Donald Hoffman

And when it's done, when it actually is like computed the square of a number or whatever it is that it's doing, it halts.

It goes into what's called a halt state.

And so when it goes into a halt state, that means it's done.

It did the computation.

But there are some computations that go on arbitrarily long.

I don't understand why.

You never come to the end of it.

There's some sort of recursive loop in it.

Yeah, where the Turing machine never halts.

You give it an input- It never thinks it's done.

And it never thinks it's done.

Got it.

Yeah, I would guess that-

Yeah, most tapes are probably you wouldn't halt, would be my guess.

But that's not an important point here.

I think that's the case, but it's not a central point.

The fact is that many won't halt.

And so the question that Turing raised was something like this.

So is there a Turing machine that can tell you if it says, given this Turing machine and all these inputs, whether this Turing machine, which one of these inputs will it halt?

Okay.