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

On 11/4/2024 6:07 AM, Richard Damon wrote:

On 11/3/24 11:03 PM, olcott wrote:

On 11/3/2024 9:57 PM, Richard Damon wrote:

On 11/3/24 10:19 PM, olcott wrote:

On 11/3/2024 7:46 PM, Richard Damon wrote:

On 11/3/24 8:38 PM, olcott wrote:

On 11/3/2024 7:26 PM, Richard Damon wrote:

On 11/3/24 8:21 PM, olcott wrote:

>
What would an unbounded emulation do?
>

>
Keep on emulating for an unbounded number of steps.
>
Something you don't seem to understand as part of the requirements.
>
Non-Halting isn't just did reach a final state in some finite number of steps, but that it will NEVER reach a final state even if you process an unbounded number of steps.

>
Would an unbounded emulation of DDD by HHH halt?

>
Not a valid question, as your HHH does not do an unbounded emulation, but aborts after a defined time.
>

>
*Now you are contradicting yourself*
YOU JUST SAID THAT HHH NEED NOT DO AN UNBOUNDED
EMULATION TO PREDICT WHAT AN UNBOUNDED EMULATION WOULD DO.

>
Right. it doesn't NEED to do the operation, just report what an unbounded emulation would do.
>
You asked about an "unbounded emulation of DDD by HHH" but that isn't possible, as HHH doesn't do that.
>

>
On 11/3/2024 12:20 PM, Richard Damon wrote:
 > On 11/3/24 9:39 AM, olcott wrote:
 >>
 >> The finite string input to HHH specifies that HHH
 >> MUST EMULATE ITSELF emulating DDD.
 >
 > Right, and it must CORRECTLY determine what an unbounded
 > emulation of that input would do, even if its own programming
 > only lets it emulate a part of that.
 >
>
*You JUST said that HHH does not need to do an unbounded emulation*
*You JUST said that HHH does not need to do an unbounded emulation*
*You JUST said that HHH does not need to do an unbounded emulation*
*You JUST said that HHH does not need to do an unbounded emulation*
>

 Right, it doesn't need to DO the unbounded emulatiohn just figure out what it would do.
 Just like we can compute:
 1 + 1/2 + 1/4 + 1/8 + ... + 1/2^n + ...
 Ether by adding the infinite number of terms, or we can notice something about it to say it will sum, in the infinite limit, to 2.
  In the same way, if HHH can see something in its simulation that tells it THIS this program can NEVER halt, it can report it.
 

Anyone with sufficient technical competence can see that
the unbounded emulation of DDD emulated by HHH can never halt.

That is what it can easily do with your Infinite_Loop program, and with a bit more intelegence with Infinite_Recursion.
 It doesn't work with DDD, as if the decider HHH aborts its simulation of DDD, then so will the copy of HHH that DDD called.
 

On 11/3/2024 12:20 PM, Richard Damon wrote:
 > On 11/3/24 9:39 AM, olcott wrote:
 >>
 >> The finite string input to HHH specifies that HHH
 >> MUST EMULATE ITSELF emulating DDD.
 >
 > Right, and it must CORRECTLY determine what an unbounded
 > emulation of that input would do, even if its own programming
 > only lets it emulate a part of that.
 >
*YOU ARE CONTRADICTING YOURSELF*
You are saying that a finite computation can predict the
behavior of an unbounded computation and then saying
that the finite computation of HHH cannot predict the
unbounded computation of DDD because it is a finite computation.
*YOU ARE CONTRADICTING YOURSELF*
*YOU ARE CONTRADICTING YOURSELF*
*YOU ARE CONTRADICTING YOURSELF*
*YOU ARE CONTRADICTING YOURSELF*
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer