[Cacti]

NFL theorems aren’t an argument about noise, they’re an argument about the uncountability of real numbers. NFL states that over all problems any optimization method performs equally poorly to any other, or equivalently, _that if an optimization method does well on some problems, it must do equally poorly on some other problems_, and those others aren’t necessarily noise, they could be anything. The problem is you don’t know which problems it is going to do poorly on in advance. You hope it does poorly on noise or on problems that you don’t care about, but you can’t tell. That is a very different statement than what you’re saying, and it’s as equally non-trivial as Godels and Turings statements in decidability.