Juergen wrote:
>One should be careful here. Discussions of sets of noncomputable numbers
>and proofs of certain theorems concerning their properties are computable.
>Such computable aspects of R, however, should not distract from the
>fundamental difference between N and R. Most of what's in R is completely
>beyond computation.
>
>Note that all your initial segments of reals simultaneously are initial
>segments of some of the few computable reals (e.g., fractions).
I'm afraid I don't follow you here. By dovetailing on all initial
segments, it seems clear to me that I am dovetailing on all finite parts
of ALL the reals.
> There are
>countable computable reals but uncountable others. Hence most reals
>are beyond dovetailing. From an information-oriented perspective, reals
>tend to complicate things. Most reals don't fit the Great Programmer
>religion, which is a simple one.
Remember that for some intuitionist (including Brouwer) the reals are
more simple than the naturals, and the continuum is considered more
primitive than the discrete. This feature is somehow reflected by the
classical theorem (by Tarski) which say that there is a complete
first-order theory of the reals. And of course (by Goedel) there is no
complete theory for the natural numbers (for exemple "Fermat theorem" is
trivial if the scope of the quantifiers is R, and very complex if the
scope is N).
But I admit this is besides the point, because we are speaking about the
elements, not the mathematical structure. Nevertheless, with infinite
dovetailing (which is what the great programmer does), all reals are
generated. The set of reals is indeed uncountable, but the set of all
finite initial segments of ALL the reals is countable. No more is used in
the proof, thanks to the PE-omega thought experiment.
>>The =
>> observer cannot be localized in a unique computation. He can only be =
>> associate with an infinity of "sufficiently similar" computations =
>
>Why? It all can happen in a particular computable world - no obvious
>need to sum over "an infinity of sufficiently similar" computations."
>Vague concepts such as "sufficiently similar" complicate things: making
>them precise requires additional bits of information.
The need to sum over "an infinity of sufficiently similar" computations
is precily provided by the PE-omega thought experiment (the UD argument
in my thesis).
>This reminds me of my brother (a theoretical physicist) who also used to
>insist on summing over all computations. I guess it's the way physicists
>get trained.
Thanks for telling me I am not the only crazy one ! (BTW I am not a
physicist, but a mathematician with biological, chemical, physical and
philosophical motivations).
>> It is necessary to concentrate ourself on the following thought =
>> experiments (PE, PE1, PE2, PE3, PE4, PE-omega).
>
>I guess I have to admit you lost me here. You mention abstract high-level
>concepts such as teletransport experiments, reconstitution, time-delays,
>expectations, undeterminism, average robots. True, some of the Great
>Programmer's universes may be interpretable (by appropriate computable
>interpreters) as being inhabited by people who write messages about such
>things. But I was not quite able to see how this affects the contents of
>my little paper, whose main objective is to keep things simple, probably
>because I am just a simple mind myself.
I don't believe my work affects the main part of your paper, it only
affects your conclusion : where you see an end I see a beginning (even
one of the most promising beginning we could ever have hoped for solving
the mind-body problem, including the problem of the origin of our belief
in universe(s)).
Don't feel sorry for not following my PE-omega thought experience. I'm
used to that. Most of those, who have (apparently) understand it, have
follow lenghty oral speech I've make, whith a lot of drawings, etc. It is
unfortunate that it is still difficult to include automatically drawings
in email !
I really intend putting more information in my URL, but I have some
problem managing time.
Now, if you agree, perhaps we can work the argument step by step.
I am sure you agree with the first PE experiment, i.e. the use of
(classical) teletransport. This follows from your paper. Indeed, you
agree that in some futur we could survive with an artificial brain. I
guess you agree that such a survival doesn't depend where and when the
artificial brain is build. So such survival experience is always a kind
of teletransport.
To sum up : I ask you if you agree with step one which just say :
STEP1: COMP entails WE CAN SURVIVE WITH AN ARTIFICIAL DIGITAL BRAIN
Obviously I use a minimal amount of "folk psychology", without which a
term like "survive" has no meaning. I just hope you belief implicitely in
step0, which is for exemple WE CAN SURVIVE READING THIS POST. If you did
survive the reading of this post, then you understand what I mean by
surviving, and you understand what I mean by minimal amount of folk
psychology.
Of course, it would be nice if any everythinger, who disagree at some
step, tell me where and why.
Bruno
Received on Tue Mar 09 1999 - 03:47:57 PST
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