I’m going to leave the mathematics mostly behind and take you on a descriptive journey.
You leave your house and go to the grocery store. Just before you enter someone walks in in front of you. Where are they going to go?
Do they turn left? Right? Do they freeze and grab a basket? Are they getting a phone call and they stop to answer the phone? How fast are they going to walk?
The scope of what they *could* do at any point is huge, and the Halting Problem basically posits that there will be no simpler way to predict what they do than to have the real live human do whatever they’re going to do, live, right in front of you. It’s easier for the universe to manufacture that exact human on that exact day than to simulate, with certainty, what the person will do.
Let’s move to computers. The Halting Problem says that there’s no better way to predict when a program will end (halt) than just running the program to see what it actually does.
This matters because it means (here comes math again) operating systems can’t predict the behavior of programs running on them in *polynomial time*–basically there’s no straightforward equation to tell you how much longer to wait for any arbitrary process to finish, become responsive, take free resources, etc… that’s better than than just letting it run.
So the best we *can* do is spinning beach balls and task managers that allow you to kill programs and frustrating progress bars that never seen to know how long something will really take. Because math says nothing will be better than letting the thing actually happen and seeing how long it takes.
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