Conversation

Nice thing about tunnels is that unlike unbroken spatial metaphors, 3 is all you need. Any graph can be embedded in 3d iirc (follows from Nash embedding theorem I think?). Even if idea space you're exploring is 10d, so long as you explore small connected patches, 3d is enough
Replying to
It’s much easier than this. You can use a fun fact about a twisted cubic: no four distinct points on a twisted cubic are coplanar. So you take n points, draw a complete graph and use induction.
1
2