On 11 Oct 2013, at 17:00, Jason Resch wrote:
On Oct 11, 2013, at 9:06 AM, Bruno Marchal <[email protected]> wrote:
On 11 Oct 2013, at 13:16, Pierz wrote:
And just to follow up on that, there are still an infinite number
of irrational numbers between 0 and 0.00001. But not as large an
infinity as those between 0.00001 and 1.
It is the same cardinal (2^aleph_zero). But cardinality is not what
count when searching a measure.
So extrapolating to universes, the very low probability, white
rabbit universes also occur an infinite number of times, but that
does not make them equally as likely as the universes which behave
as we would classically expect.
That is what remain to be seen. But if comp is true, we know the
measure has to exist, and the math gives some clues that it is
indeed the case, from machines' (consistent and/or true) points of
view.
Bruno,
Could the matter of the countably infinite number of programs be
irrelevant from the first person perspective because any given mind
contains/is aware of only a finite amount of information?
Say some mind contains a million bits of information. Then there is
a finite number (2^1000000) of distinct combinations of content for
that mind. These differations are all that matter from the first
person view, and some may be more probable than others.
(But deciding the measures for each of those finite number of
possibilities depends on infinite computations, and so would they be
real numbers?)
Even if the 3-mind ("my current 3-state") is finite, the FPI will bear
on non enumerable continuations. I will be able to "distinguish" only
finite numbers of cluster of histories in that infinity of
continuations, but the measure will bear (like in QM) on the
distinguishable in-principle continuation, so the relative
indeterminacy might depends on them all, and so it is consistent that
real numbers will be at play. Now, the real measure takes the fusion-
amnesia-backtracking into account, and the real picture is beyond our
intuition, and has to be extracted from the semantics of the (q)Hm. (q
for quantification in the logician sense, and Hm is for the relevant
material hypostases (Bp & Dt, Bp & Dt & p, but also on Bp & p, as it
gives a quantization (in the physicist sense) when p is in the UD (p
is sigma_1).
Bruno
http://iridia.ulb.ac.be/~marchal/
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