Re: Questions on Russell's "Why Occam" paper
I'm not sure I follow your reasoning, but it wouldn't surprise me if
the Turing subset of my world has additional constraints - namely the
worlds seen by observers whose O(x)'s are prefix machines, not just maps.
On Fri, Jun 10, 2005 at 05:56:50PM +0200, Bruno Marchal wrote:
>
> Le 10-juin-05, ? 14:59, Patrick Leahy a ?crit :
>
> >>Russell Standish:
> >>If the AP applies to the Sims Mark VII, then their reality will be a
> >>description containing a "body" corresponding to their intelligences.
> >>They will not be aware of the PC that their description is being
> >>generated on. We, who inhabit the world with the PC will not be aware
> >>of the countless other PCs, Macs, Xboxes, Eniacs, Turing machines,
> >>pebbles in Zen monasteries etc running Sims Mark VII. So the PC
> >>itself is actually irrelevant from the internal perspective of the
> >>Sims.
> >
> >Well at least we agree on that. No strange loops in this picture, so
> >it is unlike the picture you outline in your paper.
> >
>
>
> Aargh Bad luck! A point where I disagree with both Schmidhuber
> *and* Standish, at least here apparently.
>
> To explain I must assume comp and ... (for one) explicitly the *result*
> of my thesis. In a nutshell: it is that, if comp is assumed, then the
> correct law of physics are derivable from comp. (it makes comp
> testable: derive physics from comp and compare with empirical physics).
> I will call the physics derived from comp: the comp-physics.
>
> Please admit this if only for the sake of the argument.
>
> Suppose I build a simulated city with some self-aware entities evolving
> in that simulated environment. Then
>
> Either I simulate the correct comp physics, then apparently the
> simulated entity cannot know they are simulated by me, but actually
> this sentence has no meaning, because they are simulated by 2^aleph_0
> immaterial stories (constituting arithmetical truth), so it is only in
> a weak sense that they are failed. (actually it is not even possible to
> simulate comp physics except in the "ridiculous" sense of running
> (really) the universal dovetailer.
>
> Or I simulate incorrect comp physics, then the only way we could say
> the simulated entity are failed is
> 1) either by killing them (in some absolute way) when they discover
> discrepancies between the comp-physics they can find by herself and
> their fake environment. But in that case their story is finite and its
> measure can be shown equal to 0. Or
> 2) eithert I keep up correcting the simulation, but then in the limit I
> don't fail them. Or I limit the cognitive ability of the entities, but
> then either I will failed to genuinely fail them, or I will make them
> inconsistent (and here too the measure can be shown equal to zero, and
> that is related to the non-cul-sac phenomenon).
>
>
> It is an amazing positive consequence of machine's incompleteness that
> you cannot genuinely failed any (relatively simulated or not) machine
> having enough introspection power for a "very long time".
>
> Apparently, In machine's platonia, all lies leads soon or later to a
> (recognizable) catastroph.
>
> Tp prevent falling into an inconsistency, this last conclusion follows
> from comp, and remember that if comp is correct we cannot "know" it is
> correct, and we cannot probably know that all lies leads soon or later
> to a (recognizable) catastroph. But if you *bet* on comp, you can bet
> on it!
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
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Re: Questions on Russell's "Why Occam" paper
On Fri, Jun 10, 2005 at 01:59:16PM +0100, Patrick Leahy wrote: > > On Thu, 9 Jun 2005, Russell Standish wrote: > > >Yes, if you think there is a concrete reality in which everything exists > >(your question of where does the observer live?), then the AP is a > >tautology. > > What I meant by "where does the observer live", in more formal language, > is "how do you account for the (apparent) sense data we have?". Perhaps you ask too much. Your question is something along the lines of "what explains qualia", or "what breathes fire into the equations". I could state baldly that descriptions can conscious. This is no more preposterous than Tegmarks "mathematical systems can be conscious". Maybe that satisfies you, maybe not. What can be stated more convincingly is that all experience (including internal conscious experience) is a description, a bunch of data interpreted by an observer. Consequently, the set of all descriptions will contain a description of your current conscious experience. Hence we can make strong claims about appearances - the phenomenon. As to whether there is a Noumenon - I take Laplace's rather agnostic point of view - I have no need of that hypothesis. Perhaps you do. > I also > have a strong preference for an account where the description of at least > our "world" doesn't privilege one particular observer. In particular, this > is hard to square with your insistence that "the observer provides the > interpretation" of each of your bitstring universes. > The situation is symmetric with respect to all observers. That is hardly priveleging an observer. > As both Hal and I keep trying to emphasise, we are interested in how, or > whether, your theory can account for our own existence and the reality (or > appearance, if you prefer) that we see around us. So the case of > disembodied intelligences is a total a red herring. I don't really care > whether these feature in your theory or not, but I do care whether you can > account for (apparently) embodied intelligences. > Apparently embodied intelligences are part of the space of all descriptions by definition. The anthropic principle accounts for the fact that we observer them, and not (say) flying white rabbits. > > > >Instead, one can take the Anthropic Principle as an assertion of the > >reality we inhabit... > > Again, you are using a private language... the AP is not regarded as any > such assertion by anyone else I've ever heard of. Most people regard their > existence as proved by their own subjective experience, not some invented > principle. Of course - Decartes and all that. The AP applies to what we see in the world around us, not a proof or otherwise of our own existence. > > > ... and experimentally test it. In all such cases is has been shown to > >be true, sometimes spectacularly. > > If we know "experimentally" "the reality we inhabit" (?!), which I guess > I've just claimed that we do, why do we need a principle to assert it? > > Likely you mean something completely different, in which case please > explain (with examples of said experiments!). The experiments are the usual suspects showing fine tuning of physical parameters in the universe. Tegmark's paper is a good review of the topic. As is Barrow and Tipler's book. > > Quoting me: > >> > >>Then you are implying that the observer can, in a finite time, read and > >>attach meaning to a full (space-time) description of itself, including > >>the act of reading this description and so on recursively. > >> > > > >Not at all. Consistency is the only requirement. If the observer goes > >looking for erself, then e will find erself in the description. It > >doesn't imply the observer is doing this all the time. > > I think here we have run into the same inconsistency that you admitted in > your discussion with Hal. In your first reply to Hal you assert that the > observer O(x) attaches a unique meaning to the description string. Which > would imply processing all bits of the string up to the start of the > "don't care" region. A later reply suggest that we should in different > contexts assume (a) this and (b) what your paper actually says, i.e. the > meanings are updated as further bits are read. Now you have changed this > again, and the observer is not (modelled by) a simple mapping but is a > free agent who can choose to apply mappings to different "regions" of the > bitstring at will. Yes, as I've further clarified to Hal, O(x) is actually a function of time. One imagines that in general the region of sigificant bits of x expands as a function of (psychological) time. In my defence, the paper was written over a period of 4 years, and the O(x) was a later addition to try to clarify points in section 2. I didn't realise at the time that it introduced some ambiguities into section 3. > > And even that doesn't actually answer my problem: let's assume the > observer *does* "go looking for erself". You claim he will fi
Re: Questions on Russell's "Why Occam" paper
Le 10-juin-05, à 14:59, Patrick Leahy a écrit : Russell Standish: If the AP applies to the Sims Mark VII, then their reality will be a description containing a "body" corresponding to their intelligences. They will not be aware of the PC that their description is being generated on. We, who inhabit the world with the PC will not be aware of the countless other PCs, Macs, Xboxes, Eniacs, Turing machines, pebbles in Zen monasteries etc running Sims Mark VII. So the PC itself is actually irrelevant from the internal perspective of the Sims. Well at least we agree on that. No strange loops in this picture, so it is unlike the picture you outline in your paper. Aargh Bad luck! A point where I disagree with both Schmidhuber *and* Standish, at least here apparently. To explain I must assume comp and ... (for one) explicitly the *result* of my thesis. In a nutshell: it is that, if comp is assumed, then the correct law of physics are derivable from comp. (it makes comp testable: derive physics from comp and compare with empirical physics). I will call the physics derived from comp: the comp-physics. Please admit this if only for the sake of the argument. Suppose I build a simulated city with some self-aware entities evolving in that simulated environment. Then Either I simulate the correct comp physics, then apparently the simulated entity cannot know they are simulated by me, but actually this sentence has no meaning, because they are simulated by 2^aleph_0 immaterial stories (constituting arithmetical truth), so it is only in a weak sense that they are failed. (actually it is not even possible to simulate comp physics except in the "ridiculous" sense of running (really) the universal dovetailer. Or I simulate incorrect comp physics, then the only way we could say the simulated entity are failed is 1) either by killing them (in some absolute way) when they discover discrepancies between the comp-physics they can find by herself and their fake environment. But in that case their story is finite and its measure can be shown equal to 0. Or 2) eithert I keep up correcting the simulation, but then in the limit I don't fail them. Or I limit the cognitive ability of the entities, but then either I will failed to genuinely fail them, or I will make them inconsistent (and here too the measure can be shown equal to zero, and that is related to the non-cul-sac phenomenon). It is an amazing positive consequence of machine's incompleteness that you cannot genuinely failed any (relatively simulated or not) machine having enough introspection power for a "very long time". Apparently, In machine's platonia, all lies leads soon or later to a (recognizable) catastroph. Tp prevent falling into an inconsistency, this last conclusion follows from comp, and remember that if comp is correct we cannot "know" it is correct, and we cannot probably know that all lies leads soon or later to a (recognizable) catastroph. But if you *bet* on comp, you can bet on it! Bruno http://iridia.ulb.ac.be/~marchal/
