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klkblake comments on Open Thread: September 2011 - Less Wrong
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I'm confused about Kolmogorov complexity. From what I understand, it is usually expressed in terms of Universal Turing Machines, but can be expressed in any Turing-complete language, with no difference in the resulting ordering of programs. Why is this? Surely a language that had, say, natural language parsing as a primitive operation would have a very different complexity ordering than a Universal Turing Machine?
The Kolmogorov complexity changes by an amount bounded by a constant when you change languages, but the order of the programs is very much allowed to change. Where did you get that it wasn't?
(this is because all Turing-complete languages can simulate each other)
I knew Kolmogorov complexity was used in Solomonoff induction, and I was under the impression that using Universal Turing Machines was an arbitrary choice.
Solomonoff induction is only optimal up to a constant, and the constant will change depending on the language.