I see no reason to believe there is such a thing as an objective definition of "fair" in this case. The idea that an equal division is "fair" is based on the assumption that none of the three has a good argument as to why he should receive more than either of the others. If one has a reasonable argument as to why he should receive more, the fairness argument breaks down. In fact, none of the three really have a good argument as to why he is entitled to any of it, and I can't see why it would be wrong for any of the first one to grab it to claim the whole pie under "right of capture".

what's the standard reply to someone who says, "Friendly to who?" or "So you get to decide what's Friendly"?

This is an important question. I don't believe there is such a thing as an objective definition of friendliness, I'd doubt that "reasonable" people can come to an agreement as to what friendliness means. But I'm eager to be proven wrong, keep writing.

Well, I remember wondering as a graduate student how how one was supposed to go about deciding what problems to work on, and not coming up with a good answer . A fellow student suggested that your project is worth working on if you can get it funded, but I think he was kidding. Or maybe not.

Most experimentalists really aren't in the business of supporting or refuting hypotheses as such. It's more a matter of making a measurement, and yes they will be comparing their results to theoretical predictions, but ideally experimentalists should be disinterested in the result, that is, they care about making as accurate a measurement as possible but don't have any a priori preference of one value over another.

There's a way you could make the heat=motion concept much clearer to Carnot. When one studies kinematics, one generally makes the approximation that macroscopic bodies are rigid, and the motions of the body refer to center of mass motion, or perhaps rotation about some axis. If you explain that "heat" refers to the motion of the constituent particles relative to each other, I think a scientist of Carnot's day would understand the idea pretty quickly.

I think this sort of thing might be what people mean when they talk about a "bridging theory".

The essential idea behind reductionism, that if you have reliable rules for how the pieces behave then in principle you can apply them to determine how the whole behaves, has to be true. To say otherwise is to argue that the airplane can be flying while all its constituent pieces are still on the ground.

But if you can't do a calculation in practice, does it matter whether or not it would give you the right answer if you could?

It would certainly facilitate communication, though, if people could agree on what words mean rather than having personal definitions. No doubt it's unrealistic to expect everyone to agree on precisely where the boundary between yellow and orange lies, but tigers aren't even a yellowish orange.

For some reason this post reminds me of the Buddhist parable asceticsim now, nymphs later.

I don't think it's all that uncommon to begin cultivating an art for some specific purpose, proceed to cultivate it largely for its own sake, and eventually to abandon the original purpose.

It seems to me that your argument relies on the utility of having a probability p of gaining x being equal to p times the utility of gaining x. It's not clear to me that this should be true.

The trouble with the "money pump" argument is that the choice one makes may well depend on how one got into the situation of having the choice in the first place. For example, let's assume someone prefer 2B over 2A. It could be that if he were offered choice 1 "out of the blue" he would prefer 1A over 1B, yet if it were announced in advance that he would have a 2/3 chance of getting nothing and a 1/3 chance of being offered choice 1, he would decide beforehand that B is the better choice, and he would stick with that choice even if allowed to switch. This may seem odd, but I don't see why it's logically inconsistent.

Martin Gardner has a chapter on these "look-see" proofs in Knotted Donuts.

Ni no Tachi figured out how to use the hammer, but Bouzo only sold them without understanding their value.

"A bird in the hand is worth what you can get for it." --Ambrose Bierce

Fiction is fiction, but it seems to me that that if student objects to wearing silly clothes and his master responds by ordering him to wear yet sillier clothes, it's a lot more plausible that the student will conclude his master is a quack and drop out than that he'll decide to extend his master's teaching by taking silly clothes to a whole new level.

Maybe the whole point of this exercise is to remind us that one can't come to reliable conclusions from fictional evidence? If so, well, maybe I haven't learned anything... but at least I've learned I haven't learned anything.

"Since you are so concerned about the interactions of clothing with probability theory," Ougi said, "it should not surprise you that you must wear a special hat to understand."

But isn't this almost the exact opposite of what the student was saying? Questioning the robes indicates to me that the student felt there was not any interaction between learning probability theory and clothing, and that therefore it served some other purpose, presumably differentiating between an in group and an out group.

Or am I just nuts for trying to argue with you about the internal thoughts of your own fictional characters?