Re: Tegmark is too "physics-centric"
Hi Stephen, It seems to me that COMP is more general that computationalism since it seems to include certain unfalsifiable postulations that are independent of computationalism per say, AR, to be specific. A can be unfalsifiable, and B can be unfalsifiable, but this does not entail that A & B is unfalsifiable. Take A = "god exists", and B = "God does not exist" as an exemple. I don't know if AR per se is unfalsifiable, but I do show that comp is falsifiable. But you don't have begin to criticize the proof ... My own difficulties with Bruno's thesis hinges on this postulation. I see it as an avoidance of a fundamental difficulty in Foundation research, how to account for the 1st person experience of time if one assumes that Existence in itself is Time-less. I would like to stay modest, but this is well explained once you realise that the simplest thaetetus definition of knowledge, where (I know p) = (p and (I prove p)) leads directly toward an antisymmetric form of branching time modal theory, (S4Grz), very akin to Brouwer's theory of time/consciousness. This is somewhere else that I trip over and fall in my thinking of your work, Bruno. Is this "no mechanism can compute the output of any self-duplication" a classical version of the "no-cloning" theorem? Not so directly, but yes I do think those are related. (But it's a little out of the scope we are presently discussing). Does my comment above about how to bridge this gap of emulating a brain and emulating the entire universe? If it does it would seem to dramatically increase the computational power requirements of the emulating computation on top of the exponential slowdown. One technical question I have about this is: if we assume that the emulated universe is finite, what would be the equation showing the required computational power of the emulator given an estimate of the total algorithmic and/or information content of the universe? The main idea on which most agrees in this list is that the information content of the "everything" (or the multiverse, or UD*, ) is zero. Additionally, what are we to make of results such as the Kochen-Specker theorem that show that given any quantum mechanical system that has more than two independent degrees of freedom can not be completely represented in terms of Boolean algebra? You should say "can not be completely represented with a logical morphisme in a boolean algebra. But that does not entail that some other representation will not work. This is obvious: the theory "quantum mechanics" *is* a boolean theory; the hilbert spaces are classical mathematical object, etc. Or better, take the Goldblatt theorem (which plays a so prominent role in my thesis). It says that (where B is some modal logic): Quantum Logic proves a formula A iff the classical modal theory B proves []<>A. It's like the theorem of Grzegorczyk which says that Intuitionistic Logic proves a formula A iff the classical modal theory S4Grz proves []p. The transformation A => []<>A is just not a morphism in the Kochen & Specker sense. The "physical reality" I extract from comp cannot itself be embedded in a boolean algebra, apparently (I have not yet a totally clean proof of that statement, but let us say that only a high logical conspiracy would make boolean the "arithmetical quantum logic"). Bruno http://iridia.ulb.ac.be/~marchal/
Re: Tegmark is too "physics-centric"
Hi Russell, At 11:50 09/03/04 +1100, Russell Standish wrote: Yes, in your thesis you often talk about survival under replacement of a digital brain (cerveau digital). Digital simply means "operates with 1s and 0s". Since any analogue value can be represented arbitrarily accurately by a digital signal, this doesn't seem much of a stretch. Except that the processing is also digitalized, making things a little less trivial. In your chapter 1, you refer to a "machine universelle digitale, c'est a dire un ordinateur". The English word computer, which is the literal translation of ordinateur, can refer to an analogue computer, which is merely a device for performing computations - it needn't even be Turing complete. Not really. Ordinateur means really (in french) "*universal* computer". If not universal we say "calculateur" (and that one can be analog indeed). The fact that you used the word "universelle" previous does imply Turing completeness, but not that it is equivalent to a Turing machine. After all, I might be concerned if there was some noncomputable part of the brain that was not captured by a Turing machine, but could be built into a digital machine of some kind (eg by accurate copying of the physical layout of the brain). In that case you would be simulable by a computer at *some* level. COMP asks only that, mainly. Now I noticed you used the word "indexical". What does this mean? (I tend to skip over terms I don't understand, in the hope that I understand the gist of the argument). Indexical is an adjective which applies to word like "me", "now", "here" ... I did use "indexical" in "Conscience et Mecanisme", but I don't use it any more. It is implicit in the "Yes Doctor" part of comp where it is supposed that it is *you* who says "yes" to the doctor. Anyway, the upshot of this was that I assumed that COMP was in fact more general that computationalism. In fact I believe the first half of your thesis (chapters 1-4) indeed still hold for this more general interpretation of COMP (namely the necessity for subjective indeterminism etc). Yes. The comp hyp can be weakened. I have not try to prove the most general theorem. True computationalism is perhaps only required for the later sections where you invoke Thaetus's (is that the correct translation of Theetete?) theories of knowledge (connaissance). For here, you need Goedel's theorem, which is applicable in the case of Turing machines. I don't think so. What *is* true is that when I interview the universal machine (through the logic G and G*) I do choose "computationalist universal machine". Such machine believes in the use of classical logic in arithmetic, etc. BTW Goedel theorems apply to a lot more than simple digital machine, in particular it applies to machine with oracle(s). I agree one can simulate the Schroedinger equation of QM (albeit with irrelevant exponential slowdown). However, mapping this back to your "YD" postulate, this involves the doctor swapping the entire universe, not just your brain. Perhaps you mean that one of the options the doctor has is to upload you into a well crafted digital simulation (by a Turing machine even) of you and your complete environment (a la Matrix). This is why in the new version of the argument including those I send to the list sometimes ago I explicitely add the "NEURO" hypothesis (the hypothesis that the brain is in the skull), but then I explicitly show how the NEURO hyp. is eliminated once the Universal Dovetetailer is introduced. After all the DU will generates the many state of my brain whatever it is, if one accept just the fact that we are Turing-emulable. Reminds me of the option Arthur Dent was presented with by the pandimensional beings (aka mice) when they wanted to mince his brain to extract the question for which the answer was '42'. (And this reminds me that string theorists seems to succeed toward getting a reversible theory of black hole. See the nice "economist" summary. There is a link to an abstract from Mathur's paper with outline of the paper.) http://www.economist.com/printedition/displayStory.cfm?Story_ID=2478180 Best Regards, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Tegmark is too "physics-centric"
Dear Russell and Bruno, Interleaving. - Original Message - From: "Russell Standish" <[EMAIL PROTECTED]> To: "Bruno Marchal" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Monday, March 08, 2004 7:50 PM Subject: Re: Tegmark is too "physics-centric" On Fri, Mar 05, 2004 at 02:20:54PM +0100, Bruno Marchal wrote: > > >How does COMP entail that I am a machine? I don't follow that step at all. > > > But comp *is* the assumption that I am a machine, even a digital machine. > My last formulation of it, easy to remember is that comp = YD + CT + RA > YD = Yes doctor, it means you accept a artificial digital brain. > (and CT is Church thesis, and RA is some amount of arithmetical realism). > In "conscience et mecanisme" comp is called MEC-DIG-IND, DIG is for > digital, and IND is for indexical. It really is the doctrine that I am a > digital machine, or that I can be emulated by a digital machine. [RS] Yes, in your thesis you often talk about survival under replacement of a digital brain (cerveau digital). Digital simply means "operates with 1s and 0s". Since any analogue value can be represented arbitrarily accurately by a digital signal, this doesn't seem much of a stretch. In your chapter 1, you refer to a "machine universelle digitale, c'est a dire un ordinateur". The English word computer, which is the literal translation of ordinateur, can refer to an analogue computer, which is merely a device for performing computations - it needn't even be Turing complete. The fact that you used the word "universelle" previous does imply Turing completeness, but not that it is equivalent to a Turing machine. After all, I might be concerned if there was some noncomputable part of the brain that was not captured by a Turing machine, but could be built into a digital machine of some kind (eg by accurate copying of the physical layout of the brain). *** [SPK] I think that the key here is something like a 1st person version of a Turing Test: If you can not tell a difference between one's world of experience while in a "meat machine" - brain - and a digital machine then it is not a difference. Substantivalists will try to dispute this but that is a debate for another day. This would seem to require only that there sufficient expressiveness within the digital machine's n-ary representation to encode all of the fullness of all 1st person experiences that whatever kind of "machine" - meat or silicon or whatever - could have. *** [RS] Now I noticed you used the word "indexical". What does this mean? (I tend to skip over terms I don't understand, in the hope that I understand the gist of the argument). Anyway, the upshot of this was that I assumed that COMP was in fact more general that computationalism. In fact I believe the first half of your thesis (chapters 1-4) indeed still hold for this more general interpretation of COMP (namely the necessity for subjective indeterminism etc). True computationalism is perhaps only required for the later sections where you invoke Thaetus's (is that the correct translation of Theetete?) theories of knowledge (connaissance). For here, you need Goedel's theorem, which is applicable in the case of Turing machines. *** [SPK] It seems to me that COMP is more general that computationalism since it seems to include certain unfalsifiable postulations that are independent of computationalism per say, AR, to be specific. My own difficulties with Bruno's thesis hinges on this postulation. I see it as an avoidance of a fundamental difficulty in Foundation research, how to account for the 1st person experience of time if one assumes that Existence in itself is Time-less. > >> Computationnalism is really the "modern" digital version of "Mechanism" > >> a philosophy guessed by early Hindouist, Plato, ... accepted for animals > >> by > >> Descartes, for humans by La Mettrie, Hobbes, etc. With Church > >> thesis mechanism can leads to pretty mind/matter theories. > >> > >[RS] > >If one accepts mechanisms that go beyond the Turing machine, then > >computationalism is a stricter assumption than mere mechanism (which I > >basically interpret as "anti-vitalism"). > > > >I would counter that a Geiger counter hooked up to a radioactive > >source is a "mechanism", yet the output cannot be computed by a Turing > >machine. (Of course some people, such as Schmidhuber would disagree > >with that too, but that's another story). > [BM] > But no mechanism can compute the output of any self-duplication. > With Everett formulation of QM, a Geiger counter is emulable by a turing > machine, and the QM indeterminacy is just a f
Re: Tegmark is too "physics-centric"
On Fri, Mar 05, 2004 at 02:20:54PM +0100, Bruno Marchal wrote:
>
> >How does COMP entail that I am a machine? I don't follow that step at all.
