Bruno Marchal wrote:
>
> 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/

In keeping with the incremental interactive process, here is a first
guess.  You simply start naming off the natural numbers in order.
After naming each number you say, "That's not the largest possible
natural number", or "That's not how long I want to live."  This
statement seems to play the role of diagonalization.  The process I've
just described can be defined with a finite number of symbols (I just
did it).  Thus, in a way you can say I've just "named" the largest
natural number.

First question: Is this the same as Douglas Hoftstadter's supernatural
numbers (in his book Godel, Escher, Bach)?  It seems the only way to
really understand his book is to read it cover-to-cover (because of all
the acronyms and his defining ideas with stories, etc.).  I wish I
would have read it cover-to-cover when I was young and had lots of time
on my hands (and lots of spare brain cells).... or may I can just start
reading it cover-to-cover now and simply ask the fairy for more
(quality) time as I need it.

Second question:  When we switch over from natural numbers to "length
of life", it seems we need to specify "units of time" in order for the
specification of length of life to have any meaning.  This crosses us
over into the realm of meaning.  Length of life has no meaning apart
from an assignment of meaning or quality to the events that make up
life.  There seems to be some kind of diagonalization going on here (or
perhaps transcendence, independent from any diagonalization argument).
What good is MWI "immortality" (or any kind of "immortality") if the
infinite sum of (units of time) * (quality or meaning) adds up to some
finite number?  Is it really immortality? Life is more than existence.

Tom


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