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Re: Consciousness is information?
Jason Resch wrote:
> On Wed, Apr 29, 2009 at 1:05 AM, russell standish < lists@...> wrote:
>
>> What you are talking about is what I call the "Occam catastrophe" in
>> my book. The resolution of the paradox has to be that the
>> random/white-noise filled OMs are in fact unable to be observed. In
>> order for the Anthropic Principle to hold in a idealist theory
>> requires that the OM must contain a representation of the observer, ie
>> observers must be self-aware. Amongst such OMs containing observers,
>> ones that are the result of historically deep evolutionary processes
>> are by far the most common. And evolution of those observer moments
>> must also be constrained to be similar to those previously observed,
>> eliminating white rabbits, due to "robustness" of the observer.
>>
>> Cheers
>>
>>
>
> Hi Russell,
>
> What you said reminded me of this article, which appeared in the Boston Globe:
>
> http://www.boston.com/bostonglobe/ideas/graphics/011109_hacking_your_brain/>
> See the section on hallucinating with ping pong balls and a radio. It
> would seem the way the brain is organized it doesn't accept perception
> of pure randomness (at least not for long, I have not yet tried the
> experiment myself). If it can't find patterns from the senses it
> looks like it gives up and invents patterns of its own.
>
> Jason
There were similar reports in the late 60's when sensory deprivation
tanks were the fad. People in them reported hallucinations and
illusions and, if they stayed long enough, thought loops.
Brent
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RE: Consciousness is information?
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From: marchal@...To: everything-list@...Subject: Re: Consciousness is information? Date: Wed, 29 Apr 2009 22:19:56 +0200 >Maudlin's point is that the causal structure has no physical role
But I'm not convinced that the basic Olympia machine he describes doesn't already have a complex causal structure--the causal structure would be in the way different troughs influence each other via the pipe system he describes, not in the motion of the armature.
>But read the movie graph which shows the same thing without going through the question of the counterfactuals.
Where can I find the movie graph argument?
>If you believe that consciousness supervene on the physical implementation, or even just one universal machine computation, then you will associate consciousness to a description of that computation.
But why must I do that? Why can't I associate consciousness to a causal structure in the real world that's isomorphic to the causal structure of the computation, not just a passive description of the computation? Is there a fatal flaw in my suggestion about defining "causal structure" in terms of propositions about events and the way certain propositions logically imply others (if you take into account the basic laws of whatever 'universe' you're describing with these propositions, whether it's the laws of physics in the real universe or the laws governing a cellular automaton)?
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Re: Consciousness is information?
On 29 Apr 2009, at 23:30, Jesse Mazer wrote:
From: marchal@...To: everything-list@...Subject: Re: Consciousness is information? Date: Wed, 29 Apr 2009 22:19:56 +0200 >Maudlin's point is that the causal structure has no physical role
But I'm not convinced that the basic Olympia machine he describes doesn't already have a complex causal structure--the causal structure would be in the way different troughs influence each other via the pipe system he describes, not in the motion of the armature.
But Maudlin succeed in showing that in its particular running history, *that* causal structure is physically inert. Or it has mysterious influence not related to the computation.
>But read the movie graph which shows the same thing without going through the question of the counterfactuals.
Where can I find the movie graph argument?
Search MGA 1, MGA 2, (and forget MGA 3 I don't like it) in the recent threads on this list. Or read the french versions in my two theses. Or wait I put my last paper on my web page. Let us see:
>If you believe that consciousness supervene on the physical implementation, or even just one universal machine computation, then you will associate consciousness to a description of that computation.
But why must I do that? Why can't I associate consciousness to a causal structure in the real world that's isomorphic to the causal structure of the computation, not just a passive description of the computation?
Because in a particular running what makes the structure causal can be physically inert. This means that if you attach consciousness to it, you are attaching consciousness to something abstract. No problem, both consciousness and computations seems to me abstract or immaterial at the start. But then, unless you introduce a physical selection principle (unrelated to the abstract computation), you have to attach consciousness on all abstract realization of the computation. The machine cannot know which computation (or which mathematical universal machine) implements its states, forcing to consider the whole abstract space of all computations, which fortunately makes sense (through Church thesis).
Put in another way: a digital machine cannot distinguish between real, virtual or arithmetical. Unless magical power not present in the computations is introduced to select a reality.
Is there a fatal flaw in my suggestion about defining "causal structure" in terms of propositions about events and the way certain propositions logically imply others
No fatal flaw. On the contrary, it is the good idea. I do this too. But then you cannot rely on particular "concrete things" to select one computations among all possible one. You already move to the abstract, or mathematical or logical. I just insist to push that idea to its ultimate consequence. The seemingly realness or concreteness will have to emerge from an infinity of absract, but well defined, computations. No Token, many Types. Token are types view from inside. Comp gives an indexical (self-referential) way to explain concrete token from abstract types.
(if you take into account the basic laws of whatever 'universe' you're describing with these propositions, whether it's the laws of physics in the real universe or the laws governing a cellular automaton)?
If you survive "qua computatio", you cannot make a consciousness singular in the absolute. A concrete machine (relatively concrete with respect to you) can be endowed with consciousness, but from its first person view, its future (and past, and reality) is determined by all sublevel computations that the machine cannot distinguish.
If you attach an evolving mind to a cellular automaton states' sequence, you have to attach that same mind to all relative implementations of that sequence generated in the universal dovetailing, or in elementary arithmetic, and this change the prediction that the automaton can make about what it can find when it looks at himself or at his neighborhood below its substitution level. There are many consequence of this. For example you can deduce that whatever the physical universe is, it is not a classical cellular automaton, nor the result of any classical evolving system. At best, it could be a quantum cellular automaton, but even this should be deduced from a relative measure on *all* computations.
I hope this can help, I am aware (and Maudlin is too as he told me a long time ago) that this point is a bit subtle and rarely well understood.
Note that Maudlin concludes that there is a problem with comp, and I conclude there is a problem with the physical supervenience. We both agree that comp and physical supervenience are incompatible. I keep comp as my favorite working hypothesis, and so I attach consciousness, not to any implementation of a computation, but to all at once, and only through logical links at some level. When the computations differentiate up to the point the machine can tell the difference, consciousness bifurcate or differentiate. It remains to justify why the quantum computations seem to win the competition among all computations, but classical computer science gives clues that this could indeed be the case when we take the self-referential limitations explicitly into account (cf AUDA). This would prevent comp from solispisme: there would be a coherent notion of first person plural. There are also evidences from pure number theory.
Feel free to criticize MGA, I appreciate (rational) critics by non person eliminativist researcher.
Bruno
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MGA link
Hi Jesse,
On 30 Apr 2009, at 11:19, Bruno Marchal wrote:
Search MGA 1, MGA 2, (and forget MGA 3 I don't like it) in the recent threads on this list. Or read the french versions in my two theses. Or wait I put my last paper on my web page. Let us see:
It is more easy with this link:
Best,
Bruno
>If you believe that consciousness supervene on the physical implementation, or even just one universal machine computation, then you will associate consciousness to a description of that computation.
But why must I do that? Why can't I associate consciousness to a causal structure in the real world that's isomorphic to the causal structure of the computation, not just a passive description of the computation?