Re: Questions on Russell's "Why Occam" paper
On Thu, 9 Jun 2005, Russell Standish wrote: Yes, if you think there is a concrete reality in which everything exists (your question of where does the observer live?), then the AP is a tautology. What I meant by "where does the observer live", in more formal language, is "how do you account for the (apparent) sense data we have?". I also have a strong preference for an account where the description of at least our "world" doesn't privilege one particular observer. In particular, this is hard to square with your insistence that "the observer provides the interpretation" of each of your bitstring universes. However, if you are prepared to allow for the possibility that observers exist "nowhere", then things are not quite so simple. One can always imagine being the brain-in-the-vat observer a reality which does not contain a body, or a brain, in a vat or anywhere else. Usually in this scenario, the observer will conclude that there must be a body somewhere else, and so concludes that it is inhabiting some kind of virtual reality. However, this implicitly assumes there has to a brain somewhere, and so implies a reality somewhere else for the brain to inhabit. But what if the brain is not required? Obviously, the last conclusion is full blown solipsism, but that is hardly a knock down argument. As both Hal and I keep trying to emphasise, we are interested in how, or whether, your theory can account for our own existence and the reality (or appearance, if you prefer) that we see around us. So the case of disembodied intelligences is a total a red herring. I don't really care whether these feature in your theory or not, but I do care whether you can account for (apparently) embodied intelligences. Instead, one can take the Anthropic Principle as an assertion of the reality we inhabit... Again, you are using a private language... the AP is not regarded as any such assertion by anyone else I've ever heard of. Most people regard their existence as proved by their own subjective experience, not some invented principle. If you don't agree I think we are just arguing about the meaning of "exist"... e.g. if we happen to be living in a computer simulation, or are just features of the solution of some set of equations, I would still say that we (really) exist. ... and experimentally test it. In all such cases is has been shown to be true, sometimes spectacularly. If we know "experimentally" "the reality we inhabit" (?!), which I guess I've just claimed that we do, why do we need a principle to assert it? Likely you mean something completely different, in which case please explain (with examples of said experiments!). Quoting me: Then you are implying that the observer can, in a finite time, read and attach meaning to a full (space-time) description of itself, including the act of reading this description and so on recursively. Not at all. Consistency is the only requirement. If the observer goes looking for erself, then e will find erself in the description. It doesn't imply the observer is doing this all the time. I think here we have run into the same inconsistency that you admitted in your discussion with Hal. In your first reply to Hal you assert that the observer O(x) attaches a unique meaning to the description string. Which would imply processing all bits of the string up to the start of the "don't care" region. A later reply suggest that we should in different contexts assume (a) this and (b) what your paper actually says, i.e. the meanings are updated as further bits are read. Now you have changed this again, and the observer is not (modelled by) a simple mapping but is a free agent who can choose to apply mappings to different "regions" of the bitstring at will. And even that doesn't actually answer my problem: let's assume the observer *does* "go looking for erself". You claim he will find himself, but if the description is *complete* my original problem remains: he will never finish reading his own description. Consequently the description will remain uninterpreted. In particular, he will never get to the part which would be interpreted as "himself now". So is there any sense in which *himself now* exists? This assumes that the string description contained a complete definition of the observer, which is a natural interpretation of your phrase: "Since some of these descriptions describe self aware substructures,..." But maybe you just meant that the string contains references to (tokens of) the observer. This would be consistent with your comment a couple of posts ago that both "observers" and "descriptions" are primary. This also seems to be consistent with your other recent post in response to Hal, in which the bitstrings are treated not so much as universes in the usual sense but as either the stream of sense data entering the observer's conciousness, or as a continuously-updated description of that concio
Re: Questions on Russell's "Why Occam" paper
On Thu, Jun 09, 2005 at 01:55:32AM +0100, Patrick Leahy wrote: > > [Russell Standish wrote]: > > >The AP is a statement that observed reality must be consistent with > >the observer being part of that reality. > > Famously, this can be interpreted as either a trivial tautology (Brandon > Carter's original intention, I think), or an almost-obviously false > principle of necessity (Barrow & Tipler's SAP). If you think there's a > mystery here it suggests you go for the necessity version, but given your > infinite ensemble the tautology would suffice perfectly well. Yes, if you think there is a concrete reality in which everything exists (your question of where does the observer live?), then the AP is a tautology. However, if you are prepared to allow for the possibility that observers exist "nowhere", then things are not quite so simple. One can always imagine being the brain-in-the-vat observer a reality which does not contain a body, or a brain, in a vat or anywhere else. Usually in this scenario, the observer will conclude that there must be a body somewhere else, and so concludes that it is inhabiting some kind of virtual reality. However, this implicitly assumes there has to a brain somewhere, and so implies a reality somewhere else for the brain to inhabit. But what if the brain is not required? Obviously, the last conclusion is full blown solipsism, but that is hardly a knock down argument. Instead, one can take the Anthropic Principle as an assertion of the reality we inhabit, and experimentally test it. In all such cases is has been shown to be true, sometimes spectacularly. With the AP, one recovers some of the properties of a concrete reality, without all of it. In particular, Marchal's "shared dreaming" follows as a consequence, and it contradicts solipsism. > > You also said: > > >>>The observer _is_ the interpreter. There may well be more than one > >>>observer in the picture, but they'd better agree! > >> > >>Why does this follow? > > > >It follows from the Anthropic Principle. If O_1 is consistent with its > >observed reality, and O_2 is consistent with its observed reality, and > >O_1 observes O_2 in its reality, then O_1 and O_2 must be consistent > >with each other (at least with respect to their observed realities). > > Ah. Just to be sure, do you mean that the string the observer "attaches > meaning to" is the one which describes the very same observer? This seems > to be implied by your comment above; but you don't say it or clearly > imply it in your paper. > > Then you are implying that the observer can, in a finite time, read and > attach meaning to a full (space-time) description of itself, including the > act of reading this description and so on recursively. > Not at all. Consistency is the only requirement. If the observer goes looking for erself, then e will find erself in the description. It doesn't imply the observer is doing this all the time. > Which is impossible, of course. > Of course. > You also said: > > >I'm not entirely sure I distinguish your difference between "external > >world" and "internal representation". We're talking about observations > >here, not models. > > I'm sure you can distinguish *my* mental representation of the world from > your own. Hence if we share a world, and you can't distinguish between > that world and your internal representation, then you are not granting > equal status to other observers such as me. > I'm not sure that is the case. I have a theory of your mind. I get it most economically by observing my own mind, hence I'm self-aware. My theory of the mind says that you are doing the same thing. Isn't this symmetric? > You also said (quoting me): > > >>My problem is that you are trying to make your observers work at two > >>different levels: as structures within the universes generated > >>(somehow!) by your bitstrings, but also as an interpretive principle > >>for producing meaning by operating *on* the bitstrings. It's a bit > >>like claiming that PCs are built by "The Sims". > > > >Yes it is a bit like that. Obviously, the Anthropic Principle (or its > >equivalent) does not work with "The Sims". > > Actually I don't see why not. The existence of The Sims implies a universe > compatible with the existence of Sims. But granting this is not so for the > sake of the argument, presumably the AP *will* apply to the Sims Mark VII > which will be fully self-aware artificial intelligences. If the AP applies to the Sims Mark VII, then their reality will be a description containing a "body" corresponding to their intelligences. They will not be aware of the PC that their description is being generated on. We, who inhabit the world with the PC will not be aware of the countless other PCs, Macs, Xboxes, Eniacs, Turing machines, pebbles in Zen monasteries etc running Sims Mark VII. So the PC itself is actually irrelevant from the internal perspective of the Sims. > But it will still > be absu
Re: Questions on Russell's "Why Occam" paper
If we're allowing ourselves a little informality, then I'd appeal to
the notion of observer moment. Within any observer moment, a finite
number of bits of the bitstrings has been read, and processed by the
observer. Since only a finite number of bits have been processed to
determine the meaning of reality at that moment, the
observer map O(x) is a prefix map. Hence at any point in time the
arguments in section 2 of the paper hold.
The meaning O(x) could also be called the "observer moment". If
observer moments are enumerable, one can inject OMs into the set of
natural numbers.
