This is a fact of computer science, proven by Alan Turing using the halting problem. Undecidable problems are also far, far more numerous than decidable ones, an uncountable infinity to a countable one.
OK, I've got a bit over the top
I should have said that I believe in power of 1s and 0s simulation-wise: I say, its possible to model a brain (or create computational model of many (any?) real life events, with enough computational power and knowledge.
Halting problem is different because it does not ask question about the next state of some model - it asks whether the event will happen at any point of time from now till infinity. (unfortunately, I'm out of the university for too long to consider the whole class of other problems this one represents).
As for the mind vs algorithm ... this is still rather philosophical (as in: unanswerable by other sciences). Someone would say that the whole universe is deterministic ie. algorithmical. Others would say there's a magic happening in our heads, which cannot be described or imitated.
But in the case of the consciousness vs algorithm we can take Turing's own stance: screw the consciousness and self-awareness. Machines that can emulate intelligent behavior - appear like intelligent to observer - are good enough.
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The A.I. progression is slow but steady. You don't need to look further than google's products - "Did you mean", image search, language translation are all examples of advancements in various AI fields we use almost daily.