nothing about their relative measure. Does anyone have some principles to go by? I presume a theory of measure along the lines described by Jesse would need to account for the measure of mappings between computations. Presumably a simple correspondence would have higher weighting than some complicated mapping between two computations. - David > -Original Message- > From: Jesse Mazer [mailto:[EMAIL PROTECTED] > Sent: Saturday, 17 January 2004 4:56 AM > To: [EMAIL PROTECTED] > Subject: Re: Is the universe computable > > Eugen Leitl: > >I have trouble alternating between the internal and the external observer > >view. So we have a machine crunching bits, sequentially falling from > state > >to > >state. This spans a continous trajectory. We can make a full record of > that > >trajectory, eliminating a time axis. When does the subjective observation > >of > >existence assemble into place? The first time the computation was made? > > > >I have trouble seeing my subjective observer experience as a sequence of > >frames, already computed. Is the first run magical, and the static record > >dead meat? I'm confused. > > I think the most common theory on this list is that there is nothing > special > about the first vs. the second run--rather, the total number of runs helps > determine the measure of that subjective experience. If I scan my brain > into > a computer knowing that my first experience after being uploaded will > depend > on what environment is created for my simulated brain, I should make sure > my > friends do lots of runs where the upload wakes up in an idyllic > environment > and that my enemies don't get their hands on the program and do a lot of > runs where the upload is used as a slave or something. If my enemies do > manage to get a copy and do a few of those runs before they are caught and > stopped by the Society for the Prevention of Cruelty to Uploads, my > friends > can at least try to minimize the damage by doing so many runs of the > idyllic > environment that the probability of having that experience after I wake up > will be much greater than the probability that my first experience after > being uploaded will be waking up as a slave to my enemies (according to > this > particular theory of how measure works, anyway). > > Jesse Mazer > > _ > Get a FREE online virus check for your PC here, from McAfee. > http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963
RE: Is the universe computable?
Eugen said... > I was using a specific natural number (a 512 bit integer) as an > example for > creation and destruction of a specific integer (an instance of a class of > integers). No more, no less. > That's plenty to bring out our difference of opinion. cf "creation and destruction of a specific integer" > Existence of a specific integer has nothing to do with existence of a > production system for a class of integers. The recipe for a > series is not the > dish itself. That recipe is also just information, requiring encoding in a > material carrier. It would have taken considerably more work to > eradicate the > entire production system, as it is a bit more widespread, and has > a lot more > vested interest than conservation of a specific, random integer, destilled > from turbulent gas flow. > You say "a class of integers". Does this mean you don't believe the integers are unique? I guess this is consistent with a non-platonist. However, from the Peano axioms it can be shown that the integers are unique up to isomorphism. Does the concept of "uniqueness up to isomorphism" seem useful or important to you? > The representation (hex, need to be told that above hex string > represents an > integer (ignoring underlying representations as two's complements, > potentials, charge buckets and magnetic domains for the moment) indicates > that even that "simple" information transfer was encrusted with lots of > implicit context people take for granted. Roll back to > Sumer, and hand out little clay tablets with that hex string. What does it > mean? Nothing. Not even the alphabet to parse this exists. > > Animals evolve representations for quantities, because resource > management is > a critical survival skill. After a few iterations you get consensual > encodings for interactive transfer, then noninteractive > consensual encodings. > I used patterns of luminous pixels (translated into Braille dots, > for all what I know) > instead of scratches on a bone fragent, because that encoding is more > familiar, and easier to transmit. > > Wavefront reemitted from pebbles hitting retina, being processed > on the fly, > tranformed into a spatiotemporal electrochemical activity pattern is an > instance of a measurement of a property. It takes a specific class of > detectors to do. You cannot conduct that measurement in their absence. The platonist interpretation of the above is simply that context is needed to relate a given sentence (of symbols) back to the Platonic realm. Note that the Platonic realm is *not* itself merely a bunch of sentences. It comes with semantics! > > > You say the given integer exists because "it is it is physically > > realizable *in principle*". That sounds like the platonic view to me - > > To me, this sounds like a confusion between a specific integer, > and a recipe > for such. It is quite difficult to feed a wedding throng with > pages from a cookbook. I can't work out what you are saying! You use terms like "specific integer" and I've got no idea what you mean because you don't believe concepts exist independently of "their production systems". The integers are an example of a concept that is *decoupled* from specific instances - by definition. A great deal of our thinking and language involves generalisation. For example the word "chair" is associated with a class of objects. You use generalisation in your sentences as much as anyone else. Your lines of reasoning treat these abstractions as "things" that can be manipulated - such as when I say "the boy kicked the ball" and you form an image in your mind - even though the sentence involves generalisations such as "boy" and "ball". I presume your refutation (as a non-platonist) is that concepts only exist while someone (or something) is there to think them. The problem with that view is that many useful lines of reasoning involve the question "Does there exist a concept x such that p(x)" without instantiating x. In other words, it seems to be useful to conceptualise over the space of all possible concepts. This is exactly what happens when we generalise specific integers to the infinite set of all integers. I don't see how the non-platonist can accept any lines of reasoning that involve the set of integers because it is impossible to conceptualise every member of the set which (to them) would imply that the set doesn't exist. You agreed before with the hypothesis that a computer could exhibit awareness. Suppose we have (say on optical disk) a program and we have a computer on which we can run the program, but we haven't run the program yet. We can a-priori ask the question "On the computer monitor, will we see a simulated person laugh?". Do you believe this a-priori question has an a-priori answer? After all, there is nothing mystical in a deterministic computation. If so doesn't that mean that the simulated person exists independently of running the actual simulation? In fact, if we postulate that our univer
Re: Is the universe computable?
> Actually I tend to think that Godel's and other incompleteness > result makes comp a sort of vaccine against reductionist view of > self and reality (and arithmetic). Agreed. Godel, (as interpreted by Chaitin), precludes a "purely" reductionist view of both, IMHO. Given Reductionism as: "Belief that statements or expressions of one sort can be replaced systematically by statements or expressions of a simpler or more certain kind. Thus, for example, some philosophers have held that arithmetic can be reduced to logic, that the mental can be reduced to the physical, or that the life sciences can be reduced to the physical sciences." Self and reality are "incompressible" and thus irreducible into concise physical laws or mathematical axioms.
Re: Is the universe computable
Eugen Leitl: I have trouble alternating between the internal and the external observer view. So we have a machine crunching bits, sequentially falling from state to state. This spans a continous trajectory. We can make a full record of that trajectory, eliminating a time axis. When does the subjective observation of existence assemble into place? The first time the computation was made? I have trouble seeing my subjective observer experience as a sequence of frames, already computed. Is the first run magical, and the static record dead meat? I'm confused. I think the most common theory on this list is that there is nothing special about the first vs. the second run--rather, the total number of runs helps determine the measure of that subjective experience. If I scan my brain into a computer knowing that my first experience after being uploaded will depend on what environment is created for my simulated brain, I should make sure my friends do lots of runs where the upload wakes up in an idyllic environment and that my enemies don't get their hands on the program and do a lot of runs where the upload is used as a slave or something. If my enemies do manage to get a copy and do a few of those runs before they are caught and stopped by the Society for the Prevention of Cruelty to Uploads, my friends can at least try to minimize the damage by doing so many runs of the idyllic environment that the probability of having that experience after I wake up will be much greater than the probability that my first experience after being uploaded will be waking up as a slave to my enemies (according to this particular theory of how measure works, anyway). Jesse Mazer _ Get a FREE online virus check for your PC here, from McAfee. http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963
Re: Is the universe computable?
