On 11 Oct 2013, at 17:00, Jason Resch wrote:



On Oct 11, 2013, at 9:06 AM, Bruno Marchal <marc...@ulb.ac.be> 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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