>
>
> But comp *is* the assumption that I am a machine, even a digital machine.
> My last formulation of it, easy to remember is that comp = YD + CT + RA
> YD = Yes doctor, it means you accept a artificial digital brain.
> (and CT is Church thesis, and RA is some amount of arithmetical realism).
> In "conscience et mecanisme" comp is called MEC-DIG-IND, DIG is for
> digital, and IND is for indexical. It really is the doctrine that I am a
> digital
> machine, or that I can be emulated by a digital machine.
>
Yes, in your thesis you often talk about survival under replacement of
a digital brain (cerveau digital). Digital simply means "operates with
1s and 0s". Since any analogue value can be represented arbitrarily
accurately by a digital signal, this doesn't seem much of a stretch.
In your chapter 1, you refer to a "machine universelle digitale, c'est
a dire un ordinateur". The English word computer, which is the literal
translation of ordinateur, can refer to an analogue computer, which is
merely a device for performing computations - it needn't even be
Turing complete. The fact that you used the word "universelle"
previous does imply Turing completeness, but not that it is equivalent
to a Turing machine. After all, I might be concerned if there was some
noncomputable part of the brain that was not captured by a Turing
machine, but could be built into a digital machine of some kind (eg by
accurate copying of the physical layout of the brain).
Now I noticed you used the word "indexical". What does this mean? (I
tend to skip over terms I don't understand, in the hope that I
understand the gist of the argument).
Anyway, the upshot of this was that I assumed that COMP was in fact
more general that computationalism. In fact I believe the first half
of your thesis (chapters 1-4) indeed still hold for this more general
interpretation of COMP (namely the necessity for subjective
indeterminism etc). True computationalism is perhaps only required for
the later sections where you invoke Thaetus's (is that the correct
translation of Theetete?) theories of knowledge (connaissance). For
here, you need Goedel's theorem, which is applicable in the case of
Turing machines.
>
>
> >> Computationnalism is really the "modern" digital version of "Mechanism"
> >> a philosophy guessed by early Hindouist, Plato, ... accepted for animals
> >by
> >> Descartes, for humans by La Mettrie, Hobbes, etc. With Church
> >> thesis mechanism can leads to pretty mind/matter theories.
> >>
> >
> >If one accepts mechanisms that go beyond the Turing machine, then
> >computationalism is a stricter assumption than mere mechanism (which I
> >basically interpret as "anti-vitalism").
> >
> >I would counter that a Geiger counter hooked up to a radioactive
> >source is a "mechanism", yet the output cannot be computed by a Turing
> >machine. (Of course some people, such as Schmidhuber would disagree
> >with that too, but that's another story).
>
> But no mechanism can compute the output of any self-duplication.
> With Everett formulation of QM, a Geiger counter is emulable by a turing
> machine, and the QM indeterminacy is just a first person comp indeterminacy.
> You cannot emulate with a turing machine the *first person* knowledge
> he/she gets from looking at the Geiger counts, but no machine can
> predict the first person knowledge of a Washington/Moscow self-duplication
> either.
>
> Bruno
I agree one can simulate the Schroedinger equation of QM (albeit with
irrelevant exponential slowdown). However, mapping this back to your
"YD" postulate, this involves the doctor swapping the entire universe,
not just your brain. Perhaps you mean that one of the options the
doctor has is to upload you into a well crafted digital simulation (by
a Turing machine even) of you and your complete environment (a la
Matrix).
Reminds me of the option Arthur Dent was presented with by the
pandimensional beings (aka mice) when they wanted to mince his brain
to extract the question for which the answer was '42'.
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: Tegmark is too "physics-centric"
At 09:08 03/03/04 +1100, Russell Standish wrote: On Tue, Mar 02, 2004 at 12:28:04PM +0100, Bruno Marchal wrote: > > > >RS As I understand it, COMP refers to the conjunction of: > > > >1) Arithmetic realism > >2) Church-Turing thesis > >3) Survivability of consciousness under duplication > > > > BM...and annihilation of the "original" (if not it could be trivial). I guess > that's what you intended to mean. and I add, digital "duplication". (that's why Church thesis has to be called for) How does COMP entail that I am a machine? I don't follow that step at all. But comp *is* the assumption that I am a machine, even a digital machine. My last formulation of it, easy to remember is that comp = YD + CT + RA YD = Yes doctor, it means you accept a artificial digital brain. (and CT is Church thesis, and RA is some amount of arithmetical realism). In "conscience et mecanisme" comp is called MEC-DIG-IND, DIG is for digital, and IND is for indexical. It really is the doctrine that I am a digital machine, or that I can be emulated by a digital machine. > Computationnalism is really the "modern" digital version of "Mechanism" > a philosophy guessed by early Hindouist, Plato, ... accepted for animals by > Descartes, for humans by La Mettrie, Hobbes, etc. With Church > thesis mechanism can leads to pretty mind/matter theories. > If one accepts mechanisms that go beyond the Turing machine, then computationalism is a stricter assumption than mere mechanism (which I basically interpret as "anti-vitalism"). I would counter that a Geiger counter hooked up to a radioactive source is a "mechanism", yet the output cannot be computed by a Turing machine. (Of course some people, such as Schmidhuber would disagree with that too, but that's another story). But no mechanism can compute the output of any self-duplication. With Everett formulation of QM, a Geiger counter is emulable by a turing machine, and the QM indeterminacy is just a first person comp indeterminacy. You cannot emulate with a turing machine the *first person* knowledge he/she gets from looking at the Geiger counts, but no machine can predict the first person knowledge of a Washington/Moscow self-duplication either. Bruno
Re: Tegmark is too "physics-centric"
On Tue, Mar 02, 2004 at 12:28:04PM +0100, Bruno Marchal wrote:
> >
> >As I understand it, COMP refers to the conjunction of:
> >
> >1) Arithmetic realism
> >2) Church-Turing thesis
> >3) Survivability of consciousness under duplication
>
>
>
> ...and annihilation of the "original" (if not it could be trivial). I guess
> that's what you intended to mean.
>
>
>
> >Computationalism (as I understand it) is the strong AI principle -
> >that a program running on a Turing machine (or equivalent) is
> >sufficient to generate consciousness. A stronger version might be that
> >all conscious processes can be represented by a program. I can see how
> >3) follows from this stronger version - but I don't see how
> >computationalism follows from COMP.
>
>
>
> Well, that's really a question of vocabulary. I prefer to say Strong AI
> for ... the strong AI thesis. I guess also you intended to say that COMP
> does not follow from the Strong AI thesis, because the fact that machines
> can think does not entail that we are machine (machine can think does not
> entail that *only* machines can think). But COMP entails the strong AI
> thesis,
> because if I am a machine then machines can think. (accepting the
> perhaps foolish idea that *I* can think :)
How does COMP entail that I am a machine? I don't follow that step at all.
