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

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

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

On 4/22/2025 4:58 PM, Andy Walker wrote:

On 22/04/2025 15:57, Mr Flibble wrote:

On Tue, 22 Apr 2025 15:43:27 +0100, Andy Walker wrote:

The "real" Mr Flibble is a malevolent penguin.  I wonder why
contributors take him so seriously?  If you want to debate with a
penguin, that's your prerogative, but to me it makes more sense to add
several pinches of salt and smile or groan as appropriate to everything
he writes.  He has a knack for writing things that are just about
plausible, which is enviable, but one response to anything interesting
is surely enough?

Mr Flibble is very cross.

>
     He shouldn't be.  As hinted above, being able to write successful
satire is a rare skill.  But it loses its point if too many people take
it seriously.
>

>
Flibble <is> factually correct.
>
All computation is defined to be represented as finite string
transformations to finite strings.

 Except you are doing the logic backward.
 

>
This <is> how Turing Machine computable functions actually work.
Outputs are forced to correspond to inputs when finite string
transformation rules are applied to inputs to derive outputs.

 And you need to know that the function *IS* computable to use that.
 What the machine actually produces will be computable.
 What the machine is SUPPOSED to produce might not be.
 

>
    a function is computable if there exists an algorithm
    that can do the job of the function, i.e. given an input
    of the function domain it can return the corresponding
    output. https://en.wikipedia.org/wiki/Computable_function

 Which says if a machine exists, it is conputable.
 The machine does not need to exist.
 This seems to be a flaw in your logic, you seem to think there is a Truth Faerie that can magically make the impossible happen.
 

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

>
People here stupidly assume that the outputs are not
required to correspond to the inputs. That comes from
learn-by-rote with zero depth of understanding.
>

 The outputs DO need to correspond to the input, but not necessarily by a computable transform.
 

Yes necessarily by a computable transform.

That only exists if the function is, in fact, computable.
 

Uncomputable functions are an incoherent idea when
computable functions are defined by deriving outputs
by applying finite string transformations to input
finite strings.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer