On Jan 7, 12:09 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Hi Nick,
>
> On 07 Jan 2010, at 01:39, Nick Prince wrote:
>
>
>
> > Hi Bruno
> > OK so there is a good deal of the technical stuff that I've got to
> > catch up on yet before I can interpret what you are saying  (although
> > I think I can understand why the everettian imperative based on comp +
> > UDA is there).
>
> Nice. It is already a big part.
>
> >  However if I could for the moment get an intuitive
> > understanding of what you mean by a consistent extension then perhaps
> > that would help with what Brent brought up.  From what I gather you
> > are saying our next observer moment is based not on the laws of
> > physics but on what possibilities the UD brings up in UD*.
>
> Our "next" first person observer moment. This comes simply from the  
> fact that the UD generates my current state (at the doctor  
> substitution level or below) an infinity of times. In each computation  
> I have a well defined third person next state, but my next 1-state is  
> defined olny statistically on all my next 3-states in all computations  
> going through my current state.
>
> > As an
> > analogy, in conways game of life, the next screen output display (=OM
> > for the little inhabitants) depends on the rules put into the cellular
> > automata (I know this only accounts for a single little universe here
> > and there would be an infinity of universal numbers for the real
> > universe etc, but lets try to keep it simple for the sake of clarity).
>
> OK, but the distinction between 1-state and 3-state forces us to NOT  
> make that simplification. You will encounter a problem.
>
> > So in this game any (little) laws of physics (regularities in the
> > game) are emergent and would become evident to a conscious entity that
> > arose in the game.
>
> Only if you implement the game in an already  "self-multiplying"  
> computations. If not, then, from the first person points of view of  
> the little entities appearing in your game, they will survive  
> somewhere else in the UD*. They will survive "here" (in your game)  
> only from *your* point of view. But "your reality" is a white rabbit  
> universe from *their* point of view.
> Of course, if you do it concretely, what you will build is most  
> probably a quantum object implementing the game of life, and as such,  
> it could gives the right measure. But this is "accidental" in the  
> reasoning, and based on the fact that we know already our  
> neighborhoods are quantum (and/or comp) multiplied.
>
> > So here is a case where physics (regularities in
> > the little world) arise from "a program".  Is there any simple way
> > this analogy or example  can be adapted to demonstrate how the
> > consistent extensions we experience come about.  Does it have
> > something to do with the prescription of the UD.  If not then how does
> > my existence pick its next consistent extension.
>
> It is really the consciousness which picks the consistent extension.  
> It is your consciousness in Moscow which will pick up the consistent  
> extension "Nick + "I am in Moscow"". Similarly, your consciousness in  
> Washington will pick the Washington consistent extension. All the  
> consistent extension are picked, that is why we have to isolate a  
> measure on those extensions.
>
> > It's all to do with
> > what makes extensions "consistent".
>
> Not really. A non consistent extension does not exist, simply. Unless  
> 0 = 1. In auda, we can see that some extension lead to a belief into  
> inconsistency: those are the cul-de-sac worlds. They are consistent  
> ("0 = 1" does not belong to them, but "provable ("0 = 1")" belongs to  
> them, and they are dead end, they have no consistent extensions.
>
> This is subtle and related to the second incompleteness theorem (and  
> Löb theorem). Consistency entails the consistency of inconsistency.  
> Provable(false) does not entails false, because we cannot prove our  
> consistency (if we are consistent).
>
> If we are inconsistent we can prove everything (including the false, 0  
> = 1).
> But if we prove our inconsistency, we still cannot prove everything.  
> We may prove  only that we can prove everything, and that is  
> different, and that difference eventually plays a key role.
>
> You may think to buy the Davis Dover book "The undecidable". It  
> contains the original paper by Gödel, Turing, Church, Rosser and  
> Kleene, and also the formidable paper by Post (which initiate the  
> whole recursion theory), and also its incredible 1920-24 anticipation  
> (up to my thesis!).  And it is cheap.
>
> http://www.amazon.com/Undecidable-Propositions-Unsolvable-Computable-...
>
> His little other Dover book "computability and unsolvability" is  
> rather nice too, but you don't need it if you have the Mendelson or  
> the Cutland book.
>
> > If it's not physics then it must
> > be something
>
> It is arithmetic.
>
> > and is there  a simple analogy that can help me to grasp
> > it?  I find I can always work out the technicalities better if I have
> > a "road map" or analogy to help.
>
> Arithmetic defined all the lawful sequences of states. But from inside  
> "1-persons" do not belong to any precise computations, but to an  
> infinity of them, and their relative next 1-state is defined  
> statistically on all computations. This comes from the global 1-
> indeterminacy (cf step 7).
>
> But if we believe that our next 1-state is related to the physical  
> laws (as we have good reason to do, indeed physics comes from that  
> observation, really), we have to justify the "stable physical laws"  
> from the statistic on all computations (or to abandon comp!).
>
> A simple consequence of this, is that our physical reality has to be  
> described in term of a sum/statistics on infinity of computations, and  
> this, very startling and shocking fact,  is confirmed by QM (without  
> collapse).
>
> Then for the math, there is a need to see well the difference between  
> all points of view, and thanks to incompleteness, we get the  
> difference from the very classical definition of belief, knowledge,  
> sensations, already provided by the greeks (notably Theaetetus).
>
> But I prefer to be sure people get the uda, before embracing auda,  
> which needs more background in logic (good book for helping auda is  
> Boolos 1979, Smorynski 1985, but they requires "Mendelson").
>
> Hope this help a little bit. If you grasp that uda makes comp  
> extending Everett's imperative, you got the main thing. The rest  
> consists in using computer science and mathematical logic to make the  
> physics, or its logic, technically precise, notably the difference  
> between the points of view. Those are more subtle than a frog/bird  
> scaling difference. It is more akin to the difference between seeing  
> someone tortured and being tortured. It is very different.
>
> Bruno
>
Hi Bruno

Thanks very much for your careful answer. I think  I really do need to
get down to some more background reading and do some leg work  myself
before I can make much more progress.  Thank you (all) for your
patience with me as a newcomer.

Best wishes

Nick
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