What's wrong with admitting you can't produce such sentence? Note, I'm not saying there isn't one, Kolmogorov complexity and all, only that chances are extremely low that any human now can produce it.
As for Feynman statement, yeah, it's wrong if you read it literally (I read it as "I can't emphasize enough how important this following fact is") , but Eliezer (and all commenters I read) made the same mistake really - he produced the sentence he thought would help them most, not one that would "contain most information in the fewest words".
If we want to produce a sentence of highest compression, they probably won't be able to read it for ages, so what's the point. If we want to produce a sentence that would help them most I have no idea what should it be. Maybe some math, maybe physics, maybe agriculture or economics. Depends on the cataclysm too. Either way, I have no idea. I think the only thing the answers given so far convey is biases in people giving them ;-)
Actually, the sentence of highest compression contains direction, rather than information. The world already contains that information, all you need is a pointer to it.
So apparently Richard Feynman once said:
I could be missing something, but this strikes me as a terrible answer.
When was the atomic hypothesis confirmed? If I recall correctly, it was only when chemists started noticing that the outputs of chemical reactions tended to factorize a certain way, which is to say that it took millennia after Democritus to get the point where the atomic hypothesis started making clearly relevant experimental predictions.
How about, "Stop trying to sound wise and come up with theories that make precise predictions about things you can measure in numbers."
I noticed this on Marginal Revolution, so I shall also state my candidate for the one most important sentence about macroeconomics: "You can't eat gold, so figure out how the heck money is relevant to making countries actually produce more or less food." This is a pretty large advance on how kings used to think before economics. I mean, Scott Sumner is usually pretty savvy (so is Richard Feynman btw) but his instruction to try to understand money is likely to fall on deaf ears, if it's just that one sentence. Think about money? Everyone wants more money! Yay, money! Let's build more gold mines! And "In the short run, governments are not households"? Really, Prof. Cowen, that's what you'd pass on to the next generation as they climb up from the radioactive soil?
*Cough.* Okay, I'm done. Does anyone want to take their own shot at doing better than Feynman did for their own discipline?