Missing Shade of Blue
Posts: 62
Joined: Dec. 2008
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Keith,
I made it sound in the last post that there is no workable notion of physical simplicity. But I don't think that's true. I think some things are made out of more basic parts (and types of parts) than other things. But whether or not the syntactic simplicity of our descriptions tracks the physical simplicity of objects depends on whether our language (more generally, our set of inductive biases) carves nature at the joints. While I'm usually happy to assume that it does, I was resisting the idea that we can make this assumption when we're trying to account for the origin of those biases themselves. This was why I thought your physical simplicity proposal was question-begging. Since then, I have come to accept that there's no special problem with assuming our inductive biases are accurate when attempting to explain them. So I no longer think your proposal is question-begging.
However, the context of this discussion with Wesley is different. Here I'm responding specifically to his charge that I was wrong when I said that algorithmic information theory does not have the resources to adjudicate the relative simplicity of two finite strings without first assuming a natural language (which amounts to assuming a particular construction for the UTM). Appealing to the actual physical structure of the world we live in in order to privilege one sort of UTM over the other transcends algorithmic information theory, which is a purely syntactic measure of complexity.
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