Re: The philosophy of computation reformulates existing ideas on a new basis

Am Mon, 11 Nov 2024 09:15:09 -0600 schrieb olcott:

On 11/11/2024 5:06 AM, Mikko wrote:

On 2024-11-09 14:56:14 +0000, olcott said:

On 11/9/2024 3:53 AM, Mikko wrote:

On 2024-11-08 14:39:20 +0000, olcott said:

On 11/8/2024 6:39 AM, Mikko wrote:

On 2024-11-07 16:39:57 +0000, olcott said:

On 11/7/2024 3:56 AM, Mikko wrote:

On 2024-11-06 15:26:06 +0000, olcott said:

On 11/6/2024 8:39 AM, Mikko wrote:

On 2024-11-05 13:18:43 +0000, olcott said:

On 11/5/2024 3:01 AM, Mikko wrote:

On 2024-11-03 15:13:56 +0000, olcott said:

On 11/3/2024 7:04 AM, Mikko wrote:

On 2024-11-02 12:24:29 +0000, olcott said:

Turing Machine Halting Problem Input − A Turing machine and an input
string w.
Problem − Does the Turing machine finish computing of the string w
in a finite number of steps? The answer must be either yes or no.

The computation specified by the finite string DDD emulated by HHH
cannot possibly reach its "return"
instruction final halt state.

It can and does if HHH is a decider and otherwise does not matter.

The computation specified by the finite string DDD emulated by HHH1 IS
NOT THE ACTUAL INPUT TO HHH.

HHH1 can take same inputs as HHH. These inputs specify some behaviour.
What they do with this input may differ.

*It is the behavior of their own input that they must report on*

It is the same input.

It has always been ridiculously stupid for everyone here to require HHH
to ignore the actual behavior specified by its own input and instead
report on the behavior of the input to HHH1.

The input is the same: DDD which calls HHH.

HHH must compute the mapping FROM ITS INPUT TO THE BEHAVIOR THAT THIS
INPUT SPECIFIES.

Not to full behaviour but to one feature of that behaviour.
Doesn't HHH1 need to?

Both HHH and HHH1 must report on whether or not their simulation of
their own input can possibly reach its own "return" instruction final
halt state. They get different answers ONLY BECAUSE THE BEHAVIOR OF
THEIR INPUT DDD IS DIFFERENT!

That makes no sense. The simulators do different things to the same
input.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.