Observers find themselves embedded in a psychological time. I have not
been explicit about exactly what this time is, however I envisage it
to probably be what mathematicians call a "time scale", which is a
closed subset of the real numbers. Time could be continuous, or it
could be discrete (eg the set of natural numbers). It could be
something else, eg rational numbers or the Cantor set. All of these
are example time scales. The exact nature of time is something to be
settle later (if possible), but if you are more comfortable witrh
discrete time (as many are on this list), then you are welcome to use integers.
How this feeds back to our original observer map is that we'd expect
the map O(x) to be dependent on time, ie O(t,x). This is consistent
with time being "psychological". The description or "universe" x is
independent of time. It would correspond to what David Deutsch calls a
block universe.
Now perhaps section 3 makes some sense. What I call "robustness" of
the observer, ie that observers will not be fooled by a little noise
on the line - lions in camouflage are still observed to be lions for
instance constrains the form of time evolution of O(t,x). I haven't
formalised exactly what this constraint is, but it is something along
the lines of continuity of |O^{-1}(t,O(t,x))|, or continuity of the
observed complexity of the world.
On Wed, Jun 08, 2005 at 09:09:04AM -0700, "Hal Finney" wrote:
> Russell Standish writes:
> > On Mon, Jun 06, 2005 at 01:51:36PM -0700, "Hal Finney" wrote:
> > > In particular, if "an observer attaches sequences of meanings to sequences
> > > of prefixes of one of these strings", then it seems that he must have a
> > > domain which does allow some inputs to be prefixes of others. Isn't that
> > > what "sequences of prefixes" would mean? That is, if the infinite string
> > > is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
> > > 010, 0101, 01011, Does O() apply to this sequence of prefixes? If
> > > so then I don't think it is a prefix map.
> >
> > Yes I agree this is vague, and seemingly contradictory. I'm not sure
> > how to make this more precise, but one way to read the paper is to
> > treat observers as prefix maps for section 2 (Occam's razor), and then
> > for section 3 (White Rabbit problem) ignore the prefix property.
> >
> > It could be that the way of making this more precise is to assume
> > observers have some internal state that is constantly updated (a time
> > counter perhaps), so actually going through a sequence of prefix maps
> > in (psychological) time, but at this stage I don't have an answer.
>
> Unfortunately I still don't understand this. You agree that it is a
> seeming contradiction but that doesn't help me to see how to interpret it.
>
> Here's an idea. Would it be possible for you to explain how this
> page is meant to be understood, in an INformal way? Often when people
> present concepts they do a formal writeup, but if they give a seminar
> or explanation they will depart from the formalism and explain what is
> really going on behind the scenes. That's the kind of explanation I think
> I need.
>
> Could you explain how these concepts relate to the actual experiences
> we have as human observers? What are "descriptions" and "meanings"
> in terms of our sensory and mental experiences? Which "descriptions"
> does an observer observe? What are the "sequences of prefixes" and
> how do they relate to our day to day lives? What is the point of the
> equivalence classes and what does that have to do with what we observe?
>
> I think an informal explanation of these topics would help me, and
> perhaps Paddy, to better understand the structure that you formally
> describe. At this point I am still failing to see how it all relates
> to my experience of the world as an observer.
>
> Thanks -
>
> Hal Finney
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Re: Questions on Russell's "Why Occam" paper
[Russell Standish wrote]: The AP is a statement that observed reality must be consistent with the observer being part of that reality. Famously, this can be interpreted as either a trivial tautology (Brandon Carter's original intention, I think), or an almost-obviously false principle of necessity (Barrow & Tipler's SAP). If you think there's a mystery here it suggests you go for the necessity version, but given your infinite ensemble the tautology would suffice perfectly well. You also said: >The observer _is_ the interpreter. There may well be more than one >observer in the picture, but they'd better agree! Why does this follow? It follows from the Anthropic Principle. If O_1 is consistent with its observed reality, and O_2 is consistent with its observed reality, and O_1 observes O_2 in its reality, then O_1 and O_2 must be consistent with each other (at least with respect to their observed realities). Ah. Just to be sure, do you mean that the string the observer "attaches meaning to" is the one which describes the very same observer? This seems to be implied by your comment above; but you don't say it or clearly imply it in your paper. Then you are implying that the observer can, in a finite time, read and attach meaning to a full (space-time) description of itself, including the act of reading this description and so on recursively. Which is impossible, of course. You also said: I'm not entirely sure I distinguish your difference between "external world" and "internal representation". We're talking about observations here, not models. I'm sure you can distinguish *my* mental representation of the world from your own. Hence if we share a world, and you can't distinguish between that world and your internal representation, then you are not granting equal status to other observers such as me. You also said (quoting me): My problem is that you are trying to make your observers work at two different levels: as structures within the universes generated (somehow!) by your bitstrings, but also as an interpretive principle for producing meaning by operating *on* the bitstrings. It's a bit like claiming that PCs are built by "The Sims". Yes it is a bit like that. Obviously, the Anthropic Principle (or its equivalent) does not work with "The Sims". Actually I don't see why not. The existence of The Sims implies a universe compatible with the existence of Sims. But granting this is not so for the sake of the argument, presumably the AP *will* apply to the Sims Mark VII which will be fully self-aware artificial intelligences. But it will still be absurd to claim that the Sims are responsible for construction of PCs (assuming they are not connected to robot arms etc, for which no analogs exist in your theory). Let alone for them to construct the actual PC on which they are running, as apparently implied by your last message... even robot arms wouldn't help there. Paddy Leahy == Dr J. P. Leahy, University of Manchester, Jodrell Bank Observatory, School of Physics & Astronomy, Macclesfield, Cheshire SK11 9DL, UK Tel - +44 1477 572636, Fax - +44 1477 571618
Re: Questions on Russell's "Why Occam" paper
Russell Standish writes: > On Mon, Jun 06, 2005 at 01:51:36PM -0700, "Hal Finney" wrote: > > In particular, if "an observer attaches sequences of meanings to sequences > > of prefixes of one of these strings", then it seems that he must have a > > domain which does allow some inputs to be prefixes of others. Isn't that > > what "sequences of prefixes" would mean? That is, if the infinite string > > is 01011011100101110111..., then a sequence of prefixes might be 0, 01, > > 010, 0101, 01011, Does O() apply to this sequence of prefixes? If > > so then I don't think it is a prefix map. > > Yes I agree this is vague, and seemingly contradictory. I'm not sure > how to make this more precise, but one way to read the paper is to > treat observers as prefix maps for section 2 (Occam's razor), and then > for section 3 (White Rabbit problem) ignore the prefix property. > > It could be that the way of making this more precise is to assume > observers have some internal state that is constantly updated (a time > counter perhaps), so actually going through a sequence of prefix maps > in (psychological) time, but at this stage I don't have an answer. Unfortunately I still don't understand this. You agree that it is a seeming contradiction but that doesn't help me to see how to interpret it. Here's an idea. Would it be possible for you to explain how this page is meant to be understood, in an INformal way? Often when people present concepts they do a formal writeup, but if they give a seminar or explanation they will depart from the formalism and explain what is really going on behind the scenes. That's the kind of explanation I think I need. Could you explain how these concepts relate to the actual experiences we have as human observers? What are "descriptions" and "meanings" in terms of our sensory and mental experiences? Which "descriptions" does an observer observe? What are the "sequences of prefixes" and how do they relate to our day to day lives? What is the point of the equivalence classes and what does that have to do with what we observe? I think an informal explanation of these topics would help me, and perhaps Paddy, to better understand the structure that you formally describe. At this point I am still failing to see how it all relates to my experience of the world as an observer. Thanks - Hal Finney
Re: Questions on Russell's "Why Occam" paper
On Tue, Jun 07, 2005 at 10:15:03PM +0100, Patrick Leahy wrote:
> >>>Now an observer will expect to find a SAS in one of the descriptions
> >>>as a corrolory of the anthropic principle, which is explicitly stated
> >>>as one of the assumptions in this work. I make no bones about this - I
> >>>consider the anthropic principle a mystery, not self-evident like
> >>>many people.
> >>
> >>Very few supporters of the AP would "expect to find a SAS" in a bitstring.
> >>Until you *specify* a way of interpreting the string, it contains nothing
> >>but bits.
> >
> >The observer specifies the interpretation.
>
> But the observer is *generated* by the interpretation! Until you have an
> interpretation, you have no observers. And until you have an observer, you
> have no interpretation (at least that's how I read the sentence quoted
> above).
No the observer is somehow primary. As are the descriptions. If it
weren't for the anthropic principle, there would be no connection
between the two, and we'd have a genuine "brain-in-the-vat".
>
> How can structures which exist as some sort of pattern inside a bit string
> (or am I supposed to say in the "meaning" integer output by some (other)
> O(x)?) read a separate bitstring which exists as a parallel universe in
> Platonia?
