Re: does sqrt(2) exist in CM?

examachine_at_gmail.com
Date: 02/11/05 

Date: 11 Feb 2005 00:53:46 -0800

Jesse F. Hughes wrote:
> examachine@gmail.com writes:
>
> > Anyway, the problem is, if we swallow what I say above we have a
> > paradox: it is not possible to define a "truly random" real by
infinite
> > application of a fair coin! Which seems a little counter-intuitive.
How
> > do we explain that?
>
> Why not explain it the obvious way? Chaitin randomness isn't the
same
> thing as random.

If you think so, then you will have to conclude that Martin-Lof
randomness and Solovay randomness aren't the same thing as random,
either. What should that make us believe in? That Borel's paradox of
the undefinability of randomness was correct?

Please, let's make the discussion concrete. So, you don't think Solovay
randomness, which is provably equivalent to strong Chaitin randomness
defines randomness. In other words, Solovay randomness is just wrong,
there are other random numbers than Solovay random numbers. I require
an example, or a proof to proceed with such a thought. Because that is
ultimately an admission of the paradox I'm hinting at, rather than a
refutation of it.

Maybe that is something everybody agrees on, but I don't see how that
is obvious.

Regards, 

--
Eray

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