I think K-complexity is actually like that. For any given object you can define a Turing-complete language in which the empty program outputs that object. It could literally be “Python, except the empty program outputs this specific object”.
So when you say that K-complexity is like the function that you describe earlier, does that mean that there’s provably no minimum, or does that mean that you can’t prove that the minimal constant for Kolmogorov Complexity exists?
I can accept this as an answer, though you’d have to show why Kolmogorov Complexity’s additive constant lacks a minimum number more than you have in this comment thread.
However, “Python, except the empty program outputs this specific object” would probably be more complex than “Python”, in most programming languages. So I wonder whether it would be possible to define objective complexity as eigenvector (not sure I am using the right word here) of relative complexities. As in: “simple” means “simple, when programmed in a simple language”.
I think K-complexity is actually like that. For any given object you can define a Turing-complete language in which the empty program outputs that object. It could literally be “Python, except the empty program outputs this specific object”.
So when you say that K-complexity is like the function that you describe earlier, does that mean that there’s provably no minimum, or does that mean that you can’t prove that the minimal constant for Kolmogorov Complexity exists?
It’s still possible that I’m misunderstanding the question, but if it means what I think it means, then the answer is “provably no minimum”.
I can accept this as an answer, though you’d have to show why Kolmogorov Complexity’s additive constant lacks a minimum number more than you have in this comment thread.
However, “Python, except the empty program outputs this specific object” would probably be more complex than “Python”, in most programming languages. So I wonder whether it would be possible to define objective complexity as eigenvector (not sure I am using the right word here) of relative complexities. As in: “simple” means “simple, when programmed in a simple language”.