we may only have another 5-billion, so make every year count!

[spoonless]

It 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.

Comments

[easwaran.livejournal.com]

I'm not using the word "frequentist" here to mean an acceptance of all the theses of frequentist statistics, but just the claim that in this case, the probabilities (whether that means the degrees of belief some agent should have, or the objective chances, or something else - I'm not really sure what notion of probability they're talking about) are given by frequencies of a certain sort. In particular, the claim is that they're given by the limit of relative frequencies in certain finite regions as the size of those regions goes to infinity. But this clearly doesn't make sense if there are events that happen with frequency bounded away from zero in every finite region, which don't happen at all in the infinite region. (For instance, the event might be, "exists at a time t and not at time t+1", as in their example.) I don't see why we should expect the frequencies in certain finite regions to tell us anything about the actual probabilities, unless you're defining the probability in terms of the limit of these finite frequencies. If you're not doing that, then you should expect them to line up in many cases, but not in ones where there's a specific logical problem, like the one they come up with.

If you just extended it to the end of the life of any partially included observers, you'd end up with some ragged shape that's still finite. How does that tell you anything about the probability in the infinite case?

I don't see how any such process involving finite shapes tells you anything about the probability in the infinite case. And they're making conclusions about the infinite case using exactly this sort of process involving finite shapes. And then they end up with a conclusion that there is a positive probability that the universe ceases to exist, even though there is no boundary to the universe.

[spoonless.livejournal.com]

In particular, the claim is that they're given by the limit of relative frequencies in certain finite regions as the size of those regions goes to infinity

Actually, I don't think this is a part of their central claim. They do take the limit of a couple measures as the size goes to infinity, but that's sort of a side thing, and for the main ones like the causal patch, which I think is the one that most people think is the "right" one to use... at least moreso than any other one... they don't ever take this limit because you can't. They are just providing a way of dividing the space up into local "bins" and doing statistics on these bins, and assuming the statistics will be the same for the overall global space, if it makes sense to talk about such a space at all. You don't ever have to take a limit of bin size. I think this is a bit less arbitrary than doing the same thing for pure numbers, because spacetime automatically has this nice property of locality, which tells you what the right local bins are to use.

[spoonless.livejournal.com]

I don't see how any such process involving finite shapes tells you anything about the probability in the infinite case.

Just out of curiosity, do you know of any alternative? Is your view that probability is just meaningless for infinite sets, or is there a better way of doing this?