Hi Bruno, I meant to reply to this earlier:

From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: Consciousness is information?
Date: Sat, 2 May 2009 14:45:13 +0200


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, 
noting 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.



But what do you mean when you say the isomorphism vanishes? Do you mean that 
the causal structure of pre-Olympia would *not* be isomorphic to the causal 
structure of the original Turing machine that pre-Olympia was supposed to 
imitate (according to the definition of causal structure in terms of logical 
relations between propositions about the system's state at different moments)? 
If so, that would mean that regular Olympia (pre-Olympia + Klara) wouldn't have 
a causal structure isomorphic to the Turing machine either, since I was 
defining causal structure solely in terms of propositions about events that 
*do* occur in the system's history, meaning the extra counterfactual conditions 
provided by Klara are irrelevant to Olympia's causal structure, so Olympia's 
causal structure would be the same as pre-Olympia's.
If that's the case, why can't we postulate that consciousness supervenes on 
causal structure, since causal structure is after all part of the physical 
world? In fact one could say that physics is *only* concerned with "causality" 
in the sense of lawlike relations between propositions about observations, 
since the laws of physics tell us nothing about what particles or fields or 
wavefunctions "really are", only about how they interact with one another and 
how they can be used to predict the outcomes measurements. So if we say 
consciousness supervenes on causal structure, then Olympia would not qualify as 
an instantiation of the observer-moments that the original Turing machine 
instantiated, in much the same way that a lookup table wouldn't qualify. 
I don't have a problem with the idea that a giant lookup table is just a sort 
of "zombie", since after all the way you'd create a lookup table for a given 
algorithmic mind would be to run a huge series of actual simulations of that 
mind with all possible inputs, creating a huge archive of "recordings" so that 
later if anyone supplies the lookup table with a given input, the table just 
looks up the recording of the occasion in which the original simulated mind was 
supplied with that exact input in the past, and plays it back. Why should 
merely replaying a recording of something that happened to a simulated observer 
in the past contribute to the measure of that observer-moment? I don't believe 
that playing a videotape of me being happy or sad in the past will increase the 
measure of happy or sad observer-moments involving me, after all. And Olympia 
seems to be somewhat similar to a lookup table in that the only way to 
construct "her" would be to have already run the regular Turing machine program 
that she is supposed to emulate, so that you know in advance the order that the 
Turing machine's read/write head visits different cells, and then you can 
rearrange the positions of those cells so Olympia will visit them in the 
correct order just by going from one cell to the next in line over and over 
again.
So: why can't the idea of consciousness supervening on causal structure be a 
possible strategy for avoiding the problem you talk about in step 8 of your UDA 
argument (if I am understanding it correctly), namely the idea that even if 
there was a physical universe it wouldn't be able to tell us anything about the 
measure of different computations? If we talk about the causal structure of a 
given computation, why can't we look at how frequently sets of physical events 
with an isomorphic causal structure occur in the physical universe, and derive 
a measure on physical implementations of computations in this way? Not that I 
personally would favor this approach to a philosophical "theory of everything", 
but would you say it isn't even a coherent possibility?

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. 

Are you saying that a notion similar to my definition of "causal structure" is 
already made use of in the areas of mathematics you're talking about, or when 
you say "the history of a particular Turing machine computation" are you 
talking about something unrelated to my definition of the computation's causal 
structure?
I also wonder if anything similar to this notion of causal structure could be 
found in category theory, since in some layman's summaries I've read that 
category theory defines mathematics in a purely relational way, where any 
mathematical object (or proposition?) is defined entirely in its relationships 
to other objects.




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.
When you say "that approach", are you talking specifically about looking at 
isomorphisms between 1) logical relations among propositions about arithmetic, 
and 2) logical relations among propositions about the history of a Turing 
machine computation? Or were you saying that UDA takes an approach that is 
similar in some broader fashion?


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!
I guess it would depend on how the measure was defined. It might not just be in 
terms of the numerical frequency that a given causal structure appears in the 
world, but also in terms of things like how many other causal structures 
"remember" that causal structure in some sense (contain detailed information 
about it). That could perhaps give a measure which was biased towards more 
complex causal structures like human minds even though ants are much more 
common numerically.
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.

Well, I didn't mean to sugest that your ideas are vague, only that my own 
notions of a connection between causal structure and measure were rather 
ill-defined...there'd be a lot more math I'd need to learn if I wanted to 
seriously try to develop these ideas, or to really understand the details of 
your own ideas. By the way, do you have a bibliography somewhere of books you 
think someone could use to self-teach themselves enough math to understand the 
details of your AUDA argument?
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