> Computationnalism is really the "modern" digital version of "Mechanism"
> a philosophy guessed by early Hindouist, Plato, ... accepted for animals by
> Descartes, for humans by La Mettrie, Hobbes, etc. With Church
> thesis mechanism can leads to pretty mind/matter theories.
>
If one accepts mechanisms that go beyond the Turing machine, then
computationalism is a stricter assumption than mere mechanism (which I
basically interpret as "anti-vitalism").
I would counter that a Geiger counter hooked up to a radioactive
source is a "mechanism", yet the output cannot be computed by a Turing
machine. (Of course some people, such as Schmidhuber would disagree
with that too, but that's another story).
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
--
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: Tegmark is too "physics-centric"
Dear Bruno, - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, March 02, 2004 6:28 AM Subject: Re: Tegmark is too "physics-centric" > At 09:14 02/03/04 +1100, Russell Standish wrote: snip > >As I understand it, COMP refers to the conjunction of: > > > >1) Arithmetic realism > >2) Church-Turing thesis > >3) Survivability of consciousness under duplication > [BM] > ...and annihilation of the "original" (if not it could be trivial). I guess > that's what you intended to mean. What about 3') Survivability of consciouness under quantum teleportation? Stephen
Re: Tegmark is too "physics-centric"
At 09:14 02/03/04 +1100, Russell Standish wrote: On Mon, Mar 01, 2004 at 03:00:30PM +0100, Bruno Marchal wrote: > > > comp assumes only that the sequence 0, 1, 2, 3, 4, 5, 6, ... "lives" in > Platonia. 3-person time apparantly does not appear. 1-person time > appears through the S4Grz logic. > Fair enough - I realised it was a consequence of your mind model. OK. I should come back later on the relation between time, consciousness, Brouwer intuitionist logic and the modal logic S4Grz. > >In terms of the above assumptions, 1) is a consequence of > >computationalism, which I take is a basis of your theory (although > >I've never understood how computationalism follows from COMP). > > > > ? Wait a bit. COMP refers to computationalism. I don't understand. > As I understand it, COMP refers to the conjunction of: 1) Arithmetic realism 2) Church-Turing thesis 3) Survivability of consciousness under duplication ...and annihilation of the "original" (if not it could be trivial). I guess that's what you intended to mean. Computationalism (as I understand it) is the strong AI principle - that a program running on a Turing machine (or equivalent) is sufficient to generate consciousness. A stronger version might be that all conscious processes can be represented by a program. I can see how 3) follows from this stronger version - but I don't see how computationalism follows from COMP. Well, that's really a question of vocabulary. I prefer to say Strong AI for ... the strong AI thesis. I guess also you intended to say that COMP does not follow from the Strong AI thesis, because the fact that machines can think does not entail that we are machine (machine can think does not entail that *only* machines can think). But COMP entails the strong AI thesis, because if I am a machine then machines can think. (accepting the perhaps foolish idea that *I* can think :) Computationnalism is really the "modern" digital version of "Mechanism" a philosophy guessed by early Hindouist, Plato, ... accepted for animals by Descartes, for humans by La Mettrie, Hobbes, etc. With Church thesis mechanism can leads to pretty mind/matter theories. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Tegmark is too "physics-centric"
On Mon, Mar 01, 2004 at 03:00:30PM +0100, Bruno Marchal wrote:
>
>
> comp assumes only that the sequence 0, 1, 2, 3, 4, 5, 6, ... "lives" in
> Platonia. 3-person time apparantly does not appear. 1-person time
> appears through the S4Grz logic.
>
Fair enough - I realised it was a consequence of your mind model.
>
>
> >In terms of the above assumptions, 1) is a consequence of
> >computationalism, which I take is a basis of your theory (although
> >I've never understood how computationalism follows from COMP).
>
>
>
> ? Wait a bit. COMP refers to computationalism. I don't understand.
>
As I understand it, COMP refers to the conjunction of:
1) Arithmetic realism
2) Church-Turing thesis
3) Survivability of consciousness under duplication
Computationalism (as I understand it) is the strong AI principle -
that a program running on a Turing machine (or equivalent) is
sufficient to generate consciousness. A stronger version might be that
all conscious processes can be represented by a program. I can see how
3) follows from this stronger version - but I don't see how
computationalism follows from COMP.
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: Tegmark is too "physics-centric"
At 10:33 28/02/04 +1100, Russell Standish wrote: I deliberately leave vague what is in the theory of the mind, but simply assume a small number of things about consciousness: 1) That there is a linear dimension called (psycholgical) time, in which the conscious mind find itself embedded 2) The observations are a form of a projection from the set of subsets of possibilities onto the same set. We identify a QM "state" with a subset of possibilities. 3) The Kolmogorov probability axioms 4) The anthropic principle 5) Sets of observers are measurable Also I assume the existance of the set of all descriptions (which I call the Schmidhuber ensemble, but perhaps more accurately should be called the Schmidhuber I ensemble to distance it from later work of his). This is roughly equivalent to your Arithmetic Realism, but probably not identical. It is the form I prefer philosophically. (I think this is the exhaustive set of assumptions - but I'm willing to have other identified) I only treat continuous time in Occams razor (hence the differential equation) however I do reference the theory of timescales which would provide a way of extending this to other types of time (discrete, rationals etc). In any case, contact with standard QM is only achieved for continuous time. The justification for assuming time is that one needs time in order to appreciate differences - and differences are the foundation of information - so in order to know anything at all, one needs to appreciate differences hence the need for a time dimension. Note - computationalism requires time in order to compute mind - therefore the assumption of time is actually a weaker assumption than computationalism. comp assumes only that the sequence 0, 1, 2, 3, 4, 5, 6, ... "lives" in Platonia. 3-person time apparantly does not appear. 1-person time appears through the S4Grz logic. In terms of the above assumptions, 1) is a consequence of computationalism, which I take is a basis of your theory (although I've never understood how computationalism follows from COMP). ? Wait a bit. COMP refers to computationalism. I don't understand. 2) corresponds to your 1-3 distinction. Indeed I refer to your work as justification for assuming the projection postulate. That is not clear for me. 3) Causes some people problems - however I notes that some others start from the Kolmogorov probability axioms also. No problem at all with Kolmogorov proba axioms. 4) I know the Anthropic principle causes you problems - indeed I can only remark that it is an empirical fact of our world, and leave it as a mystery to be solved later on. No problem with the so called Weak Anthropic Principle. Although obviously I prefer a Turing-Universal-Machine--thropic principle ... 5) Measurability of observers. This is the part that was buried in the derivation of linearity of QM, that caused you (and me too) some difficulty in understanding what is going on. I spoke to Stephen King on the phone yesterday, and this was one point he stumbled on also. Perhaps this is another "mystery" like the AP, but appears necessary to get the right answer (ie QM !) Of course a more detailed theory of the mind should give a more detailed description of physics. For example - we still don't know where 3+1 spacetime comes from, or why everything appears to be close to Newtonian dynamics. Stephen King is cooking up some more ideas in this line which seems interesting... Thanks for your clarification, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Tegmark is too "physics-centric"
I deliberately leave vague what is in the theory of the mind, but simply assume a small number of things about consciousness: 1) That there is a linear dimension called (psycholgical) time, in which the conscious mind find itself embedded 2) The observations are a form of a projection from the set of subsets of possibilities onto the same set. We identify a QM "state" with a subset of possibilities. 3) The Kolmogorov probability axioms 4) The anthropic principle 5) Sets of observers are measurable Also I assume the existance of the set of all descriptions (which I call the Schmidhuber ensemble, but perhaps more accurately should be called the Schmidhuber I ensemble to distance it from later work of his). This is roughly equivalent to your Arithmetic Realism, but probably not identical. It is the form I prefer philosophically. (I think this is the exhaustive set of assumptions - but I'm willing to have other identified) I only treat continuous time in Occams razor (hence the differential equation) however I do reference the theory of timescales which would provide a way of extending this to other types of time (discrete, rationals etc). In any case, contact with standard QM is only achieved for continuous time. The justification for assuming time is that one needs time in order to appreciate differences - and differences are the foundation of information - so in order to know anything at all, one needs to appreciate differences hence the need for a time dimension. Note - computationalism requires time in order to compute mind - therefore the assumption of time is actually a weaker assumption than computationalism. In terms of the above assumptions, 1) is a consequence of computationalism, which I take is a basis of your theory (although I've never understood how computationalism follows from COMP). 