On 11 Jan 2014, at 18:57, Jason Resch wrote:
On Sat, Jan 11, 2014 at 3:14 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 11 Jan 2014, at 08:56, Stephen Paul King wrote:
Der Bruno,
The UD has no output. I guess you think to the trace of the UD,
UD*, which from the first person perspective is "entirely given",
by the 1p delay invariance."
The UD never stops. If a process lasts forever, it is eternal,
then it does not ever complete and thus its results never obtain in
any way that can be considered as accessible.
?
Then real numbers don't exist.
To belong to your first person indeterminacy domain, the UD needs
only to access the state, which, by non stopping, has to occur once.
of course we might need to look at the 10^(10^1000) nth step of the
UD. But the 1p is not aware of the "reconstitution" (in UD*) delay,
so that does not matter. Either your state is accessed, or not, and
if it is accessed it take a finite "time" (number of the UD-steps),
and belongs to the indeterminacy domain. So the global FPI does have
the whole infinite trace of the UD as domain, or if you prefer it is
the infinite union of all its finite parts. Just keep in mind the
step 2 and 4.
Bruno,
I was thinking: Shouldn't halting programs still contribute an
infinite amount of weight in the UD, since they are still reached an
infinite number of times (at least once each time the UD reaches
itself).
That will give only a denumerable set. The non enumerable set of
histories should win. The "winner" has to exploit this in some way,
like Feynman formulation of QM illustrates already for the quantum
(only in the classical case, to be sure). That is why I say that some
observable must have a continumm spectrum if comp can work. It could
be just the frequency operator (like in Graham paper in the Graham-
DeWitt book on the many-worlds, or in Hartle's paper, or in Preskill
quantum information textbook).
Perhaps there is some noticeable cut off or difference in weight
between those programs that take longer to reach than the UD itself
and those that occur multiple times before the UD reaches itself.
I am not sure. I will think about this.
Bruno
http://iridia.ulb.ac.be/~marchal/
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