Cliff Stabbert wrote:
[On a side note, I'm curious whether and if so, how, lossy compression might relate. It would seem that in a number of cases a simpler algorithm than expresses exactly the behaviour could be valuable in that it expresses 95% of the behaviour of the environment being studied -- and if such an algorithm can be derived at far lower cost in a certain case, it would be worth it. Are issues like this addressed in the AIXI model or does it all deal with perfect prediction?]
Yes, stuff like this comes up a lot in MDL work which can be viewed as a computable approximation to Solomonoff induction. Perhaps at some point a more computable version of AIXItl might exist that is similar in this sense.
Some results do exist on the relationship between Kolmogorov complexity and lossy compression but I can't remember much about it off the top of my head (I'm only just getting back into the whole area myself after a number of years doing other things!)
What I'm getting at is an attempt at an external definition or at least telltale of conscious behaviour as either "that which is not compressible" or "that which although apparently compressible for some period, suddenly changes later" or perhaps "that which is not compressible to less than X% of the original data" where X is some largeish number like 60-90.
This seems to be problematic to me. For example, a random string generated by coin flips is not compressible at all so would you say that it's alive? Back in the mid 90's when complexity theory was cool for a while after chaos theory there was a lot of talk about "the edge of chaos". One way to look at this is to say that alive systems seem to have some kind of a fundamental balance between randomness and extreme compressibility. To me this seems obvious and I have a few ideas on the matter. Many others investigated the subject but as far as I know never got anywhere. Chaitin, one of the founders of Kolmogorov complexity theory did some similar work some time ago, http://citeseer.nj.nec.com/chaitin79toward.html
Sounds to me like you need to read Li and Vitanyi's book onThe reason I'm thinking in these terms is because I suspected Ockham's razor to relate to the compressibility idea as you stated; and I've
Kolmogorov complexity theory :)
http://www.cwi.nl/~paulv/kolmogorov.html
Cheers
Shane
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