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 generate
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 distribution.
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
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
and
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 they
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 unprovable
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 last
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 distribtuion is
[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 the notion that
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
the set of all
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
[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, we only consider
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. Finite length
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.
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 length l,
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). (That is 2 to
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
-
From: Russell Standish [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
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
will make of a random
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
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 of
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.)
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 how any
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
[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
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, we
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