“There’s something really interesting going on here,” says Kenneth Pollack of Brookings Institute, a former CIA Middle East analyst and author of a new book on Iran. “We should’t dismiss this as just words.”

Pollack notes that Bill Clinton came close to an encounter with then-Iranian president Mohammed Khatami at the United Nations in 2000. At the time, Khatami was seeking better relations with the west, and Clinton was open to the meeting. Elaborate scheduling changes allowed the two men to wind up in the same room, but an actual encounter never happened—thanks to hardliners in Iran who opposed it. If Rouhani is able to pull off some direct contact with Obama, it would be a sign not only of his own thinking but of the domestic political climate in Iran.

The world may never see it, however. Even if Obama presses the flesh with Rouhani, it could happen out of the view of reporters and photographers, limiting its symbolic impact. Even good intentions could be foiled by the complex logistics of the mass diplomatic gathering. (And a substantive sit-down between the two men appears highly unlikely.)

So the main event may wind up being the speeches that will be delivered by Obama on Tuesday morning and by Rouhani late in the afternoon. Obama officials will parse Rouhani’s address for conciliatory statements—perhaps some equivalent to then-Secretary of State Madeleine Albright’s 2000 apology to Iran for America’s participation in a 1953 coup there. “Does he go beyond all the statements that he’s made already?” Pollack asks.