Juergen Schmidhuber, [EMAIL PROTECTED], writes:
> All formal proofs of number theory are computable from the axioms
> describable by a few bits. So what about Goedel's theorem? We cannot
> derive it from the axioms. But what does that mean? It just means we
> can add it as an axiom. It just means
>Or you mean "the Goedelian sentence", i.e. the statement
>constructed from the formal system saying that it will not be proved
>in the system, in which case you are correct.
I do mean "the Goedelian sentence". Sorry!
Juergen
Juergen Schmidhuber writes:
> Hal:
>
> >Approximate probabilities based on approximations to the
> >K. complexity of a string are no more computable than precise ones.
> >There is no fixed bound B which allows you to compute the K. complexity
> >of an arbitrary string within accuracy B.
>
> Yo
> Step n owns 2^(n-1) initial segments.
Bruno, why are we discussing this? Sure, in finite time you can compute
all initial segments of size n. In countable time you can compute one
real, or a countable number of reals. But each of your steps needs more
than twice the time required by the previ
Jacques M. Mallah wrote:
>On 2 Mar -1, Marchal wrote:
>> Take the self-duplication experiment as a simple illustration, where
>> after having been read I am reconstitued at two different places.
>> Nobody (not even God) can compute where I will find myself after the
>> duplication.
>
>
[EMAIL PROTECTED] (Juergen Schmidhuber) writes:
>
> Hal:
>
> >What about the fact, which I mentioned earlier, that probabilities are
> >based on Kolmogorov complexity, but that is uncomputable, or at least
> >it would require a super-TM to compute it. However we do observe
> >probabilities and th
Bruno wrote:
>Juergen Schmidhuber:
>> Even the set of all real #'s is not formally describable.
You cannot
>> write a program that lists all reals. In infinite but
countable time
>> you can write down a particular computable real,
Bruno wrote:
>Juergen Schmidhuber:
>> Even the set of all real #'s is not formally describable.
You cannot
>> write a program that lists all reals. In infinite but
countable time
>> you can write down a particular c
Juergen writes:
> UTM theory is falsifiable. It makes many predictions. One of them is
> that nobody will ever construct a Super-Turing machine based on QM.
What about the fact, which I mentioned earlier, that probabilities are
based on Kolmogorov complexity, but that is uncomputable, or at least
>>> Why assume non-computable stuff without compelling reason?
>>> Shaved by Occam's razor.
>
>Jacques:
>
>>On the contrary. Why assume the lack of *any* given type of
>>mathematical stucture? A true everything-hypothesis surely would not.
>>Occam's razor says: don't add extra distinctions such
>> Why assume non-computable stuff without compelling reason?
>> Shaved by Occam's razor.
Jacques:
>On the contrary. Why assume the lack of *any* given type of
>mathematical stucture? A true everything-hypothesis surely would not.
>Occam's razor says: don't add extra distinctions such as a res
On Tue, 26 Oct 1999, Juergen Schmidhuber wrote:
> Jacques Mallah wrote:
> > A continuous structure is a perfectly good
> > mathematical structure, but no Turing based scheme can include it.
>
> Why assume non-computable stuff without compelling reason?
> Shaved by Occam's razor.
On
Jacques Mallah wrote:
> I agree with
> Alistair Malcolm that Turing machines are not enough
> A continuous structure is a perfectly good
> mathematical structure, but no Turing based scheme can include it.
Why assume non-computable stuff without compelling reason?
Shaved by Occam'
Juergen Schmidhuber wrote:
> In absence of
>evidence to the contrary we assume that the presence of your consciousness
>(whatever that may be) is detectable by a computable process, namely, the
>one employed by you, the observer, who decides that he exists, via some
>sort of computation taking
Hal finney wrote:
>There are other ways to formalize computing: stack machines, register
>machines, cellular automata, even idealized billiard balls bouncing
>around in a giant pinball machine. Each one agrees with the others on
>computational complexity, but again only up to a "scale factor" wh
Bruno:
> Honestly it is still not clear. How could ever "S(U)=TRUE" be computable ?
> As a computer scientist I guess you know that even the apparently simple
> question "does that piece of code computes the factorial function" is not
> computable.
Sure, it's not even decidable in general whethe
In a message dated 99-10-21 11:53:14 EDT, James Higgo writes:
> Yes but the everything universe has the shortest algorithm, containing just
> one bit of information. The sub-universes do not need algorithms, just the
> WAP.
and Juergen Scmidhuber replies
> Ah! The point is: the information
[I sent this privately by accident]
James Higgo writes:
> What that postulates is that everything exists, and that means you exist and
> I exist in an infinity of all possible variations. I'm perfectly comfortable
> with this, as I am an MWI-er.
> In this view, the only reason you ever get a phy
Why can't the simplest possible program be taken as computing a universe
which includes us? We tend to say "it computes all universes" as though
it computes more than one. Then it is fair to object that the program
is too simple, because it computes more than one universe.
But this is a semanti
> It seems we're losing track of the original objection, which is to say that:
> 1. everything exists (all relationships are equally valid, all worlds
> exists, you can string 'snapshots in time' together any way you wish - with
> a glass unsmashing or whatever - and all are equally likeley, as al
Bruno wrote:
> I don't take the notion of observer for granted.
Neither do I, of course. The observer O is something computable that
evolves in some universe U.
> The problem is that "to be in a universe" has no clear meaning
But it does. There is a computable predicate S such that S(U)=TRUE
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