The Next Room

There's this great anecdote from one of the students of philosopher Ludwig Wittgenstein's. In David Embods & John Eidinow's Wittgenstein's Poker, Vinelott recounts a particular session from a philosopher club that Wittgenstein led.

Besides the puzzle of speaking to oneself, they had discussed the flexibility of the rules of mathematics. “Suppose you had all done arithmetic within this room only,” Wittgenstein had hypothesized. “And suppose you go into the next room. Mightn't this make 2+2=5 legitimate?” He had pushed this apparent absurdity further. “If you came back from the next room with 20x20=600, and I said that was wrong, couldn't you say, 'But it wasn't wrong in the other room.'”

This might seem like “apparent absurdity,” but it isn't to me. How peculiarly appropriate that Wittgenstein intuited an entire field where you sometimes walk into a room and 2+2=5 is legitimate, where you can say “It wasn't wrong in the other room.”

It just takes on a different guise:

“It works on my machine...”

I wonder how much further Wittgenstein explored this flexibility in mathematics in his own thought/writing and how it could be analogized/connected to this often parodied problem in software engineering.