Bruno Marchal wrote: > > At 10:14 13/01/04 +0100, Georges Quenot wrote: > > >Some people do argue that there is no arithmetical property > >independent of us because there is no thing on which they would > >apply independentkly of us. What we would call their arithmetical > >properties is simply a set of tautologies that do come with them > >when they are considered but exist no more than them when they > >are not considered. > > But then what would be an undecidable proposition? This is how > Russell's and Whitehead logicism has break down. There is a ladder > of arithmetical propositions which ask for more and more > ingenuity to be proved. Actually arithmetical truth extend far beyond > the reach of any consistent machine (and consistent human with > comp). There is an infinity of surprise in there. > I guess you know that there is no natural number p and q such that > (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, > why did the pythagoreans *hide* this fact for so long? > So those propositions are neither tautologies, nor conventions. > David Deutsch, following Johnson's criteria of reality, would say > that such propositions kick back. > > You know, about arithmetic, and about machines btw, a lot of > people defends idea which are just no more plausible since > Godel has proved its incompleteness theorems. > Arithmetical proposition are just not tautologies. There are three classes of (arithmetical) propositions: those who are tautologies (no matter how clever one has to be to figure that, they say nothing which is not already in the axioms), those whose negation are tautologies, and those whose neither themselves nor their negation are tautologies. It might be that we don't know which is which but it should be so in principle. > >> > Giving that I hope getting some understanding of the complex human > >> > from something simpler (number property) the approach of those > >> > people will never work, for me. > >> > >>And certainly vice versa. Though it is difficult to have them saying > >>it explicitely I have the feeling that the reason why they do not > >>want the natural numbers to be out there and even as not possibly > >>being considered as out there is that they do not accept that the > >>complex human be understood from something simpler (number property). > >>They do not even accept the idea being considered, were it as a mere > >>conjecture or working hypothesis. Their more official argument is > >>that such a view would prevent the foundation of human dignity. > > Damned!!! If there is one thing which could prevent the foundation > of human dignity, it is certainly that totalitarian idea following which > some ideas can not even be considered as an hypothesis or conjecture. This is indeed a problem. There could be more than one conception of human dignity. > But that happens all the time. There has been days you could be burned > even just because you ask yourself if by chance it was not the sun but > the earth which was moving. Unfortunately (again), yes. > Are you defending those guys? No. I am just explaining (or trying to explain) their position. > Are you asking me how to reply to those guy? I am interested in anybody's opinion on that problem. > My suggestion: if many people > thinks like that around you, just leave them. Like Valery said, those who are > not willing to use logic with you (that is to argument) are in war with you. > Run or kill them! This is a safe way to have soon everybody killing everybody. > It is not enough they have good intention, if they do not > want arguments, they are dangerous for all humans. I like to insist, in Valery > spirit, that logic is not a question of truth, but of politeness. I like the analogy. The fact is that there might be several (and possibly incompatible) protocols of politeness. > >I have not met any of them physically but I had discussion with > >some of them via Internet. There might not be so many of them but > >there are. You will find, at least in the US, a lot of people > >considering the views of evolution and/or of the big-bang as evil. > > Then what? If they disagree with dialog and argumentation, *I* will > consider them as evil. Possibly making you not better than them. But this not that simple. They do not disagree with dialog and argumentation. Rather they argue in different ways and/or with different premises. > >If they finally have to abandon these positions due to the amount > >of evidence in favor of it, the last line of defence for their > >conception of a personal God and for a significant role for Him > >could be at the level of artihmetical realism. Artihmetical > >realism by itself (not from a distinct personal God) is therefore > >seen as evil by them. As I mentionned, they usually do not put it > >that way. Rather they argue that such a view would prevent the > >foundation of human dignity and the like. > > They make probably the same confusion of those who believe > tha
Re: Is the universe computable
On Fri, Jan 16, 2004 at 02:28:27PM +0100, Bruno Marchal wrote: > of brain and the like. I of course respect completely that opinion; but I > point on the fact > that once you make the computationnalist hypothesis then it is the reverse > which becomes > true: even if locally pi is a production of the human brain, globally the > laws of physics logically > develop on the set of all possible beliefs of all possible universal and > immaterial (mathematical) > machines embedded in all possible computations (computationnal histories). I respect that opinion, I'm just interested in theories which are instrumental in solving this universe's problems. You know, trivial stuff: wars, famines and death. A TOE which says: universe is information, every possible pattern exists, observers which can observe themselves will, is a bit sterile in that respect. There's a little problem with some practical relevance I don't have an answer, though, which I'd like to have your opinion on. We have a finite system, iteratively evolving along a trajectory in state space. We have observers within that system, subjectively experiencing a flow of time. I have trouble alternating between the internal and the external observer view. So we have a machine crunching bits, sequentially falling from state to state. This spans a continous trajectory. We can make a full record of that trajectory, eliminating a time axis. When does the subjective observation of existence assemble into place? The first time the computation was made? I have trouble seeing my subjective observer experience as a sequence of frames, already computed. Is the first run magical, and the static record dead meat? I'm confused. Let's bring a little dust into the run. Let's say we use a HashLife approach, which assembles the flow from lightcone hashes. Does this screw up the subjective experience? If yes, how? What about computing a record of all possible trajectories? Is enumerating all possible states sufficient to create an observer experience? I haven't spent much time on this, so maybe you can bring some light into the matter. > That's all my thesis > is about. I don't pretend it is obvious, for sure. -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
On Fri, Jan 16, 2004 at 10:27:49AM +0800, David Barrett-Lennard wrote: > > I agree with everything you say, but did you really think I was making a > point because Eugen happened to use hex?! I've fallen behind on answering my email, so sorry if this is brief and a bit out of context. This post is not talking about the universe metalayer at all. I was using a specific natural number (a 512 bit integer) as an example for creation and destruction of a specific integer (an instance of a class of integers). No more, no less. Existence of a specific integer has nothing to do with existence of a production system for a class of integers. The recipe for a series is not the dish itself. That recipe is also just information, requiring encoding in a material carrier. It would have taken considerably more work to eradicate the entire production system, as it is a bit more widespread, and has a lot more vested interest than conservation of a specific, random integer, destilled from turbulent gas flow. The representation (hex, need to be told that above hex string represents an integer (ignoring underlying representations as two's complements, potentials, charge buckets and magnetic domains for the moment) indicates that even that "simple" information transfer was encrusted with lots of implicit context people take for granted. Roll back to Sumer, and hand out little clay tablets with that hex string. What does it mean? Nothing. Not even the alphabet to parse this exists. Animals evolve representations for quantities, because resource management is a critical survival skill. After a few iterations you get consensual encodings for interactive transfer, then noninteractive consensual encodings. I used patterns of luminous pixels (translated into Braille dots, for all what I know) instead of scratches on a bone fragent, because that encoding is more familiar, and easier to transmit. Wavefront reemitted from pebbles hitting retina, being processed on the fly, tranformed into a spatiotemporal electrochemical activity pattern is an instance of a measurement of a property. It takes a specific class of detectors to do. You cannot conduct that measurement in their absence. > You say the given integer exists because "it is it is physically > realizable *in principle*". That sounds like the platonic view to me - To me, this sounds like a confusion between a specific integer, and a recipe for such. It is quite difficult to feed a wedding throng with pages from a cookbook. > because the number is *not* actually physically realized and yet the > number is purported to have an independent existence. Are you saying > otherwise? > > I think any form of symbolic manipulation of numbers is implicitly using > the platonic view. To say they spring into existence as they are > written down (which in any case only means they are realizable in Numbers don't write down themselves. Systems generate them, translate them into specific encodings, to be parsed by other instances of systems of the same class. Use a system of a different class, and you'll only parse garbage. ATGATAGTGGCCGTCCAACGGTAGACTCTAC might be a number, it might also be a shorthand for a linear biopolymer (5'-3'? there's some implicit context for you). > principle) just seems silly to me. A cookbook is a promise of a meal, not the meal itself. > The Platonic view just says that every mathematical system free from > contradiction exists. Ie if it can exist then it does exist. There is Exists where? Two production systems of the same kind generate the same output. Surely, the output is contained within them? In there, somewhere? Mathematicians are production systems. Input is coffee, output is theorem. > no need to talk about different types of reality. -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
At 17:13 14/01/04 +, Giu1i0 Pri5c0 wrote: Please correct me if I am wrong: Bruno believes that information, for example mathematical concepts and theorems, exist independently of their encoding in some physicsl systems (arithmetic realism); in other words, that the number 4 esists independently of the presence in the physical world of sets of 4 separate objects, or that 2+2=4 is true independently of the possibility to physically verify this with 4 bottlecaps. Eugen believes that mathematics is the physics of bottlecaps, and that information cannot be said to exist if it is not carried by a physical system in the actual world. Are we sure that both mean the same thing by "existence"? I guess it is clear that in the following sentences "pi exists" and "the moon exists" the meaning of "exists" is different. But the point was the question of knowing or betting which "existence" is more fundamental. We differ on which one is reducible to the other. Eugen seems to pretend that it is obvious that "physical existence" is more fundamental than "mathematical existence", and I guess he was meaning that the existence of pi is a sort of psychological existence, that is pi exists "in" the brain of the mathematician, so that the existence of pi could be reduce to the physical existence of brain and the like. I of course respect completely that opinion; but I point on the fact that once you make the computationnalist hypothesis then it is the reverse which becomes true: even if locally pi is a production of the human brain, globally the laws of physics logically develop on the set of all possible beliefs of all possible universal and immaterial (mathematical) machines embedded in all possible computations (computationnal histories). That's all my thesis is about. I don't pretend it is obvious, for sure. By the way I am reading Bruno's thesis, the few pages that I have read are very interesting. Thanks for saying, don't hesitate to ask questions. Bruno
Re: Is the universe computable
At 17:13 14/01/04 +, Giu1i0 Pri5c0 wrote: Please correct me if I am wrong: Bruno believes that information, for example mathematical concepts and theorems, exist independently of their encoding in some physicsl systems (arithmetic realism); in other words, that the number 4 esists independently of the presence in the physical world of sets of 4 separate objects, or that 2+2=4 is true independently of the possibility to physically verify this with 4 bottlecaps. Eugen believes that mathematics is the physics of bottlecaps, and that information cannot be said to exist if it is not carried by a physical system in the actual world. Are we sure that both mean the same thing by "existence"? I guess it is clear that in the following sentences "pi exists" and "the moon exists" the meaning of "exists" is different. But the point was the question of knowing or betting which "existence" is more fundamental. We differ on which one is reducible to the other. Eugen seems to pretend that it is obvious that "physical existence" is more fundamental than "mathematical existence", and I guess he was meaning that the existence of pi is a sort of psychological existence, that is pi exists "in" the brain of the mathematician, so that the existence of pi could be reduce to the physical existence of brain and the like. I of course respect completely that opinion; but I point on the fact that once you make the computationnalist hypothesis then it is the reverse which becomes true: even if locally pi is a production of the human brain, globally the laws of physics logically develop on the set of all possible beliefs of all possible universal and immaterial (mathematical) machines embedded in all possible computations (computationnal histories). That's all my thesis is about. I don't pretend it is obvious, for sure. By the way I am reading Bruno's thesis, the few pages that I have read are very interesting. Thanks for saying, don't hesitate to ask questions. Bruno
RE: Is the universe computable?
