Hello Juergen,
>Gilles Henri (GH) writes:
>
>> I have much more objections in fact to models like Schmidhuber's one:
>> again what are these Turing machines, Big programmer and so on made of?
>
>Juergen (J) : This does not seem essential and is therefore left
> unspecified. You can
>try to make one of the stuff you find in your own universe. Note that
>many of the Great Programmer's universes indeed feature another Great
>Programmer who programs another (possibly different) Big Computer to
>run all possible universes. Obviously there are infinite chains of
>Great Programmers.
I agree. Ultimately this important point relies on Church's thesis. Below I will give a argument showing there is no stuff at all.
Consciousness AND matter are definissable only from within an infinite set of computationnal histories.
>> GH : Who is "interpreting" a string as a Universe?
>
>J : This may be a somewhat misleading question. It seems based on the
>assumption that the interpreter is not himself part of a computable
>world representable by bitstrings. E.g., your internal state changes
>and email messages and worries about "interpretations" are just part of
>the computable evolution of a particular universe. It does not matter
>that we may produce computable outputs claiming otherwise ("it doesn't
>feel like it"), to be interpreted by other computable interpreters like
>ourselves. None of us needs to be aware of the bitstring representation.
Indeed. That is equivalent to what I was trying to explain to Gilles and James in a previous post where I insist that only a person can be conscious. But of course (with comp) a person can be embedded in a string. The basic principle is indeed to embed the subject in the object. This idea begin perhaps with Galileo, but has been considerably extended by Everett. Here we generalize it by embedding the computer scientist in the set of all computations.
> GH :
>> Is it true that in this model every "state" is finite, that is the set
>> of all possible states of all possible universes is countable?
>
> J:
> Yes, definitely! Just like sqrt(2) is describable by a finite
>algorithm. Most real numbers, however, are not describable at all -
>they convey infinite information. We cannot even talk about them. No
>room for them in any of the Great Programmer's universes!
Although most real numbers are not describable at all, we can easily talk about the set of all real numbers. Now, the Great Programmer (my Universal Dovetailer UD) not only dovetails on all computations but dovetails on all computations with all real (complex, quaternionic, ...) oracles. It does so by generating all finite initial segments of all reals. At each state of the computation of the UD, there is indeed no place for a real number, BUT, I show below that from the first person perspective of an "observer", the set of all real number does play an important role. In fact our prediction will depend on the measure on all infinite computationnal histories. More below.
> GH :
>> Does it mean for example that the possible values of physical
>> constants are discrete?
>
> J :
>Discrete or at least computable. In none of the Great Programmer's
>universes there is Super-Turing computability, although the concept
>has become fashionable in our particular computable universe, and lots
>of computable people make computable noises about it.
I am not quite sure about this. Perhaps. I need to think about it. The reason why I doubt here is still the the same result I will try to explain shortly below. I show that computationnalism entails that our local expectations depend on the global set of infinite computations, and this will entail the "observation" of truly random sequence or noise. Well, this happens with QM, and physicist are used to that. The possibility remains that some "physical" constant could also be truly random. I do not find this plausible, but, from a logical point of view, it is not entirely ruled out by comp : it would mean that some special oracle would play a significant role. That would entail that our "apparent universe" is not computable ! If that is true, that would nevertheless remains unprovable ! (Such statement would be a kind of Godelian Sentence).
>> GH : The simplest program just enumerates all integer
>>numbers. If you can tell me which integer describes the existence of
>>consciousness or to the existence of anything like an electron or whatever
>>you want, I would be very grateful to you!
>
> J :
>To comment on this in the spirit above, I took a paragraph from my little
>paper and replaced every occurrence of "life" by "consciousness":
>
>What is consciousness? The answer depends on the observer. For instance,
>certain substrings of E_k may be interpretable as the evolving
>consciousness of a living thing L_k in U_k. Different observers will
>have different views though. What's consciousness to one observer will
>be noise to another. In particular, if the observer is not like the
>Great Programmer but also inhabits U_k, then its own consciousness may
>be representable by a similar substring. Assuming that recognition
>implies relating observations to previous knowledge, both L_k's and
>the observer's consciousness will have to share mutual algorithmic
>information: there will be a comparatively short algorithm computing
>L_k's from the observer's consciousness, and vice versa.
What do you mean by "an observer inhabits U_k" ? Of course, for a physicalist inclined philosopher, such an expression seem to have an obvious meaning. But I believe such an expression has no (non-ambiguous) meaning once we take seriously the comp hypothesis. An observer cannot so easily be said inhabiting a precise U_k. The observer cannot be localized in a unique computation. He can only be associate with an infinity of "sufficiently similar" computations (which all belong to UD* : the complete work of the UD). This entails a rather big localisation-indeterminism. More below.
> J :
>And Bruno wrote:
>
>> ...I will be very short. Nevertheless, about Schmidhuber, although there
>> is some superficial resemblance with my thesis, I realise Schmidhuber has
>> an inconsistant understanding of the computationnalist hypothesis. More
>> on this latter....
>
>Did I miss a follow-up message? I guess I haven't seen any subsequent
>explanation of Bruno's claim.
1) First, when I say, Juergen, that you have an inconsistant understanding of comp, I say it with all my respect and even my friendship for someone who, like me, seem to believe that indeed comp couls perhaps be the simplest explanation for "everything".
Now, I do think that you (like Tegmark, but also Everett) are missing a key point.
