| A thesis advisor entrusts his Ph.D. student with the responsibility of determining what to do with his discovery that mathematics contains inconsistencies.
This is one of several works of fiction that explore consequences of Gödel's Incompleteness Theorems. This one, like Ted Chiang's Division by Zero, is pretty sophisticated in terms of the mathematics behind it. For instance, it attempts to explain why the contradiction in mathematics has not resulted in obvious problems before:
| (quoted from On the Occasion Of Your Graduation)
It was impossible to check directly; with eight levels of Gödel encoding involved, the inconsistent statement in question, expanded out in terms of elementary operations, would have been more than ten to the trillionth characters long! Indeed, I have since discovered a heuristic argument that suggests that without such an encoding trick, any sequence of deductions less than about ten thousand pages long should be consistent. Nobody's checkbook will fail to balance.
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Mathematically, therefore, it is superior to most other works of fiction that tend to get Gödel anywhere from a little confused to completely wrong.
From a literary standpoint, however, not much happens in this story. As it takes the form of a letter from the advisor to his recently graduated student, those two characters do get "fleshed out" a little bit. But, Division by Zero addresses the same idea in a much more carefully crafted and emotionally potent story.
This story appeared in the Journal of Humanistic Mathematics (Volume 1 Issue 2) July 2011. |
