Re: HHH maps its input to the behavior specified by it --- key error in all the proofs

On 8/10/24 7:52 PM, olcott wrote:

On 8/10/2024 5:47 PM, Richard Damon wrote:

On 8/10/24 6:41 PM, olcott wrote:

On 8/10/2024 4:53 PM, Richard Damon wrote:

On 8/10/24 5:37 PM, olcott wrote:

On 8/10/2024 4:33 PM, Richard Damon wrote:

On 8/10/24 5:18 PM, olcott wrote:

On 8/10/2024 3:58 PM, Richard Damon wrote:

On 8/10/24 4:36 PM, olcott wrote:

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As I have countlessly proven it only requires enough correctly
emulated steps to correctly infer that the input would never
reach is "return" instruction halt state.

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Except that HHH does't do that, since if HHH decides to abort and return, then the DDD that it is emulating WILL return, just after HHH has stopped its emulation.
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You just confuse the behavior of DDD with the PARTIAL emulation that HHH does, because you lie about your false "tautology".
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>

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Denying a tautology seems to make you a liar. I only
say "seems to" because I know that I am fallible.

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Claiming a false statement is a tautology only make you a liar.
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In this case, you lie is that the HHH that you are talking about do the "correct emulation" you base you claim on.
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That is just a deception like the devil uses, has just a hint of truth, but the core is a lie.
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What I say is provably correct on the basis of the
semantics of the x86 language.

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Nope.
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The x86 language says DDD will Halt if HHH(DDD) returns a value.

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HHH is called by main() there is no directly executed DDD()
any where in the whole computation.
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Except in your requirements, and we can see what it does by adding a call to DDD from main, since nothing in your system calls main.
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All that you need to know is that there is not any
directly executed DDD() anywhere in the computation.

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But there ccould be, and the behavior of it is what matters.
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 The key error of the halting problem proofs all of these
years has been the false assumption that a halt decider
must report on the behavior of the computation that itself
is contained within.

But it isn't a false assemption, but an actual requirement.
A Halt Decider must be able to correctly answer for ANY Turing Machine represented as its input.
ANY includes those that are built from a copy of itself.
So, a Halt Decider needs to be able to correctly answer about programs that include copies of itself, even with contrary behavior, which is what makes it impossible to compute.
You seem to confuse non-computable with invalid, it seems in part because you don't understand the difference between knowledge and truth.

 Everyone has simply assumed that the behavior of the
input to a decider must exactly match the direct execution
of this input. They only did this because everyone rejected
simulation out-of-hand without review.

Because that is the DEFINITION of what it is to decide on.
You just don't understand what a requirement is.
Since the DEFINITION of "Correct Simulation" that you are trying to use (from a UTM) means a machine the EXACTLY reproduces the behavior of the direct exectution of the machine described by the input, the correct simulation must exactly match the behavior of the direct execution.
You can't get out of it by trying to lie about it being different.

 This caused them to never notice that the input simulated
according to its correct semantics does call its own decider
in recursive simulation thus cannot possibly return to its
caller. The Linz proof is sufficiently isomorphic so this equally
applies to the Linz TM proof.

Nope, just shows you don't know what "Correct" means.
Your proof is NOT "sufficiently isomorphic" since by your own claims it is clearly not even Turing Complete, so no where near isomorphic.

 If HHH were to report on the direct execution of DDD it would
be breaking the definition of a halt decider that only computes
the mapping from its input...

Nope. Since the mapping that it is supposed to compute is DEFINED as based on the direct exectut

 You might not be open-minded or smart enough to understand
this. Mike may be smart enough if he can manage to be
open-minded enough to pay attention to every single detail
of what I said without leaping to the conclusion that I must be
wrong. Ben understood this more deeply than anyone else.
 

Nope, you are just showing you don't understand what you are talking about.
If you want to make any of your claims, PROVE THEM by showing an ACTUAL PROOF starting from the actual definitions and established truths of the field, and then with accepted truth preserving operations show how to combine them to get to your answer.
Your problem is you just don't know any of those basics, so you can't do it, which just makes you into a liar that makes unsubstantiated claims, proving your ignorance.
Remember, you are not God, and you don't get to change the rules of the system. That means you need to work within the rules.
If you want to to try to change the rules, be honest and admit you are working on a new system, and make you definitions and then FORMALLY prove what you can do with such a system. But, since you don't understand the currect system, or it seems even how formal systems work, I don't think that is actually possible for you.