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I appreciate you correcting my terminology, but beyond that you haven't actually disagreed with anything I've said. Humans call it either the Shannon limit, or

I appreciate you correcting my terminology, but beyond that you haven't actually disagreed with anything I've said. Humans call it either the Shannon limit, or Shannon entropy, or Kolmogorov complexity of a string, or whatever other name humans have come up with for human names. The central point is there is some limit which you can't circumvent through trickery like "find it embedded within pi," regardless of what species you are, or what your species chooses to name fundamental limitations of nature. A program to generate digits of pi is small, and pi embeds every possible string. But generating up to that offset of pi is impossible in practice. And it probably won't net you any savings anyway, since you'll still need to communicate the offset. The offset's length in digits is probably close to the length of the original string (after perfect compression), so it's unlikely you'd be able to circumvent Shannon entropy. But, if you do manage to create a practical way to bypass Shannon entropy, I'd imagine it'll be headline news, along with netting you quite a lot of money.

iliis 13y ago
If you're talking about Kolmogorov Complexity here, you can't really "circumvent" it. Kolmogorov Complexitiy of a string is basically defined as the size of the shortest possible representation of said string. If you manage to"bypass" the Kolmogorov Limit you actually just "lowered" it (well, it alwayws was by definition this low). Your main point is totally valid however. You cannot compress infinitely. A simple proof: For any given N bits you can encode [at most] 2^N different strings. As there exist more than N strings there must be one which cannot be represented by N bits. As N can be arbitrarily large you'll always find strings which cannot be compressed lower than some chosen size. QED.

iliis 13y ago

If you're talking about Kolmogorov Complexity here, you can't really "circumvent" it. Kolmogorov Complexitiy of a string is basically defined as the size of the shortest possible representation of said string. If you manage to"bypass" the Kolmogorov Limit you actually just "lowered" it (well, it alwayws was by definition this low). Your main point is totally valid however. You cannot compress infinitely. A simple proof: For any given N bits you can encode [at most] 2^N different strings. As there exist more than N strings there must be one which cannot be represented by N bits. As N can be arbitrarily large you'll always find strings which cannot be compressed lower than some chosen size. QED.