<i>But sorting has a known O(N log N) algorithm. Nobody sorts by comparing all N! permutations and picking the correct one. (Well, I certainly don&#x27;t.)</i><p>That is precisely the point of the blog post. Nobody compares all N! permutation for sorting, and nobody checks all N! tours when solving a TSP. The latter is less trivial because algorithms that solve the TSP are far more sophisticated than a sorting algorithm, but they still avoid enumerating a very large subset of solutions. They cannot be claimed to run in polynomial time for any instance, but they are still quite efficient.<p><i>Saying that TSP is as hard as N! is technically wrong, but it&#x27;s much less wrong than saying sorting is as hard as N!.</i><p>I disagree, both from a practical standpoint (in both cases there are orders of magnitude between N! and actual CPU time) and a more metaphysical one (neither algorithm explores the full set of solutions).