http://www.idsia.ch/Files/idsia20/Register.html?
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
PS: Current jobs at IDSIA
(all hired persons will closely interact):
1 Postdoc and 1 PhD student in
biologically plausible reinforcement learning:
http://www.idsia.ch/~juergen/sinergia2008.html
1 Postdoc
mall universal Turing machines :-)
BTW, check out Marcus Hutter's older posting to
the Kolmogorov Complexity mailing list on whether
such machines should really count as UTMs or not:
http://mailman.ti-edu.ch/pipermail/kolmogorov/2007/000245.html
JS
http://www.idsia.ch/~juergen/computerunivers
dentifying possible mathematical
structures / universes / formally describable things.
I think some of the comments are serious enough to affect
the conclusions. Some come with quotes from papers in
http://www.idsia.ch/~juergen/computeruniverse.html
where several of your main issues are addressed
Dear colleagues,
many interesting talks
at the Zuse Symposium:
Is the universe a computer?
Berlin Nov 6-7, 2006
http://www.dtmb.de/Aktuelles/Aktionen/Informatikjahr-Zuse/
Best regards,
-JS
http://www.idsia.ch/~juergen/computeruniverse.html
the true prior from which
our universe is sampled - Schroedinger's wave
function may be an approximation thereof. But it
turns out that if the true prior is computable
at all, then we can in principle already predict
near-optimally, using the universal prior instead:
http://www.idsia.ch/~juergen/unilearn
I put everything talk slides on the web:
http://www.idsia.ch/~juergen/everythingtalk/
http://www.idsia.ch/~juergen/computeruniverse.html
And also a recent overview article:
The New AI: General & Sound & Relevant for Physics
J. Schmidhuber. TR IDSIA-04-03, arxiv:cs.AI/0302012
To app
several others)..."
Ed Clark has a nice review page on Wolfram's book:
http://www.math.usf.edu/~eclark/ANKOS_reviews.html
It includes Scott Aaronson's interesting review which also
addresses the issue of Bell's inequality.
Best,
Juergen http://www.idsia.ch/~ju
I welcome feedback on a little web page on Zuse's 1967 thesis
(which states that the universe is being computed on a cellular automaton):
http://www.idsia.ch/~juergen/digitalphysics.html
Juergen Schmidhuber
ellular automaton):
http://www.idsia.ch/~juergen/zuse.html
Bill Jefferys wrote:
>
> At 7:09 PM +0200 8/2/02, Juergen Schmidhuber wrote:
>
> >beta decay is not random but due to some fast pseudo-random
> >generator which we should try to discover.
>
> This last claim would appear to contradict some well-supported
>
following COLT paper may be old news to some
on this list.
--
The Speed Prior: a new simplicity measure yielding near-optimal
computable predictions (Juergen Schmidhuber, IDSIA)
In J. Kivinen and R. H. Sloan, eds,
s Konrad Zuse himself ("inventor of the
computer": http://www.idsia.ch/~juergen/zuse.html ) who was the first to
propose that the physical universe is running on a grid of simple
computers, each communicating with its neighbors: a cellular automaton.
He called this "Rechnender Raum,&
han P. Then predictions according to
P will be rather accurate.
For example, suppose the process computing the universe is not optimally
efficient for some reason. As long as the resource postulate holds the
true prior cannot dominate the Speed Prior, and S-based predictions
will be fine.
Juergen
Bill Jefferys wrote:
>
> At 10:59 AM +0200 4/3/02, Juergen Schmidhuber wrote:
> >The theory of inductive inference is Bayesian, of course.
> >But Bayes' rule by itself does not yield Occam's razor.
>
> "By itself?" No one said it did. Of course assum
become aware of this. It is essential to what they are
doing. And much more formal and concrete than Popper's
frequently cited but non-quantitative ideas on falsifiability.
Juergen Schmidhuberhttp://www.idsia.ch/~juergen/
results obtained."
Thus he informally invoked Occam's razor: find short descriptions that
explain a lot. Occam's razor is not the AP. It is formally treated by
the theory of inductive inference. Although this theory is at the heart
of what physicists are doing, some of them are not yet fully aware of
it.
Juergen(will be out of town for a while)
Bill Jefferys wrote:
>
> At 9:19 AM +0100 3/27/02, Juergen Schmidhuber wrote:
> >You are claiming the AP necessarily implies a specific fact about
> >nuclear energy levels? I greatly doubt that - can you give a proof?
>
> Yes, I can.
>
>
>http://adsabs.harvard.
arp loss bounds for the even more general
priors introduced in "Algorithmic Theories of Everything":
http://www.idsia.ch/~juergen/toesv2/
Similarly, if we replace M by the Speed Prior S - where S(x) is
small if x is hard to compute by any method - we obtain appropriate
loss boun
elves, letting the reader decide whether they are plausible or not.
