From: david.brown@hesbynett.no
On 09/02/2023 08:18, Richard Heathfield wrote:
> On 09/02/2023 1:09 am, Ben Bacarisse wrote:
>> Richard Heathfield writes:
>>
>>> If executed, the specified program will halt.
>>>
>>> Which it will. ALL programs halt.
>>
>> Come on! You know I know what that C program does.
>
> Yes, of course.
>
>> What I don't know
>> is in what way that C program refutes a mathematical theorem. One makes
>> statement about programs,
>
> Yes. That statement refutes the mathematical theorem by pointing out an
> obvious fact about all programs.
>
>> the other makes statements are Turing
>> machines. Presumably you don't think Turing machines all halt in the
>> same sense that you think all programs halt?
>
> Of course all Turing machines halt. You don't seriously think it is
> possible for a Turing machine *not* to halt, do you?
>
You are making up new definitions here for pretty much all of the terms.
In the mathematics of computation and computability, where the halting
problem and associated theorems live, some programs (or Turing machines)
halt and some do not.
/Real-world/ programs always halt. Most of the programs I write have an
"infinite loop" - "while (true) { .... }" in them. But they stop when
someone switches off the board they are running on. Even the last of
the Novel Netware servers will stop with the heat death of the universe.
You /could/ argue that non-halting programs are just mathematical
fantasies. But like the infinite decimal expansion of pi, or the
never-ending list of integers, they are very useful fantasies that let
people reason about all kinds of /real/ things.
So let's please stick to the normal definitions of the terms, and not
add hidden assumptions about real-world limitations to simple
mathematical concepts.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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