Re: ******** CAN ANYONE HERE DEFINE CHAITIN'S OMEGA ? ***********

From: The Ghost In The Machine (ewill_at_sirius.athghost7038suus.net)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 08:01:43 GMT

In sci.logic, |-|erc
<H@r.c>
 wrote
on Sun, 30 Jan 2005 16:14:01 +1000
<363cc1F4mt2r5U1@individual.net>:
> "The Ghost In The Machine" <ewill@sirius.athghost7038suus.net>
>> omega_U = sum(n) ( ( Halts(f(n)) ? 1 : 0) * 2^bitsize(f(n)) )
>
> Say the halt sequence is
>
> 001001001001001001001
>
> what value does your formula give, for some rudimentary bitsize function?
>
> Herc
>

I don't know. I don't have the specifics handy at this point.
This is one of the problems I have with Mr. Weisstein's
definition; it's not quite specific enough. (He does give
a reference to Sloane's papers, whoever Mr. Sloane is;
I can't say I'm familiar with them.)

I can define (and have defined) ad hoc machine specifications
in the past; whether these lead to consistent definitions
for Omega_U, I for one do not know, although I doubt it.

Not that it matters. If Omega_U depends on the halting
function, then Omega_U is inherently uncomputable, as
the halting function is uncomputable (though it is well-defined).

If you want I can exhume my machine definition (or make one
comparable thereto), and then try to compute Omega_U
for that machine definition. I'm not sure what that would
prove, if anything. 

-- 
#191, ewill3@earthlink.net
It's still legal to go .sigless.

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