Hi Eric, > >>0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780 > >> didn't exist in this universe (with a very high probability, it being a > >> 512 bit number, generated from physical system noise) before I've > >> generated it. Now it exists (currently, as a hex string (not > necessarily > >> ASCII) on many systems > (...) > > You admit a base 16 notation for numbers - which means you allow numbers > > to be written down that aren't "physically realized" by the > > corresponding number of pebbles etc. So much for talking about pebbles > > in your previous emails! > > I think that it doesn't matter what base you choose to write down the > number. > It is an integer, therefore it is physically realizable *in principle*. If > you write > '1aa3' in base 16, it means '6893' in base 10, which corresponds to a > given > number of pebbles. We may think that there is somehow more "reality" in > 6893 > in comparison to 1aa3, but they are both in the same footing, except that > we > are more used to the first representation. Why would one claim that the > corresponding decimal representation of Eugen's 512-bit number has any > more > reality that the hexadecimal one? I agree with everything you say, but did you really think I was making a point because Eugen happened to use hex?! You say the given integer exists because "it is it is physically realizable *in principle*". That sounds like the platonic view to me - because the number is *not* actually physically realized and yet the number is purported to have an independent existence. Are you saying otherwise? I think any form of symbolic manipulation of numbers is implicitly using the platonic view. To say they spring into existence as they are written down (which in any case only means they are realizable in principle) just seems silly to me. > I have no formed opinion on arithmetical realism, even though I tend to > accept that there is some external reality to the integers. But is the > "reality" that is assigned to numbers of the same kind that is assigned to > their physical representation? Are we not discussing just words without > any > meaning? The Platonic view just says that every mathematical system free from contradiction exists. Ie if it can exist then it does exist. There is no need to talk about different types of reality. - David
Re: Is the universe computable?
Eugen Leitl wrote: David Barrett-Lennard wrote: > Here is a justification of why I think arithmetical realism is at least > very plausible... I'm all ears. > Let's suppose that a computer simulation can (in principle) exhibit > awareness. I don't know whether you dispute this hypothesis, but let's > assume it and see where it leads. With you so far. We already have simulated critters with behaviour, and awareness of their environment. Computational neuroscience even attempts to do it with a high degree of biological realism. > Let's suppose in fact that you Eugin, were able to watch a computer > simulation run, and on the screen you could see "people" laughing, > talking - perhaps even discussing ideas like whether *their* physical > existence needs to be postulated, or else they are merely part of a > platonic multiverse. A simulated person may stamp his fist on a > simulated coffee table and say "Surely this coffee table is real - how > could it possibly be numbers - I've never heard of anything so That wouldn't be abstract "numbers". You'd have a system with a state, evolving along a trajectory. In your case, that system state is being rendered (in realtime, I presume) for external observers. ...but suppose we implement the same abstract program on several computers of totally different construction, like a regular computer using electronic impulses vs. a quantum computer or a gigantic babbage machine that uses only rotating gears. For the critters inside the simulation, wouldn't all these cases appear subjectively identical to them? If so, it seems the only common denominator is that all the computers were doing the same abstract computation, the physical details are apparently irrelevant in determining the experience of the simulated beings. Doesn't this lend intuitive support to the Platonic view that our own physical universe is itself just a particular abstract computation? Isn't your own belief that there is something more to our own universe, something more "physical" I guess, nothing more than faith in a certain metaphysical view of reality, with no more evidence (and considerably less parsimony, IMO) to justify it than the Platonic view? Jesse Mazer _ Scope out the new MSN Plus Internet Software optimizes dial-up to the max! http://join.msn.com/?pgmarket=en-us&page=byoa/plus&ST=1
Re: Is the universe computable?
Please correct me if I am wrong: Bruno believes that information, for example mathematical concepts and theorems, exist independently of their encoding in some physicsl systems (arithmetic realism); in other words, that the number 4 esists independently of the presence in the physical world of sets of 4 separate objects, or that 2+2=4 is true independently of the possibility to physically verify this with 4 bottlecaps. Eugen believes that mathematics is the physics of bottlecaps, and that information cannot be said to exist if it is not carried by a physical system in the actual world. Are we sure that both mean the same thing by "existence"? By the way I am reading Bruno's thesis, the few pages that I have read are very interesting.
Re: Is the universe computable?
Jesse wrote: (- Original Message - From: "Jesse Mazer" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, January 13, 2004 4:02 PM Subject: Re: Is the universe computable?) > Hal Finney wrote: Snip >As long as everything that happens in the universe's history can be represented by a finite string, this brute-force method is one that's guaranteed to work...the ultimate version of this would just be to generate all possible strings of that length, then throw out all the ones that don't match the laws/boundary conditions you've chosen. ..< Are we really smart enough to set up a 'complete' set of 'rules' to describe (restrict?) the universe(s)? I feel we are circling within our mind of a limited understanding - achieved cognitive inventory. Even our 'unreal' ideas are dreamed up by our mindset. Are we fashioning the existence (world, or nature, or Multiverse, whatever one likes to call 'everything') after our so far epistemized (!) cognitive inventory and human knowledge? Or: do we 'make up' a world as we can? John Mikes
Re: Is the universe computable?
At 13:02 14/01/04 +0100, Eugen Leitl wrote: > Also, I don't like to repeat to much arguments, so, if you want to argue "You're too dumb to get it, and I won't waste time explaining it to you." No. It is just for not boring people with arguments already send to the list. You misinterpret me. > Btw I have not perceived your argument against AR. You just keep repeating > that something abstract can exist only if some piece of matter apply it. Yeah, information doesn't exist without a material carrier. If you claim to do computation, please stick to constraints of computational physics. You repeat your assertion again. Repeating the same sentence again and again will not make it an epsilon more true. Bruno
Re: Is the universe computable?
On Wed, Jan 14, 2004 at 12:22:13PM +0100, Bruno Marchal wrote:
> Indeed I wasn't. In general I don't like to much argue on hypotheses.
"I just say lots of stuff. I don't mean it. Please attach no significance to
what I say; it's just hot air."
> Also, I don't like to repeat to much arguments, so, if you want to argue
"You're too dumb to get it, and I won't waste time explaining it to you."
Now I might be mistaken, but these are not nice attitudes. Expecially, if
taken together.
> please look at the links to the UDA (Universal Dovetailer Argument) in my
> web page (url below). Those are links to this very list.
I went there, and looked. First impression: lots of opaque lingo. This isn't
not necessarily bad in itself, but usually only mature fields develop
specialist languages. Quacks and kooks are known to use pseudospecialist
language, too.
I'll come back to you after I've actually tied to understand what it says.
I'm not sure it's worth my time, but I respect many people on this list, who
haven't come down on your argumentation, so maybe I'm wrong.
> ('course, in case you know french you can read my thesis).
Once, upon a time, the language of science was Latin. Then, it used to be
French.
Now, it is usually a very good idea to formulate your ideas in English, because it's
what any literate person in the world can be expected to understand,
currently.
> Now I am not sure you will be interested because I *assume* Arithmetical
> Realism AR (I put it in the definition of the computationalist hyp.) and it
> seems
> you consider that hypothesis as a "glib" (whatever that means: it is not in
> my dictionary but I can infer the sense.).
http://dictionary.reference.com/search?q=glib
7 entries found for glib.
glib( P ) Pronunciation Key (glb)
adj. glib·ber, glib·best
1.
1. Performed with a natural, offhand ease: glib conversation.
2. Showing little thought, preparation, or concern: a glib response
to a complex question.
2. Marked by ease and fluency of speech or writing that often suggests or
stems from insincerity, superficiality, or deceitfulness.
[Possibly of Low German origin. See ghel-2 in Indo-European Roots.]glibly
adv.
glibness n.
Synonyms: glib, slick, smooth-tongued
These adjectives mean being, marked by, or engaging in ready but often
insincere or superficial discourse: a glib denial; a slick commercial; a
smooth-tongued hypocrite.
[Buy it]
Source: The American Heritage® Dictionary of the English Language, Fourth
Edition
Copyright © 2000 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
glib
\Glib\, v. t. [Cf. O. & Prov. E. lib to castrate, geld, Prov. Dan. live, LG.
& OD. lubben.] To castrate; to geld; to emasculate. [Obs.] --Shak.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
\Glib\, a. [Compar. Glibber; superl. Glibbest.] [Prob. fr. D. glibberen,
glippen, to slide, glibberig, glipperig, glib, slippery.] 1. Smooth;
slippery; as, ice is glib. [Obs.]
2. Speaking or spoken smoothly and with flippant rapidity; fluent; voluble;
as, a glib tongue; a glib speech.
I want that glib and oily art, To speak and purpose not. --Shak.
Syn: Slippery; smooth; fluent; voluble; flippant.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
\Glib\, v. t. To make glib. [Obs.] --Bp. Hall.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
\Glib\, n. [Ir. & Gael. glib a lock of hair.] A thick lock of hair, hanging
over the eyes. [Obs.]
The Irish have, from the Scythians, mantles and long glibs, which is a thick
curied bush of hair hanging down over their eyes, and monstrously disguising
them. --Spenser.
Their wild costume of the glib and mantle. --Southey.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
adj 1: marked by lack of intellectual depth; "glib generalizations"; "a glib
response to a complex question" 2: having only superficial plausibility;
"glib promises"; "a slick commercial" [syn: pat, slick] 3: artfully
persuasive in speech; "a glib tongue"; "a smooth-tongued hypocrite" [syn:
glib-tongued, smooth-tongued]
> Btw I have not perceived your argument against AR. You just keep repeating
> that something abstract can exist only if some piece of matter apply it.
Yeah, information doesn't exist without a material carrier. If you claim to
do computation, please stick to constraints of computational physics.
Universe may very well consist of information; show why you claim to have
insight in the architecture of the metalayer.
> Giving that I don't take "matter" as granted (it's exactly what I try to
> explain) and
Are you trying to do science, or religion?
> giving that the word "apply" could only be used in an analogical, fuzzy or
> anthropomorphical way, it is hard to figure out where your argument relies.
> To be honest I don't like at all your tone which only witnesses the fact
Re: Is the universe computable?
At 18:32 13/01/04 +0100, Eugen Leitl wrote:
On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote:
> Don't tell me you were believing I was arguing.