Because in a particular running what makes the structure causal can be physically inert. This means that if you attach consciousness to it, you are attaching consciousness to something abstract. No problem, both consciousness and computations seems to me abstract or immaterial at the start. But then, unless you introduce a physical selection principle (unrelated to the abstract computation), you have to attach consciousness on all abstract realization of the computation. The machine cannot know which computation (or which mathematical universal machine) implements its states, forcing to consider the whole abstract space of all computations, which fortunately makes sense (through Church thesis).
Put in another way: a digital machine cannot distinguish between real, virtual or arithmetical. Unless magical power not present in the computations is introduced to select a reality.
Is there a fatal flaw in my suggestion about defining "causal structure" in terms of propositions about events and the way certain propositions logically imply others
No fatal flaw. On the contrary, it is the good idea. I do this too. But then you cannot rely on particular "concrete things" to select one computations among all possible one. You already move to the abstract, or mathematical or logical. I just insist to push that idea to its ultimate consequence. The seemingly realness or concreteness will have to emerge from an infinity of absract, but well defined, computations. No Token, many Types. Token are types view from inside. Comp gives an indexical (self-referential) way to explain concrete token from abstract types.
(if you take into account the basic laws of whatever 'universe' you're describing with these propositions, whether it's the laws of physics in the real universe or the laws governing a cellular automaton)?
If you survive "qua computatio", you cannot make a consciousness singular in the absolute. A concrete machine (relatively concrete with respect to you) can be endowed with consciousness, but from its first person view, its future (and past, and reality) is determined by all sublevel computations that the machine cannot distinguish.
If you attach an evolving mind to a cellular automaton states' sequence, you have to attach that same mind to all relative implementations of that sequence generated in the universal dovetailing, or in elementary arithmetic, and this change the prediction that the automaton can make about what it can find when it looks at himself or at his neighborhood below its substitution level. There are many consequence of this. For example you can deduce that whatever the physical universe is, it is not a classical cellular automaton, nor the result of any classical evolving system. At best, it could be a quantum cellular automaton, but even this should be deduced from a relative measure on *all* computations.
I hope this can help, I am aware (and Maudlin is too as he told me a long time ago) that this point is a bit subtle and rarely well understood.
Note that Maudlin concludes that there is a problem with comp, and I conclude there is a problem with the physical supervenience. We both agree that comp and physical supervenience are incompatible. I keep comp as my favorite working hypothesis, and so I attach consciousness, not to any implementation of a computation, but to all at once, and only through logical links at some level. When the computations differentiate up to the point the machine can tell the difference, consciousness bifurcate or differentiate. It remains to justify why the quantum computations seem to win the competition among all computations, but classical computer science gives clues that this could indeed be the case when we take the self-referential limitations explicitly into account (cf AUDA). This would prevent comp from solispisme: there would be a coherent notion of first person plural. There are also evidences from pure number theory.
Feel free to criticize MGA, I appreciate (rational) critics by non person eliminativist researcher.
Bruno
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Re: Consciousness is information?
2009/4/30 Bruno Marchal < marchal@...>:
> This is essentially the problem discussed by Chalmers in "Does a Rock
> Implement Every Finite-State Automaton"
> at http://consc.net/papers/rock.html ,
>
> Yes. And I don't buy that argument. I will not insist because you did it
> well in your last post. Also, if it was the case that rock implement
> sophisticated computations, it would just add some measure on some
> computations in the Universal Dovetailing. Also, a rock cannot be a
> computational object: it is a projection of an infinity of computations when
> we look at the rock at a level which would be below our common substitution
> level. Eventually we will met the quantum vacuum (assuming comp implies QM,
> as I think), and in some "parallel world" that vaccum will go through all
> accessible states, but this is part of so many variate histories that they
> interfere destructively and does not generate any classical history stable
> relatively to any observer coupled with the rock.
>
>
> and I think it's also the idea behind Maudlin's Olympia thought experiment
> as well.
>
> Maudlin's Olympia, or the Movie Graph Argument are completely different.
> Those are arguments showing that computationalism is incompatible with the
> physical supervenience thesis. They show that consciousness are not related
> to any physical activity at all. Together with UDA1-7, it shows that physics
> has to be reduced to a theory of consciousness based on a purely
> mathematical (even arithmetical) theory of computation, which exists by
> Church Thesis.
> The movie graph argument was originally only a tool for explaining how
> difficult the mind-body problem is, once we assume mechanism.
The Rock argument and the Olympia/ Movie Graph argument are
diffferent, but they lead to the same conclusion if valid, namely that
if computationalism is true then consciousness does not supervene on
physical activity. Putnam and Searle use the Rock argument to suggest
that computationalism is false: they consider it absurd that any
conscious computation supervenes on any physical activity (or
equivalently no physical activity, since at one extreme the Rock
argument allows that any computation is implemented by the null
state). Chalmers tries to rescue computationalism in the paper cited
by arguing that the Rock argument is not valid.
--
Stathis Papaioannou
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Re: Consciousness is information?
2009/4/30 Brent Meeker < meekerdb@...>:
>> It seems to me that if the seconds of my life were according to an
>> external clock being generated backwards or scrambled, I would have no
>> way of knowing this, nor any way of knowing how fast the clock was
>> running or if it was changing speed.
>
> That assumes that one second can be cleanly (no causal or other
> connection) sliced from the next second with no loss, which is what I doubt.
A virtual reality program could be run and the data saved to disk at
one second intervals. On the second run, the saved data could be
loaded out of sequence. How would the observers in the program know if
they were being implemented in sequence or out of sequence? How would
they know if their second of consciousness was generated with saved
data or with random data that just happened to be the same as the
saved data?
>> Could the question be settled by actual experiment, i.e. asking the
>> subject if they noticed anything unusual?
>>
> Yes, I think it could - if we could do the experiment. Certainly when
> I've been unconscious, either from concussion or anesthesia I've noticed
> something unusual. :-)
Of course in any experiment we might actually carry out with a human
subject in the foreseeable future there would be noticeable gaps in
consciousness, due to technical factors. What about the virtual
reality experiment above?
--
Stathis Papaioannou
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Re: Consciousness is information?
2009/4/30 Brent Meeker < meekerdb@...>:
> I see no contradiction in a "noticeable gap in consciousness". Whether
> noticing such a gap depends on having some theory of the world or is
> intrinsic seems to be the question.
You would notice a gap if the background changed, or if your level of
consciousness ramped down and ramped up again rather than
instantaneously turning off and on, but if these technical factors
could be controlled for how could you possibly notice a gap?
--
Stathis Papaioannou
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Re: Consciousness is information?
On 30 Apr 2009, at 13:30, Stathis Papaioannou wrote:
>
> 2009/4/30 Bruno Marchal < marchal@...>:
>
>> This is essentially the problem discussed by Chalmers in "Does a Rock
>> Implement Every Finite-State Automaton"
>> at http://consc.net/papers/rock.html ,
>>
>> Yes. And I don't buy that argument. I will not insist because you
>> did it
>> well in your last post. Also, if it was the case that rock implement
>> sophisticated computations, it would just add some measure on some
>> computations in the Universal Dovetailing. Also, a rock cannot be a
>> computational object: it is a projection of an infinity of
>> computations when
>> we look at the rock at a level which would be below our common
>> substitution
>> level. Eventually we will met the quantum vacuum (assuming comp
>> implies QM,
>> as I think), and in some "parallel world" that vaccum will go
>> through all
>> accessible states, but this is part of so many variate histories
>> that they
>> interfere destructively and does not generate any classical history
>> stable
>> relatively to any observer coupled with the rock.