>
That is what they do, by definition. Observers observe. Platonia is a
collection of all possible observations, hence what observers observe
is in Platonia.
>
> So you find it a mystery that you have a face, eye etc?? If so, what does
> the AP have to do with this mystery? Actually, maybe it would clarify
> things if you said what you mean by the AP; it certainly doesn't seem to
> be very like the AP that I know about.
>
The AP is a statement that observed reality must be consistent with
the observer being part of that reality.
> I'm not sure whether your "my reality" refers to the external world or
> your internal representation of it. I guess the latter, otherwise your
> body would be you, not a token representing you.
>
I'm not entirely sure I distinguish your difference between "external
world" and "internal representation". We're talking about observations
here, not models.
> >>In particular, any bitstring can be "interpreted" as any other bitstring
> >>by an appropriate map. Hence until you specify an interpreter you are
> >>simply not proposing a theory at all.
> >>
> >
> >The observer _is_ the interpreter. There may well be more than one
> >observer in the picture, but they'd better agree!
>
> Why does this follow? Your "observers" are maps O(x) from prefix strings
> to the integers. Why can't you have two inconsistent maps... or rather,
> how can you possibly avoid such? And since two different maps don't
> interact at all (how can a mapping interact with another mapping?) each of
> your observers seems to be sealed in his own little universe. In which
> case having >1 observer appears to be an unverifiable speculation, which
> is why I say it seems like solipsism.
>
It follows from the Anthropic Principle. If O_1 is consistent with its
observed reality, and O_2 is consistent with its observed reality,
and O_1 observes O_2 in its reality, then O_1 and O_2 must be
consistent with each other (at least with respect to their observed realities).
> >>Most readers of your paper would take it that you are making a strong
> >>ontological proposition, i.e. that the basis of reality is your set of
> >>bitstrings.
> >
> >This is the case.
>
> Well, if you are making an ontological proposition, you are ipso facto not
> just explaining appearances. In your model your "bitstrings" *are* the
> noumenon (in Kant's terminology).
Sorry, I don't see this. The bitstrings are phenomena. No noumenon
appears. It is possible we are arguing semantic differences only though.
> >
> >>In this case "where they live" is crucial because it
> >>defines the environment the SAS find themselves in.
> >
> >Why?
>
> An intelligent system is "intelligent" by virtue of the way it interacts
> with its environment. Think about the Turing test again: we conclude that
> the computer is (not) intelligent because of the way it interacts with us.
> To put it another way, you define these things as "observers". This
> implies something observed. Obviously your model had better account for
> people (observers) like us observing something like the world we see
> ("where we live"), and preferably interacting with other people who are
> granted equal status your ontology.
Does it not? OK, it is not exactly explicit about it, but this
situation should appear somewhere in Platonia.
>
> >It is not solipsism, if only for the reason that multiple observers
> >exist in our observed reality. They are all as real as our own
> >consciousness.
> >
> >Bruno Marchal calls this "shared dreaming". It seems apt.
>
> If that's the *only* reason it's not solipsism, then I would say you just
> don't have the courage of your convictions. Bruno's "shared dre
Re: Questions on Russell's "Why Occam" paper
On Tue, Jun 07, 2005 at 05:57:17PM +0200, Bruno Marchal wrote:
>
> Le 07-juin-05, ? 12:28, Russell Standish a ?crit :
>
> >On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:
> >>
> >>OK. it seems to me that (equation 14 at
> >>http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html )
> >>
> >>?
> >>
> >
> >In LaTeX, this equation is
> >
> >\frac {d\psi}{d t}={\cal H}(\psi)
> >
> >It supposes time, but not space (TIME postulate). Moreover, it
> >supposes continuous time,
>
>
> Yes but that is a lot of assumptions. Why a linear time capable of
> being represented by the very special line with the usual topology of
> the reals? I can imagine many topology on the reals.
>
I thought the definition of the reals defined its topology? Perhaps
you're using topology somewhat differently.
It is a good question as to why time should have a topological
dimension of 1, and I admit to not having a good answer to that. All I
can say is that computationalism also introduces a time with
topological dimension of 1. Tegmark has some arguments as to why the
topological dimension is 1, and not any other number, but these are
not overly persuasive (the argument depends on properties of 2nd order
PDEs, which already carries a greater amount of baggage)
I only assume continuity to make contact with standard QM. It is an
arbitrary assumption in my opinion, and should rightly be viewed with
suspicion.
>
>
> >but I do suggest in the paper how it might
> >be generalised to other possible timescales.
>
>
> yes but if you pretend to derive your equation, I don't understand what
> you mean by generalizing your conclusion (if only by: I have not derive
> it and it remains some work to do).
>
Of course there remains some work to be done.
>
>
> >Perhaps it also supposes
> >continuity in time for \psi, although this probably flows from
> >assuming continuity of time.
>
>
> Why should a function be continuous just because it is defined on a
> topological space (which is what I assume you are saying when you say
> continuity of time).
>
Because then it wouldn't be an evolution. For a state \psi(t') to
depend on the state \psi(t), there must be a corresponding limit
\psi(t')->\psi(t) as t'->t. Of course if t were not continuous, then
this condition is no longer necessary.
>
>
> >I do not think time is necessarily
> >continuous - I think it is interesting to explore alternative QMs
> >without this assumption.
>
>
> Sure. But again how to talk on derivation then. I mean if someone
> pretend to derive B from A, then if someone else derive something m?ore
> general than B from A, it is a critic of the assertion that B has been
> derived from A. If from facts I can derive the murderer is among John
> and Charles, I am not so interested in knowing the derivation can be
> generalized into leading that the murderer is among John, Charles, Lee,
> Bruno and Nicole!
>
To use your analogy, the situation is more like:
Assuming the murderer is John, Charles, Fred or Diana, I have shown
that the murderer must be one of John or Charles. However, if we also
consider Lee, Bruno and Nicole ... there is more work to be done.
The assumption of J,C,F or D corresponds by analogy to the continuity
assumption.
L,B and N are not continuous - does that sound right? :)
>
>
> >
> >The question is whether this is the most general evolution equation
> >for continuous time, or whether there is some more general
> >equation.
>
>
> Absolutely.
>
I think it is, for the reason above. I willing to stand corrected
should that not be the case.
>
>
> >Remember, we do have already that \psi is a member of a
> >Hilbert space, so we can write things like:
>
>
> OK, but you assume Set theory (that by itself is huge in our context).
> I show only that you have a preHilbetian space (why should "cauchy
> sequence of vectors converges).
>
>
Yes I do assume set theory. That is stated.
I prove Cauchy sequences converge in the paper. It requires the use of
Kolmogorov axiom no. 6. Hence the space of states is a Hilbert space.
>
> >
> >\psi(t')-\psi(t) = ...
> >
> >What do you mean by derivability notion for H, and topological notion?
>
>
> Topological notion are needed for talking of continuity (a continuous
> function is just a function from topological space into a topological
> space such that the inverse image of open set is an open set).. You
> "assume" the familiar topology of reals, complex number, etc.
Ah yes, you're talking about topological spaces. I just did a quick
refresher course on these using Wikipedia. Indeed, when I make the
arbitrary continuity assumption of time, it is an assumption that time
is a subset of the reals, which has the usual metric and topology
defined. When you say you can imagine many topologies on the reals,
what you are really saying is that you can imagine sets isomorphic to
the reals (1-1 corrspendence), that have many different topologies, eg
the trivial or the discrete
Re: Questions on Russell's "Why Occam" paper
On Tue, 7 Jun 2005, Russell Standish wrote:
Hal dealt with this one already, I notice. 2^\aleph_0 = c. \aleph_1 is
something else entirely.
d'oh!
Now an observer will expect to find a SAS in one of the descriptions
as a corrolory of the anthropic principle, which is explicitly stated
as one of the assumptions in this work. I make no bones about this - I
consider the anthropic principle a mystery, not self-evident like
many people.
Very few supporters of the AP would "expect to find a SAS" in a bitstring.
Until you *specify* a way of interpreting the string, it contains nothing
but bits.
The observer specifies the interpretation.
But the observer is *generated* by the interpretation! Until you have an
interpretation, you have no observers. And until you have an observer, you
have no interpretation (at least that's how I read the sentence quoted
above).
How can structures which exist as some sort of pattern inside a bit string
(or am I supposed to say in the "meaning" integer output by some (other)
O(x)?) read a separate bitstring which exists as a parallel universe in
Platonia?
Why should an observer expect to see a token of erself
embedded in reality? That is the mystery of the AP.
What ARE you talking about? Observer's don't see tokens of
themselves...
I can see that I have a body - if I look in the mirror I can see a
face, eye etc, all of which appear to be under my control. This is a
token embedded in my reality that represents me.
So you find it a mystery that you have a face, eye etc?? If so, what does
the AP have to do with this mystery? Actually, maybe it would clarify
things if you said what you mean by the AP; it certainly doesn't seem to
be very like the AP that I know about.
