There are so many things to respond to here that I have no idea where to begin. So I'll list them randomly:
- Where do you get the O(log2(n)) from? With a flat memory model, hashing algorithms are not O(log2(n)).
- Re-read my post and you'll see that I explicitly acknowledge the fact that hackers do not exactly use big-O notation in the way that Knuth did. Why do you think that he said otherwise?
- Re-read the root post and you'll discover that pg both misunderstood big-O notation as used by Knuth, and as used by hackers. As far as most people are concerned, a hash lookup is O(1). That he thought otherwise was due to a misunderstanding on his part about what big-O notation means.
- Re-read the root post and you'll find lots of incorrect attempted pedantry. When someone tries to get pedantic, I think it is fair and reasonable to be pedantic back.