On Thu Jan 18 Bruno Marchal replied:
> >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
> >Everything": http://www.idsia.ch/~juergen/toesv2/node23.html
> 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.
I certainly do not.
There is no program generating the uncountable set of all reals.
There only is a program generating countably many prefixes of reals.
How to distinguish those from the countably many prefixes of the
countable rational numbers?
> >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
I did look at it and found lots of words but no formal proof,
although it does say "QED" at some point.
You are repeatedly talking about universes generated by a dovetailer. All
these universes obviously must be computable, otherwise the dovetailer
could not compute them. So how can you claim that there is no computable
universe to which we belong, when the very tool you are using generates
lots of universes to which we belong? It does not make sense to me - my
best guess is that you mean something quite different from what you say.
Maybe you just want to say we do not know in which of the many possible
computable futures we will end, but this is obvious and precisely the
reason why we need to look at the possible probability distributions on
possible future histories, to make nontrivial predictions, e.g.:
> 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.
The infinite computational histories are countable. The continuum is not.
The concepts of dovetailing and continuum are incompatible.
The dovetailer will compute many histories featuring a Bruno or two,
but only countably many.
> 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.
You are not too short as long as your legs reach the ground :-)