alt Hacker NewsI've skimmed the result couple of weeks ago, and if I remember it states that there from all machines which takes t time to accomplish something there is one such that sqrt(t) memory is used. so it's at most but not on avg nor amorotized[not sure if et even make sense it the space where the problem lies] (you take the least memory hungry machine)
There must be more constraints, what if the problem is copying a string? Or is it only for turing tape machines where it has to backtrack during the copy, increasing number of steps?