[FOM] Mathematician in the street

Aatu Koskensilta Aatu.Koskensilta at uta.fi
Sat Aug 29 05:50:52 EDT 2009

Quoting Bill Taylor <W.Taylor at math.canterbury.ac.nz>:

> Much in the same way that there is really only one concept of
> "effective computability", or of "a universal machine", or of
> Chaitin's constant; but that the particular implementation of it
> may seem quite different according to the technical substrate,
> which is essentialy unimportant, as they all lead to "the same thing".

How is there really only once concept of Chaitin's constant? The  
"halting probability" depends in a quite extreme way on the details of  
the coding chosen. A theorem of Solovay illustrates this: there's a  
coding on which ZFC can't determine a single digit of Omega.

Your general point, that there are in mathematics -- and elsewhere --  
many ways of defining and developing essentially a single concept,  
that much we find in a typical treatment is just scaffolding of no  
intrinsic significance, and so on, is of course unobjectionable.

Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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