And you still won't have written a program that determines whether any arbitrary program goes into an infinite loop.

If we can write a program that translates said arbitrary program into the rules for an n-state, m-symbol turing machine, where n = (2|3|4|5) and m = 2, then yes - we can determine if the program terminates or not.

We can make some fuzzy guesses whether or not the program terminates or not in other state/symbol combinations.

http://en.wikipedia.org/wiki/Busy_beaver

If we ever did write said program that could determine whether any /arbitrary/ program is infinite, then we have solved the halting problem. And that would be quite something.

You're right. I wouldn't have.