There have always been two ways to interpret the interrelationship
between the physical world and our minds. The first one is to consider
the physical world to be fundamental; from this perspective, the
appearance of the mind is to be understood with the help of some
neurological theory that maps physical states of the brain to states
of the mind or observer moments. The second way starts with the mind,
denying the fundamental role of the physical world. According to this
assumption, the physical world is introduced with the help of a theory
of physics mapping mental states to physical states that reproduce the
mental state within themselves. Imprecisely speaking, the second way
questions the reality status of the physical world.
Both ways allow the elaboration of an ensemble theory. The first
approach starts from the ensemble of all physical worlds (or formally
with descriptions thereof). The second approach uses the ensemble of
all observer moments (or descriptions thereof). When Rolf expressed
the idea "UTM outputs a qualia, not a universe" (which is similar to
the second approach), I wrote: "I have always been hopeful that both
approaches will finally turn out to be equivalent."
It's a very trivial fact though that the two approaches are not
equivalent. Nonetheless it's interesting to note it. I argue that we
have good reasons to discard the second approach. The fundamental role
will be assigned to the physical worlds (hence the title of this
message). The difference between the two approaches leads to different
expections to the question "What will I experience next?".
Consequently it can be measured empirically. We find this result by
observing that different physical worlds may produce the same observer
moment (e.g. if the physical worlds differ in a detail not perceivable
by the observer). This assigns a higher probability to the observer
moment when chosen randomly in order to answer the question (it's
multiply counted because it appears more than once in the everyting
ensemble). Opposed to this, every observer moment (in the RSSA within
a given reference class) would have an equal probability to be
selected if we used the second approach.
I think that the quantum mechanical Born rule strongly supports the
first approach: Observer moments are weighted according to a specific
formula. They don't have equal probability!
Example: Both quantum states, |A> = |0>/sqrt(2) + |1>/sqrt(2) and
|B> = |0>/sqrt(3) + |1>/sqrt(1.5)
lead to the same two possible observer moments when a measurement in
the (|0>,|1>) basis is performed. According to the Born rule the
probabilites for the two observer moments are equal for |A> and
different for |B>. Starting from the second approach (observer moments
are fundamental) this result cannot be understood.
If we take this result seriously, Bostrom's self-sampling assumption
"Each observer moment should reason as if it were randomly selected
from the class of all observer moments in its reference class."
should be modified:
"Each observer moment should reason as if it were randomly selected
from the class of all observer moments in its reference class,
weighted with their frequencies in the Everything ensemble."
In order to avoid misunderstandings, I want to add that I consider the
Everything ensemble (in both approaches) as given. It's not the output
of some UTM.
Youness Ayaita
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Received on Sun Sep 23 2007 - 06:39:27 PDT