Juergen
ite interesting, and others who do not share my
belief in the Speed Prior might do so too.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
Wei Dai wrote:
>
> On Thu, Nov 15, 2001 at 10:35:58AM +0100, Juergen Schmidhuber wrote:
> > > Why do you prefer the Speed Prior? Under the Speed Prior, oracle universes
> > > are not just very unlikely, they have probability 0, right? Suppose one
> > > day w
Wei Dai wrote:
>
> Thanks for clarifying the provability issue. I think I understand and
> agree with you.
>
> On Tue, Nov 13, 2001 at 12:05:22PM +0100, Juergen Schmidhuber wrote:
> > What about exploitation? Once you suspect you found the PRG you can use
> > i
Wei Dai wrote:
>
> On Wed, Oct 31, 2001 at 10:49:41AM +0100, Juergen Schmidhuber wrote:
> > Which are the logically possible universes? Tegmark mentioned a
> > somewhat
> > vaguely defined set of ``self-consistent mathematical structures,''
> > implying p
etc. So this universe features lots of unprovable
aspects.
But why should this lack of provability matter? Ignoring this universe
just implies loss of generality. Provability is not the issue.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
> > > From: Russell Standish <[EMAIL PROTECTED]>
> > > The only reason for not accepting the simplest thing is if it can be
> > > shown to be logically inconsistent. This far, you have shown no such
> > > thing, but rather demonstrated an enormous confusion between measure
> > > and probability di
Schmidhuber:
>>It's the simplest thing, given this use of mathematical
>>language we have agreed upon. But here the power of the
>>formal approach ends - unspeakable things remain unspoken.
Marchal:
>I disagree. I would even say that it is here that the serious formal
>approach begins. Take "un
> From: Juho Pennanen <[EMAIL PROTECTED]>
> So there may be no 'uniform probability distribution' on the set of all
> strings, but there is the natural probability measure, that is in many
> cases exactly as useful.
Sure, I agree, measures are useful; I'm using them all the time. But in
general t
and how to process it. It's the simplest thing, given this use
of mathematical language we have agreed upon. But here the power of the
formal approach ends - unspeakable things remain unspoken.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
not disjoint, this doesn't imply M(x) is unnormalisable.
> Now when you realise that every finite string x is a subset of the empty
> string, it becomes clear that M(x) is normalised to precisely 1.
The point is: prob dists and measures are different things. There is a
good reason f
M(x) = M(x0)+M(x1) = M(x00)+M(x01)+M(x10)+M(x11) =
Neglecting finite universes means loss of generality though.
Hence measures mu(x) in the ATOE paper do not neglect finite x:
mu(empty string)=1
mu(x) = P(x)+mu(x0)+mu(x1) (all nonnegative).
And here P is a probability distribution indeed!
P(x)>0 pos
not by
Chaitin in 1975)
3. Measure: E.g., each x of size n gets weight 2^-n
4. Semimeasure: E.g., mu^M(x) = probability of guessing a halting or
nonhalting monotone TM program whose output starts with x
Check out: Measures and Probability Distributions
Section 4 of "Algorithmic TOEs
But there is no uniform prior over all programs!
Just like there is no uniform prior over the integers.
To see this, just try to write one down.
BTW, it's not Solomon-Levy but Solomonoff-Levin. And
it has nothing to do with resource bounds!
Juergen Schmidhuber
http://www.idsia.ch/~ju
g computable in the limit) or maybe even for the extreme prior mu^G.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
> From [EMAIL PROTECTED] Thu Oct 11 17:36:41 2001
> From: Juho Pennanen <[EM
inductive
inference and Occam's razor, which is not just a wishy-washy philosophical
framework like Popper's.
Similarly, today's string physicists accept theories for their simplicity,
not their falsifiability. Just like nobody is able to test whether
gravity is the same on Sir
some of the resulting digits as the new seed, or
whatever. So it's verifiable - we just have to discover the PRG method.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
Bruno, there are so many misleading or unclear statements
in your post - I do not even know where to start. I'll insert a few
comments below.
> Subject: Re: Predictions & duplications
> From: Marchal <[EMAIL PROTECTED]>
> Juergen Schmidhuber wrote:
>
>
because true randomness is very hard to compute, and thus has very high
Kt complexity.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
Wei, of course you should not take it too seriously -
e.g., some of the Great Programmers
in the nested universes are quite dumb devices indeed :-)
Juergen
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
> From [EM
pseudorandom generators that run extremely
slowly but produce extremely convincing results such as the enumerable but
effectively random number Omega. The speed prior, however, suggests our
universe's pseudorandom generator is much faster than the Omega generator.
