Thoughts on sentience

I have a theory that not everything that we experience is of a calculable, observable nature. Moreover, I theorize that the fact that we experience in the first place is proof of the former statement. This would disprove the theory that sentience is a product of nothing more than the results of natural physical and chemical reactions that occur in our brains, or of any thing that can be measured.

Here is my argument: If everything that occurs within our brain - the position and velocity of every atomic particle, which is theoretically both possible and impossible to measure, but for our purposes we will assume it is possible - were observable and measurable according to what we understand as the laws of the physics - as in, there were no unobservable outside forces such as the abstract idea of a soul that has "free-agency" - then theoretically one could produce a machine capable of calculating with exactness the projected path of each atomic and sub-atomic particle within the brain. This would also account for outside forces, since, according to the theory I am presently working to disprove, everything in the universe acts according to calculable natural laws and is without the idea of "magic", that which is without the boundaries of explanation; therefore everything would be calculable and thus able to be accounted for. Now, in a controlled environment, let us place a man in front of this machine that has observed the location and velocity of every particle and has calculated the paths that each will take and analyzed them to form results observable to man. Let us say that this man was out to disprove the theory I am working with right now. He asks the machine if, between 4 and 10 seconds after the machine's answer (which is given immediately after the question is made), the man will throw his hands in the air. Here we have a paradox, an impossibility. If the machine calculates that the particles in the man's brain cells or in any other outside body that would influence the act were not accelerating to create the situation where that act would be performed, and thus replies with "no", the man waits 5 seconds and then throws his hands in the air, by virtue of his desire to disprove the theory. If the machine calculates the opposite, that the man will in fact be propelled by every calculable force to throw his hands in the air in said time period, then the man keeps his hands down, by virtue of his desire to disprove the theory. Wouldn't the machine have calculated that? But if it had, and stated that the calculations dictated that he would NOT throw his hands in the air, we are back to the first circumstance. I theorize that, to avoid this paradox, one must acknowledge the existence of a force which is, by definition, external, unobservable, and incalculable, free from the government of the laws we cling to as an explanation of what appears to us as resulting from those laws. This will then free us to understand that which many refuse to accept - miracles - which are defined as that which we have observed but cannot explain with our current understanding of the universe. I theorize that included in those miracles is life itself, sentience, which is the most potent and universal evidence of the existence of them.