If some of you want to brush up on AIXI before Eli gets into that, I might suggest checking out my thesis which is now online:

http://www.vetta.org/about-me/publications

SIAI has a curiously mixed attitude towards AIXI. On the SIAI website Hutter's AIXI book and related AIXI article are among the core readings list, then among the SIAI research agenda there are two AIXI related items based on research I've done. Recently, I was awarded an SIAI academic prize worth $10,000 for, you guessed it, my research into AIXI and related topics. And yet, Eli regularly describes AIXI as a "brain malfunction", or worse!