[ExI] 11 numbers that are cooler than pi

[BillK]

On Tue, 15 Mar 2022 at 15:56, Darin Sunley via extropy-chat
<extropy-chat at lists.extropy.org> wrote:
>
> They left out my favorite: Chaitin's "Omega".
> It encodes which Turing machines halt.
> I think that might be sufficient to define the computational nature of the mathematical universe.
>

Hey!  You need to include an explanation for us poor benighted mortals
that have never heard of this. :)

<https://mathworld.wolfram.com/ChaitinsConstant.html>
Quote:
A Chaitin's constant, also called a Chaitin omega number, introduced
by Chaitin (1975), is the halting probability of a universal
prefix-free (self-delimiting) Turing machine. Every Chaitin constant
is simultaneously computably enumerable (the limit of a computable,
increasing, converging sequence of rationals), and algorithmically
random (its binary expansion is an algorithmic random sequence), hence
uncomputable (Chaitin 1975).


BillK