>>
>>
>> and I think it's also the idea behind Maudlin's Olympia thought
>> experiment
>> as well.
>>
>> Maudlin's Olympia, or the Movie Graph Argument are completely
>> different.
>> Those are arguments showing that computationalism is incompatible
>> with the
>> physical supervenience thesis. They show that consciousness are not
>> related
>> to any physical activity at all. Together with UDA1-7, it shows
>> that physics
>> has to be reduced to a theory of consciousness based on a purely
>> mathematical (even arithmetical) theory of computation, which
>> exists by
>> Church Thesis.
>> The movie graph argument was originally only a tool for explaining
>> how
>> difficult the mind-body problem is, once we assume mechanism.
>
> The Rock argument and the Olympia/ Movie Graph argument are
> diffferent, but they lead to the same conclusion if valid, namely that
> if computationalism is true then consciousness does not supervene on
> physical activity.
I don't see why. If the rock implement conscious computation, this
would just enrich the domain measure.
> Putnam and Searle use the Rock argument to suggest
> that computationalism is false: they consider it absurd that any
> conscious computation supervenes on any physical activity (or
> equivalently no physical activity, since at one extreme the Rock
> argument allows that any computation is implemented by the null
> state).
?
> Chalmers tries to rescue computationalism in the paper cited
> by arguing that the Rock argument is not valid.
He tries to rescue "materialist computationalism". But this exactly
what Olympia/movie-graph does not allow.
I guess this is also why Chalmers defends dualism, even for quantum
mechanics without collapse.
When I met Chalmers he told me he stops at UDA step 3 (and left the
room without much explanation). Some of its more recent writing
indicates that he has perhaps change its mind, I dunno.
Bruno
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Re: Consciousness is information?
2009/4/30 Bruno Marchal < marchal@...>:
>> Putnam and Searle use the Rock argument to suggest
>> that computationalism is false: they consider it absurd that any
>> conscious computation supervenes on any physical activity (or
>> equivalently no physical activity, since at one extreme the Rock
>> argument allows that any computation is implemented by the null
>> state).
>
> ?
If the vibration of atoms in a rock can be mapped onto any
computation, then there is a one to many relationship between a
physical state and a computation. That is, you can't say that the rock
implements one computation but not another. So the rock is a massively
parallel computer implementing every computation. Furthermore, any
subset (in time and space) of the rock is a massively parallel
computer implementing any computation. At the limit, a minimal subset
of the rock, such as a quark existing for one Planck interval,
implements every computation. And why not go one step further and say
that nothingness implements every computation? So you arrive at the
conclusion, computation exists independently of physical activity. Few
people seem satisfied with this conclusion, so they try to argue
either that computationalism is false or else that computationalism is
true and dependent on physical activity and therefore that the
argument is invalid.
--
Stathis Papaioannou
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Re: Consciousness is information?
On 30 Apr 2009, at 15:49, Stathis Papaioannou wrote:
>
> 2009/4/30 Bruno Marchal < marchal@...>:
>
>>> Putnam and Searle use the Rock argument to suggest
>>> that computationalism is false: they consider it absurd that any
>>> conscious computation supervenes on any physical activity (or
>>> equivalently no physical activity, since at one extreme the Rock
>>> argument allows that any computation is implemented by the null
>>> state).
>>
>> ?
>
> If the vibration of atoms in a rock can be mapped onto any
> computation, then there is a one to many relationship between a
> physical state and a computation.
But why and how should the vibration of atoms in a rock be mappable
onto any computations?
Accepting QM I can see one quantum computation: the simulation of the
rock.
Computation are global things. It is not the union of a lot of tiny
computations, it is the union of those tiny computations + the
universal state which unite them. (and then from inside the problem is
that there are an infinity of them).
> That is, you can't say that the rock
> implements one computation but not another.
I don't think it implements any computations. I could accept some tiny
apparition of tiny pieces of of tiny automata, but nothing big or
sophisticated. Some very special crystals perhaps, no doubt, but those
are, then, computer.
> So the rock is a massively
> parallel computer implementing every computation.
No, a finite rock goes in cycle and does not makes any long
computation, still less the deep one. It does at most some
computational noise. Computation, like brain are relatively rare in
the universe. If Hubble detect a computation somewhere, iy will be
taken as an argument for the presence of intelligent beings there. But
it hasn't.
The genome of a bacteria implements very simple form of computations.
There are IF ... THEN... ELSE, loops, and conditionnal (by regulatory
gene). But it took billions of year to "nature" to make them appear.
Just show me the computation of factorial(24) in a rock. No one has
shown that.
> Furthermore, any
> subset (in time and space) of the rock is a massively parallel
> computer implementing any computation.
This is probably true for something like the border of the Mandelbrot
set. But there is no concrete mandelbrot set in nature.
> At the limit, a minimal subset
> of the rock, such as a quark existing for one Planck interval,
> implements every computation.
Hard for me to think you are serious here. A case can be made that the
quantum vacuum is Turing universal, but this makes him doing
"sophisticated" computation relatively to us, only ... in the quantum
white rabbit universes.
> And why not go one step further and say
> that nothingness implements every computation?
If you stay with a physical realm, you will get only physical
nothingness, which even in classical physics is not nothingness.
> So you arrive at the
> conclusion, computation exists independently of physical activity.
That would please me, but I don't see at all the logic.
> Few
> people seem satisfied with this conclusion, so they try to argue
> either that computationalism is false
A lot of people try to argue that computationalism is false, and
usually the argument can be shown directly non valid; Searles for
example mixes levels of description (as Dennett and Hofstadter show
very well in Mind'sI).
Other have better argument, like Maudlin, but this shows only that
comp is not compatible with linking computation with the running of
one universal machine, or worse with the only physical one. It is more
interesting because it shows the real difficulty of the mind-body
problem once we take comp seriously.
But remember Jacques Mallah. He shows that there is an implementation
problem (with physicalism). Along those line a physicalist could
affirm that even a running computer does not run a "mathematical
computation". Unfortunately for Mallah, such a problem dissolves when
you understand that the physical world is not a primitive reality, but
something which emerge from the logical relations among numbers.
Indeed, through the "eyes" of the universal machines/numbers.
Arithmetical reality or alike are the only realms where computations
exists and are well defined.
> or else that computationalism is
> true and dependent on physical activity
Which is false by UDA+MGA.
> and therefore that the
> argument is invalid.
That is weird.
I think that you believe that a rock implements computations, because
you believe a computation can be decomposed in tiny computations, but
this is not true, you need much more. You need a universal machine
which links and complexify the states in a precise way.
Some alive beings do some computations (like some flowers compute tiny
part of the Fibonacci function). But again, this is sophisticated and
took time to appear. Waves do analog computations, hardly universal
digital one, or only when put in some very special condition.
Interesting and rich computations are relatively rare and exceptional
until they self-multiplied, like amoebas.
Nor do I believe the filmed movie graph do any computation, it "read"
a description of one, but does not link them logically in real time.
Today, genetical systems, brains, and computer (human or engineered)
do "concrete" computations.
The mathematical Universal Dovetailer, the splashed universal Turing
Machine, the rational Mandelbrot set, or any creative sets in the
sense of Emil Post, does all computations. Really all, with Church
thesis. This is a theorem in math. The rock? Show me just the 30 first
steps of a computation of square-root(2).
