### Re: Predictions duplications

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

### Re: Predictions duplications

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.

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

[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

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

[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

### Re: Predictions duplications

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

### Re: Predictions duplications

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) =

### Re: Predictions duplications

[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 set of

### Re: Predictions duplications

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

### Re: Predictions duplications

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.

### Re: Predictions duplications

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,

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

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.ยดยด If you try to do that then you encounter the famous halting problem. Saibal

### Re: Predictions duplications

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

### Re: Predictions duplications

Subject: Re: Predictions duplications SNIP 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

### Re: Predictions duplications

- 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

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

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.)

### Re: Predictions duplications

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

### Re: Predictions duplications

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

### Re: Predictions duplications

[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

### Re: Predictions duplications

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

### Re: Predictions duplications

In summary, it would appear that Juergen is not disputing the use of the UDA after all, but simply the use of the uniform measure as an initial prior over the everything of all description. He argues that we should use the speed prior instead. Another way of putting it is that he doesn't