I comment again a relatively old post by Juergen Schmidhuber.
>Juergen: The thing is: when you generate them all, and assume that all are
>equally likely, in the sense that all beginnings of all strings are
>uniformly distributed, then you cannot explain why the regular universes
>keep being re
Juergen Schmidhuber wrote:
>
> > > > 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 be
> > > 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 wrote:
>Why care for the subset of provable sentences?
>Aren't we interested in the full set of all describable sentences?
We are interested in the true sentences. The provable one and the
unprovable one.
>We can generate it, without caring for proofs at all.
If you mean genera
Juergen Schmidhuber wrote:
> > 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
> > a
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
Juergen Schmidhuber wrote
> Russell Standish wrote:
>> I never subscribed to computationalism at any time,
>> but at this stage do not reject it. I could conceive of us living in
>> a stupendous virtual reality system, which is in effect what your GP
>> religion Mark II is. However, as pointed o
[EMAIL PROTECTED] wrote:
>
> > From: Russell Standish <[EMAIL PROTECTED]>
> > To: [EMAIL PROTECTED]
> >
> > I think we got into this mess debating whether an infinite set could
> > support a uniform measure. I believe I have demonstrated this.
> > I've yet to see anything that disabuses me of t
juergen wrote:
> Russell, at the risk of beating a dead horse: a uniform measure is _not_ a
> uniform probability distribution. Why were measures invented in the first
> place? To deal with infinite sets. You cannot have a uniform probability
> distribution on infinitely many things.
The la
> From: Russell Standish <[EMAIL PROTECTED]>
> To: [EMAIL PROTECTED]
>
> I think we got into this mess debating whether an infinite set could
> support a uniform measure. I believe I have demonstrated this.
> I've yet to see anything that disabuses me of the notion that a
> probability distribtu
> From: [EMAIL PROTECTED]:
> [EMAIL PROTECTED] wrote:
> > > From [EMAIL PROTECTED]:
> > > [EMAIL PROTECTED] wrote:
> > > > M measure:
> > > > M(empty string)=1
> > > > M(x) = M(x0)+M(x1) nonnegative for all finite x.
> > >
> > > This sounds more like a probability distribution than a measure. In
[EMAIL PROTECTED] wrote:
>
>
>
> > From [EMAIL PROTECTED]:
> > [EMAIL PROTECTED] wrote:
> > > M measure:
> > > M(empty string)=1
> > > M(x) = M(x0)+M(x1) nonnegative for all finite x.
> >
> > This sounds more like a probability distribution than a measure. In
> > the set of all descriptions, w
> From [EMAIL PROTECTED]:
> [EMAIL PROTECTED] wrote:
> > M measure:
> > M(empty string)=1
> > M(x) = M(x0)+M(x1) nonnegative for all finite x.
>
> This sounds more like a probability distribution than a measure. In
> the set of all descriptions, we only consider infinite length
> bitstrings. Fi
Juergen wrote (on 12th Oct):
> . . . In most possible futures your computer will
> vanish within the next second. But it does not. This indicates that our
> future is _not_ sampled from a uniform prior.
I don't wish to comment directly on the computer-vanishing problem as it
applies to Juergen's
John Mikes wrote:
>Bruno, I appreciate your choice of incompressibility - as far as
>mathematical views are concerned.
And you know that with comp a case is made there is nothing
outside mathematics (even outside arithmetics) so that's ok for me.
But you know also that the determinist self-dup
Yes, in a different context, random could be applied to deterministic
chaos, however in the context of our discussion, we're not talking
about that.
Cheers
jamikes wrote:
>
> Bruno, I appreciate your choice of incompressibility - as far as
> mathe
Bruno, I appreciate your choice of incompressibility - as far as
mathematical views are concerned. How about a "random" choice of a color
from a hundred others? can this be algorithmic and incomressible?
Or a choice "at random" from available several routes, how to defend an
innocent accused in co
[EMAIL PROTECTED] wrote:
>
>
> Confusion about what's a measure?
> What's a distribution?
> Simple but important!
> For bitstrings x:
>
> M measure:
> M(empty string)=1
> M(x) = M(x0)+M(x1) nonnegative for all finite x.
This sounds more like a probability distribution than a measure. In
the
Confusion about what's a measure?
What's a distribution?
Simple but important!
For bitstrings x:
M measure:
M(empty string)=1
M(x) = M(x0)+M(x1) nonnegative for all finite x.
P probability distribution:
Sum_x P(x) = 1; P(x) nonnegative
---
M semimeasure - replace "=" by ">=":
M(x) >= M(x0)
Juergen Schmidhuber wrote:
>Bruno, there are so many misleading or unclear statements
>in your post - I do not even know where to start.
Rhetorical tricks, if not insult as usual :(
Have you read http://www.escribe.com/science/theory/m3241.html
Well, G* tells me to remain mute here, but the
Hal - that is not a uniform measure!
[EMAIL PROTECTED] wrote:
>
> Juergen Schmidhuber writes:
> > 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.
>
> I think there is. Given a program of le
Hal Finney wrote:
> Juergen Schmidhuber writes:
> > 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.
