This is a short, spoilerific rumination on the short story ‘Division by Zero’ by Ted Chiang.
We are told in the opening paragraph of this story that, unlike what we may have learned in elementary school, the result of division by zero is not infinity, but “undefined”.
This is a story about negation, about depression, about suicide. Both characters have attempted suicide at some point in their lives.
Renee is a brilliant mathematician whose world is shattered when she proves something quite basic simply isn’t true. This introduces uncertainty into the simplest of things. She has proved that any number can be equivalent to any other number. She becomes depressed and tries to kill herself.
“Her concentration was gone, and last night she had had a nightmare about discovering a formalism that let her translate arbitrary concepts into mathematical expressions: then she had proven that life and death were equivalent.”
But her partner Carl finds himself in a similar state because of his inability to help Renee. He has experience of attempted suicide, as well as comforting others who had been suicidal. His world view was that he could handle this kind of situation. He can not.
“He had always had reason to consider compassion a basic part of his character, until now. He had valued that, felt that he was nothing if not empathic. But now he’d run up against something he’d never encountered before, and it rendered all his usual instincts null and void.”
Renee’s situation is to Carl what the now-unreliable mathematics is to Renee. They are both mired in uncertainty.
The ending of the story is foreshadowed by the opening paragraph. It is, in fact, a division by zero: undefined.
(Division by Zero can be found in the collection Stories of Your Life and Others)