sleeping beauty

Recently, Sean wrote a blog post about the 'sleeping beauty problem' and came out in favor of the 1/3 solution.
Naturally, Lubos had to respond with an obvious 1/2 answer and finally Joe Polchinski jumped in defending 1/3.

I wrote about this puzzle nine years ago on that other blog and people are still discussing it, because it has all the ingredients of a nice paradoxon: i) it is easy to calculate the probabilities and ii) there is an interesting ambiguity on how to use "probability" in this case, with the same outcome unknowingly sampled twice.

It seems that Sean honestly thinks that this ambiguity can be resolved using the many worlds interpretation, but I would point out that it actually supports Bohr's philosophy of complementarity: In general we cannot assign probabilities to a local object (in this case the coin), but we have to understand them in the context of an observational situation. In other words, the 'sleeping beauty problem' supports the Copenhagen interpretation.
8-)


added later: After re-reading my old post about this, I actually like the 3/8 solution.
Btw one way to undermine the 1/3 solution based on bet size (a la Polchinski) is to point out that the same bet size optimizes the outcome if SB does not fall asleep the 2nd time (but still has to bet twice the same amount). In this case the probability surely is not 1/3.

added even later: Joe posted yet another comment "which may make it clearer" why the correct answer is 1/3, while Lubos posted a whole new blog post defending the "obvious" 1/2 solution with an interesting modification of the original puzzle: Instead of just being put to sleep twice, with small probability 1/N 'sleeping beauty' is kidnapped by the CIA and tortured - waking up and put to sleep again and again N times; as N goes to infinity, the probability of being kidnapped by the CIA should go to zero.

added much later: Finally a commenter says what needs to be said about all this. It took long enough 8-)

a certain lack of entropy

Where we live one needs an AC, especially during summer. Our apartment is not that big, but we actually have two separate ACs, one for the ground floor and the other for the bedrooms. Unfortunately, they never manage to get to the same temperature (and humidity) - so when I walk up the stairway from the ground floor I can feel the temperature drop. And such temperature differences of about 1F can last for hours, long after the AC turned off.

But how is this possible? The air in our house is pretty much an ideal gas with some water molecules added and if I can walk through the stairway (there is no door btw) then the much smaller air molecules should be able to fly from one floor to the other too. The faster molecules in one direction, the slower ones in the other until equilibrium is restored, as we learn it in school. Furthermore, should the cooler air not quickly float down to the ground floor due to gravity or something?
In general, entropy seems to work fine in our house, e.g. when I spill coffee or drop something; but where is it when we need it?

Well, Sean Carroll explained to us that entropy is actually a cosmological effect and apparently it has to do with an "arrow of time". So I have to conclude that something is not right with the universe - and perhaps I should spend more time in the upper floor, assuming that the "arrow of time" is less pointy there? (*)


(*) added later: not really...