Hi Günther,
>
> Hi Bruno,
>
> thanks for your interesting answer, I have some questions though.
>
>> course, as I said, this will depend of what you mean by "you". In
>> case
>> you accept the idea of surviving with amnesia, you can even get to a
>> state where you "know" you are immortal, because your immortality
>> is a
>> "past event".
>
>
> I would equate total amnesia with death (we've been through this
> before,
> Stathis has written about this, if I remember correctly).
I remember Quentin identifying himself with his memory, and very
logically, identifying total amnesia with death.
It is a complex matter. Total amnesia concern only some form of
declarative knowledge, you cannot loss your "procedural memory",
because it is part of ... arithmetic, and common to all elementary
knowers.
>
>
> I agree with you that you can't have a universal machine stopping
> relatively to all others from it's POV; but I don't see why we can't
> think of it having total amnesia. So, for the time being, let us take
> surviving as meaning to keep (at least large parts) of one's memory.
All right. Comp leads also to that form of immortality, at least for
awhile (if I can say).
The problem of death is intrinsically difficult, because you will
survive with amnesia or not according of the level of substitution,
which we cannot know, but only bet on (or perhaps even choose in some
circumstances?). Total amnesia seems to lead to the remembering of you
being the universal person, plausibly Plotinus "Soul-Universe", or the
arithmetical S4Grz (the third hypostase).
Total amnesia is complete fusing. We "remember" we are all the same
person. We can lost that memory only by differentiating oneself again.
>
>
>> facts, like the continuum of many-worlds. If Loop Gravity is 100%
>> correct, and if the big bang has a finitely describable origin then
>> comp is false!
>
> Could you elaborate? I don't see why LG should be bad news for comp?
> You mean because LG proposes a fundamental spacetime quantization?
> I don't see how it would falsify comp?
It is obviously an open problem. But taking literally the UDA, and
making abstraction of some still possible (logically) conspiration of
the numbers, it seems clear that comp predict that an electron, for
going from A to B, with respect to you, will be supported by a
continuum of computational histories. I have no clue how to select a
finite or countable infinity of subcomputations. But if that is the
case, the UDA shows that such a conclusion (like LG) has to be derived
from arithmetic. Otherwise, it would be treachery.
>
>
> And why the finitely describable Big Bang? It seems you have a problem
> when there are some finite limits (outside of the effective
> computation
> of mind). Is this because you need the continuum in the AUDA to get
> Quantum logic or something like that?
Not at all. That would be treachery too. If the continuum was not
possibly emerging from AUDA, I would take this as an evidence that
comp is false. The reason comes really from computer science and the
(enumerable) redundancy of the computational states, and the non
enumerable redundancy of the "1-pov" infinite stories.
>
>
>> Our bodies can be considered programmed to stop (by sex and death),
>> our soul just cannot, there is always a consistent continuation (even
>> without amnesia
>
> Why do you believe that latter?
Consider someone who dies, relatively to you. Well, La Palisse was
found of "tautology": after he died, someone said" 5 minutes avant sa
mort, Monsieur de La Paice vivait encore". "Fives minutes before he
died, Sir de La Palice was still alive". Now, from the point of view
of the dying person, the UD generates 2^aleph_zero histories going
through that state "where he is is still alive", and which are below
its computational relevant substitution level. Even with just QM, you
can see stories which will "repair anything wrong with whatever needed
to generate a short consistent computation. At his substitution level
he is finite, and finite machine can always be fixed, and that is all
the soul need to survive an instant. But this is true for all
instants, by exactly the repetition of the argument. Perhaps some Gods
can be mortal, but no souls, as supported by finite entities. That
would be like my mechanics: "no, you car is definitely broken". It is
a lie, or a simplification, what it means is "it would be more
expensive to fix it than to buy a new one". In the ud, the first
person has unbound-able resources.
I think, and Quentin disagrees, that, would I be dying, I would feel
myself surviving more probably in the "amnesic stories", probably
because I tend to believe (those days) that, if comp is true, my
substitution level could probably be rather high. So I would survive
in those "normal world" with a "lesser brain". But if Quentin is right
and all my memory are necessary for being me, I will survive in those
consistent dreams where my brain has been repaired by friendly white
rabbits.
Suggest me your substitution level (you could bet on) and specify me
the corresponding most probable universal implementation, and from
this I can "program" a generator of consistent extensions.
This could seem far stretched, but recall that the universal
dovetailing is far stretched itself. And from inside we see only the
projection of it, but of it all.
Now in auda, it is even more simple than in uda, because the soul is
defined by the knower, which modality is defined in arithmetic by the
proposition explicitly provable *and* true. Bp & p. So Bp -> p, and Bp
-> Dp (exercice), so we have Dt, and DDt, DDDt, ... in all worlds/
states. Somehow the soul is immortal quasi by definition. It is the
root of the never ending self-extension. The builder of time and
space, not yet matter, because it is logically before observation,
comprehension, and reflexion. matter arrives when Dp is added (p
Sigma_1).
