> So, at what point in time the person who is observing a running program is going to declare it doesn't halt? That "point in time" is within time itself condi

> So, at what point in time the person who is observing a running program is going to declare it doesn't halt? That "point in time" is within time itself condition on the program halting. If the program never halts, then that point in time is "never". We might disagree on whether "never" is a point in time at all... We might even disagree on whether "never" as a concept even exists or makes any sense. Yet as you say, all programs will halt, one way or another. You divide such factors into "internal" vs "external", but if we really think about, no computer program is an island; Computation is a property of the material universe. I wouldn't be so quick to draw the distinction between internal logic and external interference. The program itself wouldn't exist without external input, and its result is only meaningful in the context of the reality to which it has effect. I understand the nature of the abstract philosophical academic conundrum, but also that it's a flawed and incomplete way of modeling real world concepts. To me the halting problem is a practical engineering one; A matter of performance. A faster way to find the same answer, i.e. optimization. Consider internal errors as well. The computer can have a hardware bug that causes the program to never halt even if in theory it should. Internal interference in the flow of electrons within its circuits could throw it off. The coin in your example could be faulty, and shatter due to internal tensions upon landing.