To echo razib, I'm pretty impressed.

You know, I tried a couple times to read the "Gentle Introduction to AIXI" but didn't ever manage to get very far. I finally found a paragraph summary of the idea when someone linked to a discussion you and Ben had on the agi list. (AIXI searches through all possible algorithms up to a given length and tries each one to find the best for a given task. I'm sure that's a bit off.) It strikes me that no friendliness issues are addressed, but what's more, all of the hard parts of creating a practical AI are left unaddressed. AIXI doesn't give us any insight into what the algorithms behind human cognition are, nor into algorithms that might be more universal. In fact, there's hardly any algorithm there (which is why the theory was amenable to formal analysis). AIXI is probably interesting in some limited aspects, especially regarding theorem proving (I would guess) but I had much higher expectations given the abstract of the paper. And I guess that's sort of the point--a lot of people misunderstand what exactly AIXI means.

Anyway, I look forward to your next posts.