Youness,
hmmm.... I am not sure .... Perhaps a duality, or a Galois connection
of some sort. I'm afraid that an *equivalence* would show up only in
the case where "I" am the "world" or comp is false or in the case where
the comp level of substitution is infinitely low, roughly speaking.
In that case ASSA and RSSA are plausibly equivalent, and the indexical
comp (what I am used to call comp and which asserts that "I" am a
machine) is then plausibly equivalent with Schmiduhuberian form of comp
(the universe is a machine).
About Bostrom's unification/duplication, I think that from the first
person point of view we can have unification when the two identical
brains are running identically during a period of time dT, although
duplication---during that very period of time dT--- has still to be
considered when some histories, going through the identical states
during dT, differentiate later. This is what I like to sum up by
Y = II,
which means that a differentation/bifurcation change the measure on
states in the "logical past", a little like if the "first amoeba" did
get a high measure in the past thanks to her many descendants today.
This entails a form of anthropic teleology about which I lack the tools
for making things more precise.
I think you could make your point clearer by trying to be more precise
on what you consider to be a world and a (first person) observer moment
perhaps. Modal logic could help you here I guess.
Bruno
Youness Ayaita wrote, the 07 Apr 2008:
An Equivalence Principle
Youness Ayaita
Mon, 07 Apr 2008 07:51:31 -0700
By this contribution to the Everything list I want to argue that there
is a fundamental equivalence between the first person and the third
person viewpoint: Under few assumptions I show that it doesn't matter
for our reasoning whether we understand the Everything ensemble as the
ensemble of all worlds (a third person viewpoint) or as the ensemble
of all observer moments (a first person viewpoint). I think that this
result is even more substantial than the assumptions from which it can
be deduced. Thus, I further suggest to reverse my argument considering
the last statement as a principle, the equivalence principle.
Let me first present and explain the two viewpoints:
1. The ensemble of worlds
This approach starts from the ontological basis of all worlds (or
descriptions thereof). I am not precise to what exactly I refer by
saying "worlds" and "descriptions" for I don't want to lose wider
applicability of my arguments by restricting myself to specific
theories of the Everything ensemble. But admittedly, I mainly think of
theories similar to Russell's ideas. However, the crucial property of
theories starting from the ensemble of worlds consists in their third
person viewpoint. The ontological basis does not explicitly refer to
observers nor to observer moments. Observers are regarded as being
self-aware substructures of the worlds they inhabit.
Coming from the sciences, this approach is very natural. In the
sciences, we are used to the idea of a physical reality independent of
us humans. We are studying phenomena happening in our universe. Thus,
when we invent a theory of the Everything ensemble, we are naturally
driven to the idea that not only our universe, but a multiverse
consisting of all possible worlds exists. We already know how
observers come into the scene: As an emergent property, a huge number
of the fundamental building blocks can constitute an observer. In
order to understand this, one has to introduce a semantic language
which describes the emergent phenomenon. The description of the world
itself is expressed in the syntactic language (I adopt Russell's
nomenclature). The link between between these two languages is some
kind of neurological theory explaining how the states of the
fundamental building blocks (more precise: the description of the
world) lead to mental states (or the emergence of an observer).
Though, finding such a neurological theory is a very difficult task.
In this world, we are facing the so-called hard problem of
consciousness. And even if neurologists, psychologists and
philosophers will finally succeed to find an adequate theory in this
world, it is not clear whether we can apply the theory to other
worlds.
So, to conclude, this approach has the great advantage of being very
close to the structure of the physical worlds. The explanation of
observers and observer moments seems to be possible, but surely is
very complicated and difficult.
