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@googlegroups.com/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

http://iridia.ulb.ac.be/~marchal/




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