> ... because computers aren't Turing machines and have finite memory, so all programs are guaranteed to halt. Is this simply wrong or am I not understanding?

> ... because computers aren't Turing machines and have finite memory, so all programs are guaranteed to halt. Is this simply wrong or am I not understanding? With finite memory, the halting problem is solvable, but that's different than all programs halt. while True: pass The program doesn't halt even with finite memory. Unless he means eventually the world will end, or the power supply will die, etc. > If the halting problem was solvable, then anyone with a computer could prove Goldbach's conjecture in an afternoon. Why does he say "in an afternoon"? Maybe it would take 10^100 years? The halting problem be solvable or unsolvable is not a question of complexity or efficiency.