On 15 Oct 2011, at 05:44, Russell Standish wrote:

On Fri, Oct 14, 2011 at 06:40:04PM -0700, meekerdb wrote:
On 10/14/2011 5:50 PM, Russell Standish wrote:

I know there are only a countable number of programs. Does this entail only a countable number of histories too? Or a continuum of histories?
I did think the latter (and you seemed to agree), but I am partially
influenced by the continuum of histories available in the "no
information" ensemble (aka "Nothing").

There must be a continuum of histories since there are infinitely
long histories which go through a given state (or is it an OM - I
don't think they are the same) infinitely many times.  But if you're
only looking ahead a finite interval then it seems there would only
be a countable, or even finite, number of continuations.  That would
be the relative measure for predicting physics.


I was assuming that the histories are infinite in general. It would be
surprising if all consciousnesses were halting programs.

Just because there is an infinite number of histories passing through each OM does not imply the cardinality of the histories is greater than aleph_0.

It is bigger than aleph_0, if you accept the Y = II rule (bifurcation of history = differentiation of consciousness), and if you realize that no matter what, all UDs, stupidly enough, dovetail on the infinite real *inputs*. Those inputs being internal to the program or external (but still UD generated), being dummy argument never interfering with the computations, or interfering with them all the times. The UD does all that. You cannot diagonalized againist the UD for preventing it from doing that. The UD concept inherits the robustness of the UM concept.



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