I don't know how to answer you. It is the first time I have heard of Stosszahlansatz. I believe that the world we perceive (that is a small slice of the plenitude, consistent with ourselves) has an infinitesimally small measure compared to the chaos of the whole plenitude. As we proceed with our lives we have the 3rd person experience of increasing entropy. Our (3rd person perception of ) measure keeps increasing as well.

The assymetry of the second law is interesting. On the one hand, entropy appears from a 3rd person perspective to keeps increasing until we "die." Yet the requirement for consistency of the observed world with the observer implies that from a first person perspective, at the moment of "death" we may expect to witness a truly gigantic lowering of the entropy at a univeral scale perhaps equivalent to a reversal of the Big Bang. Measure is also expected to decrease proportionally. The magnitude of this effect depends of course on what kind of "near-death" experience we have and how the "recovery" is made. (eg. to be resussitated after being dead for for one minute requires the lucky presence of a medical team equipped with an elecroshock machine. To be dead for 1000 years would probably requires a major reorganization of the universe only found in the Bible or in science fiction books)  

The second law is applicable only to 3rd person experience. When considering first person experience, my guess is that at a universal scale, entropy fluctuates up and down depending on the need of the observer and to remain consistent with the observer. Our constitution implies that most of the time entropy ramps up. Sometimes it steps down. At the scale of the Plenitude entropy is constant.


Stephen Paul King wrote:
Daer Bruno and George,

    At the risk of being massively naive, does this idea seem to be related
to the infamous problem of Boltzmann's Stosszahlansatz?

    My reasoning is that in order to figure out how do define a universal
prior (or probability measure for the initiona conditions that led
inevitably to our common world of experience) we need to understand how to
define a ration of worlds like ours to all possible worlds, or the
computational equivalent: algorithms that generate worlds like ours as a
subset of the collection of all possible algorithms.

Kindest regards,


----- Original Message ----- 
From: "Bruno Marchal" <[EMAIL PROTECTED]>
Sent: Thursday, May 06, 2004 6:14 AM
Subject: Re: Are we simulated by some massive computer?

I agree with George, but note that I arrive at an equivalent
assertion without using that "lower levels have lower complexity
and therefore higher measure".  That is possible, but
the problem is that it is a priori hard to estimate the "dumbness"
of the universal dovetailer which is quite capable to entangle high
complexity programs with low complexity programs, so that
the "multiplication" related to low-complexity can be inherited to
high-complexity (due to dovetailing). But you may be right, I have not
proved that "a" UD could be that dumb! From a suggestion of Jacques
Bailhache (an old everythinger) I have try to build an explicit
UD which makes the measure on computations arbitrary, but I have
not succeed, in the limit (on which bears the first points of view),
the "right measure" seems to self-correct by itself. It is that
self-measure I study with provability logic.
Another problem with the idea of "low" level, or of "simple program"
is that even a program with 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^64
as minimal bit-length is quite little in comparison of almost all number
in Plato Heaven.


At 15:56 05/05/04 -0700, George Levy wrote:
This has been an interesting thread. Unfortunately I was too busy to
contribute much. However, here is a thought regarding simulation versus
first and third person points of view.

It does make sense to talk about a 3rd person point of view about
simulation of a conscious entity on a computer. However, I don't think it
applies to a first person point of view.

In the plenitude we'll have an infinite number of levels of simulation as
well as an infinite number of simulations per level (2^aleph_0 as
suggested by Bruno in a previous post, or higher)

>From a first person point of view any observer moment in any simulation
and at any level can transit to another observer moment in a different
simulation at a different level provided the transition is consistent
with the observer. Therefore from the first person point of view there
no such a thing as living in a simulator. As first persons we live in
simulators and at all levels.

In addition, since lower levels have lower complexity and therefore
measure, the number of simulations is higher at lower levels.

Therefore we are more likely to occupy ensembles of simulations located
the lower levels. Is there a lowest level in the level hierarchy, that is
a level below which there is no simulation, just the plenitude? Possibly.
If so, we are most likely to exist "most of the time" at that base level,
but we cannot exclude that "some of the time" we may be in a higher
hmmmm. This argument points to the fact that "most of the time" we do not
live in a simulator!




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