Robinson Arithmetic, Peano Arithmetic, Zermelo Fraenkel Set theory and
many theories compute, notably, all computations, through the
enumeration of the proof of all the True Sigma_1 arithmetical
sentences, but they do much more, they reason and prove more complex
propositions about them (Lobian Machine).
But again, even if rocks implements computations, this changes nothing
to the reversal reasoning. IF rocks implements all computations, it
means the Universal measure is a tiny epsilon more complex to compute,
given that the measure is put on all possible computations. It means
we have to take into account all digital rock's state accessed by the
universal dovetailer.
Bruno
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RE: Consciousness is information?
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Bruno Marchal wrote: On 29 Apr 2009, at 23:30, Jesse Mazer wrote:
But I'm not convinced that the basic Olympia machine he describes doesn't already have a complex causal structure--the causal structure would be in the way different troughs influence each other via the pipe system he describes, not in the motion of the armature.
>But Maudlin succeed in showing that in its particular running history, *that* causal structure is physically inert. Or it has mysterious influence not related to the computation.
Maudlin only showed that *if* you define "causal structure" in terms of counterfactuals, then the machinery that ensures the proper counterfactuals might be physically inert. But if you reread my post at http://www.mail-archive.com/everything-list@.../msg16244.html you can see that I was trying to come up with a definition of the "causal structure" of a set of events that did *not* depend on counterfactuals...look at these two paragraphs from that post, particular the first sentence of the first paragraph and the last sentence of the second paragraph:
>It seems to me that there might be ways of defining "causal structure" which don't depend on counterfactuals, though. One idea I had is that for any system which changes state in a lawlike way over time, all facts about events in the system's history can be represented as a collection of propositions, and then causal structure might be understood in terms of logical relations between propositions, given knowledge of the laws governing the system. As an example, if the system was a cellular automaton, one might have a collection of propositions like "cell 156 is colored black at time-step 36", and if you know the rules for how the cells are updated on each time-step, then knowing some subsets of propositions would allow you to deduce others (for example, if you have a set of propositions that tell you the states of all the cells surrounding cell 71 at time-step 106, in most cellular automata that would allow you to figure out the state of cell 71 at the subsequent time-step 107). If the laws of physics in our universe are deterministic than you should in principle be able to represent all facts about the state of the universe at all times as a giant (probably infinite) set of propositions as well, and given knowledge of the laws, knowing certain subsets of these propositions would allow you to deduce others.
>"Causal structure" could then be defined in terms of what logical relations hold between the propositions, given knowledge of the laws governing the system. Perhaps in one system you might find a set of four propositions A, B, C, D such that if you know the system's laws, you can see that A&B imply C, and D implies A, but no other proposition or group of propositions in this set of four are sufficient to deduce any of the others in this set. Then in another system you might find a set of four propositions X, Y, Z and W such that W&Z imply Y, and X implies W, but those are the only deductions you can make from within this set. In this case you can say these two different sets of four propositions represent instantiations of the same causal structure, since if you map W to A, Z to B, Y to C, and D to X then you can see an isomorphism in the logical relations. That's obviously a very simple causal structure involving only 4 events, but one might define much more complex causal structures and then check if there was any subset of events in a system's history that matched that structure. And the propositions could be restricted to ones concerning events that actually did occur in the system's history, with no counterfactual propositions about what would have happened if the system's initial state had been different.
For a Turing machine running a particular program the propositions might be things like "at time-step 35 the Turing machine's read/write head moved to memory cell #82" and "at time-step 35 the Turing machine had internal state S3" and "at time-step 35 memory cell #82 held the digit 1". I'm not sure whether the general rules for how the Turing machine's internal state changes from one step to the next should also be included among the propositions, my guess is you'd probably need to do so in order to ensure that different computations had different "causal structures" according to the type of definition above...so, you might have a proposition expressing a rule like "if the Turing machine is in internal state S3 and its read/write head detects the digit 1, it changes the digit in that cell to a 0 and moves 2 cells to the left, also changing its internal state to S5." Then this set of four propositions would be sufficient to deduce some other propositions about the history of this computation, like "at time-step 36 the Turing machine's read/write head moved to memory cell #80" and "at time-step 36 the Turing machine had internal state S5."
So if we define causal structure in terms of relationships between propositions concerning the history of the Turing machine in this way, then look at propositions concerning the history of the Olympia machine described by Maudlin when it was emulating that Turing machine program, it's not clear to me whether it would be possible to map propositions about the original Turing machine to propositions about Olympia in such a way that you'd be able to show their causal structures were isomorphic (I think it is clear that such a mapping would be impossible in the case of your MGA 1 though, so if we identify OMs with causal structures this would suggest that the brain which functioned via random cosmic rays correcting errors would not have the same inner experience as the brain which was functioning correctly and did not require these cosmic rays). But either way, what is clear is that the presence or absence of inert machinery designed to guarantee the correct counterfactuals would not affect the answer, since we'd only be looking at propositions about events that actually occurred in the course of the Olympia machine's operation. If it turned out there was an isomorphism between these propositions and the propositions about the operation of the original Turing machine, then that would show Maudlin was too quick to dismiss the original Olympia machine (the one lacking the counterfactual machinery) as giving rise to phenomenal experience (even though the armature behaves in a monotonous way, the way the troughs influence each other via pipes might be enough to ensure that the causal structure associated with Olympia's operation does depend on what program is being emulated). If there wasn't such an isomorphism, then there still wouldn't be an isomorphism even with the counterfactual machinery added, so that could make it more clear why the Olympia machine was not really "instantiating" the same computation as the original Turing machine.
One interesting thing about defining causal structure this way is that we could talk about causal structures being contained in pure mathematical structures like the set of true propositions about arithmetic. A Platonist should believe that if you take the set of all well-formed formulas concerning numbers and arithmetical operations (as well as logical symbols like 'there exists' and 'for all'), then there is a particular infinite set of WFFs which represents all true propositions about arithmetic, even if Godel showed that this infinite set cannot be generated by any finite set of initial propositions taken as axioms (and it also cannot be generated by a computable infinite set of axioms, I think). If you take any finite subset of true propositions (P1, P2, P3, ..., PN), then these propositions will be logically interrelated in some particular way--it might be that if you start out taking P2 and P3 as axioms you can deduce P5 from this but you can't deduce P4, for example. I imagine representing each proposition as a dot in a diagram, and then arrows would show which individual dots or collections of dots in this finite set can be used to deduce other dots in the same finite set. This diagram would define a unique "causal structure" for this set of propositions, and then if you have a set of propositions about something different from arithmetic, like the history of a particular Turing machine computation, you could see whether there was a subset with an isomorphic pattern of logical implications (and thus the same 'causal structure' according to my definition). And even within arithmetic you might have two different subsets of propositions (P1, P2, ..., PN) and (p1, p2, ..., pN) which could be mapped to one another in such a way that the implications within each set were isomorphic to the implications within the other, in which case they would be two different "instantiations" of the same causal structure within the Platonic set of all true propositions about arithmetic.