You were asserting a lot of stuff. That's commonly considered arguing, except
you weren't providing any evidence so far. So, maybe you weren't.
Indeed I wasn't. In general I don't like to much argue on hypotheses.
Also, I don't like to repeat to much arguments, so, if you want to argue
please look at the links to the UDA (Universal Dovetailer Argument) in my
web page (url below). Those are links to this very list.
('course, in case you know french you can read my thesis).
Now I am not sure you will be interested because I *assume* Arithmetical
Realism AR (I put it in the definition of the computationalist hyp.) and it
seems
you consider that hypothesis as a "glib" (whatever that means: it is not in
my dictionary but I can infer the sense.).
Btw I have not perceived your argument against AR. You just keep repeating
that something abstract can exist only if some piece of matter apply it.
Giving that I don't take "matter" as granted (it's exactly what I try to
explain) and
giving that the word "apply" could only be used in an analogical, fuzzy or
anthropomorphical way, it is hard to figure out where your argument relies.
To be honest I don't like at all your tone which only witnesses the fact
that you
have decided in advance what to think about this point. I guess David is right
when he says that you seem to be getting a little hot under the collar!
About AR I did send a quote by the mathematician HARDY which sums up
quite well my feeling about it. You can take a look at:
http://www.escribe.com/science/theory/m4621.html
Bruno
http://iridia.ulb.ac.be/~marchal/
Re: Is the universe computable?
Hi Georges, I got that mail before. And I did answer it. Are you sure you send the right mail? see http://www.escribe.com/science/theory/m5026.html Bruno At 10:14 13/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: > > At 13:36 09/01/04 +0100, Georges Quenot wrote: > >Bruno Marchal wrote: > > > > > It seems, but it isn't. Well, actually I have known *one* mathematician, > > > (a russian logician) who indeed makes a serious try to develop > > > some mathematics without that infinite act of faith (I don't recall > > > its name for the moment). Such attempt are known as "ultrafinitism". > > > Of course a lot of people (especially during the week-end) *pretend* > > > not doing that infinite act of faith, but do it all the time implicitly. > > > >This is not what I meant. I did not refer to people not willing > >to accept that natural numbers exist at all but to people not > >wlling to accept that natural numbers exist *by themselves*. > >Rather, they want to see them either as only a production of > >human (or human-like) people or only a production of a God. > > What I mean is that their arithmetical property are independent > of us. I don't think this is very different. I could argue that even if natural numbers were not out there, as soon as anybody consider them, their properties automatically come with and impose themselves. Even this seemingly weaker statement can be contested and it is not actually weaker but equivalent since there might be no other way than this one for natural numbers to be out there. Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. > Do you think those people believe that the proposition > "17 is prime" is meaningless without a human in the neighborhood? " "17 is prime" is meaningless without a human in the neighborhood" is exactly the kind of claim these people make (possibly generalizing the concept of human to aliens and Gods). After discussing with some of them I think they actually believe what they claim. I am not sure however that we always fully understand each other and that you or I would exactly understand such a claim in the same way as they do. > Giving that I hope getting some understanding of the complex human > from something simpler (number property) the approach of those > people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. > Also, I would take (without added explanations) an expression > like "numbers are a production of God" as equivalent to > arithmetical realism. Yes and there are several ways to understand this. > >And I said "unfortunately" because some not only do not want to > >see natural numbers as existing by themselves but they do not > >want the idea to be simply presented as logically possible and > >even see/designate evil in people working at popularizing it. > > OK, but then some want you being dead because of the color of the skin, > or the length of your nose, ... I am not sure it is not premature wanting > to enlighten everyone at once ... > I guess you were only talking about those hard-aristotelians who > like to dismiss Plato's questions as childish. Evil ? Perhaps could you be > more precise on those people. I have not met people seeing evil > in arithmetical platonism, have you? I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. Georges Quénot.
Re: Is the universe computable?
I agree with you Ben, you make a point. My objection admits indeed your wonderful generalization. Thanks. Bruno At 11:07 13/01/04 -0500, Benjamin Udell wrote: [Georges Quenot]>>Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. [Bruno Marchal]>But then what would be an undecidable proposition? >You know, about arithmetic, and about machines btw, a lot of people defends idea which are just no more plausible since Godel has proved its incompleteness theorems. >Arithmetical proposition are just not tautologies. This is how Russell's and Whitehead logicism has break down. There is a ladder of arithmetical propositions which ask for more and more ingenuity to be proved. Actually arithmetical truth extend far beyond the reach of any consistent machine (and consistent human with comp). There is an infinity of surprise in there. >I guess you know that there is no natural number p and q such that (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* this fact for so long? So those propositions are neither tautologies, nor conventions.David Deutsch, following Johnson's criteria of reality, would say that such propositions kick back. Since Georges Quenot's objection claims that nothing exists when unconsidered, be it a mathematical structure or concrete singular objects to which it applies, isn't the objection too broad to be singling out any particular physics-based cosmology as objectionable? The objection seems too powerful & broad, & seems to apply with equal force to all subject matters of mathematics & empirical research, from pointset topology to Egyptology. I wouldn't demand that a philosophical objection, in order to be valid at all, offer a direction for specific research, but I'd ask how it would at least help research keep from going wrong, & I don't see how the present objection would help keep any kind of research, mathematical or empirical, from getting onto excessively thin ice, except perhaps by inspiring a general atmosphere of skepticism in response to which people pay more attention to proofs, confirmations, corroborations, etc. -- not that any such thing could actually overcome such a ! radical objection. And the objection is stated with such generality, that I don't see how it escapes being applied to itself, since, after all, it is about things & relations. If there's nobody to consider concrete things or mathematicals, then there's nobody to consider the objection to considering any unconsidered things to exist. The objection seems to undercut itself in the scenario in which it is meant to have force. Unless, of course, I've misunderstood the argument, which is certainly possible. Best, Ben Udell
Re: Is the universe computable?
On Wed, Jan 14, 2004 at 10:38:51AM +0800, David Barrett-Lennard wrote: > You seem to be getting a little hot under the collar! Nope, just a bit polemic. I was getting tired of glib assertions, and needed to poke a stick, to find out what's underneath. > Here is a justification of why I think arithmetical realism is at least > very plausible... I'm all ears. > Let's suppose that a computer simulation can (in principle) exhibit > awareness. I don't know whether you dispute this hypothesis, but let's > assume it and see where it leads. With you so far. We already have simulated critters with behaviour, and awareness of their environment. Computational neuroscience even attempts to do it with a high degree of biological realism. > Let's suppose in fact that you Eugin, were able to watch a computer > simulation run, and on the screen you could see "people" laughing, > talking - perhaps even discussing ideas like whether *their* physical > existence needs to be postulated, or else they are merely part of a > platonic multiverse. A simulated person may stamp his fist on a > simulated coffee table and say "Surely this coffee table is real - how > could it possibly be numbers - I've never heard of anything so That wouldn't be abstract "numbers". You'd have a system with a state, evolving along a trajectory. In your case, that system state is being rendered (in realtime, I presume) for external observers. You'd be a bit pressed to enumerate all possible system trajectories, though. You'd run out of time and space even for very, very small assemblies. > ludicrous!". > > Now Eugin, you may argue that the existence of this universe depends on > the fact that it was simulated by a computer in our universe. I find Exactly. No implementation, no state, no trajectory. Information doesn't exist without systems encoding it. (This applies to this universe being the metalayer for a simulated system; I don't make any assumptions about our own metalayer, which is pretty meaningless, since unknowable unless). > this a little hard to fathom - because computer simulations are > deterministic and they give the same results whether they are run once > or a thousand times. I find it hard to imagine that they "leap into Absolutely. Provided, they're run. (In practice, you'll see system running floats are not as deterministic as you think). > existence" when they are run the first time. I'm particularly > motivated by the universal dove-tailing program - which eventually > generates the trace of all possible programs. I don't deny that this universe exists. I do deny that the metalayers is knowable in principle, provided that metalayers is not operated by cooperating beings (which is a very purple requirement). What I *am* interested in is a simple TOE, or a set of simple equivalent TOEs, which has enough predictive power to be usable with some finite amount of computation. > Do you say that most of the integers don't exist because nobody has > written them down? Yeah. I'm saying that, say, 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20d9f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems around the world, rendered in diverse fonts), as soon as I remove all its encodings it's gone again. P00f! Ditto applies to generator systems -- they're a bit more widespread within a lightday from here (though most of them are concentrated within a fraction of a lightsecond), but you take them out -- all of them -- numbers cease to exist. They're gone, until something else comes along, and reinvents them. > I can see your point when you say that 2+2=4 is meaningless without the > "physical objects" to which it relates. However this is irrelevant No, they're meaningful without observers with world models. The physical objects (unless they're infoprocessing systems) can't observe themselves. > because you are thinking of too simplistic a mathematical system! The > only mathematical systems that are relevant to the everything-list are > those that have conscious inhabitants within them. Within this "self I don't know what "conscious" means, but machine vision systems and animals can sure count. No need to use vis vitalis for that. > contained" mathematical world we *do* have the context for numbers. > It's a bit like the chicken and egg problem. (egg = number theory, > chicken = objects and observers). Both come together and can't be > pulled apart. You're anthopomorphising awfully. It sure nice to be a conscious observers, but most parts of this universe have been doing fine without, and given that multiverse exists, most of those seem to do without as well. -- Eugen* Leitl http://leitl.org";>leitl __
RE: Is the universe computable?
