The Tristram Shandy Paradox
Tristram Shandy is an auther writing an auto-biography. Unfortunately, he writes very slowly; each day of his life takes him a year to write about.
The Tristram Shandy paradox asks: If Shandy continues at this rate for eternity then will his book ever be finished?
Russell, who invented this paradox, suggested that the book would be finished. Given an infinite amount of time, for every day in Shandy’s life there is a year to spend writing about it; there are, after all, an infinite number of years in which to write the autobiography. The autobiography therefore can be completed.
This doesn’t seem right though. With each passing year, Shandy completes his writing about one day, but leaves another three hundred and sixty-four days undocumented. Every year, then, there are three hundred and sixty-four days more for Shandy to write about; the more time passess, the further behind he falls.
How can it be that Shandy ever falls further behind, and yet that given an eternity he will complete his work?