I'm not sure whether your "my reality" refers to the external world or
your internal representation of it. I guess the latter, otherwise your
body would be you, not a token representing you.
In particular, any bitstring can be "interpreted" as any other bitstring
by an appropriate map. Hence until you specify an interpreter you are
simply not proposing a theory at all.
The observer _is_ the interpreter. There may well be more than one
observer in the picture, but they'd better agree!
Why does this follow? Your "observers" are maps O(x) from prefix strings
to the integers. Why can't you have two inconsistent maps... or rather,
how can you possibly avoid such? And since two different maps don't
interact at all (how can a mapping interact with another mapping?) each of
your observers seems to be sealed in his own little universe. In which
case having >1 observer appears to be an unverifiable speculation, which
is why I say it seems like solipsism.
All that is discussed in this paper is appearances - we only try to
explain the phenomenon (things as they appear). No attempt is made to
explain the noumenon (things as they are), nor do we need to assume
that there is a noumenon.
Most readers of your paper would take it that you are making a strong
ontological proposition, i.e. that the basis of reality is your set of
bitstrings.
This is the case.
Well, if you are making an ontological proposition, you are ipso facto not
just explaining appearances. In your model your "bitstrings" *are* the
noumenon (in Kant's terminology). Kant's point was that you can't infer
the nature of "things in themselves" from observation. He didn't say that
you can't speculate about their nature, and even guess right, by chance.
In effect, this mailing list discusses nothing but the nature of the
noumenon. (Kant would probably say this is a waste of time, of course).
I think either your terminology or you model has now got very confused.
Are your "observer" TMs the observers (SAS) whose experiences your theory
is trying to explain?
Yes.
In this case "where they live" is crucial because it
defines the environment the SAS find themselves in.
Why?
An intelligent system is "intelligent" by virtue of the way it interacts
with its environment. Think about the Turing test again: we conclude that
the computer is (not) intelligent because of the way it interacts with us.
To put it another way, you define these things as "observers". This
implies something observed. Obviously your model had better account for
people (observers) like us observing something like the world we see
("where we live"), and preferably interacting with other people who are
granted equal status your ontology.
It is not solipsism, if only for the reason that multiple observers
exist in our observed reality. They are all as real as our own consciousness.
Bruno Marchal calls this "shared dreaming". It seems apt.
If that's the *only* reason it's not solipsism, then I would say you just
don't have the courage of your convictions. Bruno's "shared dreaming"
sounds very like Leibniz's pre-established harmony, but that only works if
you believe in a provident deity (if it ever worked for an
Re: Questions on Russell's "Why Occam" paper
Le 07-juin-05, à 12:28, Russell Standish a écrit :
On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:
OK. it seems to me that (equation 14 at
http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html )
?
In LaTeX, this equation is
\frac {d\psi}{d t}={\cal H}(\psi)
It supposes time, but not space (TIME postulate). Moreover, it
supposes continuous time,
Yes but that is a lot of assumptions. Why a linear time capable of
being represented by the very special line with the usual topology of
the reals? I can imagine many topology on the reals.
but I do suggest in the paper how it might
be generalised to other possible timescales.
yes but if you pretend to derive your equation, I don't understand what
you mean by generalizing your conclusion (if only by: I have not derive
it and it remains some work to do).
Perhaps it also supposes
continuity in time for \psi, although this probably flows from
assuming continuity of time.
Why should a function be continuous just because it is defined on a
topological space (which is what I assume you are saying when you say
continuity of time).
I do not think time is necessarily
continuous - I think it is interesting to explore alternative QMs
without this assumption.
Sure. But again how to talk on derivation then. I mean if someone
pretend to derive B from A, then if someone else derive something mùore
general than B from A, it is a critic of the assertion that B has been
derived from A. If from facts I can derive the murderer is among John
and Charles, I am not so interested in knowing the derivation can be
generalized into leading that the murderer is among John, Charles, Lee,
Bruno and Nicole!
The question is whether this is the most general evolution equation
for continuous time, or whether there is some more general
equation.
Absolutely.
Remember, we do have already that \psi is a member of a
Hilbert space, so we can write things like:
OK, but you assume Set theory (that by itself is huge in our context).
I show only that you have a preHilbetian space (why should "cauchy
sequence of vectors converges).
\psi(t')-\psi(t) = ...
What do you mean by derivability notion for H, and topological notion?
Topological notion are needed for talking of continuity (a continuous
function is just a function from topological space into a topological
space such that the inverse image of open set is an open set).. You
"assume" the familiar topology of reals, complex number, etc.
Derivability is a stronger requirement (although some algebraist would
introduce many nuances). Someday I will show you make also assumption
on consciousness, but that is more subtle, and then all physicist if
not almost scientist are doing them when they pretend to solve the
consciousness problem like Dennett, or when they put it under the rug
(a little bit like Lee in his last posts, I would say).
Look Russell, as I said I appreciate your attempt, it is just that, as
Hal and Paddy mentionned, there remains quite a lot of work to make it
thoroughly communicable. You should really put more clearly your
assumptions. You assume a vast part of mathematics, and I would say of
physics, mainly with your time postulate and your equation. Compare
your work with those I have mentionned (I will give the reference for
those you don't have yet). Don't compare it to quickly to mine where
the assumptions are made still at a much more basic (logical and
arithmetical) level. I assume less than Peano arithmetic. I know I
could seem a little bit presomptuous, but nuance would make the post
more long and more boring. Hope you don't mind, (actually I would be
glad someone criticize the most severely possible my work),
Bruno
http://iridia.ulb.ac.be/~marchal/
Re: Questions on Russell's "Why Occam" paper
On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:
>
> OK. it seems to me that (equation 14 at
> http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html )
>
> ?
>
In LaTeX, this equation is
\frac {d\psi}{d t}={\cal H}(\psi)
It supposes time, but not space (TIME postulate). Moreover, it
supposes continuous time, but I do suggest in the paper how it might
be generalised to other possible timescales. Perhaps it also supposes
continuity in time for \psi, although this probably flows from
assuming continuity of time. I do not think time is necessarily
continuous - I think it is interesting to explore alternative QMs
without this assumption.
The question is whether this is the most general evolution equation
for continuous time, or whether there is some more general
equation. Remember, we do have already that \psi is a member of a
Hilbert space, so we can write things like:
\psi(t')-\psi(t) = ...
What do you mean by derivability notion for H, and topological notion?
>
>
> is really presupposing a lot. Where does that come from? It presupposes
> a space/time geometry, continuity, derivability notion for H,
> topological notion, etc.
>
> To begin with.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
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Re: Questions on Russell's "Why Occam" paper
Le 07-juin-05, à 09:20, Russell Standish a écrit : On Tue, Jun 07, 2005 at 08:29:57AM +0200, Bruno Marchal wrote: Le 06-juin-05, ? 22:51, Hal Finney a ?crit : I share most of Paddy Leahy's concerns and areas of confusion with regard to the "Why Occam" discussion so far. I really don't understand what it means to explain appearances rather than reality. Well this I understand. I would even argue that Everett gives an example by providing an explanation of the appearance of a wave collapse from the SWE (Schroedinger Wave equation) and this without any *real*collapse. And I pretend at least that if comp is correct, then the SWE as an *appearance* emerges statistically from the "interference" of all computations as seen from some inner point of view of the mean universal machine. But, as I pointed a long time ago Russell is hiding (de facto, not intentionally I guess :) many assumptions. It would be nice to expose these "hidden" assumptions. As far as I'm aware, all my assumptions are exposed and upfront, where at least you as a reader can decide if you agree, but there is always the possibility of some that I've missed. OK. it seems to me that (equation 14 at http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html ) <> is really presupposing a lot. Where does that come from? It presupposes a space/time geometry, continuity, derivability notion for H, topological notion, etc. To begin with. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Questions on Russell's "Why Occam" paper
On Tue, Jun 07, 2005 at 08:29:57AM +0200, Bruno Marchal wrote:
>
> Le 06-juin-05, ? 22:51, Hal Finney a ?crit :
>
> >I share most of Paddy Leahy's concerns and areas of confusion with
> >regard to the "Why Occam" discussion so far. I really don't understand
> >what it means to explain appearances rather than reality.
>
>
> Well this I understand. I would even argue that Everett gives an
> example by providing an explanation of the appearance of a wave
> collapse from the SWE (Schroedinger Wave equation) and this without any
> *real*collapse.
> And I pretend at least that if comp is correct, then the SWE as an
> *appearance* emerges statistically from the "interference" of all
> computations as seen from some inner point of view of the mean
> universal machine.
> But, as I pointed a long time ago Russell is hiding (de facto, not
> intentionally I guess :) many assumptions.
It would be nice to expose these "hidden" assumptions. As far as I'm
aware, all my assumptions are exposed and upfront, where at least you
as a reader can decide if you agree, but there is always the
possibility of some that I've missed.