2) corresponds to your 1-3 distinction. Indeed I refer to your work as justification for assuming the projection postulate. 3) Causes some people problems - however I notes that some others start from the Kolmogorov probability axioms also. 4) I know the Anthropic principle causes you problems - indeed I can only remark that it is an empirical fact of our world, and leave it as a mystery to be solved later on. 5) Measurability of observers. This is the part that was buried in the derivation of linearity of QM, that caused you (and me too) some difficulty in understanding what is going on. I spoke to Stephen King on the phone yesterday, and this was one point he stumbled on also. Perhaps this is another "mystery" like the AP, but appears necessary to get the right answer (ie QM !) Of course a more detailed theory of the mind should give a more detailed description of physics. For example - we still don't know where 3+1 spacetime comes from, or why everything appears to be close to Newtonian dynamics. Stephen King is cooking up some more ideas in this line which seems interesting... Cheers On Fri, Feb 27, 2004 at 02:55:33PM +0100, Bruno Marchal wrote: > At 09:19 25/02/04 +1100, Russell Standish wrote: > >I think that "psychological time" fits the bill. The observer needs a > >a temporal dimension in which to appreciate differences between > >states. > > OK. That move makes coherent your attempt to derive physics, > and makes it even compatible with the sort of approach I advocate, > but then: would you agree that you should define or at least > explain what is the "psychological time". More generally: > What is your psychology or your theory of mind? This is (imo) > unclear in your Occam Paper (or I miss something). > I find that assuming time, and the applicability of differential > equation (especially with respect to a psychological time) > is quite huge. > > Bruno > > > > > >"Physical time" presupposes a physics, which I haven't done in > >"Occam". > > > >It is obviously a little more structured than an ordering. A space > >dimension is insufficient for an observer to appreciate differences, > >isn't it? > > > >Cheers > > > >On Tue, Feb 24, 2004 at 02:11:07PM +0100, Bruno Marchal wrote: > >> > >> Hi Russell, > >> > >> Let me try to be a little more specific. You say in your Occam paper > >> at http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html > >> > >> "The first assumption to be made is that observers will find themselves > >> embedded in a temporal dimension. A Turing machine requires time to > >> separate the sequence of states it occupies as it performs a computation. > >> Universal Turing machines are models of how humans compute things, so > >it is > >> possible that all conscious observers are capable of universal > >computation. > >> Yet for our present purposes, it is not necessary to assume observers are > >> capable of universal computation, merely that observers are embedded in > >> time. " > >> > >> Are you meaning physical time, psychological time, or just a (linear) > >> or
Re: Tegmark is too "physics-centric"
At 09:19 25/02/04 +1100, Russell Standish wrote: I think that "psychological time" fits the bill. The observer needs a a temporal dimension in which to appreciate differences between states. OK. That move makes coherent your attempt to derive physics, and makes it even compatible with the sort of approach I advocate, but then: would you agree that you should define or at least explain what is the "psychological time". More generally: What is your psychology or your theory of mind? This is (imo) unclear in your Occam Paper (or I miss something). I find that assuming time, and the applicability of differential equation (especially with respect to a psychological time) is quite huge. Bruno "Physical time" presupposes a physics, which I haven't done in "Occam". It is obviously a little more structured than an ordering. A space dimension is insufficient for an observer to appreciate differences, isn't it? Cheers On Tue, Feb 24, 2004 at 02:11:07PM +0100, Bruno Marchal wrote: > > Hi Russell, > > Let me try to be a little more specific. You say in your Occam paper > at http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html > > "The first assumption to be made is that observers will find themselves > embedded in a temporal dimension. A Turing machine requires time to > separate the sequence of states it occupies as it performs a computation. > Universal Turing machines are models of how humans compute things, so it is > possible that all conscious observers are capable of universal computation. > Yet for our present purposes, it is not necessary to assume observers are > capable of universal computation, merely that observers are embedded in > time. " > > Are you meaning physical time, psychological time, or just a (linear) > order? I am just > trying to have a better understanding.
Re: Tegmark is too "physics-centric"
On Wed, Feb 25, 2004 at 12:08:43AM -0500, Stephen Paul King wrote:
> Dear Russel,
>
> Could we associate this "psychological time" with the orderings that
> obtain when considering successive measurements of various measurements of
> non-commutative canonically conjugate (QM) states?
The word "successive" implies a time dimension already. I'm not sure
what you are proposing here.
> Also, re your Occam's razor paper, have you considered the necessity of
> a principle that applies between observers, more than that involved with the
> Anthropic principle? Something along the lines of: the allowable
> communications between observers is restrained to only those that are
> mutually consistent. We see hints of this in EPR situations. ;-)
>
No I haven't considered this second requirement. It would be
interesting to note whether it is a derivative concept (can be derived
from the standard QM principles say), or whether it needs to be added
in as a fundamental requirement (in which case comes the question of
why).
Cheers
> Kindest regards,
>
> Stephen
>
> - Original Message -
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: "Bruno Marchal" <[EMAIL PROTECTED]>
> Cc: "Russell Standish" <[EMAIL PROTECTED]>;
> <[EMAIL PROTECTED]>
> Sent: Tuesday, February 24, 2004 5:19 PM
> Subject: Re: Tegmark is too "physics-centric"
>
> I think that "psychological time" fits the bill. The observer needs a
> a temporal dimension in which to appreciate differences between
> states.
>
> "Physical time" presupposes a physics, which I haven't done in
> "Occam".
>
> It is obviously a little more structured than an ordering. A space
> dimension is insufficient for an observer to appreciate differences,
> isn't it?
>
> Cheers
>
> snip
>
--
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: Tegmark is too "physics-centric"
Dear Russel, Could we associate this "psychological time" with the orderings that obtain when considering successive measurements of various measurements of non-commutative canonically conjugate (QM) states? Also, re your Occam's razor paper, have you considered the necessity of a principle that applies between observers, more than that involved with the Anthropic principle? Something along the lines of: the allowable communications between observers is restrained to only those that are mutually consistent. We see hints of this in EPR situations. ;-) Kindest regards, Stephen - Original Message - From: "Russell Standish" <[EMAIL PROTECTED]> To: "Bruno Marchal" <[EMAIL PROTECTED]> Cc: "Russell Standish" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Tuesday, February 24, 2004 5:19 PM Subject: Re: Tegmark is too "physics-centric" I think that "psychological time" fits the bill. The observer needs a a temporal dimension in which to appreciate differences between states. "Physical time" presupposes a physics, which I haven't done in "Occam". It is obviously a little more structured than an ordering. A space dimension is insufficient for an observer to appreciate differences, isn't it? Cheers snip
Re: Tegmark is too "physics-centric"
I think that "psychological time" fits the bill. The observer needs a
a temporal dimension in which to appreciate differences between
states.
"Physical time" presupposes a physics, which I haven't done in
"Occam".
It is obviously a little more structured than an ordering. A space
dimension is insufficient for an observer to appreciate differences,
isn't it?
Cheers
On Tue, Feb 24, 2004 at 02:11:07PM +0100, Bruno Marchal wrote:
>
> Hi Russell,
>
> Let me try to be a little more specific. You say in your Occam paper
> at http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html
>
> "The first assumption to be made is that observers will find themselves
> embedded in a temporal dimension. A Turing machine requires time to
> separate the sequence of states it occupies as it performs a computation.
> Universal Turing machines are models of how humans compute things, so it is
> possible that all conscious observers are capable of universal computation.
> Yet for our present purposes, it is not necessary to assume observers are
> capable of universal computation, merely that observers are embedded in
> time. "
>
> Are you meaning physical time, psychological time, or just a (linear)
> order? I am just
> trying to have a better understanding.
>
> Bruno
>
>
>
>
>
>
> At 18:00 23/02/04 +1100, Russell Standish wrote:
> >Comments interspersed.
> >
> >On Sun, Jan 18, 2004 at 07:15:45AM -0500, Kory Heath wrote:
> >>
> >> I understand this perspective, but for what it's worth, I'm profoundly
> >out
> >> of sympathy with it. In my view, computation universality is the real
> >key -
> >> life and consciousness are going to pop up in any universe that's
> >> computation universal, as long as the universe is big enough and/or it
> >> lasts long enough. (And there's always enough time and space in the
> >> Mathiverse!)
