Ah, now I see how this works. Nice puzzle.
Why did the vector cross the road?
It wanted to be normal.
This can be proved by induction. For the inductive step, note that
Hence, for this problem,
In general, for , we have
This is a very neat formula. It also proves that if
then −1 ∊ M[sub]n[/sub]
Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?