I did change the strategy from whipping the Library to building it, since it was unrealistic to research Bronze Working and beeline Alphabet in time to use Slavery or chopping to build the Library starting at t26 (BC 2960). In any case, chopping the Library would be better than whipping, since that should allow at least one Citizen free to be hired as a Scientist for 17 turns.
With plentiful food, one could even hire two Scientists instead one and thus generate the Great Scientist in 9 turns rather than 17 turns. Thus, the Great Scientist could build the Academy as early as turn 47 rather than turn 55!
The more food you have the better this all works out, especially when using whipping. The best food resources (irrigated Corn, Pig or even Fish) should be used when possible.
In my current game, I generated my first Great Scientist on turn 59. I could have done it much earlier, but my Settler generation would have suffered even more than it already has.
Sun Tzu Wu
I think that the settler production is the difference. This is my typical build order:
Worker (12-15 turns)
Warriors (Allow city to grow while making cheap defenders for future cities)
Settlers (once I reach size 3-4 depending on resources)
Another worker or two
Culture buildings (For the rest of the game)
The worker finishes three turns earlier with a plains/hill city. The warriors typically take 5 turns each as the city grows while building three of them takes another 15 turns. About turn 30-35 I start to build my first settler. I build two of them at 12-17 turns each. I generally reach Alphabet by about turn 41-48 just as the second settler is finishing up. Two additional workers takes me 6-8 turns. I start building a library at about turn 50-55. Sometimes I build a wonder instead.
By the time the Library is done, it is much later than in your strategy. The only way I could see to improve the time for the library would be to build it before the second settler. With the way the AI efficiently REX the available land, I just don't see how I could delay the settler and still get three good city locations.
In the game I won, my second city was building the Pyramids (eventually gold when the AI finished before me) while the Capitol was building the Parthenon and I was delaying trading Asthetics to the AI. The third city was building a Library followed by Monistaries and Temples. The forth city was not built until about turn 85 since the location was safely within my borders. I actually had room for 2 more cities, but based on earlier discussion only built the four.
What build order do other people use to get better results?
edit: I just checked the player log from my submission. I founded York on turn 38 and Nottingham on turn 48. Hastings was founded on turn 85.