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

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?

>
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.

>
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.
>

>
And if the mapping isn't computable, like the halting function, there are no such steps.
>

>
int sum(int x, int y) { return x + y; }
The mapping from sum(3,2) to sum 5 + 6 does not
exist

 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 then I hereby overload the
term "mapping" with this new meaning.
INPUTS to functions computed by Turing Machines
must correspond to OUTPUTS via an algorithm.
The WILD GUESS that DD correctly emulated by HHH
must halt because DD(DD) halts ignores that a
specific algorithms is required.
If you cannot show every detailed step of the full
execution trace of HOW DD emulated by HHH
reaches its own emulated final halt state
THEN ALL YOU HAVE IS BLUSTER.
_DD()
[00002133] 55         push ebp      ; housekeeping
[00002134] 8bec       mov ebp,esp   ; housekeeping
[00002136] 51         push ecx      ; make space for local
[00002137] 6833210000 push 00002133 ; push DD
[0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
[00002141] 83c404     add esp,+04
[00002144] 8945fc     mov [ebp-04],eax
[00002147] 837dfc00   cmp dword [ebp-04],+00
[0000214b] 7402       jz 0000214f
[0000214d] ebfe       jmp 0000214d
[0000214f] 8b45fc     mov eax,[ebp-04]
[00002152] 8be5       mov esp,ebp
[00002154] 5d         pop ebp
[00002155] c3         ret
Size in bytes:(0035) [00002155]
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer