I did a bit of untintentional reversing once. It was my last sortie on the squadron and I was in the back of a 2-sticker running an exchange pilot through an IRT profile - whoopy doo! I started to set the aircraft up for him to do the usual 'recovery from an unusual position' on instruments. I did a couple of rolls and generally flopped about a bit to disorientate him, and then pulled up into a 70 degree climb with the engines at idle. Speed was about 250 - admired the sunset - then 130 - admired more sunset - then 130, at which point I thought 'That's not right, speedo's stuck!' just as the speed dropped off the clock. No problem, but I decided that it wouldn't be fair to hand over control at this stage so I just centralised controls with a view to doing it all again but properly. The nose began to rise so I pushed the stick forward and the nose rose even faster into the vertical. With the stick fully forward the aircraft wasn't recovering but the nose was still rising, and then I noticed smoke drifting upwards out of the intakes. It dawned on me that we were now going backwards, which is why the elevator was operating in the opposite sense. I centralised controls and held very tight, muttering something like 'Hang on!' to the the other driver. The aircraft crashed over onto its back, down through the vertical until it was about 70 degrees nose up (again), then flopped down through the vertical again until upside down and horizontal-ish, and then pendulum-ed a few times through the downward vertical, with us being shaken like peas in a pod and crashing our heads against the windows. I thought 'How embarrassing - last sortie on the squadron and I'm about to eject!' Eventually the jet steadied out with its nose pointing at the North Sea, engines still going, the speed began to increase and I levelled off. Calmly I said 'You have control. What else would you like to do?' and then we went home - quietly.
I learned about flying (backwards) from that.