Maybe you could even make a TOE based on the idea that all that really "exists" is this infinite set of propositions about arithmetic, and that this infinite set defines a unique measure on all finite causal structures, based on how easy it is to find multiple "instantiations" of each finite causal structure within the infinite set of true propositions. I don't suppose this has any resemblance to your approach? I suppose the answer is probably "no" since I'm suggesting some kind of absolute measure on all causal structures, and if you identify particular causal structures with OMs that would correspond to the ASSA, but you have said that your approach only uses the RSSA. Anyway I have no idea how you'd actually "count" the number of appearances of a given causal structure in the infinite set of propositions about arithmetic, so the idea of getting a measure on causal structures this way is very vague...but if there's one thing this list is good for it's vague speculations! ;)
Jesse
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Re: Consciousness is information?
Stathis Papaioannou wrote:
> 2009/4/30 Brent Meeker < meekerdb@...>:
>
>
>> I see no contradiction in a "noticeable gap in consciousness". Whether
>> noticing such a gap depends on having some theory of the world or is
>> intrinsic seems to be the question.
>>
>
> You would notice a gap if the background changed, or if your level of
> consciousness ramped down and ramped up again rather than
> instantaneously turning off and on, but if these technical factors
> could be controlled for how could you possibly notice a gap?
>
>
>
The same way it is proposed that continuity is established in OM's - by
memory. When I've had a concussion, I notice a memory gap.
Brent
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Re: Consciousness is information?
Stathis Papaioannou wrote:
> 2009/4/30 Bruno Marchal < marchal@...>:
>
>
>>> Putnam and Searle use the Rock argument to suggest
>>> that computationalism is false: they consider it absurd that any
>>> conscious computation supervenes on any physical activity (or
>>> equivalently no physical activity, since at one extreme the Rock
>>> argument allows that any computation is implemented by the null
>>> state).
>>>
>> ?
>>
>
> If the vibration of atoms in a rock can be mapped onto any
> computation, then there is a one to many relationship between a
> physical state and a computation. That is, you can't say that the rock
> implements one computation but not another. So the rock is a massively
> parallel computer implementing every computation. Furthermore, any
> subset (in time and space) of the rock is a massively parallel
> computer implementing any computation. At the limit, a minimal subset
> of the rock, such as a quark existing for one Planck interval,
> implements every computation. And why not go one step further and say
> that nothingness implements every computation? So you arrive at the
> conclusion, computation exists independently of physical activity. Few
> people seem satisfied with this conclusion, so they try to argue
> either that computationalism is false or else that computationalism is
> true and dependent on physical activity and therefore that the
> argument is invalid.
>
>
>
I'd say that computation is relative to action within an environment.
We say that molecular vibrations in a rock isn't computing anything
because it doesn't act. Compare this to a virtual reality simulation
that includes rocks, people, etc. Within the interpreted simulation
people act and rocks don't. But if we didn't know the interpretation of
the program we might interpret it in a completely different way such
that it didn't even contain people and rocks, or the part of the
computation that corresponded to the rock now was interpreted as a
person who was acting. Notice that in the reinterpretation a step that
formerly was "do nothing" may now be a link in a causal chain of action.
I think the implication for Comp is that, while you might say "yes" to
the doctor who proposed to replace your brain with a computer, you
should say "no" if he proposes to replace you and your whole world with
a virtual reality simulation that will be self contained and will no
more interact with this world.
Brent
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Re: Consciousness is information?
Bruno Marchal wrote:
> On 30 Apr 2009, at 15:49, Stathis Papaioannou wrote:
>
>
>> 2009/4/30 Bruno Marchal < marchal@...>:
>>
>>
>>>> Putnam and Searle use the Rock argument to suggest
>>>> that computationalism is false: they consider it absurd that any
>>>> conscious computation supervenes on any physical activity (or
>>>> equivalently no physical activity, since at one extreme the Rock
>>>> argument allows that any computation is implemented by the null
>>>> state).
>>>>
>>> ?
>>>
>> If the vibration of atoms in a rock can be mapped onto any
>> computation, then there is a one to many relationship between a
>> physical state and a computation.
>>
>
>
> But why and how should the vibration of atoms in a rock be mappable
> onto any computations?
> Accepting QM I can see one quantum computation: the simulation of the
> rock.
> Computation are global things. It is not the union of a lot of tiny
> computations, it is the union of those tiny computations + the
> universal state which unite them. (and then from inside the problem is
> that there are an infinity of them).
>
>
>
>
>
>
>> That is, you can't say that the rock
>> implements one computation but not another.
>>
>
> I don't think it implements any computations. I could accept some tiny
> apparition of tiny pieces of of tiny automata, but nothing big or
> sophisticated. Some very special crystals perhaps, no doubt, but those
> are, then, computer.
>
>
>
>
>> So the rock is a massively
>> parallel computer implementing every computation.
>>
>
>
> No, a finite rock goes in cycle and does not makes any long
> computation, still less the deep one. It does at most some
> computational noise. Computation, like brain are relatively rare in
> the universe. If Hubble detect a computation somewhere, iy will be
> taken as an argument for the presence of intelligent beings there. But
> it hasn't.
> The genome of a bacteria implements very simple form of computations.
> There are IF ... THEN... ELSE, loops, and conditionnal (by regulatory
> gene). But it took billions of year to "nature" to make them appear.
> Just show me the computation of factorial(24) in a rock. No one has
> shown that.
>
>
>
>
>> Furthermore, any
>> subset (in time and space) of the rock is a massively parallel
>> computer implementing any computation.
>>
>
>
> This is probably true for something like the border of the Mandelbrot
> set. But there is no concrete mandelbrot set in nature.
>
>
>
>
>> At the limit, a minimal subset
>> of the rock, such as a quark existing for one Planck interval,
>> implements every computation.
>>
>
> Hard for me to think you are serious here. A case can be made that the
> quantum vacuum is Turing universal, but this makes him doing
> "sophisticated" computation relatively to us, only ... in the quantum
> white rabbit universes.
>
>
>
>
>
>> And why not go one step further and say
>> that nothingness implements every computation?
>>
>
>
> If you stay with a physical realm, you will get only physical
> nothingness, which even in classical physics is not nothingness.
>
>
>
>
>> So you arrive at the
>> conclusion, computation exists independently of physical activity.
>>
>
> That would please me, but I don't see at all the logic.
>
>
>
>
>> Few
>> people seem satisfied with this conclusion, so they try to argue
>> either that computationalism is false
>>
>
>
> A lot of people try to argue that computationalism is false, and
> usually the argument can be shown directly non valid; Searles for
> example mixes levels of description (as Dennett and Hofstadter show
> very well in Mind'sI).
> Other have better argument, like Maudlin, but this shows only that
> comp is not compatible with linking computation with the running of
> one universal machine, or worse with the only physical one. It is more
> interesting because it shows the real difficulty of the mind-body
> problem once we take comp seriously.
> But remember Jacques Mallah. He shows that there is an implementation
> problem (with physicalism). Along those line a physicalist could
> affirm that even a running computer does not run a "mathematical
> computation". Unfortunately for Mallah, such a problem dissolves when
> you understand that the physical world is not a primitive reality, but
> something which emerge from the logical relations among numbers.
> Indeed, through the "eyes" of the universal machines/numbers.
> Arithmetical reality or alike are the only realms where computations
> exists and are well defined.
>
>
>
>
>> or else that computationalism is
>> true and dependent on physical activity
>>
>
> Which is false by UDA+MGA.
