Here is my response to Bruno's UDA argument as described in the links
from http://www.escribe.com/science/theory/m3044.html.

I agree with the general idea, that if we assume that a UDA program
exists in some sense (Platonic or otherwise), then each observer moment
is instantiated multiple times (probably a countably infinite number of
times) throughout the structure generated by the UDA.  In that case we
have to accept that our mental experiences are not unique to some universe
(by "universe" I mean the output of one program being simulated by the
UDA) but are present in infinitely many of them.

However there are a few places where I would expand upon the steps, and
take issue with some of them.  First, as far as the basic idea of COMP,
I do agree that functional substitution is enough for consciousness
indistinguishable from my own.  I would expand on this to explain that
the reason for this belief is not due to philosophy, but to biology.

The way the brain works appears to be a matter of processing information
via electrochemical signals transmitted by neural cells.  Each such cell
is acting as an information processor.  The collection of these cells
in the brain takes in information on incoming nerves, and sends out
commands on outgoing nerves.  Everything is information.  So it seems to
me that replacing this system with something that can process information
in a functionally equivalent way would produce an equivalent system.
If I didn't know that the brain worked in this way, I would probably
not accept COMP.

However, based on some arguments which Wei Dai gave (and which I'm not
sure if he accepts), I believe there are some aspects of consciousness
which are not fully captured by a purely functional substitution.
Specifically, as we get into the questions about duplications, I
believe that some details of the functional substitution may affect the
first-person likelihood of experiencing that implementation.  Issues such
as the speed, size and degree of redundancy of an implementation may
affect how much "measure" it has, that is, how much of a contribution
it makes to the space of all my first-person experiences.

If we jump to the end of Bruno's argument, step 10 or 11, and accept
that we are instantiated in multiple forms, it is obvious that not
all ways we could be instantiated are equally probable.  Otherwise the
universe we observe would be chaotic.  So somehow it must be the case
that implementations which exist in simple and lawful universes are more
probable (in the first person sense) than those in random universes.

Given that we accept the reality of different measures for different
implementation states, I think we need to consider the possibility that
not all functional substitutions have equal measure (i.e. first-person
probability).  I won't go into the details here, but I think a detailed
argument shows that different sizes and speeds of the functional
substitution must make a difference in measure.

Several of Bruno's questions raise the idea of quantifying the first
person probability of various duplication scenarios.  In the comment
preceding question 7 in http://www.escribe.com/science/theory/m2992.html,
he writes:

> The way to quantify the indeterminacy is the unknown. Although we can
> argue that the {W, M} duplication gives a sort of perfect 1-coin, simple
> probabilty reasoning leads quickly to hard problems.

I think Bruno agrees here that you can't just say that if you have 2
duplicates made, you therefore have a 50% first-person probability of
experiencing each of them.  We have discussed various paradoxes and
problems that arise with this kind of reasoning.

Nevertheless he asks in questions 7 and 8, *if* we accept a 50%
probability in one experiment, will we also see it in another?  I am not
sure how to answer these, because I don't have a good understanding of
how to begin to quantify the probabilities.  So I cannot answer in the
affirmative, but I can't deny the possibility either.  I have to answer
that I need to get a better understanding of what aspects are relevant
in understanding probabilities.

Likewise in question 10, where we assume a UDA is actually implemented
in the physical universe, I believe it is possible that the measure
of the implementations in the UDA may be smaller than the measure of
biological physical implementations.  So while the UDA machine will
produce copies of my mental state, it might turn out that they make
an insignificant contribution in terms of first-person probability,
compared to the contributions from the physical universe.  (For the
purposes of question 10, we assume that the physical universe exists.)

To sum up, I agree with Bruno (I think) on the following points:

 - Functional substitution is adequate to maintain consciousness

 - Mental states must be (in some sense) shared across all equivalent
   functional implementations

 - The UDA program produces multiple functional equivalents of all possible
   observers

 - If we accept a certain view of Platonic reality of mathematics, then the
   UDA exists even if it is not implemented in our reality

 - In that case our current mental states can be viewed as being created
   by a UDA or some similar program

I may disagree on some points:

 - Not all functional substitutions have equal measure

 - Universes are well defined: each universe is the output of one of the
   programs which are simulated in "dovetailed" fashion by the UDA

 - Each observer-moment spans a specific set of universes - that is, those
   specific programs which functionally implement it

And my very tentative theory for measure, which was first proposed by
Wei Dai:

 - The measure of an observer-moment is proportional to the fraction of
   programs that implement it, and proportional to the fraction of each
   programs' trace that it occupies.  That is, observer moments have
   higher measure if they are implemented by more programs, and also if
   they use up more of the "resources" of the universe created by each
   of these programs.

Hal Finney

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