> >
> >Computational universality is not sufficient for open-ended evolution
> >of life. In fact we don't what is sufficient, as evidenced by it being
> >an open problem (see Bedau et al., Artificial Life 6, 363.)
> >
> >I also suspect that it is not necessary for the evolution of SASes,
> >but this is obvious a debatable point.
--
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: Tegmark is too "physics-centric"
Hi Russell, Let me try to be a little more specific. You say in your Occam paper at http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html "The first assumption to be made is that observers will find themselves embedded in a temporal dimension. A Turing machine requires time to separate the sequence of states it occupies as it performs a computation. Universal Turing machines are models of how humans compute things, so it is possible that all conscious observers are capable of universal computation. Yet for our present purposes, it is not necessary to assume observers are capable of universal computation, merely that observers are embedded in time. " Are you meaning physical time, psychological time, or just a (linear) order? I am just trying to have a better understanding. Bruno At 18:00 23/02/04 +1100, Russell Standish wrote: Comments interspersed. On Sun, Jan 18, 2004 at 07:15:45AM -0500, Kory Heath wrote: > > I understand this perspective, but for what it's worth, I'm profoundly out > of sympathy with it. In my view, computation universality is the real key - > life and consciousness are going to pop up in any universe that's > computation universal, as long as the universe is big enough and/or it > lasts long enough. (And there's always enough time and space in the > Mathiverse!) Computational universality is not sufficient for open-ended evolution of life. In fact we don't what is sufficient, as evidenced by it being an open problem (see Bedau et al., Artificial Life 6, 363.) I also suspect that it is not necessary for the evolution of SASes, but this is obvious a debatable point.
Re: Tegmark is too "physics-centric"
At 18:00 23/02/04 +1100, Russell Standish wrote: Comments interspersed. On Sun, Jan 18, 2004 at 07:15:45AM -0500, Kory Heath wrote: > > I understand this perspective, but for what it's worth, I'm profoundly out > of sympathy with it. In my view, computation universality is the real key - > life and consciousness are going to pop up in any universe that's > computation universal, as long as the universe is big enough and/or it > lasts long enough. (And there's always enough time and space in the > Mathiverse!) Computational universality is not sufficient for open-ended evolution of life. In fact we don't what is sufficient, as evidenced by it being an open problem (see Bedau et al., Artificial Life 6, 363.) How do you know then that comp universality is not sufficient? (Giving that comp universality entails the non existence of a complete theory of comp-universality; I mean computer science is provably not completely unifiable; there is no general theory for non stopping machines or non stopping comp processes). Are you thinking about something specific which is lacking in comp universality? I also suspect that it is not necessary for the evolution of SASes, but this is obvious a debatable point. Are you saying that "comp" is entirely irrelevant to explain the origin of life, the origin of the universe(s) ? Bruno
Re: Tegmark is too "physics-centric"
Comments interspersed.
On Sun, Jan 18, 2004 at 07:15:45AM -0500, Kory Heath wrote:
>
> I understand this perspective, but for what it's worth, I'm profoundly out
> of sympathy with it. In my view, computation universality is the real key -
> life and consciousness are going to pop up in any universe that's
> computation universal, as long as the universe is big enough and/or it
> lasts long enough. (And there's always enough time and space in the
> Mathiverse!)
Computational universality is not sufficient for open-ended evolution
of life. In fact we don't what is sufficient, as evidenced by it being
an open problem (see Bedau et al., Artificial Life 6, 363.)
I also suspect that it is not necessary for the evolution of SASes,
but this is obvious a debatable point.
> (countably?) infinite. So why would I be more likely to find myself in one
> of those universes rather than the other?
>
> -- Kory
>
The issue of where physics comes from is addressed in my paper "Why
Occams Razor". Dynamics on complex-valued hilbert spaces is the most
likely observed universe. I have just had another discussion with
Stephen King re why we should observe 3+1 spacetime. I am somewhat
unconvinced like you by the arguments put forward in Tegmark's paper
(which aren't due to him at all), but at present its the best we
have. There should be an anthropic reason why 3+1 spacetime is
necessary, or even the most likely dimensionality seen by observers.
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: Tegmark is too "physics-centric"
I don't think there are many intelligent beings per cubic Plank length in our universe at all! In fact, string theorists don't know how to get to the standard model from their favorite theory, yet they still believe in it. Simple deterministic models could certainly explain our laws of physics, as 't Hooft explains in these articles: Determinism beneath Quantum Mechanics: http://arxiv.org/abs/quant-ph/0212095 Quantum Mechanics and Determinism: http://arxiv.org/abs/hep-th/0105105 How Does God Play Dice? (Pre-)Determinism at the Planck Scale: http://arxiv.org/abs/hep-th/0104219 - Original Message - From: Kory Heath <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, January 18, 2004 1:15 PM Subject: Re: Tegmark is too "physics-centric" > At 1/17/04, Hal Finney wrote: > >But let me ask if you agree that considering Conway's 2D > >Life world with simply-specified initial conditions as in your example, > >that conscious life would be extraordinarily rare? > > I certainly agree that it would be "extraordinarily rare", in the sense > that the size of the lattice would need to be very big, and the number of > clock-ticks required would need to be very large. But "big" and "large" are > such relative terms! Clearly, our own universe is very, very big. The > question is, how can we sensibly determine whether life is more likely in > our universe or in Conway's Life universe? > > I don't believe we have anywhere near enough data to answer this question, > but I don't think it's unanswerable in principle. Fredkin actually believes > that our universe is a 3+1D cellular automata, and if anyone ever found > such a description of our physics (or some other fundamentally > computational description), then we could directly compare it with Conway's > Life, determining for each one how big the lattice needs to be, and how > many clock-ticks are required, for life to appear with (say) 90% > probability. (Of course, this determination might be difficult even when we > know the rules of the CAs. But we can try.) > > One thing that you'd have to take into account is the complexity of the > rules you're comparing, including the number of states allowed per cell. > Not only are the rules to Conway's Life extremely simple, but the cells are > binary. All things being equal, I would expect that an increase in the > complexity of the rules and the number of cell-states allowed would > decrease the necessary lattice-size and/or number of clock-ticks required > for SASs to grow out of a pseudo-random initial state. I mention this to > point out a problem with our intuitions about our universe vs. Conway's > Life: the description of our universe is almost certainly more complex than > the description of Conway's Life with a simple initial state. If Fredkin > actually succeeds in finding a 3+1D CA which describes our universe, it > will almost certainly require more than 2 cell-states, and its rules will > certainly be more complex than those of the Life universe. We have to take > this difference into account when trying to compare the two universes, but > we have nowhere near enough data to quantify the difference currently. We > really don't know what size of space in the Life universe is equivalent to > (say) a solar system in this universe. > > In a way, this is all beside the point, since I have no problem believing > that one CA can evolve SASs much more easily than some other CA whose rules > and initial state are exactly as complex. (In fact, this must be true, > since for any CA that supports life at all, there's an equally complex one > that isn't even computation universal.) I have no problem believing that > the Life universe is, in some objective sense, not very conducive to SASs. > Perhaps it's less conducive to SASs than our own universe, although I'm not > convinced. What I have a problem believing is that CAs as a class are > somehow less conducive to observers than quantum-physical models as a > class. In fact, I think it's substantially more likely that there are > relatively simple CA models (and other computational models) that are much > more conducive to SASs than either Conway's Life universe or our own. > Models in which, for instance, neural-net structures arise much more > naturally from the basic physics of the system than they do in our > universe, or the Life universe. > > >In many ways, our universe seems tailor made for creating observers. > > I understand this perspective, but for what it's worth, I'm profoundly out > of sympathy with it. In my view, computation universality is the real key - > life and consciousness ar
Re: Tegmark is too "physics-centric"
