Tom wrote

> My "beside myself" statement was a punny reference to self-reference.
> I meant that I am looking forward to your post(s) with positive
> eagerness.


Thanks. Also, I will follow your suggestion to force me writing little 
post. I will first answer an older post by George (not to confuse with 
Georges).



Le 25-mars-06, à 00:51, George Levy a écrit :

> I have read or rather tried to read Smullyan's book. His examples are
> totally fabricated. I will never meet the white knight in the island of
> liars and truthtellers. I need examples which are relevant to life, at
> least the way I understand it in the context of the many-worlds.


The role of the knight-knave island is just to give an easy way to 
produce self-referential sentences? This is explain on page 48 in 
Forever Undecided (hereafter FU).



>
> Einstein (or maybe someone writing about relativity) came up with the
> paradox of the travelling aging twin.


Was it not Langevin?




> Schroedinger came up with his
> cat's paradox. Tegmark came up with the quantum suicide experiment.


I came up first with the comp suicide, and much later after with the 
quantum suicide and with the "kill the user" sort of quantum 
computation, well before Tegmark, and I am not sure this has helped to 
make my work more "acceptable" or "comprehensible". For me "quantum 
suicide" was a confirmation of the fact, easily derivable from comp, 
that even for purely empirical reason we can doubt "mortality", or 
doubt that the mortality issue is simple, like so many materialist tend 
to think.




> Granted, I will never travel near the speed of light; I will never put 
> a
> cat in a box equipped with a random and automatized killing device; and
> I will not attempt suicide; my wife would just kill me. However, these
> examples fired up my imagination: travelling near the speed of light,
> existing in a superposition of state, surviving a nuclear bomb under
> your chair.
>
> Smullyan's white knigth had the mission to teach me about the logic of 
> G
> and G*. Sorry, he failed. The white knight does not fire up my
> imagination. I don't care about his island and about his questions.


It is exactly with the "diagonal principle" (FU page 211) that the 
logical role of the Knight-knave Island is eventually eliminated. Now 
his "diagonal principle" arises in the context of his "Godelized 
Universe" for which Smullyan don't provide motivation (it still look 
like a fairy tale). What makes Universe *Godelized* is really Church 
Thesis, and that is really the missing key in FU (and actually in the 
whole work of Smullyan). I make those steps more transparent in my SANE 
paper. have you print it? It should help.



> However I do care about life, death and immortality. The many-world 
> does
> seem to guarantee a form of immortality, at least according to some
> interpretations.


Yes, we have discuss this a lot. I think most people agree on this in 
the list, both with the quantum MWI, or with some "all computations 
exist". I think the most serious involved people in this list just 
disagree on how to quantify the (quantum or comp) indeterminacy. Of 
course progress have been made on the quantum part of that problem, but 
hardly on the comp part, which is actually presupposed in the quantum 
MWI (cf Everett, Deutsch, ...).




>  I consider this issue to be very relevant since sooner
> or later each one of us will be facing the issue of death or of 
> non-death.


Be careful with such motivation because it could lead t wishful 
thinking. I am not sure you can appreciate the comp "lesson" which 
shows above all the abyssal googelplexity or our ignorance. But then 
such an ignorance appears to have a mathematical shape capable of 
providing information, but this leads today just to hard mathematical 
questions.



>
> I would like someone to come up with an extreme adventure story like 
> the
> travelling twin, Schroedinger's cat, or Tegmark's suicide experiment to
> illustrate G and G*.


I think the whole UDA (Universal Dovetailer Argument) and the movie 
graph paradox (or argument), and/or Maudlin's Olympia device are going 
in that direction. G and G* are just the tools for making this 
technical enough so that it leads to testable propositions. UDA is 
really the intuitive (and rigorous although informal) path for an 
understanding of the reversal between physics and numbers, including 
the showing of how hard the comp (im)mortality puzzle is.




> For example this story would describe a close brush
> with death.. It would create a paradox by juxtaposing 1) classical or
> common sense logic assuming a single world,


It seems to me that the UDA just does that. Do you see that classical 
physics is a priori untenable with comp once we take the 1-3 person 
distinction into account? I mean Classical physics is just 
epistemologically incompatible with common sense, once comp is assumed.




> 2) classical or common sense
> logic assuming the many-world, and


See just above.



>  3) G/G* logic assuming the many-world.


Well, we get G and G* assuming just the natural numbers (and 
classicality in Platonia, but this is generaly assumed under the comp 
hyp).


>
> What would the white knight do if he were living in the many-world?


Please, the white knight is just a "logical tool" for getting G and G* 
without learning some heavy introduction to recursion theory or 
mathematical logic. Read my SANE paper(*)  for a quick elimination of 
it. You can ask question.
But the white knight is nothing more than that. As an entity it is not 
even definable in the language of a lobian machine. I explain this in 
my paper.
I realize also that I explain the "real" heart of the matter 
(diagonalization *and* Church thesis) in my last paper, which is not 
yet in my web page (which I should update anyway).



> What
> kind of situations would highlight his talent to think in G. Would his
> behavior appear to be paradoxical from our logical point of view?


The white knight does not exist, not even in Platonia. It is the price 
Smullyan asks to pay for making G and G* easily accessible without 
studying too much mathematical logic.

Now I think I should train you with diagonalization. I give you an 
exercise: write a program which, if executed, will stop on the biggest 
possible natural number. Fairy tale version: you meet a fairy who 
propose you a wish. You ask to be immortal but the fairy replies that 
she has only finite power. So she can make you living as long as you 
wish, but she asks precisely how long. It is up too you to describe 
precisely how long you want to live by writing a program naming that 
big (but finite) number. You have a limited amount of paper to write 
your answer, but the fairy is kind enough to give you a little more if 
you ask.
You can ask the question to very little children. The cutest answer I 
got was "7 + 7 + 7 + 7 + 7" (by a six year old). Why seven? It was the 
age of his elder brother!

Hint: try to generate an infinite set S of more and more growing and 
(computable) functions, and then try to diagonalize it. S can be 
{addition, multiplication, exponentiation,  .... (?)....}. More hints 
and answers later. I let you think a little bit before. (Alas it looks 
I will be more busy in may than I thought because my (math) students 
want supplementary lessons this year ...).

Hope this can help; feel free to make *any* comments.

Remember that if all this is too technical, you can also just read 
Plotinus and the (neo)platonist which, accepting comp or weaker form of 
Pythagorism,  do have a tremendous advance on most materialist of today 
... I think it could even provide more light on the practical death 
issue. The role of G and G* is just to get the math correct for some 
notion of quantifying the 1-person probabilities.

Bruno

(*)SANE paper html:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.htm
SANE paper pdf:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf

http://iridia.ulb.ac.be/~marchal/


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