Juergen
http://www.idsia
10^30 in the ongoing century. More and more people, especially kids, are
in regular contact with virtual realities, and to them the new religion
may seem just like a natural extrapolation.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/toesv2/
http://www.idsia.ch
ny of them. Any real number computable in the limit
(such as Pi) has a finite nonhalting program; the set of all such programs
cannot have higher cardinality than the integers.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
> From: "Joel Dobrzelewski" <[EMAIL PROTECTED]>
> Subject: Re: Countable vs Continuous
> Date: Thu, 21 Jun 2001 08:41:13 -0400
>
> Juergen:
> > There is the rather harmless kind: the countable one. And some say
> > there is another kind, a strange one,
We cannot formally describe other probabilities, and therefore cannot
write reasonable papers about them. This apparently harmless restriction
is the very reason that any complex future (among all the possible
futures compatible with the anthropic principle) necessarily is unlikely.
Juergen Schmidh
ot agree, of course. Since you keep insisting on this, I suggest
you clearly write down all implicit assumptions and why exactly you
believe Bell's inequality is not compatible with pseudorandomness and
algorithmic TOEs.
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
O OO OO - if complexity is too high, then life doesn't
> OOO OOO OO evolve - and we don't see it.
According to the weak anthropic principle, the conditional probability
of finding ourselves in a universe compatible with our existence equals
1. But most futures compatible
> O O> ??? - There is no way of assigning equal
> OO O O O > nonvanishing probability to infinitely
> O O O O > many mathematical structures, each being
> O O O > represented by a finite set of axioms.
> OO O O O
> O okay - s
- most are maximally random and unpredictable. Any irregular
future, however, must have small measure, given the rather harmless
assumption of formal describability or computability in the limit.
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
e also that observers evolving within the universe may write
books about all kinds of unprovable things; they may also write down
inconsistent axioms; etc. All of this is computable though, since the
entire universe history is. So again, why should provability matter?
Juergen Schmidhuber
ural
measures of function complexity are used to show that the most efficient
program computing some function f is also among the shortest programs
provably computing f.
ftp://ftp.idsia.ch/pub/techrep/IDSIA-16-00.ps.gz
-----
que theorems?
Hal, here is an infinite chain of provable unique theorems:
1+1=2, 2+1=3, 3+1=4, 4+1=5, ...
Juergen
Hal, Chaitin just says "you cannot prove 20 pound theorems with 10 pound
axioms". But the infinite cascade of all provable theorems of number
theory collectively does not convey more information than the axioms.
> But what if you declare theorems which say the same thing to be the
> _same theorem
But this reference does not say what you say.
There is an infinite cascade of provable
theorems of, say, number theory.
> From Hal Ruhl <[EMAIL PROTECTED]> Wed Apr 11 05:02:30 2001:
> For the cite to Chaitin see "The Limits to Mathematics" page 17 note 1 at
> the bottom of the page.
Hal, you wrote:
> I believe that attempting an extensive detailed formal description of
> the Everything is the wrong approach. IMO - at least in this case - the
> more information used to describe, the smaller the thing described.
I was not able to follow this, but informal and vague descriptio
cient time most long histories involving him will
be fast ones.
Some consequences are discussed in
http://www.idsia.ch/~juergen/toesv2/node39.html
Juergen Schmidhuber
Bruno Marchal "explained" to Jesse Mazer:
> Schmidhuber's solution is based on a belongness relation between
> observer and universes which is impossible to keep once we take
> comp seriously. But even if we make sense to such a relation, it
> would only eliminates third person white rabbits and
niverse, but it ignores that multiple copies of me might exist in
> > > one universe. Let's consider a simple example. The prior probability
> > > of universe i (i>0) is denoted as P(i), and i copies of me exist in
> > > universe i. In this case, Juergen computes
ther it won't
because some of its output bits will flip back and forth forever:
http://rapa.idsia.ch/~juergen/toesv2/node9.html
But what do such undecidability results really mean? Are they relevant in
any way? They do not imply that I cannot write down finite descriptions
of the describable re
[EMAIL PROTECTED] to [EMAIL PROTECTED] :
> Certainly things that we can imagine even slightly, like real-valued
> observers, already have a kind of existence, in that they cause us
> to argue about them.
[EMAIL PROTECTED] to [EMAIL PROTECTED] :
> That's a bit like saying there is some truth to
ple example. The prior probability
> of universe i (i>0) is denoted as P(i), and i copies of me exist in
> universe i. In this case, Juergen computes the propability that if you
> pick a universe at random, sampled with the prior P, you pick universe
> i. This probability is, of cour
ual real" is not equivalent to
"generating all prefixes of all reals." "Generating an individual real"
means "generating all prefixes of that individual real, AND NOTHING
ELSE". Generating a real means you somehow have to be able to identify
and completely desc
r refinements, but the current debate has not explored
this space; it has focused on other things instead.
