Re: Random reals are not computable!

examachine_at_gmail.com
Date: 01/25/05 

Date: 25 Jan 2005 15:25:51 -0800

Torkel Franzen wrote:
> examachine@gmail.com writes:
>
> > Strictly speaking, I do not think it's correct to say that the two
> > numbers are Turing-equivalent, which kind of got me confused in my
> > statements...
>
> So what's your private definition of "Turing equivalent"?

Torkel, as far as I know "Turing equivalent" means the equivalence of a
formalization of computation to the Turing Machine formalization.

See for example
http://www.j-paine.org/students/lectures/lect7/node13.html

"I'll say that any computer which is equivalent in power to a Turing
machine is Turing equivalent. This covers all digital computers. It is
also an upper limit on connectionist systems. Some (e.g. the linear
associator) may have less power than a Turing machine, in that they
can't compute something it can. But none have more power. "

There is no such thing as the Turing-equivalence of two numbers that I
know of, so I assumed he meant something roughly like "computable by
similar algorithms", or perhaps he meant reducibility, e.g. wrt to the
way he defined the number with less entropy than Omega.

Now, it's your turn to explain what it means for two numbers to be
Turing-equivalent. I won't accept a 'private definition'. URL please. 

--
Eray Ozkural

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