you're right that the isolated assertion is not at all sensible, but the wider context is that you are considering all possible algorithms and the sequences tha

you're right that the isolated assertion is not at all sensible, but the wider context is that you are considering all possible algorithms and the sequences that they generate, and looking for some way of compressing as many of those as possible. you should read one of chaitin's books for a better idea (they're generally "accessible", but at some point you just give up trying to make complete sense of it all...) in other words, you are choosing your compression for one particular algorithm (the one that generates omega - you could go further and say it's 1 for omega and 0 for everything else). this is a common problem in arguments about compressibility (if we're only trying to compress beethoven's ninth then i can do that in one bit too) - you have to be talking in an "average" or statistical sense for things to be useful. having said that, the exact nature of what they're saying is still not clear to me (ie it's not clear exactly how the details of the argument work out, or how this eventually ties back to http://en.wikipedia.org/wiki/Shannons_source_coding_theorem http://en.wikipedia.org/wiki/Shannons_source_coding_theorem).