2. The ensemble of observer moments
When I first thought of the Everything ensemble, I did not come from
the sciences, but from philosophy. I judged that the concept of
absolute "existence" was a dubious extension of the concepts of
subjective accessibility and perceptibility. So, it was natural for me
to start from the ensemble of observer moments, a first person
viewpoint. The class of all observer moments constitutes the
ontological basis of this second approach. Later, I realized that the
theory of the Everything ensemble could be used to draw conclusions
about the physical world. But this seemed to be unfeasible starting
from observer moments: the relatively simple laws of nature that we
find in our universe are obscured by the complex properties of our
senses. Starting from observer moments seemed to be a complication.
Consequently, I switched viewpoints and studied the ensemble of
worlds. I always hoped that both approaches would finally turn out to
be equivalent.
Even in principle, it is very difficult to think of "worlds" when
starting from observer moments only. This task is similar to
understanding observer moments when starting from the descriptions of
worlds. Starting from worlds, we must identify the observer moments as
substructres. Starting from observer moments, we must somehow extract
information that allows us to meaningfully talk about a world. From
the sciences, we know how difficult this is because there we try to
find a description of our world given our observer moments. We see how
complementary the two approaches are: The first approach needed some
kind of neurological theory to explain the appearance of observer
moments within a world, the second approach needs some kind of
physical theory to explain the appearance of a world when first
studying observer moments. The two approaches are another
manifestation of the deep connection between laws of physics and
properties of an observer.
The assumptions
My first assumption is related to our reasoning. The equivalence of
the two approaches does not mean that they are identical. I will say
that they have identical implications for our reasoning. To clarify
this, I must first explain how we shall reason. Here, I take the ASSA
(maybe we can check during the discussion whether or not my argument
generalizes to other versions of the self-sampling assumption):
'Each observer moment should reason as if it were randomly selected
from the class of all observer moments.'
The second assumption is more subtle. Suppose we take the first
approach, with all worlds as ontological basis. We explain observer
moments with the help of some neurological theories. At first, it is
not clear whether we can find every possible observer moment under
these emergent observer moments. The assumption is that we can. Every
possible observer moment is realized in at least one world.
Perhaps, some of you remember that I wrote about this topic September
last year. At that time, I came to the conclusions that the
equivalence did not exist. But yesterday, I read Bostrom's paper that
is currently analyzed on this list ("Quantity of experience: brain-
duplication and degrees of consciousness") and I understood that
September last year I took for granted what Bostrom calls
"Duplication". His arguments in favor of Duplication didn't convince
me, quite the opposite happened: I have adopted the other position,
"Unification".
The question Bostrom raises is the following: "Suppose two brains are
in the same conscious state. Are there two minds [Duplication], two
streams of conscious experience? Or only one [Unification]?"
This may seem to be a matter of definition. But let us return to the
ASSA: Which measure should be assigned to each observer moment? Given
Unification it is natural to assign a uniform measure: no observer
moment is more likely to be selected than any other. Given Duplication
it is natural to assign a measure to each observer moment proportional
to the number of its occurences in the Everything ensemble.
I assume a uniform measure. Surely, we can soften this assumption.
Nonetheless, it is decisive that the measure does not fundamentally
depend on the worlds but can also be deduced when taking the class of
observer moments as ontological basis. This is why I think that the
RSSA does not do any worse than the ASSA.
The equivalence principle
'Our reasoning does not depend on whether the ensemble of worlds or
the ensemble of observer moments is considered fundamental.'
I assumed that our reasoning should follow from the ASSA (or any other
version of the SSA compatible with my argument). Due to Unification,
we cannot detect any difference between the two different approaches:
The measure for each observer moment is the same.
The equivalence principle is a fundamental expression of what Russell
so eloquently explained in his book: "Not only is our psyche emergent
from the eletrical and chemical goings on in our brain, but the laws
governing that chemico-electrical behaviour in turn depend on our
psyche."
I speculate that both approaches to the Everything ensemble, the
ensemble of worlds and the ensemble of observer moments, are two
different windows to the same theory.
Youness Ayaita
http://iridia.ulb.ac.be/~marchal/
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Received on Mon Apr 14 2008 - 09:46:03 PDT