On Jan 7, 12:09 pm, Bruno Marchal <[email protected]> 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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