“I assume you’ve taken to calling Hilbert’s box ‘Hilbert space.’
“I hope Hilbert — ‘plainly the intellectual type’ — is not disappointed that his space has only finitely many dimensions.”
[Derb] I have fond memories of my Functional Analysis lecturer, Hymie Kestelman (whose daughter, like mine, was named Eleanor), walking us through the analog to Pythagoras’ Theorem in a space of infinitely many dimensions. When he was done, he turned from the chalkboard and said with much glee: “If old Pythagoras could see that, he’d sacrifice a chicken on the spot!”
There’s a write-up on Hilbert space here.