I mean, translated to algorithmic description land, my claim was: It’s often difficult to prove a negative and I think the non-existence of a short algorithm to compute a given object is no exception to this rule. Sometimes someone wants to come up with a simple algorithm for a concept for which I suspect no such algorithm to exist. I usually find that I have little to say and can only wait for them to try to actually provide such an algorithm.
So, I think my comment already contained your proposed caveat. (“The concept has K complexity at least X” is equivalent to “There’s no algorithm of length <X that computes the concept.”)
Of course, I do not doubt that it’s in principle possible to know (with high confidence) that something has high description length. If I flip a coin n times and record the results, then I can be pretty sure that the resulting binary string will take at least ~n bits to describe. If I see the graph of a function and it has 10 local minima/maxima, then I can conclude that I can’t express it as a polynomial of degree <10. And so on.
I mean, translated to algorithmic description land, my claim was: It’s often difficult to prove a negative and I think the non-existence of a short algorithm to compute a given object is no exception to this rule. Sometimes someone wants to come up with a simple algorithm for a concept for which I suspect no such algorithm to exist. I usually find that I have little to say and can only wait for them to try to actually provide such an algorithm.
So, I think my comment already contained your proposed caveat. (“The concept has K complexity at least X” is equivalent to “There’s no algorithm of length <X that computes the concept.”)
Of course, I do not doubt that it’s in principle possible to know (with high confidence) that something has high description length. If I flip a coin n times and record the results, then I can be pretty sure that the resulting binary string will take at least ~n bits to describe. If I see the graph of a function and it has 10 local minima/maxima, then I can conclude that I can’t express it as a polynomial of degree <10. And so on.