2 ms·

Yeah I get that, but if we're inventing magic infinite computers, why not invent magic halting algorithms? > the halting problem was solvable, then anyone wit

• lmm 2y ago
  > Yeah I get that, but if we're inventing magic infinite computers, why not invent magic halting algorithms? Do you object to doing geometry because it involves a magic infinite plane? The point is that by studying the behaviour of this simple model we can learn useful things. > This paragraph is essentially saying this - if we had magic computers then we could magic things we them, but we don't so we can't. If you knew what a program would do on a magic computer, you could do very interesting things. The point isn't to have an actual magic computer.
• Dylan16807 2y ago
  > This paragraph is essentially saying this - if we had magic computer Not at all. A halting algorithm very specifically wouldn't need magic computers. Heck, if you had a magic infinite computer then you wouldn't need a halting algorithm. It's the opposite of a prerequisite. A halting algorithm requires the concept of an infinite computer. No more, no less. It's like a calculus program solving some category of infinite sum. It uses the concept of infinite math, it doesn't need or want a computer that's actually capable of infinite additions. And detecting divergence is a lot like detecting halting.