George Levy wrote:

>> > GL: The MWI  gives us the chance to go all the way
>> >and places each "I" at the center.
>> BM: How weird. That would have been a nice sum up of what I try to say;
>> with COMP instead of MWI.
>Could you please elaborate. Why can't you just say it in the context of COMP?
>Or maybe you can say it.

I can say it indeed. With comp (or some weakening) I *must* say it.

>> BM: But COMP implies MWI (Note that Schmidhuber and me agree on that,
>> but we disagree on what *are* the (many) worlds MW).

More precisely: COMP implies MWI in two senses.

1) Everett's sense: SE + COMP gives MW.
2) COMP sense: COMP gives SE + MW (my thesis, look at my CC&Q paper)

>This is interesting and I just want to clarify this in my mind... You say 
>you and Schmidhuber do not agree on the "size" of the MW...what it 

No. Basically we agree with the size of the "ontology". We disagree on
the meaning of the word "world". I pretend that with comp a world is a
first person (plural) construct. He does not defined them but he 
them with their generating programs. Observers belongs to worlds, with
Schmidhuber. I pretend with comp that observers's infered worlds are 
defined by the set of the consistent extensions. I think at it as some
kind of model (in the logician sense). I don't get classical (boolean)
realities, but some sort of quantum one.

>> Schmidhuber associate worlds to some programs, I associate
>> worlds on machine's projection from shared computational histories
>> The projection is first person plural.
>Again to clarify... the word "machine" means that consciousness arises from
>simple (Turing-like) computations. This is the COMP hypothesis.

In first approximation YES. In second approximation NOT REALLY.
By comp I mean I survive with an artificial digital brain/body/universe.
As a counter-intuitive conclusion, consciousness does not really
supervenes on a computation but on an infinite cloud of "similar" 
computations existing in UD*. Locally a brain/body/universe only makes it
possible for a person (the one conscious) to accelerate himself 
relatively to its most probable possible extensions. Note that this gives
a role to consciousness : self-speeding up abilities. 
And this is linked to another result by Godel. If you add an undecidable
true statement to the theory (in which that sentence is undecidable), not
only an infinity of new formula become decidable, but an infinity of
provable formula get shorter proofs.

>I am not sure I understand  "shared computational histories". Why would past
>computational states be relevant? A current state could be reached from
>different past points (OMs) unless "merging" is not allowed

Merging is allowed through amnesia. In some sense personal memories
help you to stay into no merging histories. There is something
similar with quantum mechanics and the quantum eraser. Saibal Mitra
proposes a similar idea in the discussion.

>...Isn't the 
>state only of relevance?

Relevance with respect to what? A state is not enough, you need a 
machine to support it. Now a single state defines its accessible 
extensions in UD*, in that sense you are (platonically) right.
State are relative, in both Everett or Comp.

>In addition, "shared computational histories" seems
>to imply that two people have "now" the same thought pattern. 

 I was meaning *partially* shared computational histories. Like
telepathic dreamers (if that exists!) or like a video game net where 
different persons interact with a program.

>Do you mean that
>a "world" is the view (of the plenitude) by two observers sharing a "common
>frame of reference?" 

It is more "sharing a common history" like the bifurcation W and M.
Biological multiplication gives a simple model of tree like
developpement where individuals share a long common history. The more you
leave the leaves (!) the more the histories are shared. This is an image
because both with comp and/or QM, we must take into account merging.
(I know you agree with that).
>From inside UD* (i.e. from the average first person point of view of
machines) I make the conjecture that there is no ultimate well-defined
trunk for these barnches and leaves. From the third person view there
is one which is just the trivial one: UD.

>How is this frame of reference defined? 

All the histories are in the block comp universe (UD* or just 
platonic numberland). But they makes sense as "histories" only 
viewed by the machines inside. It is the main purpose of the UDA TE
to explain that. Mathematical logic is needed for defining 
formally those inside views. 

>Should they have
>the same thinking mechanism and laws of nature, but not necessarily the same
>specific thoughts? 

Er... Yes like W and M.

>(It's hard to know where to draw the line... 

It is *impossible* to draw the line with certainty and from a third
person point of view. Of course if you feel pain or joy you can know

>One could argue
>that two different people sharing the same laws of nature and thinking
>mechanisms, but having different specific thoughts will perceive different

*partially* different. They can both refer to a common moon of 
things like that.

>Why the word "projection?"

Or "common anticipation". Like F=ma, or SE, ... We take it as a trunk,
when it is perhaps just a branch. See above.


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