[32bitkid]

This one is interesting, because if I recall correctly, if you are using the single symbol they more or less mean the same thing. You can do ~~~ or ^^^ and get to the same spot

The difference is in their numerical notion. ~N means go to my Nth first parent. Where ^N means my Nth parent, which is really only valuable/useful on merge commits (Or more specifically octopus merges that merge more than two commits)

This is why ~ and ^ in the single form mean the same thing.

So, in one mental model of the DAG you can think of ^ as horizontal navigation (Right) and ~ as vertical (Down)

[rjtobin]

Oh cool! That's good to know. Sadly too late to edit my original message, but have upvoted yours so people won't learn from my errors :)