Hi Jacques,
Thank you for your commentary on my (old) UDA
argument. I must say you have a curious style for asking me
to refresh the key definitions.
You should not excite so much my teacher professional
deformation :)
The tricky term is the term "survive". The point is that we don't
need a definition of it in UDA although it helps using grandma
definition for the first few steps. No doubt at later steps
grandma is more and more astonished living the gap between
what she feels to be herself (1-person) and her doubles (3-person).
But ok, the 1-person and the 3-person is what you ask me
definitions of.
If you read my posts you will see that I have given more than
one definition of the 1-person. The simple one is enough for
both Everett's justification of the appearance of probability with
pure QM (SE + comp) and enough for my (ok, sorry) justification of the
appearance of probability in "pure comp" (through the grandma UDA.
You can say I borrow it from Everett if you want.
[BTW thanks for your "grandma" expression I love it. I recall for the
others that in the cognitive/mind science the grandmother or folk
psychology is what you need for following a Mickey comics (american
definition) or a "Tintin and Milou" (Belgium definition).
Grandma psychology accept explanation like "John postponed the
operation because he was afraid by anesthesia", etc. In the second
part of my thesis I substitute grandma for an arithmetical
grandma driven by the Godel Lob modal logic G and G*. It makes
possible the translation of UDA in arithmetic through Kleene's
arithmetical Metamathematics. I say a little more below].
1-person (simple definition working for UDA and Everett):
I suppose an observer has a memory. A way to record result of
experiment. Let us symbolize it by a diary
(but the observer's brain works aswell).
In the frame of duplication experiments (resp. the quantum
superposition). The 1-person discourse is defined by the content
of the diary *<which is supposed to accompany the candidate of
the duplication>*, i. e. the diary is duplicated too.
And then the 3-person discourse is defined to be the content
of the diary of an external observer of the duplication experiment.
He is just an observer NOT entering the duplication
machine, but still trying to describe the experiment.
(In QM the 3-person is given by the SE).
Illustrations:
Look at the following experiences.
There are two rooms quite identical except that one has a zero
painted on the wall, and the other has a one painted on the wall.
In the experience A I duplicate the candidate, that is I *cut* him
and *paste* him, with his diary, in both rooms. I ask the candidate
to write in his diary the number painted on the wall in front of him).
I repeat that experience 64 times, staying outside of the
duplication machine (I play the role of the scientist here, accepting
only 3-descriptions).
Now here is my 3-description of the 1-discourses: About 18 thousand
billions of billions of diaries, in most of which, by simple arithmetic
it is just incompressible noise. A typical diary content is not unlike
1100100100001111110110101010001000100001011010001100001000110100
(except this one is compressible! Do you recognize or guess?).
In experience B I have a Stern Gerlach Device and I send silver
atom. You are asleep (with you diary in your pocket).
We use like above two rooms with 1 and 0 painted on the wall.
If the atom goes up I put you in the first room, then wait you wake
up and you are here also supposed to write the number on the wall
in your diary. I repeat the experience 64 times.
The 3-description, i.e. SE gives a superposition of about 18 thousand
billions of billions of diaries.
But here SE entails the observer duplicate too, and SE applied to me
and the candidate gives, for a typical observer a typical diary content:
noise.
In QM the observer cannot stay outside the duplication machine, but the
UDA shows that it is the same with comp, we cannot stay outside the
universal dovetailing, and that is why 3-person sharable discourse
comes first from 1-person *plural* sharing histories. (But I anticipate
perhaps too much ... on my preceding post!).
Although the definition of the 1-3 difference presented here is enough
for the UDA (the main and key point being that the diaries does not
contains comments on *delays* of reconstitution so that the search of the
measure must be done on the whole UD* (the whole platonistic work of the
UD), I cannot resist giving more elaborate definition useful for the
understanding of the ultimate description of the 1-person in arithmetical
term.
A nice one, using more deeply grandma psychology though, is based on the
following fact: I cannot prove to you that I am conscious. Or, if you
prefer, if you decide to believe I am a zombie, there is no way for me
(if comp is true) to refute your assertion.
Still I bet most people like you and me are NOT zombie.
Now the first person is everything you know about you but that you
cannot prove to others, and which makes yourself NOT being a zombie.
I let you the exercice of showing that this definition is stronger than
the simple one.
Hoping that can help you.
The last definition (in my thesis) of the 1-person is the one given by
Thaetetus in Plato. It is the knower. I say a honest machine
communicates p, if the
machine gives me a proof of p. And I say, with Thaetetus that the
machine knows p, if it communicates p and p is true.
Unfortunately "p is true" cannot be translated in the language of the
machine (by Tarski theorem). But then I use a trick (found independently
by Boolos, Goldblatt, and Kusnestsov and Muravitskii) which leads to
identify somehow the 1-person with sort of intuitionist Brouwerian
creative subject. Here we got a theory of antisymmetrical time.
But that subject collapses into just propositional logic in UD*,
but then the miracle is that a minimal weakening of Thaethetus trick
makes possible to marry the antisymmetrical knower with its
quasi completely symmetrical surroundings in UD*.
Well this need G and G* ... (see "modalities" in the archive).
Hoping that can open your appetite :)
And the term "survive"? Forget it if you don't like it.
A computationalist is just someone saying "yes" to its surgeon
for an artificial digital brain/body/"universe" transplant,
He/She or the doctor he/she trusts (unfortunately perhaps), is
*betting* on a level of functional substitution relatively
to the more probable consistent extensions.
The real question is not the question of comp being true or
false, but the (relative) measure on the possible diaries content.
To sum up the main point, the absence of account of the UD delays
in the first person (classical memories of UTM's diaries) forces
us to search the measure on the computational continuations
on the *whole* UD*.
The key of the translation of the UDA in arithmetic is that the
nuance between the person point of views is literaly forced on us
by the necessary nuance between provability, truth, and
consistency forced by the incompleteness phenomenon on the self
referentially correct machine.
Adding consistency to provability throughout UD* gives rise to
(arithmetical) sort of quantum probabilities (to describe the
mathematical content of my thesis in a nutshell).
Bruno
http://iridia.ulb.ac.be/~marchal
Received on Fri Sep 07 2001 - 06:53:54 PDT