>
> I think there is. Given a program of length l, the prior probability
> is 2^(-l). (Tha
Saibal wrote:
> Hal Finney wrote:
> > Juergen Schmidhuber writes:
> > > 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.
> >
> > I think there is. Given a program of length l, the prior pro
"According to whim or taste" implies a conscious entity performing
choices according to a free will. This need not be the case. In my
mind, random means selected without cause (or without
procedure/algorithm)."
Russell picked my example from a language which has no equivalent to the
word "random"
Juergen Schmidhuber writes:
> 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.
I think there is. Given a program of length l, the prior probability
is 2^(-l). (That is 2 to the power of negative
Hal Finney wrote:
>Isn't this fixed by saying that the uniform measure is not over all
>universe histories, as you have it above, but over all programs that
>generate universes? Now we have the advantage that short programs
>generate more regular universes than long ones, and the WAP grows teeth
Saibal Mitra wrote:
>John Mikes wrote:
>`` If you say: a sequence defying all
>rules, then it is not random, it is calculable. You have to consider all
>rules and cut them out.´´
>
>If you try to do that then you encounter the famous halting problem.
Exactly. So why not defined random by inc
Juergen writes
> 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.
This is of course true (if uniform measure is a
measure that gives the same, non-zero, probability
for each program. I got no idea
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/~juergen/
ht
nd others, too) would agree .
> Till then I wish you luck to use the word - at random.
>
> Best wishes
> John Mikes
> - Original Message -
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: <[EMAIL PROTECTED]>
> Cc: <[EMAIL PROTECTED]>; <
John Mikes wrote:
`` If you say: a sequence defying all
rules, then it is not random, it is calculable. You have to consider all
rules and cut them out.´´
If you try to do that then you encounter the famous halting problem.
Saibal
t;
Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Sunday, October 14, 2001 4:36 AM
Subject: Re: Predictions & duplications
>>>>>>>SNIP<<<<<<<<<
> That is almost the correct solution, Hal. If we ask what an observer
>
That is almost the correct solution, Hal. If we ask what an observer
will make of a random description chosen at random, then you get
regular universes with probability exponentially related to the
inferred complexity. It is far clearer to see what happen when the
observer is a UTM, forcibly termi
Juergen writes:
> Some seem to think that the weak anthropic principle explains the
> regularity. The argument goes like this: "Let there be a uniform measure
> on all universe histories, represented as bitstrings. Now take the tiny
> subset of histories in which you appear. Although the measure
In reply to Russell Standish and Juho Pennanen I'd just like to
emphasize the main point, which is really trivial: by definition, a
uniform measure on the possible futures makes all future beginnings of
a given size equally likely. Then regular futures clearly are not any
more likely than the irr
[EMAIL PROTECTED] wrote:
>
>
>
> Huh? A PDF? You mean a probability density function? On a continuous set?
Probability Distribution Function. And PDF's are defined on all
measurable sets, not just continuous ones.
> No! I am talking about probability distributions on describable objects.
>
I tried to understand the problem that doctors Schmidhuber
and Standish are discussing by describing it in the most
concrete terms I could, below. (I admit beforehand I couldn't
follow all the details and do not know all the papers and
theorems referred to, so this could be irrelevant.)
So
> > > From [EMAIL PROTECTED] :
> > > [EMAIL PROTECTED] wrote:
> > > >
> > > > So you NEED something additional to explain the ongoing regularity.
> > > > You need something like the Speed Prior, which greatly favors regular
> > > > futures over others.
> > >
> > > I take issue with this state
[EMAIL PROTECTED] wrote:
>
>
>
> > From [EMAIL PROTECTED] :
> > [EMAIL PROTECTED] wrote:
> > >
> > > So you NEED something additional to explain the ongoing regularity.
> > > You need something like the Speed Prior, which greatly favors regular
> > > futures over others.
> >
> > I take issue
> From [EMAIL PROTECTED] :
> [EMAIL PROTECTED] wrote:
> >
> > So you NEED something additional to explain the ongoing regularity.
> > You need something like the Speed Prior, which greatly favors regular
> > futures over others.
>
> I take issue with this statement. In Occam's Razor I show ho
[EMAIL PROTECTED] wrote:
>
> So you NEED something additional to explain the ongoing regularity.
> You need something like the Speed Prior, which greatly favors regular
> futures over others.
>
I take issue with this statement. In Occam's Razor I show how any
observer will expect to see regula
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:
>
>
Juergen Schmidhuber wrote:
>We need a prior probability distribution on possible histories.
OK. I agree with that. But of course we differ on the meaning of
"possible histories". And we tackle also the "prior probability"
in quite different ways.
>Then, once we have observed a past history,
iable -
no sequence can be proven to be truly random - there is always the
possibility of some pseudo random generator being found to be the
source.
Cheers
[EMAIL PROTECTED] wrote:
>
>
>
> Predictions & duplications
>
>
> > Fro
Predictions & duplications
> From: Marchal <[EMAIL PROTECTED]> Thu Oct 4 11:58:13 2001
> [...]
> You have still not explain to me how you predict your reasonably next
> experience in the simple WM duplication. [...]
> So, how is it that you talk like if you do have
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