> There are a lot of "derivation" of the SWE in the literature, it would
> be interesting that Russell compares them with its own. My favorite one
> is the one by Henry and another one by Hardy.
The only thing I was aware of by Henry was a derivation of the
correspondence principle from gauge invariance in a paper you sent me,
something I think that Stenger does better in his book (which is
almost published now!).
And as for Hardy, I never found his axioms terribly "reasonable",
unfortunately.
> Note the incredible derivation of QM from just 5 experiments + a
> natural principle of simplicity by Julian Swinger in his QM course
> (taken again by Towsend in its QM textbook). I will give reference once
> less busy.
>
Sure - I'm not aware of that.
> I agree with Hal and Paddy about the lack of clarity in many passages.
> Note that my result is infinitely more modest (despite the
> appearance!).
Hardly infinitely more modest. You start from a slightly different
basis (COMP thesis vs all descriptions ensemble), derive the
existence of what I assume, and end up not quite where I end
up. Perhaps if you adopted Kolmogorov probability axioms, you could
get the full QM theory to result. The other things I assume tend to be
assumed by you also - COMP => TIME, and I think you assume PROJ. Not
sure where your work stand with the Anthropic Principle.
> I just prove that if comp is assumed to be correct then a
> derivation of the SWE *must* exist, without providing it. Well, in the
> interview of the Lobian machine I do extract some 'quantum logic' from
> comp, but it is too early to judge if the SWE can be extracted from it.
> But it should be, in principle, if comp is true. Advantage: I just
> assume natural numbers and classical logic, I don't assume any geometry
> or temporality, which for me are really the miraculous things in need
> to be explained.
>
> Bruno
>
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Re: Questions on Russell's "Why Occam" paper
Le 06-juin-05, à 22:51, Hal Finney a écrit : I share most of Paddy Leahy's concerns and areas of confusion with regard to the "Why Occam" discussion so far. I really don't understand what it means to explain appearances rather than reality. Well this I understand. I would even argue that Everett gives an example by providing an explanation of the appearance of a wave collapse from the SWE (Schroedinger Wave equation) and this without any *real*collapse. And I pretend at least that if comp is correct, then the SWE as an *appearance* emerges statistically from the "interference" of all computations as seen from some inner point of view of the mean universal machine. But, as I pointed a long time ago Russell is hiding (de facto, not intentionally I guess :) many assumptions. There are a lot of "derivation" of the SWE in the literature, it would be interesting that Russell compares them with its own. My favorite one is the one by Henry and another one by Hardy. Note the incredible derivation of QM from just 5 experiments + a natural principle of simplicity by Julian Swinger in his QM course (taken again by Towsend in its QM textbook). I will give reference once less busy. I agree with Hal and Paddy about the lack of clarity in many passages. Note that my result is infinitely more modest (despite the appearance!). I just prove that if comp is assumed to be correct then a derivation of the SWE *must* exist, without providing it. Well, in the interview of the Lobian machine I do extract some 'quantum logic' from comp, but it is too early to judge if the SWE can be extracted from it. But it should be, in principle, if comp is true. Advantage: I just assume natural numbers and classical logic, I don't assume any geometry or temporality, which for me are really the miraculous things in need to be explained. Bruno It's hard to get my mind around this kind of explanation and what to expect from it. Also the way the Anthropic Principle applies to infinite strings seems extremely vague until we have a clearer picture of how those strings relate to reality. One area I differ: Paddy Leahy writes, quoting Russell: However, as the cardinality of "my" ensemble is actually "c" (cardinality of the real numbers), it is quite probably a completely different beast. There you go again with your radical compression. Without the reading I've been doing in the last two weeks, I wouldn't have been able to decode this statement as meaning: 2^\aleph_0 = \aleph_1 (by definition) To assume c = \aleph_1 is the Continuum Hypothesis, which is unprovable (within standard arithmetic). Actually Russell did not bring aleph_1 into the picture at all. All that he referred to was aleph_0 and c which by definition is 2^aleph_0. c is the cardinality of the reals and of infinite bit strings. This is all just definitional. Whether c is the "next" infinite cardinal after aleph_0 is the Continuum Hypothesis, but that is not relevant here. Another area I had trouble with in Russell's answer was the concept of a prefix map. I understand that a prefix map is defined as a mapping whose domain is finite bit strings such that none of them are a prefix of any other. But I'm not sure how to relate this to the infinite bit strings that are "descriptions". In particular, if "an observer attaches sequences of meanings to sequences of prefixes of one of these strings", then it seems that he must have a domain which does allow some inputs to be prefixes of others. Isn't that what "sequences of prefixes" would mean? That is, if the infinite string is 01011011100101110111..., then a sequence of prefixes might be 0, 01, 010, 0101, 01011, Does O() apply to this sequence of prefixes? If so then I don't think it is a prefix map. I want to make it clear by the way that my somewhat pedantic and labored examination of this page is not an attempt to be difficult or stubborn. Rather, I find that by the third page, I don't understand what is going on at all! Even the very first sentence, "In the previous sections, I demonstrate that formal mathematical systems are the most compressible, and have highest measure amongst all members of the Schmidhuber ensemble," has me looking to see if I skipped a page! I don't see where this is discussed in any way. So I hope that by pinning down and crystalizing exactly what the first page is claiming, it will help me to see what the more interesting third page is actually able to establish. I think Paddy is in much the same situation. Hal Finney http://iridia.ulb.ac.be/~marchal/
Re: Questions on Russell's "Why Occam" paper
On Mon, Jun 06, 2005 at 01:51:36PM -0700, "Hal Finney" wrote:
>
> Another area I had trouble with in Russell's answer was the concept of
> a prefix map. I understand that a prefix map is defined as a mapping
> whose domain is finite bit strings such that none of them are a prefix
> of any other. But I'm not sure how to relate this to the infinite bit
> strings that are "descriptions".
A prefix map attaches the same output to all strings that share a
common finite length prefix.
>
> In particular, if "an observer attaches sequences of meanings to sequences
> of prefixes of one of these strings", then it seems that he must have a
> domain which does allow some inputs to be prefixes of others. Isn't that
> what "sequences of prefixes" would mean? That is, if the infinite string
> is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
> 010, 0101, 01011, Does O() apply to this sequence of prefixes? If
> so then I don't think it is a prefix map.
>
Yes I agree this is vague, and seemingly contradictory. I'm not sure
how to make this more precise, but one way to read the paper is to
treat observers as prefix maps for section 2 (Occam's razor), and then
for section 3 (White Rabbit problem) ignore the prefix property.
It could be that the way of making this more precise is to assume
observers have some internal state that is constantly updated (a time
counter perhaps), so actually going through a sequence of prefix maps
in (psychological) time, but at this stage I don't have an answer.
> I want to make it clear by the way that my somewhat pedantic and labored
> examination of this page is not an attempt to be difficult or
> stubborn.
Even being difficult and stubborn has its place (to help winkle out
subtle errors of logic eg), so long as you relax enough at other times to
obtain understanding. I appreciate the effort in any case.
> Rather, I find that by the third page, I don't understand what is going
> on at all! Even the very first sentence, "In the previous sections, I
> demonstrate that formal mathematical systems are the most compressible,
> and have highest measure amongst all members of the Schmidhuber ensemble,"
> has me looking to see if I skipped a page! I don't see where this is
> discussed in any way.
This is pretty much a tautology. Formal mathematical systems are a
means of compressing data in the form of facts about numbers. If one
were to include all such possible compression schemes, rather than
just the systems studies by mathematicians to date, one would end up
with the set of Turing machines, or equivalently of computable
functions. The Occam's razor result clearly relates measure to the
amount of compressibility in the description.
Perhaps such a view of mathematics is strange. Certainly I find it
strange when Stephen Wolfram says mathematics is incapable of
understanding complex phenomena, and one should cellular automata
instead. To me, cellular automata are just another example of a
mathematical system.
> So I hope that by pinning down and crystalizing
> exactly what the first page is claiming, it will help me to see what
> the more interesting third page is actually able to establish. I think
> Paddy is in much the same situation.
>
> Hal Finney
I hope so too.
--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.
