He made an actual test of it, that involved generating random brainfuck programs. And then tested various reinforcement learning algorithms on it to measure their intelligence, and even tested humans.
That is an actual computable test that can be run.
The no free lunch theorems apply to a completely uninformative prior. We have a prior. The Solomonoff prior, where you assume the environment was generated by a computer program. And that simpler programs are more likely than more complex ones. With that, some AI programs will be objectively better than others. You can have a free lunch.
The output of this procedure would be at least as good as the best approximation of AIXI we can make with the same amount of computing power. In fact it basically would be the best approximation of AIXI possible, since it assumes the same prior and task.
Though of course it's totally impractical, since it would require unimaginably huge computers to perform this brute force search.
The Kolmogorov complexity ("K") of a string ("S") specifies the size of the smallest Turing machine that can output that string. If a Turing machine (equivalently, by the Church-Turing thesis, any AI) has size smaller than K, it can rewrite its code as much as it wants to, it won't be able to output S. To be specific, of course it can output S by enumerating all possible strings, but it won't be able to decide on S and output it exclusively among the options available. Now suppose that S is the source code for an intelligence strictly better than all those with complexity <K. Now, we are left with 3 options: