I think I discovered another thing about our Persian friends: they've researched Sailing. In my test game and the one Irgy just posted, it takes 4 turns to research Sailing at turn 40 (100% research). In both the test and the actual game our tech rate is 38 beakers/turn at that point. However, in the real game researching Sailing only takes 3 turns at turn 40. I was trying to figure out what was different between the test and the real game, when I realized we'd met another civ, and if they had researched Sailing, we'd get the discount. Sure enough, if I give the other civ (Korea) in Irgy's test game Sailing, it then only takes 3 turns to research at turn 40.
The Persians must have researched Sailing.
Does this make getting a settler out to the neighboring island more of a priority (that is, do we build the settler before the worker)?
Edit: Given AlphaShard's observation about Slavery (nice going, I didn't think to check the victory conditions window), we know they've self-researched Fishing, Sailing, and BW, at least. I'm wondering how much besides Mysticism they can offer us in trade at this point.
Edit2: I forgot Mining. And most likely, Animal Husbandry.