Not really, Komogorov complexity difference between various languages is bounded (for everything languages L1 and L2, there is a constant D for which, for every algorithm A, |K(L1, A) - K(L2, A)| < D, D being at most the complexity of writing a L2 compiler in L1 or vice-versa). So while it may not give exactly the same results with different languages, it doesn’t “fall apart”, but stays mostly stable.
Yes, but it’s still true that for any two distinct finite strings S1 and S2, there will always be some description language in which S1 has lower Kolmogorov complexity than S2. So by appropriate choice of language I can render any finite string simpler than any other finite string.
Turing complete languages rarely vary much. If you take the string domain to be binary data, and compare most major programming languages, there will probably be a high between the lengths of equivalent programs.
Any language for which description of 30000 zero bits is longer than say, 30000 bits with zero-separated prime-length clusters of one bits (110111011111011111110...) is not general purpose.
This problem exists for all reasoning, e.g., Komogorov complexity falls apart when some bozo comes along with a different language.
Not really, Komogorov complexity difference between various languages is bounded (for everything languages L1 and L2, there is a constant D for which, for every algorithm A, |K(L1, A) - K(L2, A)| < D, D being at most the complexity of writing a L2 compiler in L1 or vice-versa). So while it may not give exactly the same results with different languages, it doesn’t “fall apart”, but stays mostly stable.
Yes, but it’s still true that for any two distinct finite strings S1 and S2, there will always be some description language in which S1 has lower Kolmogorov complexity than S2. So by appropriate choice of language I can render any finite string simpler than any other finite string.
Turing complete languages rarely vary much. If you take the string domain to be binary data, and compare most major programming languages, there will probably be a high between the lengths of equivalent programs.
Any language for which description of 30000 zero bits is longer than say, 30000 bits with zero-separated prime-length clusters of one bits (110111011111011111110...) is not general purpose.