Re: Who here understands that the last paragraph is Necessarily true?

Am Tue, 16 Jul 2024 08:50:12 -0500 schrieb olcott:

On 7/16/2024 3:17 AM, joes wrote:

Am Mon, 15 Jul 2024 15:56:21 -0500 schrieb olcott:

On 7/15/2024 3:51 PM, joes wrote:

Am Mon, 15 Jul 2024 08:51:14 -0500 schrieb olcott:

On 7/15/2024 3:37 AM, Mikko wrote:

On 2024-07-15 03:41:24 +0000, olcott said:

On 7/14/2024 9:04 PM, Richard Damon wrote:

On 7/14/24 9:27 PM, olcott wrote:

Turing machines only operate on finite strings they do not operate
on other Turing machines *dumbo*

That's right. But the finite string can be a description of a
Turing machine.

No that is wrong. The finite string must encode a Turing machine.

Same difference.

Not at all. The huge mistake of all these years is that people
stupidly expected that HHH to report on the behavior of its own
executing Turing machine. The theory of computation forbids that.

Encoding = description.
HHH isn't executed by anything.

// HHH is not allowed to report on this DDD int main() { DDD(); }
invokes HHH(DDD);

The outer DDD? HHH doesn't report on that. That DDD isn't even a TM
that executes (simulates) HHH.

It simply reports on a string that represents itself.
 

That way a Turing machine can say someting about another Turing
machine,

Not exactly. It can only report on the behavior that the input
finite string specifies.

Which is that other TM.

 Do you agree?

even simulate its complete execution. Or it can count something
simple like the number of states or the set of symbols that the
described Turing machine may write but not erase. But there are
questions that no Turing machine can answer from a description of
another Turing machine.

All of the questions that a TM cannot answer are logical
impossibilities

Not true. Some interesting questions are undecidable.

It is a despicable lie that it even be called "undecidable". It is
like no one can "make up their mind" about the square root of a dead
rat.

You may dislike the term; it means there is no program that gives the
answer for every input.

The term "undecidable input" incorrectly cites the decider as the source
of the issue instead of rejecting incorrect input.
The problem is that no program gives the answer whether a
self-contradictory input is true or false because the correct answer is
neither. It isn't that the decider "couldn't make up ts mind" it is that
the input was invalid.

The counterexample input has a well-defined halting status determined
by the decider that it calls.

--
Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.