According to the Time Hierarchy theorem ( http://en.wikipedia.org/wiki/Time_hierarchy_theorem http://en.wikipedia.org/wiki/Time_hierarchy_theorem ), for each nu

According to the Time Hierarchy theorem ( http://en.wikipedia.org/wiki/Time_hierarchy_theorem http://en.wikipedia.org/wiki/Time_hierarchy_theorem ), for each number k > 1, there exists a problem in P that can be decided (solved) in O(n^k), and not decided (solved) in O(n^j) for each j in [1, k). This was the first time I heard of this theorem (was googling for something I thought would weaken the author's point), and it really strengthens the authors argument - I thought his example of O(n^10) algorithms was sort of a fallacy but it appears not. If I'm properly understanding the Time Hierarchy Theorem, it is a very strong argument for what the author is suggesting (and somewhat disappointing for me, because I wish he were wrong).