On Fri, Sep 29, 2006 at 11:46:20AM +0200, Bruno Marchal wrote:
> 
> 
> Le 26-sept.-06, à 16:03, Russell Standish a écrit :
> 
> > I would say also that interpretations could be inconsistent,
> 
> 
> ? ? ?
> I guess you are using the word "interpretation" in some non standard 
> way.
> It would help us, and you, if you could work on a glossary.
>

"Interpretation of something" means "meaning an observer attaches to
something".
 
Is this nonstandard? I wouldn't have thought so.

> 
> > Indeed - however we do have a difference in emphasis. Yours is towards
> > more formal models, but with obscure modeling relations,
> 
> My emphasis is on machine which are formal by construction, and the 
> obscure modeling relation are old and new theorems in mathematical 
> logic. It is just applied mathematics.
> The modelling relations are strange and mysterious, but this is just 
> because Godel and Lob theorems are somehow themselves strange and 
> mysterious.

But so are your postulates, for example the Theatetus notion of
knowledge is far from obvious. I can follow the logic as a formal
system, but I struggle to make sense of it (interpret it).


> 
> 
> 
> > But is this 1-3 distinction implicit within your statement of COMP?
> > I'm not sure that it is.
> 
> I think it is, and the following quote makes me thing you believe this 
> too, at least in the quantum framework, when you say:
> <<Collapse is conceived of as a physical process, and as such is
> problematic. Nonphysical collapse is just the 1 POV of the
> Multiverse. That's all I'm talking about.>>
> 

But I have an explicit 1-3 distinction in the format of my PROJECTION
postulate, and that quoted statement is taken in that context.

Obviously I have no objection to the 1-3 distinction, but I failed to
see how it follows explicitly from AR+CT+YD, or even from "I am a
machine" (in the Turing sense).


> > It is not new, it underlies all of Chapter 2 of my book, and also of
> > "Why Occams Razor". Perhaps I'm guilty of assuming it without
> > explicitly stating it, but by way of challenge can you give me a piece
> > of knowledge that doesn't come in the form of a string?
> 
> Knowledge comes from third person finite strings, with a measure 
> determined by *some* infinite strings (the non halting immaterial 
> computations) generating them.
> 

But finite strings are just sets of infinite strings.


> > It is
> > certainly hard, given we live on the opposite sides of a digital world
> > - a record of a telephone conversation we have will be a a string of
> > bits, as will any emails we use, any my book left my hands in the form
> > of a string of bits and so on.
> 
> OK, but that are finite strings conceived and manipulated (by your 
> computer and your brain with some high level comp assumption) as 
> numbers. Most test editor manipulate a structure of finite strings 
> together with a concatenation or substitution structure. Again this is 
> infinitely richer that your set of all infinite strings.
> 

No - sets have subsets, and all finite strings can be found as a
subset of the set of all infinite strings.

> > I use the usual one (excluded middle), and I don't use any infinity
> > axiom that I'm aware of.
> 
> Now I am very confused. I thought you were assuming infinite strings. A 
> glossary would really help, I am not sure you are not changing the 
> meaning of your term from paragraph to paragraph.
> 

You introduced the term infinity axiom. If by a infinity axiom you
mean the existence of infinite strings, or the existence of infinite
sets, then yes I have an infinity axiom.

> > Yes - I appreciate the ontological difference. I would say that only
> > "Nothing" exists (in ontological meaning). Strings and sets of strings
> > only exist in the same sense that the number "1" exists.
> 
> This contradict the definition of "Nothing" you gave us.
> 

The set of all strings is a model of the Nothing (or equivalently the
Everything). It is meant to be the ultimate model, capturing all that
is possible to know about it.

> >
> > About the only difference I see is that the measure might be 
> > different...
> 
> 
> And that *is* the key issue, I think.
> 
> > I more or less always assumed this. Either COMP is more specialised
> > (you can derive some my postulates from COMP, and others are compatible
> > with it), or COMP is the only way of deriving these same postulates,
> > or COMP in some way contradicts these postulates.
> 
> As you admit yourself there is a lot of work to get enough precision in 
> your approach to compare it with the consequence of the 
> computationalist hypothesis.
> As I do have a lot of work to compare the comp-physics with the 
> experimental physics.
>

Yes - in that respect, my work ties more closely to physics. However,
there is a distinct difference between my string ensemble and
Schmidhuber's speed prior one, particularly with respect to randomness.
 
> Sometimes I define strong comp by saying yes to the doctor, and weak 
> comp by accpetoing your child marry someone who has say yes to the 
> doctor. Surely you have an opinion on that, no?
> 

To be quite frank, I don't know what to make of that. What does it
matter who my child marries, so long as they are happy with that.


-- 
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