A/Prof Russell Standish Phone 8308 3119 (mobile)
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UNSW SYDNEY 2052 [EMAIL PROTECTED]
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Re: Questions on Russell's "Why Occam" paper
On Mon, Jun 06, 2005 at 12:06:06PM +0100, Patrick Leahy wrote: > > > On Mon, 6 Jun 2005, Russell Standish wrote: > > >I am beginning to regret calling the all descriptions ensemble with > >uniform measure a Schmidhuber ensemble. I think what I meant was that > >it could be generated by a standard dovetailer algorithm, running for > >2^\aleph_0 timesteps. > > It can't! Timesteps are denumerable, hence this statement is just a > contradiction in terms. You better postulate your ensemble without > reference to any algorithm to generate it. Indeed I do. Only Schmidhuber uses the dovetailer. Hence my "regret". ... > > 2^\aleph_0 = \aleph_1 (by definition) > Hal dealt with this one already, I notice. 2^\aleph_0 = c. \aleph_1 is something else entirely. > > > > >Now an observer will expect to find a SAS in one of the descriptions > >as a corrolory of the anthropic principle, which is explicitly stated > >as one of the assumptions in this work. I make no bones about this - I > >consider the anthropic principle a mystery, not self-evident like > >many people. > > Very few supporters of the AP would "expect to find a SAS" in a bitstring. > Until you *specify* a way of interpreting the string, it contains nothing > but bits. The observer specifies the interpretation. > > >Why should an observer expect to see a token of erself > >embedded in reality? That is the mystery of the AP. > > What ARE you talking about? Observer's don't see tokens of > themselves... I can see that I have a body - if I look in the mirror I can see a face, eye etc, all of which appear to be under my control. This is a token embedded in my reality that represents me. > if anyone (God?) has a 3rd-person/bird's eye view, it is certainly not > someone who is included in any particular reality. No way is anything like > this implied by the AP. All the AP requires is that there *be* > observers/SAS in (real) universes, which is true in our case at least. > Sorry - you lost me here ... oh well. > > > >>And now we find not only that the bit string is > >>a description, but it is a complex enough description to describe SAS's? > >>How does that work? > >> > > > >The bitstrings are infinite in length. By reading enough bits, they can > >have arbitrarily complex meanings attached to them. > > > > In particular, any bitstring can be "interpreted" as any other bitstring > by an appropriate map. Hence until you specify an interpreter you are > simply not proposing a theory at all. > The observer _is_ the interpreter. There may well be more than one observer in the picture, but they'd better agree! > > > > >All that is discussed in this paper is appearances - we only try to > >explain the phenomenon (things as they appear). No attempt is made to > >explain the noumenon (things as they are), nor do we need to assume > >that there is a noumenon. > > Most readers of your paper would take it that you are making a strong > ontological proposition, i.e. that the basis of reality is your set of > bitstrings. This is the case. If this is *not* the case, and you think the bitstrings may be > represented in some deeper reality (or maybe are just metaphors), then > what is the motivation for your proposal? Why do we need to think about > this intermediate layer of bitstrings? The original simplicity goes out > the window. This latter extrapolation is not the case. > > BTW I'm with Kant: you can't have an appearance without an underlying > reality, even if that is unknowable. > I'm not sure Kant says this, but in any case that's not important. I'm with Marchal, who says if there is an underlying reality which is not only unknowable, but also unnecessary to explain phenomena, then why assume that particular hypothesis? It makes no sense. > >Bruno Marchal has a detailed discussion on this in his thesis, and > >concludes that he "has no need for this hypothesis" (what he calls the > >extravagant hypothesis). > > > >So the former statement is true :[the description strings are] things > >that "observer" TM's observe and map to integers. It is also true that > >descriptions of self aware observers will appear within the description > >by the Anthropic Principle. The phenomenon of observerhood is included. > >However where the observers actually live is not a meaningful question > >in this framework. > > I think either your terminology or you model has now got very confused. > Are your "observer" TMs the observers (SAS) whose experiences your theory > is trying to explain? Yes. > In this case "where they live" is crucial because it > defines the environment the SAS find themselves in. Why? > If you are not > careful your theory becomes effectively that we are all "brains in > bottles" or Leibnizian monads, which is solipsism by another name. It is not solipsism, if only for the reason that multiple observers exist in our observed reality. They are all as real as our own consciousness. Bruno Marchal cal
Re: Questions on Russell's "Why Occam" paper
I share most of Paddy Leahy's concerns and areas of confusion with regard to the "Why Occam" discussion so far. I really don't understand what it means to explain appearances rather than reality. It's hard to get my mind around this kind of explanation and what to expect from it. Also the way the Anthropic Principle applies to infinite strings seems extremely vague until we have a clearer picture of how those strings relate to reality. One area I differ: Paddy Leahy writes, quoting Russell: > > However, as the cardinality of "my" ensemble is actually "c" > > (cardinality of the real numbers), it is quite probably a completely > > different beast. > > There you go again with your radical compression. Without the reading I've > been doing in the last two weeks, I wouldn't have been able to decode this > statement as meaning: > > 2^\aleph_0 = \aleph_1 (by definition) > > To assume c = \aleph_1 is the Continuum Hypothesis, which is unprovable > (within standard arithmetic). Actually Russell did not bring aleph_1 into the picture at all. All that he referred to was aleph_0 and c which by definition is 2^aleph_0. c is the cardinality of the reals and of infinite bit strings. This is all just definitional. Whether c is the "next" infinite cardinal after aleph_0 is the Continuum Hypothesis, but that is not relevant here. Another area I had trouble with in Russell's answer was the concept of a prefix map. I understand that a prefix map is defined as a mapping whose domain is finite bit strings such that none of them are a prefix of any other. But I'm not sure how to relate this to the infinite bit strings that are "descriptions". In particular, if "an observer attaches sequences of meanings to sequences of prefixes of one of these strings", then it seems that he must have a domain which does allow some inputs to be prefixes of others. Isn't that what "sequences of prefixes" would mean? That is, if the infinite string is 01011011100101110111..., then a sequence of prefixes might be 0, 01, 010, 0101, 01011, Does O() apply to this sequence of prefixes? If so then I don't think it is a prefix map. I want to make it clear by the way that my somewhat pedantic and labored examination of this page is not an attempt to be difficult or stubborn. Rather, I find that by the third page, I don't understand what is going on at all! Even the very first sentence, "In the previous sections, I demonstrate that formal mathematical systems are the most compressible, and have highest measure amongst all members of the Schmidhuber ensemble," has me looking to see if I skipped a page! I don't see where this is discussed in any way. So I hope that by pinning down and crystalizing exactly what the first page is claiming, it will help me to see what the more interesting third page is actually able to establish. I think Paddy is in much the same situation. Hal Finney
Re: Questions on Russell's "Why Occam" paper
On Mon, 6 Jun 2005, Russell Standish wrote: I am beginning to regret calling the all descriptions ensemble with uniform measure a Schmidhuber ensemble. I think what I meant was that it could be generated by a standard dovetailer algorithm, running for 2^\aleph_0 timesteps. It can't! Timesteps are denumerable, hence this statement is just a contradiction in terms. You better postulate your ensemble without reference to any algorithm to generate it. However, as the cardinality of "my" ensemble is actually "c" (cardinality of the real numbers), it is quite probably a completely different beast. There you go again with your radical compression. Without the reading I've been doing in the last two weeks, I wouldn't have been able to decode this statement as meaning: 2^\aleph_0 = \aleph_1 (by definition) To assume c = \aleph_1 is the Continuum Hypothesis, which is unprovable (within standard arithmetic). Now an observer will expect to find a SAS in one of the descriptions as a corrolory of the anthropic principle, which is explicitly stated as one of the assumptions in this work. I make no bones about this - I consider the anthropic principle a mystery, not self-evident like many people. Very few supporters of the AP would "expect to find a SAS" in a bitstring. Until you *specify* a way of interpreting the string, it contains nothing but bits. Why should an observer expect to see a token of erself embedded in reality? That is the mystery of the AP. What ARE you talking about? Observer's don't see tokens of themselves... if anyone (God?) has a 3rd-person/bird's eye view, it is certainly not someone who is included in any particular reality. No way is anything like this implied by the AP. All the AP requires is that there *be* observers/SAS in (real) universes, which is true in our case at least. And now we find not only that the bit string is a description, but it is a complex enough description to describe SAS's? How does that work? The bitstrings are infinite in length. By reading enough bits, they can have arbitrarily complex meanings attached to them. In particular, any bitstring can be "interpreted" as any other bitstring by an appropriate map. Hence until you specify an interpreter you are simply not proposing a theory at all. All that is discussed in this paper is appearances - we only try to explain the phenomenon (things as they appear). No attempt is made to explain the noumenon (things as they are), nor do we need to assume that there is a noumenon. Most readers of your paper would take it that you are making a strong ontological proposition, i.e. that the basis of reality is your set of bitstrings. If this is *not* the case, and you think the bitstrings may be represented in some deeper reality (or maybe are just metaphors), then what is the motivation for your proposal? Why do we need to think about this intermediate layer of bitstrings? The original simplicity goes out the window. BTW I'm with Kant: you can't have an appearance without an underlying reality, even if that is unknowable. Bruno Marchal has a detailed discussion on this in his thesis, and concludes that he "has no need for this hypothesis" (what he calls the extravagant hypothesis). So the former statement is true :[the description strings are] things that "observer" TM's observe and map to integers. It is also true that descriptions of self aware observers will appear within the description by the Anthropic Principle. The phenomenon of observerhood is included. However where the observers actually live is not a meaningful question in this framework. I think either your terminology or you model has now got very confused. Are your "observer" TMs the observers (SAS) whose experiences your theory is trying to explain? In this case "where they live" is crucial because it defines the environment the SAS find themselves in. If you are not careful your theory becomes effectively that we are all "brains in bottles" or Leibnizian monads, which is solipsism by another name. Or are your "observers" the missing "interpreters" in your theory which give it meaning, and allow us to find (in principle) the SAS within the bitstrings that represent actual observers like us? In this case it's unhelpful to call these meta-entities "observers"; rather, in effect, they constitute the (meta-)laws of physics. Incidentally, a TM by itself can't generate meaning, as it is only a map from integers to integers. You still have to specify externally how to interpret the code as something more than a mere number. (E.g. in the Turing test the output bits have to be processed into English language text). The page then goes on to make some comments about measure applied to universes. Here again I am confused about how to relate it to all that has been descibed. What are the analogs of universes, in this model? Is it "descriptions", the infinite bit strings? From what h
