OFF : Physics *is* fun.

[Paul Mather]

On 4 May 2007, at 6:00 PM, M Holmes wrote:

> Then he went into Omega, the number which
> answers every question in the universe but which has an infinite  
> number
> of digits which are unpredictable and can't be calclated. Except that
> someone has used a quantum computer to calculate sixty digits,  
> which is
> great because that answers *some* of the questions in the universe.
> unfortunately we don't know which those are.

That wouldn't happen to have been Chaitin's Omega, would it, or some  
other Omega?  (Chaitin of Algorithmic Information Complexity fame,  
that is, which is an offshoot of Kolmogorov Complexity.)  Dim  
recollection tells me Chaitin's Omega has the property that it is the  
most compressed string in existence (mathematically possible), i.e.,  
no other string contains more information than Omega.  Further dim  
recollection tells me this property springs from the fact that the  
first N bits of Omega encodes the halting probability of universal  
Turing Machines (i.e., programs) of N bits or smaller.  Of course,  
because the halting problem is unsolvable, it makes computing Omega,  
um... difficult, but means that Omega encodes a heck of a lot of  
information (besides being very useful as an oracle).

Dear me, this is taking me back years...

Cheers,

Paul.

e-mail: paul at gromit.dlib.vt.edu

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