This may be accurate when you're still dealing with a hemisphere, but if you accept the principle that it would work, the probabilities are different with a single neuron. The inputs of one neuron over the course of one calculation are far simpler than the rest of the brain. In fact, any combination of inputs would correspond to something from some brain.

Technically, I guess even one neuron might be too much. It has a lot of inputs. Get it down to a few atoms and it definitely works.