Re: A computable function that reports on the behavior of its actual self is not allowed

On 5/13/24 10:10 AM, olcott wrote:

On 5/13/2024 8:55 AM, Fred. Zwarts wrote:

Op 13.mei.2024 om 15:39 schreef olcott:

On 5/13/2024 4:34 AM, Fred. Zwarts wrote:

Op 12.mei.2024 om 21:27 schreef olcott:

Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that 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
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A computable function that reports on the behavior of its actual
self (or reports on the behavior of its caller) is not allowed.

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So, olcott uses his authority to create a new problem. Why would anybody be interested in such limitation?
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The definition of computable function is an axiomatic basis
not any mere authority.

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I was referring to the "is not allowed". If olcott uses his authority to introduce a new axiom with this sentence, a new problem is created. Who is interested in a system with this new limitation?
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 No decider can take an actual Turing Machine as its input.
 

But the HALTING function that it is trying to compute DOES, thus the Turing Machine takes some from of representation / description / specification of that input.
Like MOST inputs to Turing Machines trying to compute some Function.
The only Functions that don't need this are the (relatively few) Functions whose input IS a finite string, and even then, often the Turing Machine will need to answer with a representation unless that output was also a finite string.