>
>
>
>
>
>> and therefore that the
>> argument is invalid.
>>
>
>
> That is weird.
>
> I think that you believe that a rock implements computations, because
> you believe a computation can be decomposed in tiny computations, but
> this is not true, you need much more. You need a universal machine
> which links and complexify the states in a precise way.
> Some alive beings do some computations (like some flowers compute tiny
> part of the Fibonacci function). But again, this is sophisticated and
> took time to appear. Waves do analog computations, hardly universal
> digital one, or only when put in some very special condition.
> Interesting and rich computations are relatively rare and exceptional
> until they self-multiplied, like amoebas.
>
Does the universe compute its states? How is the evolution of the wave
function of the universe or of a flower not a computation?
> Nor do I believe the filmed movie graph do any computation, it "read"
> a description of one, but does not link them logically in real time.
> Today, genetical systems, brains, and computer (human or engineered)
> do "concrete" computations.
>
But that seems like introducing a "magic" similar to the magic of
physical existence, except now it is the magic of computational connection.
Brent
> The mathematical Universal Dovetailer, the splashed universal Turing
> Machine, the rational Mandelbrot set, or any creative sets in the
> sense of Emil Post, does all computations. Really all, with Church
> thesis. This is a theorem in math. The rock? Show me just the 30 first
> steps of a computation of square-root(2).
> Robinson Arithmetic, Peano Arithmetic, Zermelo Fraenkel Set theory and
> many theories compute, notably, all computations, through the
> enumeration of the proof of all the True Sigma_1 arithmetical
> sentences, but they do much more, they reason and prove more complex
> propositions about them (Lobian Machine).
>
> But again, even if rocks implements computations, this changes nothing
> to the reversal reasoning. IF rocks implements all computations, it
> means the Universal measure is a tiny epsilon more complex to compute,
> given that the measure is put on all possible computations. It means
> we have to take into account all digital rock's state accessed by the
> universal dovetailer.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/>
>
>
>
> >
>
>
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Re: Consciousness is information?
2009/5/1 Bruno Marchal < marchal@...>:
>> That is, you can't say that the rock
>> implements one computation but not another.
>
> I don't think it implements any computations. I could accept some tiny
> apparition of tiny pieces of of tiny automata, but nothing big or
> sophisticated. Some very special crystals perhaps, no doubt, but those
> are, then, computer.
If your computer has to interact with the external world then that
imposes some constraints on what counts as an implementation of a
computation. But without this constraint you are free to interpret any
activity as any computation. You could pick three trees and, observing
the movement of birds on and off the trees, interpret this as a logic
gate. Three birds land on the first tree, and that's a "zero" input.
Two birds alight from the second tree, that's a "zero" input also.
Three birds land on the third tree, that's a "one" output. A minute
later, five birds alight from the first tree, one bird lands on the
second tree and two birds land on the third tree, which is interpreted
as two "one" inputs giving a "zero" output. Looks like it might be a a
NAND gate! Not very useful, of course, but is there any reason why my
interpretation is wrong, or why the birds flying around won't give
rise to whatever consciousness is associated with the operation of the
logic gate?
--
Stathis Papaioannou
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Re: Consciousness is information?
On Thu, Apr 30, 2009 at 10:35 AM, Bruno Marchal < marchal@...> wrote:
>
>
> The mathematical Universal Dovetailer, the splashed universal Turing
> Machine, the rational Mandelbrot set, or any creative sets in the
> sense of Emil Post, does all computations. Really all, with Church
> thesis. This is a theorem in math. The rock? Show me just the 30 first
> steps of a computation of square-root(2). ...
Bruno,
I am interested about your statement regarding the Mandelbrot set
implementing all computations, could you elaborate on this?
Thank you,
Jason
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RE: Consciousness is information?
Some parts of this message have been removed.
Learn more about Nabble's security policy.
I found a paper on the Mandelbrot set and computability, I understand very little but maybe Bruno would be able to follow it:
http://arxiv.org/abs/cs.CC/0604003
The same author has a shorter outline or slides for a presentation on this subject at http://www.cs.swan.ac.uk/cie06/files/d37/PHP_MandelbrotCiE2006Swansea_Jul2006.pdf and at the end he asks the question "If M (Mandelbrot set) not Q-computable, can the Halting Problem be reduced to determining membership of (intersection of M and Q^2), i.e. how powerful a 'hypercomputer' is the Mandelbrot set?" I believe Q^2 here just refers to the set of all possible pairs of rational numbers. Maybe by "reducing" the Halting Problem he means that for any Turing machine + input, there might be some rule that would translate it into a pair of rational numbers such that the computation will halt iff the pair is included in the Mandelbrot set? Whatever he means, it sounds like he's saying it's an open question...
Jesse
> > > On Thu, Apr 30, 2009 at 10:35 AM, Bruno Marchal < marchal@...> wrote: >> >> >> The mathematical Universal Dovetailer, the splashed universal Turing >> Machine, the rational Mandelbrot set, or any creative sets in the >> sense of Emil Post, does all computations. Really all, with Church >> thesis. This is a theorem in math. The rock? Show me just the 30 first >> steps of a computation of square-root(2). ... > > Bruno, > > I am interested about your statement regarding the Mandelbrot set > implementing all computations, could you elaborate on this? > > Thank you, > > Jason > >
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Re: Consciousness is information?
On Apr 29, 2:26 am, russell standish < li...@...> wrote:
>
> What extra information do you have in mind? I'd gladly update my
> priors with anything I can lay my hands on.
So changes to neural structure and the concentrations of various
chemicals within neurons and around neural synapses is known to change
conscious experience in humans. Ants have neurons that work along
similar lines as human neurons. Surely this must affect the
probability that is assigned to the question of whether ants are able
to experience things like pain in a similar way that humans do. It
certainly seems to me to be significant.
So how does this extra information show up in your assessment of ant
consciousness?
Again, it seems to me that SSA arguments are better than nothing. But
their usefulness fades quickly as more sources of data become
available. They might be a good first stab at answering a question,
but ideally will never be the final word.
For instance, why would I believe your argument over something like
this:
Fish Feel Pain, Study Finds
When you hook a fish, does it hurt? Yes, a new study suggests.
Some researchers have previously concluded that fish react to painful
stimuli without actually feeling pain in the conscious way humans do.
In the new study, researchers gave morphine to one group of fish, and
injected the other group with a placebo (saline). Then the fish were
treated to burning sensations that were expected to be painful but
which did not damage any fish tissue.
Both groups reacted the same, by wriggling.
However, the fish that had been on morphine later went on about
business as if nothing had happened. The fish that had gotten the
saline were wary after the test.
"They acted with defensive behaviors, indicating wariness, or fear and
anxiety," said Joseph Garner, an assistant professor at Purdue
University.
"The experiment shows that fish do not only respond to painful stimuli
with reflexes, but change their behavior also after the event," said
Janicke Nordgreen, a doctoral student in the Norwegian School of
Veterinary Science. "Together with what we know from experiments
carried out by other groups, this indicates that the fish consciously
perceive the test situation as painful and switch to behaviors
indicative of having been through an aversive experience."
A study last month indicated that crabs feel pain, too.
Garner and Nordgreen published their results in the online version of
the journal Applied Animal Behaviour Science.
