This runs into strongly believed theoretical comp sci limits such as the likelyhood that P != NP.
Does it? There are certainly situations (breaking encryption) where the problem statement looks something like "I'd like my program to be able to get the single exact solution to this problem in polynomial time", but for optimization we're often perfectly happy with "I'd like my program to be able to get close to the exact solution in polynomial time", or even just "I'd like my program to be able to get a much better solution than people's previous intuitive guesses".
Yes, this is one of the issues that does need to be thought about. But there are limits to this. However, there's been work in the last few years (especially for problems in graph theory) where one can show that being able to find close to optimal solutions is equivalent to being able to find optimal solutions.
The encryption example is also an interesting one, in that many foom scenarios involve the hypothetical AI gaining control over lots of the world's computer systems. And in fact, no known encryption system rest on a problems which is NP-complete, so...
Link: johncarlosbaez.wordpress.com/2011/04/24/what-to-do/
His answer, as far as I can tell, seems to be that his Azimuth Project does trump the possibility of working directly on friendly AI or to support it indirectly by making and contributing money.
It seems that he and other people who understand all the arguments in favor of friendly AI and yet decide to ignore it, or disregard it as unfeasible, are rationalizing.
I myself took a different route, I was rather trying to prove to myself that the whole idea of AI going FOOM is somehow flawed rather than trying to come up with justifications for why it would be better to work on something else.
I still have some doubts though. Is it really enough to observe that the arguments in favor of AI going FOOM are logically valid? When should one disregard tiny probabilities of vast utilities and wait for empirical evidence? Yet I think that compared to the alternatives the arguments in favor of friendly AI are water-tight.
The problem why I and other people seem to be reluctant to accept that it is rational to support friendly AI research is that the consequences are unbearable. Robin Hanson recently described the problem:
I believe that people like me feel that to fully accept the importance of friendly AI research would deprive us of the things we value and need.
I feel that I wouldn't be able to justify what I value on the grounds of needing such things. It feels like that I could and should overcome everything that isn't either directly contributing to FAI research or that helps me to earn more money that I could contribute.
Some of us value and need things that consume a lot of time...that's the problem.