>
>
>> In arithmetic there are even histories where each time your
>> "brain" dysfunction some alien white rabbits give you a new suitable
>> brain, update it with suitable subroutines, and let you continue your
>
> What continuations are possible in arithmetic? I would like to warn
> against the approach of taking conceivability/ "humand mind" logical
> possibility as a criterion (as you seem to suggest with saying that
> "the
> transporter failed" is a consistent extension). The criterion for
> continuation must be arithmetic possibility,
In uda, the accessible, by the UD, states, and their points of view
on their statistics, bearing on the conputations going through them.
In auda, this will depend from the eigth hyspostases. But it is always
an interplay of provability, consistency, and truth (Bp, Dp, and p).
> and here, I don't see any
> formal or even informal way to get to "worlds" in the
> anthropocentric sense.
It is the place where indeed many can confuse the map and the
territory, or accuse me of doing so. The key advantage of comp, is
that when you say yes to the doctor, you do indeed identify your self
with a local relative map of you. Then, in uda we reason informally,
hopefully rigorously, in term of intuitive description of
computational histories. In auda, we do it formally, by interviewing
an ideally correct universal self-referring machine with elementary
betting abilities, and a world is just a consistent extensions, but
the geometry of the relation between worlds if dependent from the
chosen point of view. Auda gives 8 (16, 32, ...) very different view
of the same arithmetic. Only one of them gives physics, another gives
physical sensibility, etc.
>
>
>> opportunity to go through the UDA (seventh step) again with Kim. I
>> suggest you polish your argument against comp-immortality until then,
>> perhaps.
>
> Will do :-) But I think beforehand we should clear up any mutual
> misunderstandings; you have obviously been thinking about these things
> for a long time, and you have made connections/inferences which may
> not
> be as obvious as you think.
>
> BTW: thanks for your modal logic post (the Dt explanation), here again
> the above mentioned issue crops up: while the modal logic may be
> elemental, your interpretation of them is certainly not.
By Solovay theorem, G and G* gives the "intelligible world" of the
machine. Or its propositional skeleton. The interpretation are
mathematical structures, and I am interested in what the machine
proves, and bet, about them. The interpretations somehow are the
consistent extensions themselves (I use in the background the
COMPLeteness (not INCOMPLeteness) theorem of Gödel, and a more recent
theorem by Orey which shows that Loebianne machine prove the
completeness theorem.
The comp hyp is the link between you and machine, and Solovay theorem
is the link between machine and the logic G and G*.
As far as we are self-referentially correct, Solovay theorem applies
to us. If you bet on your correct level of substitution you are self-
referentially correct, for example.
The completeness theorem say that a theory is consistent (does not
prove the false, = Dt) if and only if the theory has a model. That is
there is a mathematical world which satisfies (in a mathematical
sense) the theory. So Dt is really "I believe in a reality, or in a
world, state, etc."
>
>
> Often it is the interpretation that does all the work (consider for
> instance Einstein's SR: the mathematics was there before, he "just"
> suggested a new interpretation by adding postulates (Principle of
> Relativity for electrodynamics, c as constant speed of light)).
>
> These interpretation issues are often played down, but they are in
> fact
> essential.
Take quantum mechanics, like Everett and Dewitt, I don't believe in
human interpretations, I believe in the interpretation, or the
corresponding discourses, made by the "relatively statistically
relevant" entities described by the theory.
With comp, you have to proceed in that way, too. You can do it
mathematically with respect to the correct level of self-description.
What is impossible in practice, is to guaranty any precise chosen
level, you have to bet, pray, ... on something. This I never hide.
Like consistency, the truth of comp guaranties the consistency of the
falsity of comp. It is really a "theology", but a mathematical one.
It is even possible that the level is a matter of personal
convenience. You could fuse by amnesia, and then come back in this or
that reality to finish this or that job, like if you could chose
between Mitra's backtracking and Anciaux's wish to keep its books,
CDs, hard and wet disk full of all its memories.
Dying? The Loebian machine is confronted to a gigantic arithmetical
Bardo Thodol, yet with infinitely many shortcuts. The arithmetical and
analytical hierarchies provide good approximation, for the correct
Lobian machine. The full first person of the lobian machine is not a
machine, its vastly more deep, powerful ... unnameable also (like the
knower is already not definable by the machine).
It is new, and relates three non obvious fields, don't worry. I'm
sorry I can't help more quickly. Logic is the most subtle branch of
math, and is not well taught, when it is. Hope this helped a bit. I
will go through this very slowly with Kim, so in the worst case, just
be patient, but don't hesitate to ask questions. If you study logic
(the Mendelson book, or Boolos, or Smoryinski) don't hesitate to ask
question.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Sun Mar 15 2009 - 17:06:15 PDT