The brain is based on physics, and we can simulate physics on a computer, so what is to stop us eventually simulating human beings in a computer, your whole body including your brain? Many researchers, and science fiction writers have come to the conclusion that it is just a matter of time, and increasing computer power before we can do this.
However - there are some gaps in this reasoning. Are the laws of physics as we know them complete? Could there be laws physics that we can't simulate using a computer program?
Roger Penrose, a specialist in quantum gravity, thinks that our understanding of quantum mechanics is incomplete and will need to involve gravity along with the other forces of nature. Also he thinks this new physics will arise, not just in extreme situations such as black holes (if they exist) and Hawking radiation. He thinks that these interactions of gravity with quantum mechanics happen all the time, in a much more ordinary sense, at the "Planck Scale".
Until we can do that, we can't simulate a human brain, and he has reasons that suggest, he thinks even proves, that when we do finally understand the physics, we will find out that it is "non computable", i.e., that it can't be simulated using a computer program as ordinarily understood.
He has written about this in the Empire's New Mind and Shadows of the Mind. But I think his ideas have been often misunderstood. Decided to write this after finding a summary of his ideas in Wikipedia which got them completely wrong (now corrected), and after various discussions.
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But he is not the first. Godel also had this belief. After he completed his proof, thinking over his results, he came to the view that a computer could not be programmed to understand mathematical truth - though he didn't think this could be proved.
