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spoonlessIt seems that top notch physicists have now discovered Nick Bostrom's ingenius "Doomsday Argument".
Eternal Inflation Predicts That Time Will End
http://arxiv.org/abs/1009.4698
"If you accept that the end of time is a real event that could happen to you, the change in odds is not surprising: although the coin is fair, some people who are put to sleep for a long time never wake up because
they run into the end of time first. So upon waking up and discovering that the world has not ended, it is more likely that you have slept for a short time. You have obtained additional information upon waking—the information that time has not stopped—and that changes the probabilities. However, if you refuse to believe that time can end, there is a contradiction. The odds cannot change unless you obtain additional information. But if all sleepers wake, then the fact that you woke up does not supply you with new information."
Lending some weight to this theory is the fact that both Peter Woit and Lubos Motl think the paper is complete nonsense (Motl's rant on it is particularly entertaining and vacuous), since both of them are idiots (although usually in polar opposite ways)!
I've always thought of Raphael Bousso as a better physicist than ex physicist Lubos Motl was, and certainly better than mathematics lecturer Peter Woit. I suppose that doesn't guarantee that it's right though.
Normally I wouldn't pay much attention to a headline like this, but Bousso is actually someone I have a lot of respect for. And to add to that, I have found Bostrom's Doomsday Arguments in the past fairly persuasive (at least more convincing than not), which have a similar flavor... although Bostrom's arguments were far less technical in nature. This may give a more solid, physical basis to the idea that being a good Bayesian entails believing we are all doomed.
Eternal Inflation Predicts That Time Will End
http://arxiv.org/abs/1009.4698
"If you accept that the end of time is a real event that could happen to you, the change in odds is not surprising: although the coin is fair, some people who are put to sleep for a long time never wake up because
they run into the end of time first. So upon waking up and discovering that the world has not ended, it is more likely that you have slept for a short time. You have obtained additional information upon waking—the information that time has not stopped—and that changes the probabilities. However, if you refuse to believe that time can end, there is a contradiction. The odds cannot change unless you obtain additional information. But if all sleepers wake, then the fact that you woke up does not supply you with new information."
Lending some weight to this theory is the fact that both Peter Woit and Lubos Motl think the paper is complete nonsense (Motl's rant on it is particularly entertaining and vacuous), since both of them are idiots (although usually in polar opposite ways)!
I've always thought of Raphael Bousso as a better physicist than ex physicist Lubos Motl was, and certainly better than mathematics lecturer Peter Woit. I suppose that doesn't guarantee that it's right though.
Normally I wouldn't pay much attention to a headline like this, but Bousso is actually someone I have a lot of respect for. And to add to that, I have found Bostrom's Doomsday Arguments in the past fairly persuasive (at least more convincing than not), which have a similar flavor... although Bostrom's arguments were far less technical in nature. This may give a more solid, physical basis to the idea that being a good Bayesian entails believing we are all doomed.
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no subject
Date: 2010-09-30 12:55 am (UTC)Not at all. Just take the Borel sigma-algebra of regions, and put any probability measure at all that you like on it. This gives you a consistent definition of probability.
In fact, talking about probabilities by using the limits of frequencies in finite cutoffs explicitly gives you something that doesn't satisfy the probability axioms. In particular, there are two events that have a well-defined probability, such that their conjunction doesn't have a well-defined probability. I'll give an example with the natural numbers instead of in physical space, but you can generalize it fairly straightforwardly, I would think.
If you define probability in the limit way, then the probability that a number is even is 1/2, since as n goes to infinity, the limit of the number of numbers up to n that are even goes to 1/2. (At every odd n there is a slight deviation, but the size of the deviation goes to 0.)
Now if you let S be the set of natural numbers that have an even number of bits in their binary expansion and are even, or an odd number of bits in their binary expansion and are odd, then the probability that a number is in S is also 1/2. (There are slight deviations, but again the size goes to 0 as n goes to infinity.)
But the probability that a number is even and in S is undefined. This is because when n is exactly an even power of 2, the frequency is close to 1/3, and when n is exactly an odd power of 2, the frequency is close to 1/6, and it fluctuates back and forth as n increases, so there is no well-defined probability.
no subject
Date: 2010-09-30 01:34 am (UTC)Not at all. Just take the Borel sigma-algebra of regions, and put any probability measure at all that you like on it. This gives you a consistent definition of probability.
Ok, I guess I should have used the word "unique" instead of "consistently". It's the arbitrariness here that's the issue. I should have said that there is no unique way to define probability on an infinite space.
Yes, you can consistently do whatever you want. The problem is that no matter how you do it, it's going to be arbitrary, right? So you might as well do it in a way that makes some physical sense, like looking at how statistics works in a physically local region of spacetime, and then generalizing from there. If you can think of a way that makes more sense, or is somehow less arbitrary, then I'm sure lots of people would be interested.