When Raymonda Tawil and Ruth Dayan met in 1970, they seemed well-primed to be enemies. Dayan, the then-wife of Israeli war hero and Minister of Defense Moshe Dayan, was visiting a hospital in the Palestinian city of Nablus to deliver dolls to children. Tawil, of Palestinian aristocracy and Yasser Arafat’s mother-in-law, was there to witness this exercise in diplomacy. She was not impressed. Today, these elder stateswomen are dear friends. From Malta, where they most recently met up, they share the story of how they won each other over in “R & R,” Act I of this week’s episode of Israel Story. In his recent book, An Improbable Friendship, Anthony David tells their full story.

Act II, “The Center for Rationality,” introduces us to economist Eytan Sheshinski and mathematician Yisrael Aumann, both of them at the top of their fields who, nevertheless, seem to leave clear thinking behind when it comes to their favorite pastime: hiking together.

In Act III, Danna Harman brings us “Girls’ Night In,” the story of two women in their forties who have been acquaintances, but by no means friends, since childhood. It took a pair of tragedies to draw them close.