On Sat, Jan 17, 2004 at 11:05:18PM -0800, Hal Finney wrote: > Yes, I see that that is true. I think it points to a problem with some > of the simple conceptualizations of measure, about which I will say > more below.But let me ask if you agree that considering Conway's 2D > Life world with simply-specified initial conditions as in your example, > that conscious life would be extraordinarily rare? Life is an universal CA (it is possible to implement Life in Life e.g.), but not all universal CAs are suitably structure to support emergence of life from a random pattern. Biggest problem is translation, Life doesn't support translation of large blocks, so you have to implement storage/copy, it doesn't have noniteractive particles natively, it doesn't conserve noise naturally (you get increasingly rare splotches of noise of gliders colliding with stationary/evolving structures). You could implement a more suitable CA (or any other machine) in Life, but it couldn't emerge naturally (it would have a huge cell unit size), and it's not obvious it could eventually overgrow the entire substrate, once emerged (there might be tricks with perimeter guards, etc., but the whole point is that Life is pretty hostile to emergence of life. > I want to say, vastly more rare than in our universe, but of course we > don't know how rare life actually is in our universe, so that may be a It would be nice if we could find several independently emerged life nucleation points in our solar system (difficult, given the high rates of crosscontamination through impact ejecta). If we don't find them, the emergence of local life is of course causally linked to us, so it's still biased by the anthropic principle. We need other data points, maybe from nearby systems. > hard claim to justify. But the point is that our universe has stable > structures; it has atoms of dozens of different varieties, which can form > uncountable millions of stable molecules. It has mechanisms to generate > varieties of these different molecules and collect them together in > environments where they can react in interesting ways. We don't have a > full picture of how life and consciousness evolved, but looking around, > it doesn't seem like it should have been THAT hard, which is where the > Fermi paradox comes from. In many ways, our universe seems tailor made There's not much of a paradox, if you look at Fermi from anthropic principle angle. And we absolutely can't say how probable emergence of an advanced culture is (given the above). We have been leading unusually sheltered lifes, and there's nothing particularly obvious about us coming into being scant few 100 megayears before the curtain falls on life in the local environment. > for creating observers. > > In contrast, in the Life world there are no equivalents to atoms or > molecules, no chemical reactions. It's too chaotic; there's not enough Life's about patterns, not atoms or reactions. I agree that Life is sterile, however, and there are no obvious tweaks in how make it work better. However, most digital physics people seem to think the unit cell is at Planck scale, or below, and I have absolutely no idea how a Plack scale life would look like on macroscale, considering how much volume one has, and how many iterations occur there. I never figured out how to get rid of grid assymetries shining through to macroscale, and how to generate rule tables with conservation laws intact, but then there are perfectly spherical sound waves, and wave interferece in stupid lattice gas automata, of all things. That's pretty surprising, so perhaps it doesn't make sense to rule out too much yet. > structure. Replicators and life seem to require a balance between > chaos and stasis, and Life is far too dynamic. It just looks to me > like it would be almost impossible for replicators to arise naturally. > Almost impossible, but not absolutely impossible, so if you tried enough > initial conditions as you suggest, it would happen. I won't belabor > this argument unless you disagree about the ease with which life might > arise in a Life universe, and consciousness evolve. I'd rather amazed to see large assemblies capable of translation in Life universe, already. > that those are too parochial. But as I recall he had a number of broad > arguments that would apply even to a Life-like universe. > > This was the motivation for the idea I proposed a few days ago, that > for applying anthropic reasoning, a universe should get a "bonus" if > it had a high density of observers, rather than merely a high absolute I'm not sure how that follows, using anthropic principle and relativistic pioneer expansion wavefront (which directly follows from Darwin, and current knowledge of propulsion methods) the Fermi paradoxon completely disappears. > number of them. It's too easy to create universes with low-density > observers, as your example of Life suggests. But just as the existence > of a counting progr
Re: Tegmark is too "physics-centric"
At 1/17/04, Hal Finney wrote: But let me ask if you agree that considering Conway's 2D Life world with simply-specified initial conditions as in your example, that conscious life would be extraordinarily rare? I certainly agree that it would be "extraordinarily rare", in the sense that the size of the lattice would need to be very big, and the number of clock-ticks required would need to be very large. But "big" and "large" are such relative terms! Clearly, our own universe is very, very big. The question is, how can we sensibly determine whether life is more likely in our universe or in Conway's Life universe? I don't believe we have anywhere near enough data to answer this question, but I don't think it's unanswerable in principle. Fredkin actually believes that our universe is a 3+1D cellular automata, and if anyone ever found such a description of our physics (or some other fundamentally computational description), then we could directly compare it with Conway's Life, determining for each one how big the lattice needs to be, and how many clock-ticks are required, for life to appear with (say) 90% probability. (Of course, this determination might be difficult even when we know the rules of the CAs. But we can try.) One thing that you'd have to take into account is the complexity of the rules you're comparing, including the number of states allowed per cell. Not only are the rules to Conway's Life extremely simple, but the cells are binary. All things being equal, I would expect that an increase in the complexity of the rules and the number of cell-states allowed would decrease the necessary lattice-size and/or number of clock-ticks required for SASs to grow out of a pseudo-random initial state. I mention this to point out a problem with our intuitions about our universe vs. Conway's Life: the description of our universe is almost certainly more complex than the description of Conway's Life with a simple initial state. If Fredkin actually succeeds in finding a 3+1D CA which describes our universe, it will almost certainly require more than 2 cell-states, and its rules will certainly be more complex than those of the Life universe. We have to take this difference into account when trying to compare the two universes, but we have nowhere near enough data to quantify the difference currently. We really don't know what size of space in the Life universe is equivalent to (say) a solar system in this universe. In a way, this is all beside the point, since I have no problem believing that one CA can evolve SASs much more easily than some other CA whose rules and initial state are exactly as complex. (In fact, this must be true, since for any CA that supports life at all, there's an equally complex one that isn't even computation universal.) I have no problem believing that the Life universe is, in some objective sense, not very conducive to SASs. Perhaps it's less conducive to SASs than our own universe, although I'm not convinced. What I have a problem believing is that CAs as a class are somehow less conducive to observers than quantum-physical models as a class. In fact, I think it's substantially more likely that there are relatively simple CA models (and other computational models) that are much more conducive to SASs than either Conway's Life universe or our own. Models in which, for instance, neural-net structures arise much more naturally from the basic physics of the system than they do in our universe, or the Life universe. In many ways, our universe seems tailor made for creating observers. I understand this perspective, but for what it's worth, I'm profoundly out of sympathy with it. In my view, computation universality is the real key - life and consciousness are going to pop up in any universe that's computation universal, as long as the universe is big enough and/or it lasts long enough. (And there's always enough time and space in the Mathiverse!) When I think about the insane, teetering, jerry-rigged contraptions that we call life in this universe - when I think about the tortured complexity that matter has to twist itself into just to give us single-celled replicators - and when I think about the insane reaches of space we see around us (even if we end up finding life in practically every solar system, there's a crazy amount of space even between planets, not to mention stars) - I find it easy to believe that our universe is just one of those countless universes out there in Mathspace which isn't especially conducive to life at all, but is simply computation universal, so life pops up eventually. Because of the above conclusions, the problem of measure is a serious one for me. I don't have a clue why I would be more likely to find myself in a universe like this one instead of some CA universe. Regarding your suggestion that we might judge universes not only by the complexity of their rules and initial states, but also by the com
Re: Tegmark is too "physics-centric"
Kory Heath, <[EMAIL PROTECTED]>, writes: > It is very likely that even Conway's Life universe has this feature. Its > rules are absurdly simple, and we know that it can contain self-replicating > structures, which would be capable of mutation, and therefore evolution. We > can specify very simple initial conditions from which self-replicating > structures would be overwhelmingly likely to appear, as long as the lattice > is big enough. (The binary digits of many easily-computable real numbers > would work.) Yes, I see that that is true. I think it points to a problem with some of the simple conceptualizations of measure, about which I will say more below.But let me ask if you agree that considering Conway's 2D Life world with simply-specified initial conditions as in your example, that conscious life would be extraordinarily rare? I want to say, vastly more rare than in our universe, but of course we don't know how rare life actually is in our universe, so that may be a hard claim to justify. But the point is that our universe has stable structures; it has atoms of dozens of different varieties, which can form uncountable millions of stable molecules. It has mechanisms to generate varieties of these different molecules and collect them together in environments where they can react in interesting ways. We don't have a full picture of how life and consciousness evolved, but looking around, it doesn't seem like it should have been THAT hard, which is where the Fermi paradox comes from. In many ways, our universe seems tailor made for creating observers. In contrast, in the Life world there are no equivalents to atoms or molecules, no chemical reactions. It's too chaotic; there's not enough structure. Replicators and life seem to require a balance between chaos and stasis, and Life is far too dynamic. It just looks to me like it would be almost impossible for replicators to arise naturally. Almost impossible, but not absolutely impossible, so if you tried enough initial conditions as you suggest, it would happen. I won't belabor this argument unless you disagree about the ease with which life might arise in a Life universe, and consciousness evolve. And the main point is that these are exactly the kinds of considerations which Tegmark discusses. Issues of stability of the building blocks of life, of providing the right amounts and kinds of interactions. These