Garner figures the morphine blocked the experience of pain, but not
behavioral responses to the heat stimulus itself, either because the
responses were reflexive or because the morphine blocked the
experience of pain, but not the experience of an unusual stimulus.
"If you think back to when you have had a headache and taken a
painkiller, the pain may go away, but you can still feel the presence
or discomfort of the headache," Garner said.
"The goldfish that did not get morphine experienced this painful,
stressful event. Then two hours later, they turned that pain into fear
like we do," Garner said. "To me, it sounds an awful lot like how we
experience pain."
Then again, scientist don't fully understand pain in humans. It is
felt when electrical signals are sent from nerve endings to your
brain, which in turn can release painkillers called endorphins and
generate physical and emotional reactions. The details remain unclear,
which his why so many people suffer chronic pain with no relief.
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Re: Consciousness is information?
On 30 Apr 2009, at 18:29, Jesse Mazer wrote:
Bruno Marchal wrote: On 29 Apr 2009, at 23:30, Jesse Mazer wrote:
But I'm not convinced that the basic Olympia machine he describes doesn't already have a complex causal structure--the causal structure would be in the way different troughs influence each other via the pipe system he describes, not in the motion of the armature.
>But Maudlin succeed in showing that in its particular running history, *that* causal structure is physically inert. Or it has mysterious influence not related to the computation.
Maudlin only showed that *if* you define "causal structure" in terms of counterfactuals, then the machinery that ensures the proper counterfactuals might be physically inert. But if you reread my post at http://www.mail-archive.com/everything-list@.../msg16244.html you can see that I was trying to come up with a definition of the "causal structure" of a set of events that did *not* depend on counterfactuals...look at these two paragraphs from that post, particular the first sentence of the first paragraph and the last sentence of the second paragraph:
>It seems to me that there might be ways of defining "causal structure" which don't depend on counterfactuals, though. One idea I had is that for any system which changes state in a lawlike way over time, all facts about events in the system's history can be represented as a collection of propositions, and then causal structure might be understood in terms of logical relations between propositions, given knowledge of the laws governing the system. As an example, if the system was a cellular automaton, one might have a collection of propositions like "cell 156 is colored black at time-step 36", and if you know the rules for how the cells are updated on each time-step, then knowing some subsets of propositions would allow you to deduce others (for example, if you have a set of propositions that tell you the states of all the cells surrounding cell 71 at time-step 106, in most cellular automata that would allow you to figure out the state of cell 71 at the subsequent time-step 107). If the laws of physics in our universe are deterministic than you should in principle be able to represent all facts about the state of the universe at all times as a giant (probably infinite) set of propositions as well, and given knowledge of the laws, knowing certain subsets of these propositions would allow you to deduce others.
>"Causal structure" could then be defined in terms of what logical relations hold between the propositions, given knowledge of the laws governing the system. Perhaps in one system you might find a set of four propositions A, B, C, D such that if you know the system's laws, you can see that A&B imply C, and D implies A, but no other proposition or group of propositions in this set of four are sufficient to deduce any of the others in this set. Then in another system you might find a set of four propositions X, Y, Z and W such that W&Z imply Y, and X implies W, but those are the only deductions you can make from within this set. In this case you can say these two different sets of four propositions represent instantiations of the same causal structure, since if you map W to A, Z to B, Y to C, and D to X then you can see an isomorphism in the logical relations. That's obviously a very simple causal structure involving only 4 events, but one might define much more complex causal structures and then check if there was any subset of events in a system's history that matched that structure. And the propositions could be restricted to ones concerning events that actually did occur in the system's history, with no counterfactual propositions about what would have happened if the system's initial state had been different.
For a Turing machine running a particular program the propositions might be things like "at time-step 35 the Turing machine's read/write head moved to memory cell #82" and "at time-step 35 the Turing machine had internal state S3" and "at time-step 35 memory cell #82 held the digit 1". I'm not sure whether the general rules for how the Turing machine's internal state changes from one step to the next should also be included among the propositions, my guess is you'd probably need to do so in order to ensure that different computations had different "causal structures" according to the type of definition above...so, you might have a proposition expressing a rule like "if the Turing machine is in internal state S3 and its read/write head detects the digit 1, it changes the digit in that cell to a 0 and moves 2 cells to the left, also changing its internal state to S5." Then this set of four propositions would be sufficient to deduce some other propositions about the history of this computation, like "at time-step 36 the Turing machine's read/write head moved to memory cell #80" and "at time-step 36 the Turing machine had internal state S5."
So if we define causal structure in terms of relationships between propositions concerning the history of the Turing machine in this way, then look at propositions concerning the history of the Olympia machine described by Maudlin when it was emulating that Turing machine program, it's not clear to me whether it would be possible to map propositions about the original Turing machine to propositions about Olympia in such a way that you'd be able to show their causal structures were isomorphic (I think it is clear that such a mapping would be impossible in the case of your MGA 1 though, so if we identify OMs with causal structures this would suggest that the brain which functioned via random cosmic rays correcting errors would not have the same inner experience as the brain which was functioning correctly and did not require these cosmic rays).
But either way, what is clear is that the presence or absence of inert machinery designed to guarantee the correct counterfactuals would not affect the answer, since we'd only be looking at propositions about events that actually occurred in the course of the Olympia machine's operation. If it turned out there was an isomorphism between these propositions and the propositions about the operation of the original Turing machine, then that would show Maudlin was too quick to dismiss the original Olympia machine (the one lacking the counterfactual machinery) as giving rise to phenomenal experience (even though the armature behaves in a monotonous way, the way the troughs influence each other via pipes might be enough to ensure that the causal structure associated with Olympia's operation does depend on what program is being emulated). If there wasn't such an isomorphism, then there still wouldn't be an isomorphism even with the counterfactual machinery added, so that could make it more clear why the Olympia machine was not really "instantiating" the same computation as the original Turing machine.
Maudlin shows that you can reduce almost arbitrarily the amount of physical activity for running any computation, and keep their computational genuineness through the use of inert material. So the isomorphism you introduce vanish on the original Olympia (Pre-olympia).
Olympia *is* "Pre-Olympia" + Klara (the inert (for the computation PI) machinery needed for the counterfactuals) OK? Olympia run the computation PI.
The point of Maudlin is that for any computation there exists a a Klara machinery such that you can built a "Pre-Olympia" which will execute, with an arbitrarily small amount of physical activity (even with none) that computation. And this in the usual sense that the counterfactuals are preserved, thanks to the Klara.
The price for keeping your "causal structure" isomorphism not vanishing consists, indeed, in making consciousness supervening on the logical and immaterial relations bringing a local story about a probable local relatively consistent <self-environment> structure.
Again, see the Movie graph for a simpler (and older) argument not based on the counterfactual issue.
One interesting thing about defining causal structure this way is that we could talk about causal structures being contained in pure mathematical structures like the set of true propositions about arithmetic. A Platonist should believe that if you take the set of all well-formed formulas concerning numbers and arithmetical operations (as well as logical symbols like 'there exists' and 'for all'), then there is a particular infinite set of WFFs which represents all true propositions about arithmetic, even if Godel showed that this infinite set cannot be generated by any finite set of initial propositions taken as axioms (and it also cannot be generated by a computable infinite set of axioms, I think).
Yes.
