Pigeons are sweet. I used to feed them from my apartment window, and got to know a few of them pretty well. They would come and find me all over the city, and gather outside of the window when I was having coffee downtown. It was fun having little birdie groupies.
Pigeons have an incredible sense of hearing, and are especially good at detecting low sounds created by electrical storms and so on. They also have incredible eyesight, and can be trained to distinguish between different styles of paintings. They are slow moving birds, but they are by no means stupid. The reason that there are pigeons everywhere is that their natural habitat is a bunch of rock walls in China. They spread everywhere because human buildings are basically a bunch of ledges going up into the sky, which is more or less hat looks like home to a pigeon.
If pigeons realize that you are trying to communicate with them, they will try to communicate back. It takes a lot of time and patience, but it is possible.