Re: Occam's Razor now published
"Why Occam's Razor" can be viewed at
http://parallel.hpc.unsw.edu.au/rks/docs/occam/
The abstract:
"Ensemble theories have received a lot of interest recently as a means of
explaining a lot of the detailed complexity observed in reality by a vastly
simpler description ``every possibility exists'' and a selection principle
(Anthropic Principle) ``we only observe that which is consistent with our
existence''. In this paper I show why, in an ensemble theory of the
universe, we should be inhabiting one of the elements of that ensemble with
least information content that satisfies the anthropic principle. This
explains the effectiveness of aesthetic principles such as Occam's razor in
predicting usefulness of scientific theories. I also show, with a couple of
reasonable assumptions about the phenomenon of consciousness, the linear
structure of quantum mechanics can be derived. "
- Original Message -
> At 15:16 27/01/04 +1100, Russell Standish wrote:
> >A brief heads up that my paper "Why Occam's Razor" will appear in the
> >June issue of Foundations of Physics Letters. The full reference is:
> >
> >Standish, R.K. (2004) ``Why Occam's Razor'' Foundations of Physics
> >Letters, 17, 255-266.
> >
>
>---
-
> >A/Prof Russell Standish Director
> >High Performance Computing Support Unit, Phone 9385 6967, 8308 3119
(mobile)
> >UNSW SYDNEY 2052Fax 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: Modern Physical theory as a basis for Ethical and Existential Nihilism
The big difference between ethical and aesthetic axioms and the axioms of empirical science is that the latter are so widely accepted that they are not even recognised as axioms, for the most part. If I say "water boils at 100 degrees celcius", this can be proved or disproved to the satisfaction of just about anyone by measuring the temperature of boiling water on several different occasions with several different thermometers. The means of verification contains as it were "hidden" axioms: that checking the boiling point several times with different equipment and obtaining consistent results allows one to generalise about the boiling point of a substance under certain conditions. One could go a level deeper and point out the (axiomatic) assumption that a physical law proved here and now applies to all time and space, the assumption that a logical deduction applies to all possible universes, the "axioms" of logic itself, including rules for using the term "axiom", definition of "rule", definition of "definition"... Fortunately, we hardly ever have to go to such lengths in scientific fields because everyone agrees on the basic axioms. Now that I think of it, this could be used to define a field as a science: a field is a scientific field when the underlying axioms are well-defined and not in dispute by the scholars in that field. This all stands in stark contrast to ethics and aesthetics, where axiomatic statements (defined as statements taken as given, not dependent on any more basic assumptions) are in dispute all the time. For the record, I am all in favour of being nice to people, opposed to torture and murder, etc. I take these as "axiomatic", meaning that I cannot give a more basic reason behind my acceptance of these beliefs. Some philosophers may push the axiom one level lower, and say, for example, "murder is wrong _because_ it decreases the net happiness in the world". In that case, the axiom is the utilitarian belief that "the good is the greatest happiness of the greatest number". However - and this is the point of this extended reply - there are many who would reject these axioms, especially if they are not of a liberal democratic bent, and there is no way to argue against them as being "irrrational" because if the axiom were rational or irrational it wouldn't be an axiom! If an advanced alien species decided to wipe us out because they regard us in the same way as we regard bacteria, do you seriously think you have a chance of convincing them they are doing something "evil"? What will your argument be when they point out the clause in the Handbook of Intergalactic Ethics which says (after the preamble where it says "we hold these truths to be self-evident") "...more advanced species have the right to enslave, consume or destroy less advanced species." It isn't the same as if they got the boiling point of H2O wrong, is it? From: Bruno Marchal <[EMAIL PROTECTED]> To: "Stathis Papaioannou" <[EMAIL PROTECTED]>, [EMAIL PROTECTED] CC: [EMAIL PROTECTED] Subject: Re: Modern Physical theory as a basis for Ethical and Existential Nihilism Date: Tue, 27 Jan 2004 15:05:48 +0100 At 22:17 26/01/04 +1100, Stathis Papaioannou wrote: Yes, this is exactly what I mean. I could be the most rational of people and still consistently hold the evil views I have described (for the sake of argument, of course!). You cannot "prove" that a moral axiom is correct or incorrect, nor can you assume that it will be self-evident to everyone else just because it appears so to you. OK, but is that not true for any axiom of any theory? Let us make a try. Would you accept the following axiom for moral obligation and permission: Obligatory(p) implies permitted(p) No? (it is one of the deontic axiom most people working theoretically on laws accept; obviously a society in which that principle is not respected make it possible for the power in place to put anyone in jail, by just making some service obligatory and also interdicted !) Bruno _ Protect your inbox from harmful viruses with new ninemsn Premium. Click here http://ninemsn.com.au/premium/landing.asp
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: Occam's Razor now published
Congratulations! B.t.w., I don't like the doublespaced version on http://arxiv.org/abs/physics/0001020 - Original Message - From: Russell Standish <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, January 27, 2004 5:16 AM Subject: Occam's Razor now published
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: Modern Physical theory as a basis for Ethical and Existential Nihilism
At 22:17 26/01/04 +1100, Stathis Papaioannou wrote: Yes, this is exactly what I mean. I could be the most rational of people and still consistently hold the evil views I have described (for the sake of argument, of course!), because good and evil. You cannot "prove" that a moral axiom is correct or incorrect, nor can you assume that it will be self-evident to everyone else just because it appears so to you. OK, but is that not true for any axiom of any theory? Let us make a try. Would you accept the following axiom for moral obligation and permission: Obligatory(p) implies permitted(p) No? (it is one of the deontic axiom most people working theoretically on laws accept; obviously a society in which that principle is not respected make it possible for the power in place to put anyone in jail, by just making some service obligatory and also interdicted !) Bruno
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/theory/m3038.html Re:UDA... http://www.escribe.com/science/theory/m3042
Re: Occam's Razor now published
Congratulation Russell, I am very happy for you, it did take some time,
isn't it?
Best regards,
Bruno
At 15:16 27/01/04 +1100, Russell Standish wrote:
A brief heads up that my paper "Why Occam's Razor" will appear in the
June issue of Foundations of Physics Letters. The full reference is:
Standish, R.K. (2004) ``Why Occam's Razor'' Foundations of Physics
Letters, 17, 255-266.
Cheers
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052Fax 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
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
