I have asked another question on Hebbian learning before, and I guess I got a good answer which I accepted, but, the problem is that I now realize that I've mistaken about Hebbian learning completely, and that I'm a bit confused.

So, could you please explain how it can be useful, and what for? Because the way Wikipedia and some other pages describe it - it doesn't make sense! Why would we want to keep increasing the weight between the input and the output neuron if the fire together? What kind of problems can it be used to solve, because when I simulate it in my head, it certainly can't do the basic AND, OR, and other operations (say you initialize the weights at zero, the output neurons never fire, and the weights are never increased!)