Hi Eugin, > I see, we're at the "prove that the Moon is not made from green cheese > when > nobody is looking" stage. > > I thought this list wasn't about ghosties'n'goblins. > Allright, I seem to have been mistaken about that. You seem to be getting a little hot under the collar! Here is a justification of why I think arithmetical realism is at least very plausible... Let's suppose that a computer simulation can (in principle) exhibit awareness. I don't know whether you dispute this hypothesis, but let's assume it and see where it leads. Let's suppose in fact that you Eugin, were able to watch a computer simulation run, and on the screen you could see "people" laughing, talking - perhaps even discussing ideas like whether *their* physical existence needs to be postulated, or else they are merely part of a platonic multiverse. A simulated person may stamp his fist on a simulated coffee table and say "Surely this coffee table is real - how could it possibly be numbers - I've never heard of anything so ludicrous!". Now Eugin, you may argue that the existence of this universe depends on the fact that it was simulated by a computer in our universe. I find this a little hard to fathom - because computer simulations are deterministic and they give the same results whether they are run once or a thousand times. I find it hard to imagine that they "leap into existence" when they are run the first time. I'm particularly motivated by the universal dove-tailing program - which eventually generates the trace of all possible programs. Do you say that most of the integers don't exist because nobody has written them down? I can see your point when you say that 2+2=4 is meaningless without the "physical objects" to which it relates. However this is irrelevant because you are thinking of too simplistic a mathematical system! The only mathematical systems that are relevant to the everything-list are those that have conscious inhabitants within them. Within this "self contained" mathematical world we *do* have the context for numbers. It's a bit like the chicken and egg problem. (egg = number theory, chicken = objects and observers). Both come together and can't be pulled apart. - David > -Original Message----- > From: Eugen Leitl [mailto:[EMAIL PROTECTED] > Sent: Wednesday, 14 January 2004 1:32 AM > To: [EMAIL PROTECTED] > Subject: Re: Is the universe computable? > > On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote: > > > > What is the point? Do we have experimental procedure to validate > > the opposite of the fanciful scenario? Giving that we were talking about > > I see, we're at the "prove that the Moon is not made from green cheese > when > nobody is looking" stage. > > I thought this list wasn't about ghosties'n'goblins. > Allright, I seem to have been mistaken about that. > > > first person scenario, in any case it is senseless to ask for > > experimental procedure. (experience = first person view; experiment = > > third person view). > > So the multiverse is not a falsifyable theory? > > > Don't tell me you were believing I was arguing. > > You were asserting a lot of stuff. That's commonly considered arguing, > except > you weren't providing any evidence so far. So, maybe you weren't. > > > About logic, it is a branch of mathematics. Like topology, algebra, > analysis > > it can be *applied* to some problem, which, through some hypothesis, > > can bear on some problem. With the comp hyp mathematical logic makes > > it possible to derive what consistent and platonist machine can prove > about > > themselves and their consistent extension. > > Except that machine doesn't exist in absence of implementations, be it > people, machines, or aliens. > > > >My point is that formal systems are a very powerful tool with very > small > > >reach, > > >unfortunately. > > > > But I never use formal system. I "modelise" a particular sort of machine > by > > formal system, so I prove things *about* machines, by using works > > *about* formal system. I don't use formal systems. I prove things in > > informal > > ways like all mathematicians. > > Above passage is 100% content-free. > > > >Because we know that QM is not a TOE. You haven't heard? > > > > How could be *know* QM is not a TOE? (I ask this independently of > > the fact that I find plausible QM is not a *primitive* TOE). > > Because general relativity and quantum theory are mutually incompatible. > So > both TOE aren't. We
Re: Is the universe computable?
Dear Wei, Georges, et al, Where does the notion of computational resources factor in this? Stephen - Original Message - From: "Wei Dai" <[EMAIL PROTECTED]> To: "Georges Quenot" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Monday, January 12, 2004 8:50 PM Subject: Re: Is the universe computable? > On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: > > Many other way of simulating the universe could be considered like > > for instance a 4D mesh (if we simplify by considering only general > > relativity; there is no reason for the approach not being possible in > > an even more general way) representing a universe taken as a whole > > in its spatio-temporal aspect. The mesh would be refined at each > > iteration. The relation between the time in the computer and the time > > in the universe would not be a synchrony but a refinement of the > > resolution of the time (and space) in the simulated universe as the > > time in the computer increases. > > > > Alternatively (though both views are not necessarily exclusive), one > > could use a variational formulation instead of a partial derivative > > formulation in order to describe/build the universe leading again to > > a construction in which the time in the computer is not related at > > all to the time in the simulated universe. > > Do you have references for these two ideas? I'm wondering, suppose the > universe you're trying to simulate contains a computer that is running a > factoring algorithm on a large number, in order to cryptanalyze somebody's > RSA public key. How could you possibly simulate this universe without > starting from the beginning and working forward in time? Whatever > simulation method you use, if somebody was watching the simulation run, > they'd see the input to the factoring algorithm appear before the output, > right? > >
Re: Is the universe computable?
Jesse Mazer wrote: > Hal Finney wrote: > >Suppose we sought to construct a consistent history of such a CA system > >by first starting with purely random values at each point in space and > >time. Now, obviously this arrangement will not satisfy the CA rules. > >But then we go through and start modifying things locally so as to > >satisfy the rules. We move around through the mesh in some pattern, > >repeatedly making small modifications so as to provide local obedience > >to the rules. Eventually, if we take enough time, we ought to reach a > >point where the entire system satisfies the specified rules. > > Would this be guaranteed to work? You might get local regions of space and > time that internally follow the rules but that are incompatible at their > boundaries, like domains in a magnet. The algorithm would keep trying to > modify things to make them globally consistent of course, but isn't it > possible it'd get stuck in a loop? Yes, you might have to do it carefully in order to avoid that. I think that if you had a stochastic (random) element to the algorithm then it would avoid loops. And you'd also have to be prepared to change your boundary conditions so that you weren't trying to solve an impossible state. (I think this part is implicit in Georges' idea of maximizing some criterion rather than using fixed boundary conditions.) Wolfram observationally divided CA universes (and more general computational systems) into four categories: static, cyclic, random and structured. Only the last class would allow for computation. I suspect that those universes capable of computation would be among the hardest ones to solve in this non-sequential way, that they would have the most global dependencies. Universes which were restricted to regular patterns would be easy. (Maybe the random ones would be hard, too, since they tend to be chaotic.) > >Now, I'm not sure how to combine this process with Georges' proposal to > >maximize some criterion such as the gradient of orderliness. I suppose > >you could simply repeat this process many times, saving or remembering > >the best solution found so far. > > As long as everything that happens in the universe's history can be > represented by a finite string, this brute-force method is one that's > guaranteed to work...the ultimate version of this would just be to generate > all possible strings of that length, then throw out all the ones that don't > match the laws/boundary conditions you've chosen. This method could also be > used to generate histories satisfying global constraints that could be hard > to simulate in a sequential way, like a universe where backwards time travel > is possible but history must be completely self-consistent, where it is > possible to influence the past but not to change it. Yes, that's a good idea, and it would probably be a shorter and simpler program than my suggestion. I like your idea of time travel universes; this is a mechanism for generating them that shows that they are not logically impossible or contradictory. Several science fiction writers have explored this concept, that time travel is possible and paradoxes will not occur, no matter how unlikely are the events which conspire to keep things consistent. I'm not sure how to estimate the measure of time travel universes. The program to generate them is not necessarily large, but there would be many fewer consistent solutions to the equations than in universes without time travel. So perhaps there would be fewer observers in time travel universes compared even to ones that might have ad hoc rules forbidding time travel. Such rules might make non time travel universes' programs more complex and the universes of lower measure, but this might be more than compensated for by the greater numbers of observers in universes that forbid time travel. Hal Finney
Re: Is the universe computable?
Hal Finney wrote: Suppose we sought to construct a consistent history of such a CA system by first starting with purely random values at each point in space and time. Now, obviously this arrangement will not satisfy the CA rules. But then we go through and start modifying things locally so as to satisfy the rules. We move around through the mesh in some pattern, repeatedly making small modifications so as to provide local obedience to the rules. Eventually, if we take enough time, we ought to reach a point where the entire system satisfies the specified rules. Would this be guaranteed to work? You might get local regions of space and time that internally follow the rules but that are incompatible at their boundaries, like domains in a magnet. The algorithm would keep trying to modify things to make them globally consistent of course, but isn't it possible it'd get stuck in a loop? Now, I'm not sure how to combine this process with Georges' proposal to maximize some criterion such as the gradient of orderliness. I suppose you could simply repeat this process many times, saving or remembering the best solution found so far. As long as everything that happens in the universe's history can be represented by a finite string, this brute-force method is one that's guaranteed to work...the ultimate version of this would just be to generate all possible strings of that length, then throw out all the ones that don't match the laws/boundary conditions you've chosen. This method could also be used to generate histories satisfying global constraints that could be hard to simulate in a sequential way, like a universe where backwards time travel is possible but history must be completely self-consistent, where it is possible to influence the past but not to change it. Jesse Mazer _ Find out everything you need to know about Las Vegas here for that getaway. http://special.msn.com/msnbc/vivalasvegas.armx
Re: Is the universe computable?
