“A rare example of a well-defined, useful, but noncomputable problem is the halting problem. Imagine that I want to write a computer program that will examine another computer program and determine whether or not that program will eventually stop. If the program being examined has no loops or recursive subroutine calls, it is bound to finish eventually, but if it does have such constructs the program may well go on forever. It turns out that there is no algorithm for examining a program and determining whether or not it is fatally infected with an endless loop. Moreover, it’s not that no one has yet discovered such an algorithm; rather, no such algorithm is possible. The halting problem is noncomputable.”