Also, maybe the Babylonians simply rushed some advanced tech before getting the ones left from the previous eras ?
I know I sometime go for Archeology, which you can get with simply 1 tech per column in the last 2, and only a few before; then the old techs go very quickly, because of the higher science/turn and the bonus because everybody researched them.
Before Babylon's tech spike starts, they have 38 techs. This means that the tech they rush can't be further than late industrial. If that is the case, they would have 4 first column renaissance techs, 2 second column renaissance techs, 1 first column industrial tech and 1 second column tech when they get their 39th tech and the spike starts. Had they filled the tech tree as evenly as possible, they would have 5 first column reneissance techs and 3 second column reneissance techs. Even with maximum rush on the tech tree, they can only have substituted 2 reneissance techs to 2 industrial techs. It can't explain the pace in which Babylon managed to get 28 techs or in other words, advanced 3 eras.
If I'm looking at the graph correctly, it seems that Babylon got 28 techs in 31 or 32 turns. The x-axis is split to 40 parts and as there were just less than 300 turns in the game according to the OP, each part consists of around 7.5 turns. Babylon's tech spike took just over 4 parts and they got from 38 to 66 techs during that time. For me it seems like something is not working. I edited OP's screen shot a little to show what I'm talking about.
Spoiler :
