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The Mount of Olives is a large hill, east of the city, separated from it by the Kidron Valley. Kidron is a wadi, it only has water during part of the year, in this case, the winter. So Jesus crosses this winter flow.
Gethsemane (lit. oil press) means a place where there were oil vats. There are olive trees about, and they need oil presses to press out the oil. Gethsemane is a place where this is done. This seems to be part of the earliest tradition, that there was this place called Gethsemane. Mount of Olives has interesting theologizing around it, and it’s mentioned in Luke that on Easter Sunday night Jesus ascends to heaven there, and in Acts, he again does this after 40 days. It’s usually inferred that he will come back to that spot in the future.
There is an interesting thing here with King David and it’s certain that the Evangelists understood it. In 2 Sam. 15, there is this tragic moment in Daivd’s life. His son Absalom is attempting a coup. And David’s trusted and sagacious advisor, Ahitophel the Gilonite, betrays him and goes to Absalom and tells him how to get to David and kill him. David escapes his city (Jerusalem is the city of David–he conquers it as a strategic site to rule the tribes, so that it doesn’t appear that he favors Judah, his own tribe) and the Samuel passage says David crossed the winter-flowing Kidron. And he goes to the Mount of Olives and weeps and prays. Now there is the “Son of David,” betrayed by his trusted companion and advisor (Judas), and he crosses the Kidron (John says) and goes to the Mount of Olives (Mk and Mt) and there his soul is sorrowful and he prays. Matthew continues the parallel. Ahitophel the betrayer of David eventually concludes that Absalom is an idiot, and Ahitophel goes and hangs himself. It’s the only OT person to hang himself. Matthew says the same of Judas. He hangs himself. It’s this kind of thing that makes the event with Jesus one to be remembered. He is, especially for Matthew, the Son of David. This is another instance of Johannine and Markan traditions crossing somewhere in the past. John isn’t using Mark (like Mt and Lk do) but there’s a commonality in the past.
There’s more parallel. As David goes up to the Mount, he has companions, but he starts to tell them to go back, and he ends out alone. Jesus does the same thing. He finally gets down to three (in Mark), and then he leaves them to be by himself.
As Jesus leaves the supper and the disciples follow him (John: he crosses the Kidron) (Mk and Mt: he goes to Mt. of Olives) (Lk: having gone out he goes according to his custom to Olives, his disciples follow). Only Mk and Mt have Jesus speaking anything on this journey. This speech consists of predictions about the disciples. There’s a general prediction, and a particular one. Luke and John place some of this in the supper itself and it’s the statement about Peter betraying Jesus when the cock crows.
 There’s a lot of discussion about these two ascensions (is there just one somehow?) and whether Luke was appealing to two sources, or whether he’s using the event symbolically in two different ways or something (end of Jesus’ earthly career, or beginning of the earthly church). Luke seems to like the 40 day thing: 40 days of preparation with Jesus at the beginning of the ministry, 40 days as preparation for the Holy Spirit event in Acts. In Acts there are angels present at the ascension they tell the disciples that there is no need to look up into heaven, Jesus will return as he left, to judge the world. In a lot of the Gospel stories, the book of Zechariah is heavily deployed: cleansing of the temple, God standing on the Mount of Olives facing the city and he divides the people in the Kidron Valley, so Jesus will come back to that spot and judge the world. Of course its parochial in a way, but we see it in varying degrees as allegory I suppose. Luke sees this as a symbolic place and it’s based on the tradition he has of Jesus departing from the Mount. We have this vision of the Twelve going out through the world, preaching. But the actual reports of their activities suggest that they essentially stayed at Jerusalem. Peter goes around some. It fits their office in a way. Jesus chooses them at judges of the tribes of Israel and that’s why there are twelve. They are witnesses both for and against.
 Certainly, Jesus doesn’t say this twice, that seems wholly unlikely. The question then is, which way was it? Does one of them represent the earlier tradition about the predictions? The supper predictions are three: Judas will betray, and that can’t be moved to the journey, because it’s connected to breaking bread. The other two, “strike the shepherd and the sheep scatter, all of you will be offended” (it means scandalized) Peter says not me, Jesus says, want to bet? One way of thinking about this is that all of them take place at the supper. Why would Mark move the last two to the journey to Olives? It’s a good way to preface what is going to take place there, Jesus is terribly troubled, experiences horrors, then he’s arrested. Mark’s vision of everything to come is deathly somber–it’s a powerful theme of weakness, and he has his reasons perhaps. John is utterly the reverse of this. The image is one of triumph even at the supper, and John basically skips Gethsemane altogether. I’ll come back to this contrast.