On Tue, Sep 18, 2007 at 04:23:58PM +0200, Bruno Marchal wrote:
> 

> OK. You know I like your little book as an introduction to the field, 
> but, as you have already acknowledge, there is some lack in rigor in 
> it, and it is not even clear if eventually you are of the ASSA type or 
> RSSA type, or if you accept comp or not. Use of Bayes and Prior, for 

I am clearly on the record, both in the book and also in the list
archives as an "RSSA type".

As far as comp is concerned, I do not assume it, but accept it as a
model of what's going on. See page 79 of my book.

> example, is a symptom of ASSA type reasoning. Distinction between 1 and 
> 3 person points of view is symptom of the RSSA type of reasoning, (and 
> favored with comp).

Not if the prior were actually given by the observer erself. This is
the main point of departure between Schmidhuber's and my approach.

> >
> > Not equivalent. Equivalent status. Assumption of the set of all
> > infinite strings plays the same role as your assumption of
> > arithmetical realism, and that is of the ontological background.
> 
> 
> I don't know. Let us fix a simple alphabet: {0, 1}. Then an infinite 
> string like
>    111101000100111000000010100101100001101001 ..... (infinite on the 
> right) can be seen as the chracteristic function of a subset of N (the 
> first 1 in the string means then that 0 is in the set,, the second one 
> that 1 is in the set etc. The resulting set is
>   {0, 1, 2, 3, 5, 9, 12, 13, 14, 22, 24, 27, 29, 34, 35, 37, 40, ...}
> So there is a bijection between the set of infinite strings on the 
> {0,1} alphabet, and the subset of N. So without putting any 
> extra-stcruture on the set of infinite strings, you could as well have 
> taken as basic in your ontology the set of subset of N, written  P(N). 
> Now, such a set is not even nameable in any first order theory. In a 
> first order theory of those strings you will get something equivalent 
> to Tarski theory of Real: very nice but below the turing world: the 
> theory is complete and decidable and cannot be used for a theory of 
> everything (there is no natural numbers definable in such theories). 
>  From this I can deduce that your intuition relies on second order 
> arithmetic or analysis (and this is confirmed by the way you introduce 
> time). But then this again is really a strong assumption, far stronger 
> than arithmetical realism.

Stronger in what sense? I have only assumed just enough to make sense
of the notion of complexity.

> To be sure, I still don't know if your ontic base is just "nothing" 
> (but then in which theory?) or the infinite strings (again, in which 
> theory and as I said you will to use rich mathematics for that), etc.
> As you know, I am trying to go a little beyond the UDA result so as to 
> give a little smell of the real thing. The trouble is that the basic 
> tools of logic and axiomatic are not very well known by anybody but the 
> professional logicians.
> 

Its not so much that, but in how you interpret the logical
results. Calling G*/G an angel for instance might be colourful
rhetoric, but it doesn't really mean much to me.

> 
> 
> 
> > It might seem like such uncountable sets are too much to assume, but
> > in fact it is the simplest possible object. It has precisely zero
> > information.
> 
> Zero information. Zero justification. Occam razor ... I do agree with 
> these major motivations for the everything idea, but I disagree with 
> the proposition saying that the the set of strings needs 
> zero-information. Why not the infinite strings on both right and left 
> (coding the integers), or infinite many-dimensional lattices fit with 
> zero and one on the vertex, or etc. ?

Information theory is defined on one-sided strings. It would be
possible to redefine complexity to use two-sided strings, or subsets
of N, or real numbers, but you just end up with an isometric theory,
it wouldn't be saying anything different/

> There is just a lack of enough precise definition so as to verify your 
> statements that strings needs zero-information, and as I say above, 
> from some standard and traditional view points, infinite strings needs 
> a lot of information to be define.
> 
> 
> > No countable set has this property.
> 
> Why?
> 

For finite sets, one has the objection - why that finite number? For
infinite countable sets, can one even define a measure?

> 
> > I put your objection
> > into the same category as those who claim the multiverse is
> > ontologically profligate. Apologies to intuistionists out there.
> 
> 
> Apologies to intutionists and also to constructivist like Schmidhuber, 
> but also to weak arithmetical platonist like, imo, digital mechanist 
> ought to be.
> 
> 
> 
> >>> Obviously I'm departing from
> >>> Schmidhuber at that point, and whilst in "Why Occam's Razor" I use 
> >>> the
> >>> term Schmidhuber ensemble to refer to this, in my book I distinguish
> >>> between Schmidhuber's Great Programmer idea
> >>
> >>
> >> (which you confuse some time with the UD, I think).
> >>
> >
> > He does actually dovetail,
> 
> 
> We have discuss this. In the first paper the "great programmer" is not 
> a dovetailer, and indeed there is nothing in the ASSA approach for 
> which dovetailing could play a role.
> 

No the great programmer writes and runs a dovetailer on er great computer.

