[Madison]

Okay, I'll concede that, unless I'm about to devise derailleur: part deux, shifting while moving backward is out of the question.

However, I don't think that moving backward itself is impossible.
The problem, as best as I can see, is that when there's resistance against the back sprockets due to, say, the wheels, the torque transmitted by the chain is taken up by the torsion springs in the tensioner part of the derailleur. Thus, you don't move.

But, there's no written rule that says, really, that tensioning mechanism needs to be a part of the derailleur, right? It serves to pick up the slack that is given off because of the smaller diameter sprockets. What if this slack were taken up elsewhere?

There are lots of robots with simple, similar tensioning mechanisms, and *they* can go backwards. I think a derailleur sort of mechanism doesn't preclude the ability to go backwards. We'll see, I guess.