If you take any finite subset of true propositions (P1, P2, P3, ..., PN), then these propositions will be logically interrelated in some particular way--it might be that if you start out taking P2 and P3 as axioms you can deduce P5 from this but you can't deduce P4, for example. I imagine representing each proposition as a dot in a diagram, and then arrows would show which individual dots or collections of dots in this finite set can be used to deduce other dots in the same finite set. This diagram would define a unique "causal structure" for this set of propositions, and then if you have a set of propositions about something different from arithmetic, like the history of a particular Turing machine computation,
The history of a particular Turing machine computation does belong to arithmetic. Already to Robinson Arithmetic. (Roughly: Peano Arithmetic without the induction axioms). You need just a Sigma_1 complete theory for the ontology. It is enough to (meta)define a richer internal epistemology justifying why, "from inside" things appear (and in some sense are) much richer. This is not obvious and technically relies on Gödel's compeleteness and incompleteness theorem, or Skolem theorem. It is long to explain, yet very short to understand, and utterly clear, if you are aware of Solovay theorem.
you could see whether there was a subset with an isomorphic pattern of logical implications (and thus the same 'causal structure' according to my definition). And even within arithmetic you might have two different subsets of propositions (P1, P2, ..., PN) and (p1, p2, ..., pN) which could be mapped to one another in such a way that the implications within each set were isomorphic to the implications within the other, in which case they would be two different "instantiations" of the same causal structure within the Platonic set of all true propositions about arithmetic.
Exactly. The movie graph and/or Olympia just show that if we are machine, we rely only on arithmetic. And physics became a measure problem on or relatively probable arithmetical histories. With the provability logic, or the self-reference logic you can explain why arithmetic divides, for each universal machine into sharable and doubtable quanta, and non sharable non doubtable qualia. (AUDA) UDA, which I have explained often here is an argument showing why it has to be so, and AUDA is the math exploiting UDA in the case of ideally monotonic machine observers.
Maybe you could even make a TOE based on the idea that all that really "exists" is this infinite set of propositions about arithmetic, and that this infinite set defines a unique measure on all finite causal structures, based on how easy it is to find multiple "instantiations" of each finite causal structure within the infinite set of true propositions. I don't suppose this has any resemblance to your approach?
UDA is an argument that if we (human) are machine it has to be that approach. It is the reversal physics/number theory. Physics is eventually the projection or limit of what the number can see when they look at themselves.
(AUDA is the about the same, but I use the opportunity of Gödel, Löb, Kleene, Feferman, Grzegorczyk, Boolos, Goldblatt, Visser, ... and the key Solovay works in self-reference (in arithmetic, first order, second order, in set theory and beyond) to exploit the many nuances (between truth, provability, knowability, observability, ...), due to internal incompleteness, and to show we don't have to leave arithmetic, yet get a sufficiently precise theology including physics so as to compare it with the empirical world). One of lmy main point is that comp, is a "scientific" theory in the sense of Popper. It leads to observable conclusions, and most (alas not yet all) quantum weirdness confirm comp.
I suppose the answer is probably "no"
The answer is "yes"!
since I'm suggesting some kind of absolute measure on all causal structures, and if you identify particular causal structures with OMs that would correspond to the ASSA, but you have said that your approach only uses the RSSA.
There is no absolute measure on all "causal structures" , still less on OM, right! I would ba an ants or a bacteria in two seconds! But for all "causal structure" rich enough to develop a "personal first person" there is a more relatively probable computational stories.
Your two sets above (p1, p2, ..., pn) and (P1, P2, P3, ... PN), if isomorphic (in your vague (theory dependent) sense, but ok) will give rize, in Platonia, to the same first person experience (same consciousness), but with different measure in case they can bifurcate or differentiate, into something like
(p1, p2, ..., pn, pn+1, pn+2, ...) (P1, P2, P3, ... PN, PN+1, PN+2, ...)
where (pn+1, pn+2, ...) and (PN, PN+1, PN+2, ...) are both consistent extension of the preceding propositions, and are no more isomorphic above the level of substitution (different and distinguishable experiences like feeling to be in Seattle and feeling to be in Melbourne after a self-duplication experiment).
There is an absolute conditionalisation, or relativisation. Physics became superglobal in search of the invariant for the recursive permutations. If you want I am using ARSSA. The probability of being Jesse Mazer does not make sense in the absolute, only the (absolute) probability of being Jesse Mazer in an instant, from the point of view of Jesse Mazer, here and now.
Anyway I have no idea how you'd actually "count" the number of appearances of a given causal structure in the infinite set of propositions about arithmetic, so the idea of getting a measure on causal structures this way is very vague...
Vague? I don't think so. Church thesis makes this purely mathematical. Difficult? Sure. That is why UDA is followed by AUDA where the case of "probability or credibility (whatever) ONE, is made entirely clear and formal. It is already proved that the physical local observations cannot be boolean, and there is already a well defined notion of quantization. UDA is also completely clear, even if it take some time for some people to grasp some steps. It is normal given that is new and counterintuitive.
but if there's one thing this list is good for it's vague speculations! ;)
Given that we address a very difficult problem in the list it is all normal that some posts can be more vague than others. That is the reason why we discuss: to clarify, and clarify, and clarify up to crystal clarity. If you have trouble in UDA, please say so. I think most people on the list understand the seven first steps. For AUDA you need to invest more deeply in computer science, mathematical logic, quantum logic, and (the harder and not very well known by the average scientist) cognitive science.
And frankly, mechanism seems to me less speculative than any form non mechanism in the cognitive science, given our current working theories, be it physical or neurophysiological.
Bruno
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Re: Consciousness is information?
On 30 Apr 2009, at 19:39, Brent Meeker wrote:
>
> Bruno Marchal wrote:
>> On 30 Apr 2009, at 15:49, Stathis Papaioannou wrote:
>>Marchal wrote
>> That is weird.
>>
>> I think that you believe that a rock implements computations, because
>> you believe a computation can be decomposed in tiny computations, but
>> this is not true, you need much more. You need a universal machine
>> which links and complexify the states in a precise way.
>> Some alive beings do some computations (like some flowers compute
>> tiny
>> part of the Fibonacci function). But again, this is sophisticated and
>> took time to appear. Waves do analog computations, hardly universal
>> digital one, or only when put in some very special condition.
>> Interesting and rich computations are relatively rare and exceptional
>> until they self-multiplied, like amoebas.
>>
> Does the universe compute its states?
Open problem, but most probably not, given that the universe
appearance emerge from a statistic bearing on a infinite set of
(finite and infinite) computations.
> How is the evolution of the wave
> function of the universe or of a flower not a computation?
For a reason similar to the fact that there is no algorithm capable of
predicting if you will see an electron up or down when prepared in the
state up+down. But comp makes the "wave" itself resulting from
apparent (for the 1-person) arithmetical collapses.
>
>
>> Nor do I believe the filmed movie graph do any computation, it "read"
>> a description of one, but does not link them logically in real time.
>> Today, genetical systems, brains, and computer (human or engineered)
>> do "concrete" computations.
>>
>
> But that seems like introducing a "magic" similar to the magic of
> physical existence, except now it is the magic of computational
> connection.
Ok, but the magic of computational connection can be entirely reduce
to the magic of succession, addition and multiplication of positive
integers.
And it is magic, but it is a magic which explains why it has to be a
magic. A TOE which does not postulate the natural numbers is a TOE
without natural numbers. We have to assume the numbers, they cannot be
reduced to anything simpler/
Bruno
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