I missed the dovetailer on my first reading, as indeed it doesn't seem
too important. I suspect the Scvmidhuber intended the dovetailer to
"breathe fire" into the ensemble.

> 
> 
> > so it is a universal dovetailer in all but
> > name perhaps. But the ontological basis of the "Great Programmer"
> > differs very much from COMP.
> 
> 
> Again this is not corect. Schmidhuber and me do agree on comp (100% 
> agreement: we have the same hypothesis). 

I'm not sure that Schmidhuber accepts arithmetical realism. His
ontology is that the great programmer exists, whatever e may be. The
GP is not necessarily a machine, or an arithmetical formula.

> And relatively to the comp hyp 
> and the importance of the universal machine Schmidhuber and me are much 
> closer than with Tegmark whi is just very naïve about notion of 
> mathematical reality. Now the problem is that, unlike many people in 
> this list, Schmidhuber does not address neither the mind body problem 
> nor the 1-3 person distiinction, and the relativity of states which 
> derives from that distinction. This forces him to literally defend the 
> idea that randomness in nature never really exist, which is hard to 
> justify in front of the physical branch of history we are living. This 
> does not makes his work wrong, but at least incomplete (and then he 
> should use Bennett notion of depth for the cosmological/geographical 
> aspect (like I do in Conscience et mécanisme: using just Kolmogorov is 
> not enough, but here I am going out topic.
> 
> 
> 
> 
> 
> 
> > Of course, although you'd better say the Standish ensemble so as not
> > to misattribute it to Bertie. Also, it is quite clearly a set (I think
> > you've read enough English papers to know the difference between and
> > ensemble and a set in English, I hope?)
> 
> 
> Well, I hope you are not referring to the notion of "ensemble" as it 
> occurs in physical statistics. 

Not at all! Ensemble is usually used in mathematical terms to refer to
a collection that need not satisfy set axioms.

> Again, this would mean that you endow 
> the space of infinite strings with a structure of a measure space 
> (boolean sigma-algebra, for example). because this means that your 
> basic ontology is much richer than just the strings. I am trying to 
> understand a bit more clearly how you view of the everything thing.
> 
> 
> 
> >>>>
> >>> All of these concepts are more precise and have additional properties
> >>> to the set of all infinite strings. For instance, the reals have
> >>> group properties of addition and multiplication that the strings
> >>> don't.
> >> But as sets, they are isomorphic, and if you don't have 
> >> extra-structure
> >> on your "ensemble", the relation between your "observers" and your
> >> "ensemble"  is even more obscure, it seems to me.
> >>
> >
> > You've lost me here.
> 
> 
> I'm the one saying that I'm lost here. I am just asking: how do you 
> define "observer" in the infinite strings setting. (Actually with or 
> without extra-strcuture, like what you need to have a measure space).
> 

I don't define the observer at all! If I knew enough to define this,
I'd probably be very rich. I merely postulate what I need, and
hopefully the postulates are reasonable.

For the Occam's razor (and White rabbit argument), the observer
defines a map O from the set of strings (descriptions, things which
are observed) to concepts, or interpretations (results of
observations). This latter set is assume discrete, and can therefore be
indexed by N, so we can consider O: {0,1}^\infty->N.

The requirement that the measure of O^{-1}(n) be non-zero is needed
for the dewabbiting. It also ensures a positive complexity value for concepts.

> 
> 
> >> So here you do explicitly accept extra-structure, a measure, on your
> >> ensemble, making them again quite close to the reals.
> >> You cannot derive the existence of a measure from just a definition of
> >> a set. (There are *many* possible measures on any set).
> >>
> >
> > Yes of course. The uniform measure has always been part of the 
> > definition.
> 
> 
> This was not clear, sorry. Now you definitely need analysis or second 
> order arithmetic. This is everything but nothing!
> 

It sounds like we have a different idea of "nothingness". I call the
all-strings ensemble "nothing" as a rhetorical device to stress how
wrong the "metaphysical profligates" are.

