Re: How computable functions actually work. (was Flibble)

On 4/23/2025 6:15 AM, Richard Damon wrote:

On 4/23/25 12:14 AM, olcott wrote:

On 4/22/2025 9:33 PM, Richard Damon wrote:

On 4/22/25 6:19 PM, olcott wrote:

>
On Turing Machines inputs <are> finite strings, and
finite string transformation rules <are> applied to
these finite strings to derive corresponding outputs.

>
Yes, so the results can only BE what is computable, but as pointed out, the correct answer need not be.
>

>
That would seem to indicate an error in the original
problem specification.

 No, just in your understanding of it.
 

>
Whatever can be derived by applying finite string
transformation to input finite strings <is> computable.

 No, and the problem is you don't actually understand the meaning of the words you are using.
 The point it that your phrase "Computations are finite string transformations" is not a definition, but just a description.

int sum(int x, int y) { return x + y; }
It does conclusively prove that HHH is not allowed
to report on the behavior of the direct execution
of DD for the same reason that sum(3,2) cannot report
on the sum of 4 + 3.
The finite string transformations to the machine code
of DD according the definition of the x86 language
ALREADY SPECIFIES BEHAVIOR THE IS NOT THE BEHAVIOR
OF THE DIRECTLY EXECUTED DD.
The call to HHH(DD) from the directly executed DD returns.
The call to HHH(DD) from DD emulated by HHH cannot possibly return.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer