Comment on Open Thread: October 2009

DanB
Thu, 01 Oct 2009 23:51:28 GMT

But by smearing its optimality over the entire Platonic space of computable functions, it is significantly worse than those algorithms tuned for this world's function. And not surprisingly, AIXI has very little practical application.

Let's do another thought experiment. Say that humanity has finally resolved to send colonists to nearby star systems. The first group is getting ready to head out to Alpha Centauri.

The plan is that after the colonists arrive and set up their initial civilization, they will assemble a data archive of size T about the new world and send it back to Earth for review. Now it is expensive to send data across light-years, so obviously they want to minimize the number of bits they have to send. So the question is: what data format do the two parties agree on at the moment of parting?

If T is small, then it makes sense to think this issue over quite a bit. What should we expect the data to look like? Will it be images, audio, health reports? If we can figure something out about what the data will look like in advance (ie, choose a good prior), then we can develop a good data format and get short codes.

But if T is large (terabytes) then there's no point in doing that. When the Alpha Centauri people build their data archive, they spend some time analyzing it and figuring out ways to compress it. Finally they find a really good compression format (=prior). Of course, Earth doesn't know the format - but that doesn't matter, since the specification for the format can just be prepended to the transmission.

I think this thought experiment is nice because it reveals the pointlessness of a lot of philosophical debates about Solomonoff, Bayes, etc. Of course the colonists have to choose a prior before the moment of parting, and of course if they choose a good prior they will get short codes. And the Solomonoff distribution may not be perfect in some metaphysical sense, but it's obviously the right prior to choose in the large T regime. Better world-specific formats exist, but their benefit is small compared to T.

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