On 2/14/2012 03:00, Stephen P. King wrote:
On 2/13/2012 5:54 PM, acw wrote:
On 2/12/2012 17:29, Stephen P. King wrote:
Hi Folks,

I would like to bring the following to your attention. I think that we
do need to revisit this problem.


The Anthropic Trilemma


I gave a tentative (and likely wrong) possible solution to it in
another thread. The trillema is much lessened if one considers a
relative measure on histories (chains of OMs) and their length. That
is, if a branch has more OMs, it should be more likely.

The first horn doesn't apply because you'd have to keep the copies
running indefinitely (merging won't work).
The second horn, I'm not so sure if it's avoided: COMP-immortality
implies potentially infinite histories (although mergers may make them
finite), which makes formalizing my idea not trivial.
The third horn only applies to ASSA, not RSSA (implicit in COMP).
The fourth horn is acceptable to me, we can't really deny Boltzmann
brains, but they shouldn't be that important as the experience isn't
spatially located anyway(MGA). The white rabbit problem is more of a
worry in COMP than this horn.
The fifth horn is interesting, but also the most difficult to solve:
it would require deriving local physics from COMP.

My solution doesn't really solve the first horn though, it just makes
it more difficult: if you do happen to make 3^^^3 copies of yourself
in the future and they live very different and long lives, that might
make it more likely that you end up with a continuation in such a
future, however making copies and merging them shortly afterwards
won't work.


This solution only will work for finite and very special versions of
infinite sets. For the infinities like that of the Integers, it will not
work because any proper subset of the infinite set is identical to the
complete set as we can demonstrated with a one-to-one map between the
odd integers and the integers.
Hence why it's a measure, not a sets cardinality. Although, you're right, it's not obvious to me how this can be solved in a satisfactory manner with infinite non-merging histories. One could give up on finding a computable measure and just consider each history as it is, without trying to quantify directly over all histories. Such a measure would be most likely uncomputable, although it'd still be better than nothing. It's not obvious that some histories wouldn't be finite if one considers their mergers with other histories (consider the case of humans which have finite brains and memories, eventually a loop/merge would exist if they don't self-modify somehow, simply because of finite amount of memory, even in the case of a SIM which never dies or deteriorates due to biological issues).

Given that the number of computations that a universal TM can run is at
least the countable infinity of the integers, we cannot use a comparison
procedure to define the measure. (Maybe this is one of the reasons many
very smart people have tried, unsuccessfully, to ban infinite sets...)

Unfortunately (or maybe fortunately?), one cannot avoid the countable infinity of naturals.


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