@Throwback: Again I could argue with you forever but we are getting NOWHERE. If you don't think young prodigy programmers exist look at Mark Zuckerburg. Many of these people have a natural nag for this. As far as unpredictability it's really how you define it. For example a program can be created to generate a random integer. Thus it is "unpredictable" in a sense. However the fact that the program will always generate a random integer is 100% predictable (pseudorandom number generator ). When you look at it like this then yes, it is predictable. However if you define behaviour strictly of this one integer then it's value is unpredictable. This is a very rudimentary example but it does serve to show that the behaviour of a program does not have to be predictable. The reason that so many make the claim that you have is because of the binary nature of computers. If there is only 2 possibilities (On, Off, Stop, Start.) then how can any program be unpredictable...I can understand this view but if any mathematical operations can replicated in binary then I refuse to believe that algorithms haven't been developed that cause computer programs to behave in a way that are impossible to predict.
Also with in theory quantum computing can solve many of the problems that weren't possible to solve before (problems not in polynomial time for example Shore's algorithm). This may mean that everything we think we know about the binary nature of computers is changed.
@MikeAKATheBoss: I really should have cited my sources regardless. But yeah I know that small fact from personal experience. =p