Re: Functions computed by Turing Machines MUST apply finite string transformations to inputs +++

On 5/4/2025 2:17 PM, olcott wrote:

On 5/4/2025 12:48 PM, dbush wrote:

On 5/4/2025 1:38 PM, olcott wrote:

On 5/4/2025 11:57 AM, dbush wrote:

On 5/4/2025 12:06 PM, olcott wrote:

On 5/3/2025 4:28 PM, dbush wrote:

On 5/3/2025 3:45 PM, Richard Heathfield wrote:

>
I am conscious that you have already explained to me (twice!) that Mr O's approach is aimed not at overturning the overarching indecidability proof but a mere detail of Linz's proof. Unfortunately, your explanations have not managed to establish a firm root in what passes for my brain. This may be because I'm too dense to grok them, or possibly it's because your explanations are TOAST (see above).
>
You have said, I think, that Olcott doesn't need a universal decider in order to prove his point. But a less ambitious decider doesn't contradict Linz's proof, surely? So once more for luck, what exactly would PO be establishing with his non-universal and impatient simulator if he could only get it to work?

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The core issue is that PO, despise being nearly 70 and having worked as a programmer, fundamentally doesn't understand proof by contradiction.
>

>
The actual issue is the NO ONE here (or perhaps anywhere)
sufficiently understands the key details about
COMPUTING THE MAPPING FROM AN INPUT TO AN OUTPUT.
>
Many here know that a mapping from the input must be
computed.

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False.  There is no requirement that a mapping is computable.  The halting function is one such mapping, as Linz and others have proved and you have *explictly* agreed is correct.
>
>

What they don't know are ALL of the tiny
detailed steps required to compute this mapping.
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And if the mapping isn't computable, like the halting function, there are no such steps.
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int sum(int x, int y) { return x + y; }
The mapping from sum(3,2) to sum 5 + 6 does not
exist

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Category error.  A mapping is an association between an input domain and an output domain, not a C function call to a value.
>

 We can be more vague and say there is a mapping
from pairs of integers to their integer sum value.
 The mapping from sum(3,2) is much more specific it
only maps to 5 by the rules of arithmetic.
 If there is no preexisting term for the mapping from
one specific input to one specific output via a specific
set of transformation rules

There is.  It's called an algorithm.

INPUTS to functions computed by Turing Machines
must correspond to OUTPUTS via an algorithm.

And not all functions can be computed, such as the halting function, as Linz and other have proved and as you have *explicitly* agreed is correct.

 The WILD GUESS that replacing the code of HHH with an unconditional simulator and subsequently running HHH(DD)
must halt because DD(DD) halts ignores that a
specific algorithms is required.

We know that changing the input results in an algorithm that does not halt.
Changing the input is not allowed.

 If you cannot show every detailed step of the full
execution trace of HOW replacing the code of HHH with an unconditional simulator and subsequently running HHH(DD)
reaches its own emulated final halt state
THEN ALL YOU HAVE IS BLUSTER.

Of course the changed input doesn't halt.
Changing the input is not allowed.