physics-like considerations are precisely the correct issues to consider in looking at how easily observers will arise, and that is Tegmark's point. I haven't read Tegmark's paper in detail recently, and to the extent that his arguments are based on string theory or QM then I would agree that those are too parochial. But as I recall he had a number of broad arguments that would apply even to a Life-like universe. Now I'll get back to the question above about measure. There are universes, as in your example, where life is intrinsically unlikely, but if you make the universe large enough, and provide all possible initial conditions for finite-sized regions, then in all that vastness, somewhere life will exist. The problem is, this is not too different from separately implementing alternate, smaller versions of that universe, with different initial conditions for each, so that all possible initial conditions are tried in some universe. A small fraction of those universes will have life. To specify just one of the life-containing universes will typically take a lot of information, while specifying all of the universes takes less information. This is analogous to the even broader picture of the "universal dovetailer (UD)" program, the program that runs all programs (on all initial conditions). It's a very small program, yet it creates all possible universes. Even universes with incredibly complex laws of physics and initial conditions are created by this extremely small UD program. Does this mean that all universes have the same measure, and it is large, since this small program creates them? The answer has to be no. It's not enough to find a small program which generates a desired structure, somewhere in the vastness that it creates. Otherwise all integers would have the same complexity because they are all created by a simple counting program. Wei Dai once suggested a heuristic that the measure of a structure ought to have two components: the size of the program that creates it; and the size of a program which locates it in the output of the first program. By this argument, you could have a big program which output just the structure in question, which was then located by a trivial one; or you could have a small program which output the structure among a vastness, which then required a big program to locate it. Either way, the structure has a large measure. This was the motivation for the idea I proposed a few days ago, that for applying anthropic reasoning, a universe should get a "bonus" if it had a high density of observ
Re: Tegmark is too "physics-centric"
At 1/17/04, Eric Hawthorne wrote: Well here's the thing: The onus on you is to produce a "physical theory" that describes some subset of the computations of a 4D CA and which can explain (or posit or hypothesize if you will) properties of observers (in that kind of world), and properties of the space that they observe, which would be self-consistent and descriptive of "interesting, constrained, lifelike behaviour and interaction with environment and sentient representation of environment aspects" etc. I'm not sure I really understand what you're asking for here. I'm applying the very same concepts of "lifelike" and "sentient" that I apply to configurations of matter here in our own universe. These concepts certainly have to do with the things you mention - perception of surrounding environment, information processing, the building of internal representations, action within the environment, etc. All of these concepts are essentially computational, and are highly general. They should be applicable to substructures in any computation-universal system. If you're asking how we would be able to recognize SASs (or even just lifelike substructures) in a 4D cellular automata, there's clearly no simple answer to that question. We can imagine running a giant computer implementation of a 4D world, with lots of software tools at our disposal. Obviously, we could examine the state of any bit in the lattice, and we could also build higher-level pattern-matching tools that would help us to recognize higher-level structures (like gliders, and perhaps larger molecule-like structures). To recognize lifelike substructures in the lattice, we would bring everything we know about computation, self-replication, information processing, etc., to bear on the subject. We already have some conception of what a self-replicating structure in Conway's Life universe would look like. I don't see any reason why we couldn't recognize such things if they arose naturally in some 4D CA that we were studying. I have no doubt that the problem would be difficult. I am also fully aware that we have no precise "definition" which infallibly distinguishes all "living" sub-structures from "non-living" ones. This is true for any universe, including our own. We know that elephants are intelligent, but do we really have a clear picture of what kind of sentience they possess? The science-fiction author Stanislaw Lem suggests that alien intelligences in our own universe might be as big as galaxies, and might look to us simply like clouds of cosmic dust. My guess is that that physical theory (and that subset of computations or computed states) would end up being proven to be essentially equivalent to the physical theory of OUR universe. We may be starting a game of what Dennett calls "burden tennis", but it seems to me that the burden is entirely upon you to support such an extraordinary claim. Are you suggesting that, for any CA we discover that contains SASs, if we analyze how those SASs gain information about their environment and how they affect it, if we analyze how their environment must seem *to them*, we will find that it looks essentially like our own quantum-physical, relativistic universe? I find that highly implausible, to put it mildly. Maybe you're simply arguing that our definitions of "life" and "sentience" are so tied to our particular physics that we simply wouldn't find SASs when we explore CA worlds. (Or, we'd only find them in those CA that manage to behave very much like our own universe, with QM and GR and all the rest.) Again, I find that highly implausible. I think our standard (fuzzy) conceptions of life and sentience are substantially more "substrate neutral" than that. You can't just say "there could be life and sentience in this (arbitrarily weird) set of constraints" and then not bother to define what you mean by life and sentience. They aren't self-explanatory concepts. Our definitions of them only apply within universes that behave at least roughly as ours does. As I've said, my definitions of life and sentience are essentially computational, and they're the same ones I apply to groups of molecules in our own local universe. I think these definitions are applicable within any universes that are computation-universal. Of course, it should be obvious that my position rests on underlying positions about the possibility of computational models of life, consciousness, etc. If you don't believe, for instance, that hard-AI is possible, even in principle, then obviously you won't accept my conclusions, at least when it comes to intelligent SASs. But in that case, we're really talking past each other, and we need to back up - way up. (And frankly, I'm not interested in backing up that far.) -- Kory
Re: Tegmark is too "physics-centric"
> My guess is that that physical theory (and that subset of computations > or computed states) would end up being proven to > be essentially equivalent to the physical theory of OUR universe. In > other words, I believe in parochialism, because > I believe everywhere else is a devilish, chaotic place Perhaps, but hydro-thermal vents are rather devilish locales relative to our raher narrow comfort zones. > You can't just say "there could be life and sentience in this > (arbitrarily weird) set of constraints" and then not bother to > define what you mean by life and sentience. They aren't self-explanatory > concepts. Our definitions of them only apply > within universes that behave at least roughly as ours does. > Fair enough. How about, say, if a given universe can harbour phenomena that meet at least this criteria: "Life is the result of the non random replication of randomly varying replicators" (Dawkins) Then the possibility of emergent sentience can be entertained, IMHO. CMR
Re: Tegmark is too "physics-centric"
> I agree that this is what Tegmark is trying to say. If we look at it > in terms of measure, there are (broadly speaking) two ways for creatures > to exist: artificial or natural. By artificial I mean that there could > be some incredibly complex combination of laws and initial conditions > built into the simulated universe so that the creature's existence was in > effect pre-ordained. (If we ever build a simulation containing conscious > entities, our first attempts will almost certainly be of this type, > where we have carefully crafted the program to create consciousness.) > By natural I mean that we could have simple laws of physics and initial I agree that the "consciousness" (assuming our definitions of same correspond) would likely result from "complex combination of laws and initial conditions built into the simulated universe", but I submit that it is just as likely to be an incidental emergent phenom of an everymore complex interconnected distributed computational network as the result of any planned process. Would we even recognize such an "entity", or it us? Possibly, but Wolfram alludes to the challenges of percieving the intelligence of "beings" whose ecology operates on spacial and/or temporal scales foreign to our sensory receptivity. >Of course, there's always a risk in such arguments that we may be falling >victim to parochialism, thinking that our own way of life is the only >one possible. It may be that there are some possible life forms that >exist in a very different mode than we have imagined, in a universe with >different dimensionality, or perhaps one where dimensionality doesn't >even make sense. But I think overall Tegmark does a good job in avoiding >at least the most obvious flaws of parochialism and anthropomorphism. Indeed. The constraints to, and requirements for, terrestrial life have had to be revised and extended of late, given thermophiles and the like. Though they obviously share our dimensional requisites, they do serve to highlight the risk of prematurely pronouncing the "facts of life". CMR
Re: Tegmark is too "physics-centric"
