Sharingan Prediction Method (as well as others) I explained my theory here:
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As for a "matrix effect" that's actually a good description. All peoples eyes work based off of a matrix of sensors in the back of your eyes. I believe the two main parts of the Sharingan's function is that there is a cone/rod hybrid (that doesn't exist in the real world) that is unique to the Sharingan user and could be a genetic deformity. As well, the increasing tomoe's (eventually into the MS/EMS state) each represent greater areas of focused light. I believe that chances are these areas are clusters of sensors which help to draw light down to the nerve faster.
As for the rapid reactions, in real life goalies train to react to a puck being shot at them and making various movements. Because of the years of training, professional goalies tested have shown that when they react they don't use their secondary nervous system as per a normal person, instead they use their central nervous system (reserved mostly for breathing and stuff like that) to send the signals for reacting to what they see. This increases their reaction time in such a way that they can actually catch a puck moving so fast that the human eye isn't registered to be able to see. This is called the plasticity of the brain. The brain is reprograms itself to work differently based on the way we need it to work. If the Sharingan existed this could explain how their bodies were capable of reacting to the high number of signals which were being sent from the eyes.
Now as for if Madara only has one eye or not, we don't know that for sure. they've only ever showed us one eye (I think he only has one eye though)... I've talked to various people and we share the same theory that Madara only took one eye from his brother and his brother took the other from him. I think his brother probably died later on, it's just not been mentioned yet. I personally, think that Madara is infact his younger brother who stole the other eye and watched Shodaime kill his older brother, then took his older brothers body away and left the village only later to become Mizukage. But that's just my sick and twisted mind on the matter.