Juergen
This time I'll repeat only a fraction of the 500 lines in your reply:
>From [EMAIL PROTECTED]:
> Suppose you "survive" only through a simulation of
> the big bang at the level of the quantum superstring, membrane, etc.
> then the "correct level of substitution" is the level of the quantum
> s
>From Wei Dai, Thu, 15 Feb 2001 05:00:23:
<<<
Sentient beings can follow the same decision procedure used by the oracle.
Suppose you are faced with a bet involving a tossed coin. There is no need
to consider probabilistic questions like "what is the probability that the
coin landed heads?" which w
This time I'll annotate your entire message to demonstrate how many
things I tend to find unclear in your texts.
> From: Marchal <[EMAIL PROTECTED]>
> Juergen wrote (among things):
>
> >But how to answer an ill-posed question? You promise that "time and
>
> From [EMAIL PROTECTED] Wed Feb 14 23:34:18 2001
> [EMAIL PROTECTED]:
> > Yes. My point is: as long as we are not forced by evidence, why
> > assume the existence of something we cannot describe or analyze in
> > principle?
>
> In the spirit of this list, shouldn't we assume the existence (insof
> [EMAIL PROTECTED]:
>
> But stuff indescribable by us ought to be constructible by observers
> with real-valued input, output and memory living in real-valued
> worlds. They might communicate identities of arbitrary real numbers
> as naturally as we refer to a points on a line, and execute anal
universe, where x^k represents the state of the
universe at discrete time step k, and x^1 the "Big Bang" (compare
http://www.idsia.ch/~juergen/everything/node1.html ). Suppose there is
a finite algorithm A that computes x^{k+1} (k \geq 1) from x^{k} and
additional information noise^k (t
omething, namely,
I can exclude almost all infinite futures (those without finite
descriptions) with probability one. And among those I cannot exclude,
the weird ones with very long minimal descriptions are very unlikely.
Maybe you now say you don't buy the describability assumption. Then the
theory can't say nothing nontrivial no more. Neither can you though.
Juergen
tion that can't be
> simulated on a Turing machine.
Much of http://rapa.idsia.ch/~juergen/toesv2/ is about
things uncomputable on traditional Turing machines. That's why
we need to introduce General Turing Machines or GTMs:
http://rapa.idsia.ch/~juergen/toesv2/node6.html
> Som
reasonable anyway, by definition.
So we shouldn't give it up unless evidence forces us.
Juergen
> From Russell Standish Thu Feb 8 23:52:51 2001
> Guys,
> I'm getting great enjoyment out of the titanic battle between
> Juergen and Bruno over the meaning of the UD. I'm learning a lot from
Battle? The case is clear.
You cannot battle over whether 2+2 equals 4
Your vague answers to questions I did not ask keep evading the issue of
continuum vs computability in the limit. I give up. JS
ories of
> >Everything": http://www.idsia.ch/~juergen/toesv2/node23.html
>
> A program which generates all the reals is shorter than a program which
> generates Pi, which is itself shorter than a program which generates
> a particular real (for most "particular" reals).
tempted to call this wishful thinking.
Juergen
speed prior for some strings. So a similar question is, how do you
>pick which classic TM to base S on?
Good point. Simulating a k-tape TM on a 1-tape TM may cause a quadratic
slowdown indeed. Simulating a k-tape TM on a 2-tape TM, however, causes
at most logarithmic slowdown. One should use a TM with several work tapes.
Juergen
>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
e. But Occam's razor also motivates
us to consider just the computable universes as opposed to those based on,
say, non-computable real numbers. The ensemble of computable universes is
both compatible with known data AND simple. The ensemble of non-computable
universes is not!
Cheers,
Juergen
the previous step. Therefore you need
more than countable time to compute all reals.
> Now, could you give me a bitstring which is not generated
> by this countably infinite process ?
Sure. The output of the program "While TRUE print 1" won't
be computed in countable time by your procedure.
Juergen
ates things, so much that we cannot even talk about
it in a formal way.
Juergen Schmidhuber www.idsia.ch
?
Shaved by Occam's razor.
Juergen
____
Juergen Schmidhuber www.idsia.ch
gument has some problems, but it is appealing and
> if the holes can be filled it seems to offer an answer to the question.
> What do you think?
Where exactly are the holes?
Juergen
ire universe, except in that there's nothing
> stopping temporary minor abberations such as a flying rabbit.
To repeat, given the universal Solomonoff-Levin distribution U, the simple
universes (those with short algorithms) are much more likely. That's
why flying rabbits are so improbable.
Juergen
etc.
Now we have a formally defined, conditional probability distribution
on all universes satisfying S. I thought this to be clear, but maybe
I should have written it down explicitly.
Juergen
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