Re: Questions on Russell's "Why Occam" paper
On Fri, Jun 03, 2005 at 04:22:07PM -0700, "Hal Finney" wrote: > Russell Standish recently mentioned his paper "Why Occam's Razor" which > can be found at http://parallel.hpc.unsw.edu.au/rks/docs/occam/ . Among > other things he aims to derive quantum mechanics from a Schmidhuber type > ensemble. I have tried to read this paper but never really understood it. > Here I will try to ask some questions, taking it slowly. > > On this page, http://parallel.hpc.unsw.edu.au/rks/docs/occam/node2.html , > things get started. Russell describes a set of infinite bit strings he > calls "descriptions". He writes: > > "By contrast to Schmidhuber, I assume a uniform measure over these > descriptions -- no particular string is more likely than any other." > > This surprises me. I thought that Schmidhuber assumed a uniform measure > over bit strings considered as programs for his universal computer. So > what is the "contrast" to his work? Nowhere in Schmidhuber (1997) does he propose a measure over the "input programs". What he does is is justify the appearance of a universal prior in the set of descriptions by passing the raw data through a reference UTM. Presumably the set of descriptions is sampled uniformly by the observer. In Schmidhuber (2000), the set of descriptions is generated by a machine which has resource bounds. This leads to the notion of "speed prior" which differs from the universal prior in several important respects. I sometimes refer to the two different ensembles as Schmidhuber I and Schmidhuber II. I am beginning to regret calling the all descriptions ensemble with uniform measure a Schmidhuber ensemble. I think what I meant was that it could be generated by a standard dovetailer algorithm, running for 2^\aleph_0 timesteps. However, as the cardinality of "my" ensemble is actually "c" (cardinality of the real numbers), it is quite probably a completely different beast. It is also not generated by a program, Schmidhuber style, it simply is (in the sense of being the simplest set - equivalent to nothing). > > It seems that the greater contrast is that while Schmidhuber assumed that > the bit strings would be fed into a computer that would produce outputs, > Russell is taking the bit strings directly as raw data. > Quite true. > But I am confused about their role. > > "Since some of these descriptions describe self aware substructures..." > > Whoa! This is a big leap for me. First, I am not too happy that mere bit > strings have been elevated with the title "descriptions". A bit string on > its own doesn't seem to have the inherent meaning necessary for it to be > considered a description. Many apologies for deploying terminology in a different way to you expect. A description (in my terminology) does not necessarily have meaning. It is simply data. This is in accord with how I use the term in casual English usage too - a description is simply a string of letters, and may or may not be meaningful. Meaning is attached by an observer. Now an observer will expect to find a SAS in one of the descriptions as a corrolory of the anthropic principle, which is explicitly stated as one of the assumptions in this work. I make no bones about this - I consider the anthropic principle a mystery, not self-evident like many people. Why should an observer expect to see a token of erself embedded in reality? That is the mystery of the AP. > And now we find not only that the bit string is > a description, but it is a complex enough description to describe SAS's? > How does that work? > The bitstrings are infinite in length. By reading enough bits, they can have arbitrarily complex meanings attached to them. > It's especially confusing to read the introductory word "since" as though > this is all quite obvious and need not be explained. To me it is very > confusing. > Sorry for not going slow enough. The habits of concise expression are hard to shake. > The page goes on to identify these SAS's as observers. Now they are mappings, > or equivalently Turing Machines, which map finite bit strings to integers. > These integers are the "meanings" of the bit strings. Not equivalently. Not all maps can be represented by a Turing machine, only computable ones. > > I believe the idea here is that the bit strings are taken as prefixes > of the "description" bit strings in the ensemble. It is as though the > "observers" are observing the "descriptions" a bit at a time, and mapping > them to a sequence of integer "meanings". Is that correct? > Indeed that is one interpretation. The most important point is that the observer map is a "prefix" map, in the sense of prefix machines of Algorithmic Information Theory. In reading a bit string one bit at a time, once a meaning is attached to the string, that is the meaning for evermore - the observer cannot change er mind after reading a few more bits. Schmidhuber (2000) deals with machines that do "change their mind", so perhaps there is some extension
Questions on Russell's "Why Occam" paper
Russell Standish recently mentioned his paper "Why Occam's Razor" which can be found at http://parallel.hpc.unsw.edu.au/rks/docs/occam/ . Among other things he aims to derive quantum mechanics from a Schmidhuber type ensemble. I have tried to read this paper but never really understood it. Here I will try to ask some questions, taking it slowly. On this page, http://parallel.hpc.unsw.edu.au/rks/docs/occam/node2.html , things get started. Russell describes a set of infinite bit strings he calls "descriptions". He writes: "By contrast to Schmidhuber, I assume a uniform measure over these descriptions -- no particular string is more likely than any other." This surprises me. I thought that Schmidhuber assumed a uniform measure over bit strings considered as programs for his universal computer. So what is the "contrast" to his work? It seems that the greater contrast is that while Schmidhuber assumed that the bit strings would be fed into a computer that would produce outputs, Russell is taking the bit strings directly as raw data. But I am confused about their role. "Since some of these descriptions describe self aware substructures..." Whoa! This is a big leap for me. First, I am not too happy that mere bit strings have been elevated with the title "descriptions". A bit string on its own doesn't seem to have the inherent meaning necessary for it to be considered a description. And now we find not only that the bit string is a description, but it is a complex enough description to describe SAS's? How does that work? It's especially confusing to read the introductory word "since" as though this is all quite obvious and need not be explained. To me it is very confusing. The page goes on to identify these SAS's as observers. Now they are mappings, or equivalently Turing Machines, which map finite bit strings to integers. These integers are the "meanings" of the bit strings. I believe the idea here is that the bit strings are taken as prefixes of the "description" bit strings in the ensemble. It is as though the "observers" are observing the "descriptions" a bit at a time, and mapping them to a sequence of integer "meanings". Is that correct? So here is another confusion about the role of the "description" bit strings in the model. Are they things that "observer" TM's observe and map to integers? Or are they places where observers live, as suggested by the "Since" line quoted above? Or both? Now it gets a little more complicated: "Under the mapping O(x), some descriptions encode for identical meanings as other descriptions, so one should equivalence class the descriptions." The problem I have is, O takes only finite bit strings. So technically a "description", which is an infinite bit string, does not encode a meaning. What I think is meant here, though, is that two "descriptions" (i.e. infinite bit strings) will be considered equivalent if for every finite prefix of the strings, the O() mapping is the same. So if we think of O as "observing" the "description" bit strings one by one, it will go through precisely the same sequence of integer "meanings" in each case. Is that right? "In particular, strings where the bits after some bit number n are ``don't care'' bits, are in fact equivalence classes of all strings that share the first n bits in common." I think what this considers is a special O() and a special string prefix such that if O sees that particular n-bit prefix, all extensions of that prefix get mapped to the same "meaning" integer. In that case the condition described in my previous paragraph would be met, and all strings with this n-bit prefix would be equivalent. "One can see that the size of the equivalence class drops off exponentially with the amount of information encoded by the string." That seems a little questionable because the size of the equivalence class is infinite in all cases. However I think Russell means to use a uniform measure where the collection of all strings with a particular n-bit prefix have a measure of 1/2^n. It's not clear how well this measure really works or whether it applies to all sets of infinite strings. "Under O(x), the amount of information is not necessarily equal to the length of the string, as some of the bits may be redundant." Now we have this new concept of "the amount of information" which has not previously been defined. This sentence is really hard for me. What does it mean for bits to be redundant? We just discussed strings where all those after bit n are "don't care", but this sentence seems to be envisioning other kinds of redundancies. "The sum P_O(s) = [sum over p such that O(p)=s of] 2^(-|p|) where |p| means the number of bits of p consumed by O in returning s, gives the size of the equivalence class of all descriptions having meaning s." Boy, that's a tough one now. We consider all bit strings p such that O(p) = s. Now, is this supposed to just be those cases described earlier where the bits after |p|
