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

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?
>

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Keep on emulating for an unbounded number of steps.
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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.

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Would an unbounded emulation of DDD by HHH halt?

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

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

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Right. it doesn't NEED to do the operation, just report what an unbounded emulation would do.
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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.
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.
Your "logic" of CHANGING HHH, and thus the input, is INVALID, and you claims it is correct is just a LIE (can't be an Honest Mistake, you have been told too many time, at best you can plead incompetence with a reckless disregard for the facts). HHH must look at the HHH that IS THERE, and that is the aborting one, especially if HHH does decide to abort.