Bruno Marchal wrote: > > At 13:36 09/01/04 +0100, Georges Quenot wrote: > >Bruno Marchal wrote: > > > > > It seems, but it isn't. Well, actually I have known *one* mathematician, > > > (a russian logician) who indeed makes a serious try to develop > > > some mathematics without that infinite act of faith (I don't recall > > > its name for the moment). Such attempt are known as "ultrafinitism". > > > Of course a lot of people (especially during the week-end) *pretend* > > > not doing that infinite act of faith, but do it all the time implicitly. > > > >This is not what I meant. I did not refer to people not willing > >to accept that natural numbers exist at all but to people not > >wlling to accept that natural numbers exist *by themselves*. > >Rather, they want to see them either as only a production of > >human (or human-like) people or only a production of a God. > > What I mean is that their arithmetical property are independent > of us. I don't think this is very different. I could argue that even if natural numbers were not out there, as soon as anybody consider them, their properties automatically come with and impose themselves. Even this seemingly weaker statement can be contested and it is not actually weaker but equivalent since there might be no other way than this one for natural numbers to be out there. Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. > Do you think those people believe that the proposition > "17 is prime" is meaningless without a human in the neighborhood? " "17 is prime" is meaningless without a human in the neighborhood" is exactly the kind of claim these people make (possibly generalizing the concept of human to aliens and Gods). After discussing with some of them I think they actually believe what they claim. I am not sure however that we always fully understand each other and that you or I would exactly understand such a claim in the same way as they do. > Giving that I hope getting some understanding of the complex human > from something simpler (number property) the approach of those > people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. > Also, I would take (without added explanations) an expression > like "numbers are a production of God" as equivalent to > arithmetical realism. Yes and there are several ways to understand this. > >And I said "unfortunately" because some not only do not want to > >see natural numbers as existing by themselves but they do not > >want the idea to be simply presented as logically possible and > >even see/designate evil in people working at popularizing it. > > OK, but then some want you being dead because of the color of the skin, > or the length of your nose, ... I am not sure it is not premature wanting > to enlighten everyone at once ... > I guess you were only talking about those hard-aristotelians who > like to dismiss Plato's questions as childish. Evil ? Perhaps could you be > more precise on those people. I have not met people seeing evil > in arithmetical platonism, have you? I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. Georges Quénot.
Re: Is the universe computable?
Georges Quenot writes: > I do not believe in either case that a simulation with this level > of detail can be conducted on any computer that can be built in > our universe (I mean a computer able to simulate a universe > containing a smaller computer doing the calculation you considered > with a level of accuracy sufficient to ensure that the simulation > of the behavior of the smaller computer would be meaningful). > This is only a theoretical speculation. What about the idea of simulating a universe with simpler laws using such a technique? For example, consider a 2-D or 1-D cellular automaton (CA) system like Conway's "Life" or the various systems considered by Wolfram. Suppose we sought to construct a consistent history of such a CA system by first starting with purely random values at each point in space and time. Now, obviously this arrangement will not satisfy the CA rules. But then we go through and start modifying things locally so as to satisfy the rules. We move around through the mesh in some pattern, repeatedly making small modifications so as to provide local obedience to the rules. Eventually, if we take enough time, we ought to reach a point where the entire system satisfies the specified rules. Now, I'm not sure how to combine this process with Georges' proposal to maximize some criterion such as the gradient of orderliness. I suppose you could simply repeat this process many times, saving or remembering the best solution found so far. But it would be nice if you could combine the two steps somehow, looking for valid solutions which also scored highly in the desired optimization property. Among simple CA models are ones which have been shown to be universal, meaning that you can set up systems which do computation within the CA "universe", and those systems could do various sorts of sequential calculations. Let's suppose, as Georges' ideas might suggest, that some optimization principle can implicitly promote the formation of such sequential computational systems within the simulated universe. To get back to Wei's question, it would seem that when we do manage to create such a universe using non-sequential optimization as described above, there would be no particular need for the early steps of the simulated computation to be stabilized before the later steps. The order in which stabilization occurs in any given run could be essentially arbitrary or random. Hal
Re: Is the universe computable?
On Tue, Jan 13, 2004 at 05:30:10PM +0100, Georges Quenot wrote: > No. They actually came to me while I was figuring some other > ways of simulating a universe than the sequential one that seemed > to give rise to many problems to me. The second one is influenced What's your take on how subjective timeflow looks like in a HashLife universe? http://www.ericweisstein.com/encyclopedias/life/HashLife.html -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Wei Dai wrote: > > On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: > > Many other way of simulating the universe could be considered like > > for instance a 4D mesh (if we simplify by considering only general > > relativity; there is no reason for the approach not being possible in > > an even more general way) representing a universe taken as a whole > > in its spatio-temporal aspect. The mesh would be refined at each > > iteration. The relation between the time in the computer and the time > > in the universe would not be a synchrony but a refinement of the > > resolution of the time (and space) in the simulated universe as the > > time in the computer increases. > > > > Alternatively (though both views are not necessarily exclusive), one > > could use a variational formulation instead of a partial derivative > > formulation in order to describe/build the universe leading again to > > a construction in which the time in the computer is not related at > > all to the time in the simulated universe. > > Do you have references for these two ideas? No. They actually came to me while I was figuring some other ways of simulating a universe than the sequential one that seemed to give rise to many problems to me. The second one is influenced by the prossibility to consider the whole universe within a variational formulation as suggested by Hawking in "A brief history of time" where he also considered the possibility of a boundaryless universe (that makes much sense to me) that would make difficult the use of any (initial or other) boundary condition. Among other problems are the one of defining a global time within a universe ruled by general relativity and including time singularities within black holes for instance. Last but not least is the problem of the emergence of the flow of time itself from the gradient of order within the universe. There might be references which I do not know of and I would say probably for the case of simple physics (possibly fluid dynamics or heat transfer for instance) phenomena which could be simulated in a 3+1 (or 2+1 or 1+1) dimensional meshes as wholes. I think the refining mesh could be practically experimented in a 1D+1D and possibly up to 2D+1D for heat conduction within a solid object with various boundary conditions. While it could much less efficient (but is it even so obvious ?) than a sequential approach, implementing a finite element mesh including the time dimension and solving the partial derivative heat diffusion equations by standard linear algebra on the whole spatio-temporal domain seems perfectly feasable to me (at least for small amounts of time). > I'm wondering, suppose the > universe you're trying to simulate contains a computer that is running a > factoring algorithm on a large number, in order to cryptanalyze somebody's > RSA public key. How could you possibly simulate this universe without > starting from the beginning and working forward in time? Whatever > simulation method you use, if somebody was watching the simulation run, > they'd see the input to the factoring algorithm appear before the output, > right? I would say there is a strong anthropomorphic bias in this view. I suggest you to read my other posts in which I comment a bit about this kind of things. Indeed, the practical implementation of the simulation of the whole universe including the considered computer would be very heavy if a variational formulation and/or a 4D iteratively refining mesh had to be used. But I do not see why it should fail to simulate the computer calculation. What is very difficult is to guarantee that all interactions propagate at the appropriate level of accuracy through all of the 4D mesh and/or through all of the action paths which can be very large and interconnected. No doubt that "close (up to an unimaginable level) to singular" matrices will be encountered. But is this very different if one is to simulate the universe from the big bang up to this computer calculation with the appropriate accuracy needed to ensure that from the big bang initial conditions through stellar formation and human evolution this computer would be built and would run this particular calculation ? I am not so sure. I do not believe in either case that a simulation with this level of detail can be conducted on any computer that can be built in our universe (I mean a computer able to simulate a universe containing a smaller computer doing the calculation you considered with a level of accuracy sufficient to ensure that the simulation of the behavior of the smaller computer would be meaningful). This is only a theoretical speculation. Georges Quénot.
Re: Is the universe computable?
On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote: > > What is the point? Do we have experimental procedure to validate > the opposite of the fanciful scenario? Giving that we were talking about I see, we're at the "prove that the Moon is not made from green cheese when nobody is looking" stage. I thought this list wasn't about ghosties'n'goblins. Allright, I seem to have been mistaken about that. > first person scenario, in any case it is senseless to ask for > experimental procedure. (experience = first person view; experiment = > third person view). So the multiverse is not a falsifyable theory? > Don't tell me you were believing I was arguing. You were asserting a lot of stuff. That's commonly considered arguing, except you weren't providing any evidence so far. So, maybe you weren't. > About logic, it is a branch of mathematics. Like topology, algebra, analysis > it can be *applied* to some problem, which, through some hypothesis, > can bear on some problem. With the comp hyp mathematical logic makes > it possible to derive what consistent and platonist machine can prove about > themselves and their consistent extension. Except that machine doesn't exist in absence of implementations, be it people, machines, or aliens. > >My point is that formal systems are a very powerful tool with very small > >reach, > >unfortunately. > > But I never use formal system. I "modelise" a particular sort of machine by > formal system, so I prove things *about* machines, by using works > *about* formal system. I don't use formal systems. I prove things in > informal > ways like all mathematicians. Above passage is 100% content-free. > >Because we know that QM is not a TOE. You haven't heard? > > How could be *know* QM is not a TOE? (I ask this independently of > the fact that I find plausible QM is not a *primitive* TOE). Because general relativity and quantum theory are mutually incompatible. So both TOE aren't. We have several TOE candidates, and an increased number of blips heralding new physics, but no heir apparent yet. > You believe that the theorem "there is an infinity of primes" is a human > invention? (as opposed to "a human discovery"). Of course. Not necessarily human; there might be other production systems which invented them. Then, maybe there aren't. Infinity is something unphysical, btw. You can't represent arbitrary values within a finite physical system -- all infoprocessing systems are that. You'll also notice that imperfect theories are riddled with infinities; they tend to go away with the next design iteration. So infinities is something even more primatish than enumerable natural numbers. > >I do not see how arithmetic realism (a special case of Platonic realism, is > >that correct?) is an axiom. I agree with the rest of > >your list. > > Perhaps I have been unclear. By Arithmetic Realism I mean that Arithmetical > Truth is independent of me, you, and the rest of humanity. There exist Oh, I disagree with that allright. Nonliving systems don't have an evolutionary pressure to develop enumerable quantities representation. > weaker form of that axiom and stronger form. Tegmark for instance > defends a much larger mathematical realism (so large that I am not sure > what it could mean). As I said some ultrafinitist defends strictly > weaker form of mathematical realism. > The more quoted argument in favour of arithmetical realism is the one based > on Godel's theorem, and presented by him too) which is that any formal > systems (and so any ideally consistent machines) can prove, even in > principle, > that is with infinite time and space, all the true proposition of > arithmetic. Sure. Notice that infinite time and space is unphysical, and of course a machine which doesn't exist doesn't produce anything. I was hoping for a falsifyable argument, showing that this spacetime is an operation artifact of some finite production system. > But look also to the site of Watkins > http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm Oh, basically you're arguing that the unreasonable applicability of mathematics in physics is anything but unreasonable, and that a TOE arisen from a formal system is in fact the universe itself? > for a lot of evidence for it (evidence which are a priori not related to > my more theoretical computer science approach). > Now my goal (here) is not really to defend AR as true, but as sufficiently > plausible > that it is interesting to look at the consequences. You can read some I do not deny that a TOE can be immensely useful (but not necessarily so, higher levels of theory tend to require increasing amounts of crunch to predict anything useful), but that TOE has anything to do with the metalayer, or that in fact that distinction is meaningful. You don't seem to disagree, so we're not actually arguing. > main post I send to this list where I present the argument according to > which if we take comp seriously (comp = AR + TC + "yes docto
Re: Is the universe computable?
[Georges Quenot]>>Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. [Bruno Marchal]>But then what would be an undecidable proposition? >You know, about arithmetic, and about machines btw, a lot of people defends idea >which are just no more plausible since Godel has proved its incompleteness theorems. >Arithmetical proposition are just not tautologies. This is how Russell's and >Whitehead logicism has break down. There is a ladder of arithmetical propositions >which ask for more and more ingenuity to be proved. Actually arithmetical truth >extend far beyond the reach of any consistent machine (and consistent human with >comp). There is an infinity of surprise in there. >I guess you know that there is no natural number p and q such that (p/q)(p/q) is >equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* >this fact for so long? So those propositions are neither tautologies, nor >conventions.David Deutsch, following Johnson's criteria of reality, would say that >such propositions kick back. Since Georges Quenot's objection claims that nothing exists when unconsidered, be it a mathematical structure or concrete singular objects to which it applies, isn't the objection too broad to be singling out any particular physics-based cosmology as objectionable? The objection seems too powerful & broad, & seems to apply with equal force to all subject matters of mathematics & empirical research, from pointset topology to Egyptology. I wouldn't demand that a philosophical objection, in order to be valid at all, offer a direction for specific research, but I'd ask how it would at least help research keep from going wrong, & I don't see how the present objection would help keep any kind of research, mathematical or empirical, from getting onto excessively thin ice, except perhaps by inspiring a general atmosphere of skepticism in response to which people pay more attention to proofs, confirmations, corroborations, etc. -- not that any such thing could actually overcome such a ! radical objection. And the objection is stated with such generality, that I don't see how it escapes being applied to itself, since, after all, it is about things & relations. If there's nobody to consider concrete things or mathematicals, then there's nobody to consider the objection to considering any unconsidered things to exist. The objection seems to undercut itself in the scenario in which it is meant to have force. Unless, of course, I've misunderstood the argument, which is certainly possible. Best, Ben Udell
Re: Is the universe computable?
At 10:14 13/01/04 +0100, Georges Quenot wrote: Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. But then what would be an undecidable proposition? You know, about arithmetic, and about machines btw, a lot of people defends idea which are just no more plausible since Godel has proved its incompleteness theorems. Arithmetical proposition are just not tautologies. This is how Russell's and Whitehead logicism has break down. There is a ladder of arithmetical propositions which ask for more and more ingenuity to be proved. Actually arithmetical truth extend far beyond the reach of any consistent machine (and consistent human with comp). There is an infinity of surprise in there. I guess you know that there is no natural number p and q such that (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* this fact for so long? So those propositions are neither tautologies, nor conventions. David Deutsch, following Johnson's criteria of reality, would say that such propositions kick back. > Giving that I hope getting some understanding of the complex human > from something simpler (number property) the approach of those > people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. Damned!!! If there is one thing which could prevent the foundation of human dignity, it is certainly that totalitarian idea following which some ideas can not even be considered as an hypothesis or conjecture. But that happens all the time. There has been days you could be burned even just because you ask yourself if by chance it was not the sun but the earth which was moving. Are you defending those guys? Are you asking me how to reply to those guy? My suggestion: if many people things like that around you, just leave them. Like Valery said, those who are not willing to use logic with you (that is to argument) are in war with you. Run or kill them! It is not enough they have good intention, if they does not want arguments, they are dangerous for all humans. I like to insist, in Valery spirit, that logic is not a question of truth, but of politeness. I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. Then what? If they disagree with dialog and argumentation, *I* will consider them as evil. (btw I think there are much more people like that in France and in Belgium, especially in Belgium, but that's another story). If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. They make probably the same confusion of those who believe that determinism is in contradiction with free will. Actually I tend to think that Godel's and other incompleteness result makes comp a sort of vaccine against reductionist view of self and reality (and arithmetic). You know "reason" works only through doubt, and through the ability to listen to different opinions. Now with Godel we can say more, which is that "good faith" never fears "reason" and rationality. Sincere Faith can only extend Ratio, and is always open to dialog. Bruno
Re: Is the universe computable?
At 14:08 13/01/04 +0100, Eugen Leitl wrote: > you be able to do a thing like that. I will not insist on this > startling consequence of COMP or QM, giving that you > postulate physicalism at the start. See my thesis for a proof that > physicalism is incompatible with comp. We have discuss the > immortality question a lot in this list. Do we have an experimental procedure to validate these fanciful scenarios? What is the point? Do we have experimental procedure to validate the opposite of the fanciful scenario? Giving that we were talking about first person scenario, in any case it is senseless to ask for experimental procedure. (experience = first person view; experiment = third person view). If you insist to label me thusly. But, really, instead of glib assertions and pointers to your thesis (what has formal logic to do with reality?) you are not being very convincing so far. Don't tell me you were believing I was arguing. About logic, it is a branch of mathematics. Like topology, algebra, analysis it can be *applied* to some problem, which, through some hypothesis, can bear on some problem. With the comp hyp mathematical logic makes it possible to derive what consistent and platonist machine can prove about themselves and their consistent extension. My point is that formal systems are a very powerful tool with very small reach, unfortunately. But I never use formal system. I "modelise" a particular sort of machine by formal system, so I prove things *about* machines, by using works *about* formal system. I don't use formal systems. I prove things in informal ways like all mathematicians. Because we know that QM is not a TOE. You haven't heard? How could be *know* QM is not a TOE? (I ask this independently of the fact that I find plausible QM is not a *primitive* TOE). This is ridiculous. You're referring to a specific notation, which needs systems to produce and to parse. Remove all instances of such systems, and everything is instanstly meaningless. You believe that the theorem "there is an infinity of primes" is a human invention? (as opposed to "a human discovery"). > Perhaps we should put our hypothesis on the table. Mine is > comp by which I mean arithmetical realism, Church thesis, and > the "yes doctor" hypothesis, that is the hypothesis that there is > a level of description of myself such that I don't detect any differences > in case my parts are functionaly substituted by digitalizable device. > Do you think those postulates are inconsistent? I do not see how arithmetic realism (a special case of Platonic realism, is that correct?) is an axiom. I agree with the rest of your list. Perhaps I have been unclear. By Arithmetic Realism I mean that Arithmetical Truth is independent of me, you, and the rest of humanity. There exist weaker form of that axiom and stronger form. Tegmark for instance defends a much larger mathematical realism (so large that I am not sure what it could mean). As I said some ultrafinitist defends strictly weaker form of mathematical realism. The more quoted argument in favour of arithmetical realism is the one based on Godel's theorem, and presented by him too) which is that any formal systems (and so any ideally consistent machines) can prove, even in principle, that is with infinite time and space, all the true proposition of arithmetic. But look also to the site of Watkins http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm for a lot of evidence for it (evidence which are a priori not related to my more theoretical computer science approach). Now my goal (here) is not really to defend AR as true, but as sufficiently plausible that it is interesting to look at the consequences. You can read some main post I send to this list where I present the argument according to which if we take comp seriously (comp = AR + TC + "yes doctor") then physics is eventually a branch of machine's psychology (itself a branch of computer science" itself a branch of number theory. If you find an error, or an imprecision, please show them. Or, if there is a point you don't understand, it will be a pleasure for me to provide more explanations. Also, I thought you were postulating an universe, aren't you? (I just try to figure out your philosophical basic hypothesis). Regards, Bruno
Re: Is the universe computable?
