>Pi is enumerable. Most reals are not. Most of the dummy data is much
>less likely than extraordinary data (such as Pi),
>if the dummy data probability is approximable by a computer.
>Compare "Algorithmic Theories of
A program which generates all the reals is shorter than a program which
generates Pi, which is itself shorter than a program which generates
a particular real (for most "particular" reals).
Perhaps you confuse program generating reals and programs
generating *set* of reals.
>Instead of giving examples, could you just provide a short proof of your
>claim that there is no computable universe to which we belong?
Tell me what you don't understand in my UDA post (which is the beginning
of the shortest proof I know).
UDA is at http://www.escribe.com/science/theory/m1726.html
Let 3-you be your current computational state and 1-you your actual
What happens is that "3-you" belongs to an infinity of computational
histories (generated by the UD) and the UDA shows that your expected
futur 1-you is undetermined and that the domain of indeterminacy is
given by that set of computational histories.
So "we" belongs to an infinity (a continuum) of
infinite computational histories.
(Remember that from our personal 1-point of view we are not aware
of the number of steps the UD makes for generating "our" 3-states).
There is no reason to associate a "universe" neither to a
computational history nor to the set of all computational histories.
The physical predicate (time space temperature ...) emerges from some
sum or averaging on all histories.
For me it is not even clear how to make sense of the word "universe"
in the computationalist frame.
PS I am rather buzy, so I am sorry if I am to short or if I take time
for answering. Don't hesitate to make any remarks, though.