In particular, although I agree with almost your whole paper, I completely disagree with your philosophical conclusion. Like Hal Finney (see the very beginning of this discussion list), I belief you are "throwing the baby with the bathwater" when you told us that "... adopting the great Programmer's point of view, classic problems of philosophy go away".
On the contrary, I believe that, with comp, we are just beginning to make it possible to build clearer formulations of these classic problems.
For example, my thesis,
http://iridia.ulb.ac.be/marchal/, consists in a reformulation of the classic Mind-Body problem in the frame of comp (along with some light on the qualitative aspects of the solution).
2) You did miss follow-up messages. In fact almost everybody in the list "miss" them. That is because some people send me private mail with more technical questions, and I have answer them privately (thinking it would have been indecent to explain my thesis in the discussion list). But now I guess it was key questions which bear on "your missing point". So I make my answer public.
====================
UD, the Universal Dovetailer, is equivalent to your Great Programmer. UD is a finite program. UD* is the infinite extension of the UD.
The question most people ask me was
>Bruno, you say "you can only associate mind with the whole UD*." - I'm not
>sure why.
Here is a short answer. Take your time to read it, and please tell me if you disagree at some point.
It is necessary to concentrate ourself on the following thought experiments (PE, PE1, PE2, PE3, PE4, PE-omega).
The "practitionners" of computationnalism can use classical teletransport as a mean to move from one place A to another place B. This mean he is "read" at A, send (by wave radio, for exemple) at B, annihilated at A, and reconstituted at B. Let us call that experience : the primitive experience or simply the PE.
Let us look first at two independent changes of the PE.
PE1 : if, knowing it or without knowing it, the reconstitution is time-delayed at B, this doesn't change anything from his first-person point of view. In particular if he is certain to get B with PE, he must be certain to get B, in PE1. (The delay is supposed to be finite).
PE2 : if he is told he will be reconstituted at B and B', his first-person futur is undetermined. The domain of undeterminism is {B, B'}.
Of course, from a third person point of view, everything is determined.
Do you agree until here ?
Now, consider the following experience PE3 which mixed PE1 and PE2.
He is told that he will be reconstituted at B and at B' (like PE2), but a time-delay of reconstitution is introduced at B (like PE1).
Now, if you agree with what I say about PE1 and PE2,
you should agree with :
IF he quantifies the indeterminism on {B, B'} in some way for PE2, THEN he must give the same quantification for the indeterminism on {B, B'} with PE3.
For exemple, if he quantifies {B, B'} with a uniform probability distribution with PE2, he must quantify {B, B'} with a uniform probability distribution with PE3. To sum up, the delay doesn't change his expectation.
This follows from comp (think on the first-person communication by the average robot instead of you, for exemple). The average robot = the normal (gaussian) robot when these duplication experiences are iterated.
OK ?
I guess you will also accept that nothing will change, in neither PE nor PE1 nor PE2, nor PE3, if at B (for exemple) he is reconstituted in a perfect virtual environment (which could exist by COMP). This is PE4.
If you agree, you are ready for "PE-omega", which is just the infinite running of the UD.
Suppose that you are in some state of mind s, captured at some digital level by a computationnal state S (which exist by COMP, and there is no restriction on the level other than permitting digitalisable capture).
Now suppose the UD is running, and that it never ends (accidentally). Then you will be virtually reconstituted, in the state S, an infinite number of times in the all UD*.
>From the conclusion of PE to to PE4, it follows that you must quantify the undeterminism (relatively to S) on the infinite set of reconstitutions, which is an infinite set which is include in the whole UD*. This implies a very big form of indeterminism (the UD*-indeterminism).
Because your mind (consciousness) includes your immediate expectations, your effective mind is really defined by the whole UD*, which has a (platonist) arithmetical reality.
With Church's thesis, and the compiler theorem, the whole UD* is embedded in Arithmetical Truth (or in the standart model of Peano Arithmetic as the logician like to put it).
This (platonist) arithmetical reality should convince any "occamist" (like you or like James Higgo) that the "concrete running" of the UD is not necessary. (In my thesis I am much more cautious about that point).
Of course the mind body problem is not solved here, as I said above, we 've got just a beginning of a formulation of the problem in the computationnalist framework.
With comp the mind aspect is not so difficult. It admits even a positivist account as the study of the limit discourses of (self referentially sound) machines, but we 've got a real matter problem : we must explain our determinist belief from the a priori very big UD*-indeterminism.
If I put it in some poetical way, we must extract our physical beliefs from all our possible (computationnal) dreams. Note also that a comp solution of the mind-body problem would provide a solution to the "other mind" problem (as philosopher of mind put it). This will provide a kind of computationnalist vaccin against solipsism.
The high non triviality of computer science and of the logic of provability(°) suggest ways toward solutions as I illustrate in the chapter 5 of my thesis
http://iridia.ulb.ac.be/marchal
I hope I have not been too short (nor too long !).
Bruno
-------------------
(°) A classical treatise on godelian provability logic is "THE LOGIC OF PROVABILITY" by Georges Boolos, 1993, Cambridge University Press.
(It is a revised and considerably extended version of his classic book "THE UNPROVABILITY OF CONSISTENCY" 1979, Cambridge University Press).
There is also a recreative introduction to this provability logic by Raymond Smullyan : FOREVER UNDECIDED. 1987, Knopf, New York.
A graduate text is the book by Smorinsky 'Modal logic and Self-Reference", 1985, Springer-Verlag, New York.
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Received on Fri Feb 26 1999 - 08:15:42 PST