On Tue, Jan 13, 2004 at 12:24:07PM +0100, Bruno Marchal wrote: > >If I'd kill you, you'd have no chance of thinking that thought. > > Actually this is pure wishful thinking, unless you mean succeeding I was referring to a gedanken experiment, of course. > to kill me and my counterparts in some absolute way, but how would There are several ways imaginable, I'll point you to http://www.foresight.org/NanoRev/Ecophagy.html I don't see how the manner of destruction of the local pocket of biological life (which seems to be the only one in the visible universe) has anything to do with the validity of the argument. It's just implementation details. > you be able to do a thing like that. I will not insist on this > startling consequence of COMP or QM, giving that you > postulate physicalism at the start. See my thesis for a proof that > physicalism is incompatible with comp. We have discuss the > immortality question a lot in this list. Do we have an experimental procedure to validate these fanciful scenarios? Multiverses are nice and all; so what flavour of kool aid do you prefer? > >If I killed > >all animals capable of counting, "abstract immaterial numbers" would become > >exactly that: immaterial. > > OK. But "immaterial" does not mean "not existing". Even a physicalist can > accept that. Only very reductionist forms of physicalism reject that. If you insist to label me thusly. But, really, instead of glib assertions and pointers to your thesis (what has formal logic to do with reality?) you are not being very convincing so far. > >The universe does what it does, it certainly doesn't solve equations. > > So we agree. (but note that anything does what it does, so what is your > point). My point is that formal systems are a very powerful tool with very small reach, unfortunately. > > > >People > >solve equations, when approximating what universe does. As such, QM is a > >fair > >approximation; it has no further reality beyond that. > > > That is your opinion, which is not really relevant for the question > we are talking about. Because we know that QM is not a TOE. You haven't heard? We don't have a TOE. If there's such a thing as a TOE, there might be several equivalent. I would really like to see an algorithm, showing that any TOEs are equivalent. > >H\psi=E\psi in absence of context is just as meaningless as 2+2=4. > > > I can understand that point and respect that opinion, but > what makes you so sure. Could you give me a context in > which H\psiis not equal to E\psi ? Could you give me a context in > which 2+2 is not equal to 4, and where 2, +, 4, = have their > usual standard meaning? This is ridiculous. You're referring to a specific notation, which needs systems to produce and to parse. Remove all instances of such systems, and everything is instanstly meaningless. > Perhaps we should put our hypothesis on the table. Mine is > comp by which I mean arithmetical realism, Church thesis, and > the "yes doctor" hypothesis, that is the hypothesis that there is > a level of description of myself such that I don't detect any differences > in case my parts are functionaly substituted by digitalizable device. > Do you think those postulates are inconsistent? I do not see how arithmetic realism (a special case of Platonic realism, is that correct?) is an axiom. I agree with the rest of your list. -- Eugen* Leitl http://leitl.org";>leitl __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Hi John, At 10:39 12/01/04 -0500, John M wrote: Bruno, in the line you touched with 'numbers: I was arguing on another list 'pro' D.Bohm's "there are no numbers in nature" position ... But what is "nature" ? I have never said that numbers exist in nature. The word "nature" or the word "universe" are sort of deities for atheist or naturalist (as I said in the FOR list recently). Such concept, it seems to me, explain nothing, and I have not yet see definitive evidence for those things to exist. Now, when I say that number property exist independently of me, just mean that 2+2 = 4 wil remain true even if Eugen kill me. The concept of life-insurance would not have meaning without such an act of faith. To believe that "2+2=4" would be meaningless aafter a meteor strikes earth seems to me a very large anthropomorphism. ... when a listmember asked: "aren't you part of nature? then why are you saying that numbers - existing in your mind - are not 'part of nature'?" Since then I formulate it something like: numbers came into existence as products of 'our' thinking. (Maybe better worded). OK John, you are not the only one, but you know I try to explain thinking in term of turing programs which relies on number properties. Also I believe that 317 is a prime number, even when no one thinks about it. That the AR (Arithmetical Realism) part of comp, which I *postulate*. You wrote: > What I mean is that their arithmetical property are independent of us. ..< That may branch into the question how much of 'societal' knowledge is part of an individual belief - rejectable or intrinsically adherent? (Some may call this a fundamental domain of memes). With the 'invention' of numbers (arithmetical, that is) human mentality turned into a computing animal - as a species-characteristic. I separate this from the assignment of quantities to well chosen units in numbers. Quantities may have their natural role in natural processes - unconted in our units, just mass-wise, and we, later on - in physical laws - applied the arithmetical ordering to the observations in the quantized natural events. But I do not the nature postulate at all. I follow Plato, not Aristotle. Such quantizing (restricted to models of already discovered elements) renders some processes 'chaotic' or even paradoxical, while nature processes them without any problem in her unrestricted (total) interconnectedness (not included - even known ALL in our quantized working models). Sorry for the "physicistically" unorthodox idea. It seems to me physicalism is quite orthodox these days, honestly. Best Regards, Bruno
Re: Is the universe computable?
At 16:37 12/01/04 +0100, Eugen Leitl wrote: If I'd kill you, you'd have no chance of thinking that thought. Actually this is pure wishful thinking, unless you mean succeeding to kill me and my counterparts in some absolute way, but how would you be able to do a thing like that. I will not insist on this startling consequence of COMP or QM, giving that you postulate physicalism at the start. See my thesis for a proof that physicalism is incompatible with comp. We have discuss the immortality question a lot in this list. If I killed all animals capable of counting, "abstract immaterial numbers" would become exactly that: immaterial. OK. But "immaterial" does not mean "not existing". Even a physicalist can accept that. Only very reductionist forms of physicalism reject that. > Pebbles can't count themselves, obviously. But it is not because > pebbles can't count that two pebbles give an even number of pebbles. > Electron cannot solve schroedinger equation (only a physicist can do that), > nevertheless electron cannot not follow it (supposing QM). The universe does what it does, it certainly doesn't solve equations. So we agree. (but note that anything does what it does, so what is your point). People solve equations, when approximating what universe does. As such, QM is a fair approximation; it has no further reality beyond that. That is your opinion, which is not really relevant for the question we are talking about. H\psi=E\psi in absence of context is just as meaningless as 2+2=4. I can understand that point and respect that opinion, but what makes you so sure. Could you give me a context in which H\psiis not equal to E\psi ? Could you give me a context in which 2+2 is not equal to 4, and where 2, +, 4, = have their usual standard meaning? Perhaps we should put our hypothesis on the table. Mine is comp by which I mean arithmetical realism, Church thesis, and the "yes doctor" hypothesis, that is the hypothesis that there is a level of description of myself such that I don't detect any differences in case my parts are functionaly substituted by digitalizable device. Do you think those postulates are inconsistent? Bruno
Re: Is the universe computable?
On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: > Many other way of simulating the universe could be considered like > for instance a 4D mesh (if we simplify by considering only general > relativity; there is no reason for the approach not being possible in > an even more general way) representing a universe taken as a whole > in its spatio-temporal aspect. The mesh would be refined at each > iteration. The relation between the time in the computer and the time > in the universe would not be a synchrony but a refinement of the > resolution of the time (and space) in the simulated universe as the > time in the computer increases. > > Alternatively (though both views are not necessarily exclusive), one > could use a variational formulation instead of a partial derivative > formulation in order to describe/build the universe leading again to > a construction in which the time in the computer is not related at > all to the time in the simulated universe. Do you have references for these two ideas? I'm wondering, suppose the universe you're trying to simulate contains a computer that is running a factoring algorithm on a large number, in order to cryptanalyze somebody's RSA public key. How could you possibly simulate this universe without starting from the beginning and working forward in time? Whatever simulation method you use, if somebody was watching the simulation run, they'd see the input to the factoring algorithm appear before the output, right?
Re: Is the universe computable?
Bruno, in the line you touched with 'numbers: I was arguing on another list 'pro' D.Bohm's "there are no numbers in nature" position when a listmember asked: "aren't you part of nature? then why are you saying that numbers - existing in your mind - are not 'part of nature'?" Since then I formulate it something like: numbers came into existence as products of 'our' thinking. (Maybe better worded). You wrote: > What I mean is that their arithmetical property are independent of us. ..< That may branch into the question how much of 'societal' knowledge is part of an individual belief - rejectable or intrinsically adherent? (Some may call this a fundamental domain of memes). With the 'invention' of numbers (arithmetical, that is) human mentality turned into a computing animal - as a species-characteristic. I separate this from the assignment of quantities to well chosen units in numbers. Quantities may have their natural role in natural processes - unconted in our units, just mass-wise, and we, later on - in physical laws - applied the arithmetical ordering to the observations in the quantized natural events. Such quantizing (restricted to models of already discovered elements) renders some processes 'chaotic' or even paradoxical, while nature processes them without any problem in her unrestricted (total) interconnectedness (not included - even known ALL in our quantized working models). Sorry for the "physicistically" unorthodox idea. Best regards John Mikes - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, January 12, 2004 9:50 AM Subject: Re: Is the universe computable? > At 13:36 09/01/04 +0100, Georges Quenot wrote: > >Bruno Marchal wrote: > > > > > It seems, but it isn't. Well, actually I have known *one* mathematician, > > > (a russian logician) who indeed makes a serious try to develop > > > some mathematics without that infinite act of faith (I don't recall > > > its name for the moment). Such attempt are known as "ultrafinitism". > > > Of course a lot of people (especially during the week-end) *pretend* > > > not doing that infinite act of faith, but do it all the time implicitly. > > > >This is not what I meant. I did not refer to people not willing > >to accept that natural numbers exist at all but to people not > >wlling to accept that natural numbers exist *by themselves*. > >Rather, they want to see them either as only a production of > >human (or human-like) people or only a production of a God. > > > What I mean is that their arithmetical property are independent > of us. Do you think those people believe that the proposition > "17 is prime" is meaningless without a human in the neighborhood? > Giving that I hope getting some understanding of the complex human > from something simpler (number property) the approach of those > people will never work, for me. > Also, I would take (without added explanations) an expression > like "numbers are a production of God" as equivalent to > arithmetical realism. Of course if you add that God is a > mathematical-conventionalist and that God could have chose > that only even numbers exist, then I would disagree. > (Despite my training in believing at least five impossible > proposition each day before breakfast ;-) > > > >And I said "unfortunately" because some not only do not want to > >see natural numbers as existing by themselves but they do not > >want the idea to be simply presented as logically possible and > >even see/designate evil in people working at popularizing it. > > > OK, but then some want you being dead because of the color of the skin, > or the length of your nose, ... I am not sure it is not premature wanting > to enlighten everyone at once ... > I guess you were only talking about those hard-aristotelians who > like to dismiss Plato's questions as childish. Evil ? Perhaps could you be > more precise on those people. I have not met people seeing evil > in arithmetical platonism, have you? > > Bruno >
