How complex can it be? If you have a bare minimum background in basic physics and control theory, and a bicycle in your hands, the qualitative reasons for balance and stability will jump at you in under 10 minutes...
Please don't post unsubstantive dismissals of others' work to HN.
If you know more than the rest of us, it would be good to post an informative comment that teaches the reader something. If you don't want to do that, it's fine to post nothing.
If you feel that something is trivial and potentially wasting other people's time by means of wasting pixels, I think it's fine to speak up. (Explaining why something is trivial may not be that effective, in general).
I was clearly wrong in that many people disagreed and found this to be an interesting and nontrivial subject.
Ok, I guess I could have provided more info. Do this if you own a bicycle: hold it by the saddle perfectly straight, front of the bike forward. Make it lean on the left (no forward movement). Look at the handle, it steers left.
When you're moving this means that when you lean left there will be a torque, due to your circular path you'll be following, that will try to make the bike lean right.
Bend left -> torque to the right, bend right -> torque to the left. Here you have the basic ingredient for stability: the one torqueless angle is the bike going straight perfectly vertical wrt the ground, while any perturbation leads to a torque in the opposite direction.
If you know more than the rest of us, it would be good to post an informative comment that teaches the reader something. If you don't want to do that, it's fine to post nothing.