Who can name the largest number?
On Friday, Jan. 26, two philosophers, MIT Associate Professor Agustin Rayo (The Mexican Multiplier) and Princeton Associate Professor Adam N. Elga (Dr. Evil) engaged in the Large Number Duel, in which they attempted to one-up each other by inscribing the largest finite number ever to be written on an ordinary-sized chalkboard. The feat, if successfully accomplished, would be worthy of a note in the Guinness Book of World Records. (...)
The rules of the duel gave free rein to the contestants’ creativity and humor, maintaining only a ban on the use of infinity, and restricting statements about the number proposed to a primitive semantic vocabulary. The battle itself was intense and the room in the Dreyfoos wing of the Stata Center was packed, with people standing on chairs and at least 20 students craning their necks from the doorway.
The contest opened in the style of a boxing match, with competitors presented “in the red corner” and “in the blue corner.” Elga went first, writing the number one. “Ha!” announced Rayo, as he countered with a string of ones across the board. Elga retaliated with a clever trick, erasing a line through the base of half of the ones to turn them into factorials. (...)
Near the end of the duel, Rayo furiously scribbled on the whiteboard: “The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with less than a googol (10100) symbols.”
Although this definition took a bit of tweaking, including what Rayo described as his “second order logic trick,” it soon won him the duel.
As Elga collapsed, slain, the referee closed the ceremony.