> 
> 
> 
> >>> see Li & Vitanyi example 4.2.1 for a detailed
> >>> discussion. The idea is simple enough, however.
> >>
> >>
> >> ... where they describe how to put a measure on some set of *subsets*
> >> of an uncountable sets. You have to define a Borel structure on it,
> >> etc.
> >> It is indeed explained in Li & Vitanyi (page 214q).
> >>
> >
> > We must have different editions. On mine its page 243 :). So there
> > must be some non-measurable subsets.
> 
> This is not even provable in formal set theory like ZF (Zermelo 
> Fraenkel). You need the axiom of choice, if I remember well. This means 
> you presuppose set theory (a vastly bigger and richer ontology than 
> arithmetic).
> 

It strikes me as unimportant if these sets exist or not. But I could
be wrong - sometimes corner cases are very important.

> 
> 
> > But I fail to see how these can
> > be inverse images of an observers interpretation (O^{-1}(n)) must be
> > measurable). But then I admit I am acting like a physicist in glossing
> > over these sorts of details.
> 
> 
> I would not have dare to call you a physicist, but now that you admit 
> you are acting a bit like them, I can understand better :)
> 

OK - I thought you'd appreciate the reference :)

> 
> 
> 
> >>> Since this appears to be the point of departure between you
> >>> and he, I'll state that I've always followed you in this point, that
> >>> the 1st person pov (what I call the semantic level) is important.
> >>
> >>
> >> OK. But again it could be misleading to call that "the semantic 
> >> level",
> >> because a relation between "semantic" and first person would be a very
> >> interesting things to dig on, but nobody has done that yet.
> >> All hypostases (first person, third person, first person plural, etc.)
> >> have syntax and semantics.
> >
> > Yes but again we're mixing terminologies. When I refer to syntactic
> > level, I'm refer to what stuff is,
> 
> 
> You can do that. I see the point. But it is not standard at all and has 
> to be explained in all detail, especially if you are not clear if you 
> follow comp or not. Even with comp this is highly ambiguous.
> 
> 
> > and when I refer to semantic level,
> > I mean how it is interpreted.
> 
> This is even less standard, and although I could put sense on it, this 
> is only because I have tools for doing that. A term like 
> "interpretation" can be seen as syntactical at some level and 
> semantical at some other level.
> 
> 
> 
> > This can be applied to all situations
> > where emergence is occurring.
> 
> 
> I knwo a lot of people who are searching their gun when they hear the 
> word "emergence".  I mean this is a word which can be used once you 
> take many precautions. Also, if comp is correct, as you know, it is 
> matter (stuff) which emerges from consciousness/meaning (cf the 
> reversal result).
> 

Sure there is a lot of confusion on the subject of emergence, so it is
not surprising if there are people "reaching for the gun" when hearing
the term. However, the term actually is quite well defined, and the
way I use it is pretty consistent with what other recent thinkers have
written, such as Bedau, or Ronald, or Fromm.

> 
> 
> > So in the case of an ideal gas, the
> > molecular description is syntactic, and its thermodynamic description
> > is semantic.
> 
> Hmmm....  I cannot really accept this. Here is a case where emergence 
> is far better than semantics.
> 

I'm not sure what this has to do with "semantics", but everything to
do with emergence. Semantic means "meaning". The "semantic layer" is
the descriptive layer that means something to the observer. The
"syntactic layer" is typically what the system is specified on
(although it need not be). The terms are my invention, but really of
the other terms I've across, microscopic/macroscopic will not do, as
it often doesn't relate to size, and L_1/L_2 (This is Ronald, Sipper
and Capcarre's term) - I mean WTF?

I have actually read quite a lot of literature on the subject, and
there aren't any accepted terms for describing the levels of
description in emergence. I'm trying to propose the semantic/syntactic
level labels, but you know its a market of ideas out there.

> 
> Another point where your fuzziness does not help is that you are not 
> clear on the comp hyp. 

I never assume the comp hyp. I believe comp is consistent with what
I've developed, and note that you can pretty much get the consequences
of the UDA from a more general functionalist position.

> Schmidhuber is clear on comp, even if he has 
> disagreed when discussing online in the list with the consequences I 
> derive from it. But the disagreement comes not from what comp means, 
> but from the 1/3 distinction, which Schmidhuber does not consider. 
> Tegmark does introduce an embryo of 1/3 distinction (but quite 
> different from mines (see below)), but Tegmark still uses some identity 
> thesis implicitly for making observer belonging to universe, and minds 
> to brain. Such identities have just no meaning at all once you 
> postulate the comp hyp (or even strong weakening of it btw). OK? (by 
> UDA). Yes?

Yes, but there is still some reason tying the observer to the
universe. Otherwise you get the Occam catastrophe. (again my term, and
others have called it differently) I do not know what that reason is,
but suspect self-awareness has something to do with it.

> 
> Bruno
> 

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