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Daniel_Burfoot comments on Significance of Compression Rate Method - Less Wrong
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Re: "The key realization is that lossless data compression can only be achieved through empirical science. This is because data compression is impossible for arbitrary inputs: no compressor can ever achieve compression rates of less than M bits when averaged over all M-bit strings."
Well, you only need one empirical observation to build a general purpose compressor - that inputs are more likely than not to be the result of executing short programs. Aftter noticing that you can obtain impressive compression ratios while ignoring the real world completely.
Want to bet? :-)
An implicit point of my whole story is the rejection of the idea that good compression rates can be achieved using theory alone. I suppose you can disagree with this, but the history of science seems to be on my side - science never really started making progress until people started systematically checking their theories against empirical data.
Why bet? This is a maths debate - and not a very complex one.