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From: Alan Mackenzie <acm@muc.de>
Newsgroups: comp.theory
Subject: Re: Simulating termination analyzers by dummies --- criteria is met
Date: Tue, 25 Jun 2024 14:06:00 -0000 (UTC)
Organization: muc.de e.V.
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Mikko <mikko.levanto@iki.fi> wrote:
> On 2024-06-24 20:27:55 +0000, Alan Mackenzie said:

>> joes <noreply@example.com> wrote:

>> [ .... ]

>>> --
>>> Man kann mit dunklen Zahlen nicht rechnen. F=C3=BCr die eigentliche=20
>>> Mathematik> sind sie vollkommen nutzlos. --Wolfgang M=C3=BCckenheim

>> Or, in English, "You can't do arithmetic with dark numbers.  For actua=
l
>> mathematics, they're completely useless.".

>> Wolfgang M=C3=BCckenheim is a crank in sci.math and de.sci.mathematik,=
 one of
>> the few remaining ones after Google shut down their Usenet servers in
>> February.  He insists on the existence of something he calls "dark
>> numbers" and gives crank-like justifications for them, which do not ho=
ld
>> up under more robust questioning.

> From the first order Peano axioms it is not possible to prove that ther=
e
> are no non-standard numbers. It is possible to construct (for example i=
n
> ZF) a model of the first order Peano arithmetic that has a proper subse=
t
> that is another model of the same Peano artichmetic. And it is possible
> to do arithmetic with those numbers. Whether useful, I don't know.

Yes.  All that is over Wolfgang M=C3=BCckenheim's head.  He doesn't have =
a
degree in maths, but I believe he has a Phd in physics.  His intuitions
in set theory are those of a rebellious teenager, and he refuses to
accept many established mathematical results.  The threads he gets
involved in in sci.math feel similar to the threads in comp.theory
involving Peter Olcott.

Such people completely miss the fascination of surreal numbers, Robinson
integers, and the rest.  Other posters just wish they could get the
cranks to learn new (for them) things.  Personally, I never learnt much
about mathematical logic and the foundations in my maths degree, but I
could catch up if I could be bothered, and I'm broadly aware of what I've
missed.  That distinguishes me from the cranks.

> --=20
> Mikko

--=20
Alan Mackenzie (Nuremberg, Germany).