Kory Heath wrote: Tegmark goes into some detail on the problems with other than 3+1 dimensional space. Once again, I don't see how these problems apply to 4D CA. His arguments are extremely physics-centric ones having to do with what happens when you tweak quantum-mechanical or string-theory models of our particular universe. Well here's the thing: The onus on you is to produce a "physical theory" that describes some subset of the computations of a 4D CA and which can explain (or posit or hypothesize if you will) properties of observers (in that kind of world), and properties of the space that they observe, which would be self-consistent and descriptive of "interesting, constrained, lifelike behaviour and interaction with environment and sentient representation of environment aspects" etc. My guess is that that physical theory (and that subset of computations or computed states) would end up being proven to be essentially equivalent to the physical theory of OUR universe. In other words, I believe in parochialism, because I believe everywhere else is a devilish, chaotic place. You can't just say "there could be life and sentience in this (arbitrarily weird) set of constraints" and then not bother to define what you mean by life and sentience. They aren't self-explanatory concepts. Our definitions of them only apply within universes that behave at least roughly as ours does. You'll have to come up with the generalized criteria for generalized N-D SAS's (what would constitute one) before saying "they could exist." Eric
Re: Tegmark is too "physics-centric"
At 1/17/04, Hal Finney wrote: By natural I mean that we could have simple laws of physics and initial conditions in which the creatures evolve over a long period of time, as we have seen in our universe. It is very likely that even Conway's Life universe has this feature. Its rules are absurdly simple, and we know that it can contain self-replicating structures, which would be capable of mutation, and therefore evolution. We can specify very simple initial conditions from which self-replicating structures would be overwhelmingly likely to appear, as long as the lattice is big enough. (The binary digits of many easily-computable real numbers would work.) Moving from this 2D world, in which each cell can be pictured as a square with 4 orthogonal neighbors, we can consider 3D CA in which each cell is a cube with 6 orthogonal neighbors. There are rule sets and initial conditions for this lattice structure that are just as simple as Conway's life, which can similarly contain evolving self-replicating structures. We can go further and envision a 4D CA in which each cell is a hypercube with 8 orthogonal neighbors. Without a doubt, there are absurdly simple rulesets for this lattice structure which are computation universal, support stable structures like gliders, and support self-replicating structures which would grow and evolve. Universes of the natural type would seem likely to have higher measure, because they are inherently simpler to specify. If that's true, then the CA universes described above should have very high measure, because they are extremely simple to specify. Tegmark goes into some detail on the problems with other than 3+1 dimensional space. Once again, I don't see how these problems apply to 4D CA. His arguments are extremely physics-centric ones having to do with what happens when you tweak quantum-mechanical or string-theory models of our particular universe. -- Kory
Re: Tegmark is too "physics-centric"
At 1/17/04, Eric Hawthorne wrote: 1. All cellular automata which are computationally universal are reducible to each other, by the definition of universality, so it doesn't matter which D the automaton program itself is. The subject matter that they can represent and compute is equivalent. That's correct on one level, but what we're really interested in is the dimensionality of space that SASs within the computation would perceive their world as having. For instance, we know that there is a very simple 1D CA that's computation universal (Wolfram's rule 110), so we know that we can implement any higher-dimensional cellular automata in rule 110. However, if we implement in rule 110 some 3D CA which contains SASs, these SASs would go right on moving around in their 3D world and perceiving their space as 3D. In an important sense, it would be incorrect to say that those SASs live in a 1D world, even though ultimately their "substrate" is 1D. This is really just another example of the familiar concept of "substrate neutrality". So at the least the 2D or 4 or 5D sentient creatures would be frustrated (remember, they are SUBSTRUCTURES, they're not computing the space itself, they're part of the space and perceiving and acting on other parts of it). But what possible reason do we have for believing that 4D or 5D cellular automata (or, to be more careful, cellular automata which would be perceived as 4D or 5D by the SASs within them) are somehow hostile to the existence of SASs? The arguments in Tegmark's paper about how universes with more than 3 spacial dimensions can't support stable structures like atoms simply don't apply to 4D cellular automata. Those arguments are very specific, applying only to quantum-physical and string-theory models. -- Kory
Re: Tegmark is too "physics-centric"
Eric Hawthorne writes: > 2. SAS's which are part of a 3+1 space may not have higher measure than > SAS's in other spaces, but perhaps the SAS's > in the other spaces wouldn't have "a decent way to make a living". In > other words, maybe they'd have a hard time > perceiving the things in their space, existing coherently "physically" > in it, being able to "incrementally impact and survival-optimize" > their surroundings in the space etc. > In other words they'd be inhabiting (and trying to perceive and act on) > a world of NOISE, or of LIMITED DEGREES OF FREEDOM AND EVOLUTION, > or of UNRULY, untameable hyperbolic physical laws and functions. I agree that this is what Tegmark is trying to say. If we look at it in terms of measure, there are (broadly speaking) two ways for creatures to exist: artificial or natural. By artificial I mean that there could be some incredibly complex combination of laws and initial conditions built into the simulated universe so that the creature's existence was in effect pre-ordained. (If we ever build a simulation containing conscious entities, our first attempts will almost certainly be of this type, where we have carefully crafted the program to create consciousness.) By natural I mean that we could have simple laws of physics and initial conditions in which the creatures evolve over a long period of time, as we have seen in our universe. Universes of the natural type would seem likely to have higher measure, because they are inherently simpler to specify. It is in those universes where Tegmark's physics-based arguments come into play. For creatures to evolve, to become complex, to optimize for survival, things like dimensionality are very relevant. Tegmark goes into some detail on the problems with other than 3+1 dimensional space. Of course, there's always a risk in such arguments that we may be falling victim to parochialism, thinking that our own way of life is the only one possible. It may be that there are some possible life forms that exist in a very different mode than we have imagined, in a universe with different dimensionality, or perhaps one where dimensionality doesn't even make sense. But I think overall Tegmark does a good job in avoiding at least the most obvious flaws of parochialism and anthropomorphism. Hal Finney
Re: Tegmark is too "physics-centric"
Kory Heath wrote: I greatly enjoyed Tegmark's "Is 'the theory of everything' merely the ultimate ensemble theory?", and there are parts of it that I agree with wholeheartedly (for instance, his arguments against the idea that the AUH is "wasteful"). However, whenever he talks about the testability of the AUH, his views seem unjustifiably physics-centric to me. For instance, he seems impressed by the fact that versions of our physics with more than 3 dimensions are insufficiently stable to support atoms (and presumably, therefore, self-aware substructures), and those with less than 3 dimensions are insufficiently complex to support SASs. These are interesting facts, but I fail to see their importance when you consider the entire ensemble of possible mathematical structures. For instance, consider the infinitely many cellular automata that exist in the Mathiverse. We know of very simple 1D, 2D, and 3D cellular automata that are computation universal, and therefore (I believe) capable of containing SASs. Undoubtedly there an infinite number of 4D cellular automata that are computation universal and contain SASs that perceive their surroundings as 4D. Ditto for CA with dimensions higher than 4. Perhaps it's true that within the ensemble of all quantum-physical universes in Mathspace, only those with 3+1 dimensionality contain SASs. But what possible reason do we have for believing that these SASs (or the observer-moments of those SASs) have a greater measure than those in the ensemble of all cellular automata? Notes: 1. All cellular automata which are computationally universal are reducible to each other, by the definition of universality, so it doesn't matter which D the automaton program itself is. The subject matter that they can represent and compute is equivalent. 2. SAS's which are part of a 3+1 space may not have higher measure than SAS's in other spaces, but perhaps the SAS's in the other spaces wouldn't have "a decent way to make a living". In other words, maybe they'd have a hard time perceiving the things in their space, existing coherently "physically" in it, being able to "incrementally impact and survival-optimize" their surroundings in the space etc. In other words they'd be inhabiting (and trying to perceive and act on) a world of NOISE, or of LIMITED DEGREES OF FREEDOM AND EVOLUTION, or of UNRULY, untameable hyperbolic physical laws and functions. So at the least the 2D or 4 or 5D sentient creatures would be frustrated (remember, they are SUBSTRUCTURES, they're not computing the space itself, they're part of the space and perceiving and acting on other parts of it). At worst, their own "physical" existence in the flat or unruly space would be impossible to define coherently, so they couldn't BE anything that we would recognize as a perceiving-acting lifeform. Maybe there's still room for some other ultra-weird form of self-contemplative (4Dimensional navel-gazing) Ent-lifeform thingy, but I don't think so. -- I, like Tegmark, believe that the constraints for life, and sentient life in particular, are are EXTREMELY ONEROUS. There are so many constraints, I believe, that it is possible but only just so, and so expected to be extremely rare even in a very large universe (note, the universe may be infinite but the event horizon of intercommunicable beings or parts of beings and their environment is not (at any given time, for a finite-lifetime creature). Each "liveable part" of the universe is constrained to that subspace reachable by lightspeed interaction. Within each interreachable event horizon, i.e. each observable universe, life and sentience should be rare because of the need to satisfy a very large number of constraints simultaneously to get environment-interactive life and sentience and to retain them. Eric
