Proof That Computers Can't Do Everything (The Halting Problem)
Notice the way the walker twists its upper torso ever so slightly while it is walking (starts at 25 seconds, runs through 31). That little bit on motion conveys something, perhaps a little bit of sass? Don't bother watching the whole video, short as it is, it's an effing waste of time.
The Halting Problem itself is stupid. It's one of those philosophical questions that computer science wienies like to argue over, kind like the old "how many angels can you fit on the head of a pin" question that old time religious philosophers used to argue about.
Can you build a machine that won't work? Sure, easy. Pick up a rock. Declare that this rock is a rocket and can fly to the moon. Let go of the rock. Will it fly to the moon? No, it will not.
Can you build a machine that will count to infinity? No, you can't. You can't even build something that would hold the answer because it would have to be infinitely big.
Consideration of some of the fundamental questions about what computers can do have provided real insight into the nature of the universe and have led to real benefit. This is not one of them.