From: Vladimir Nesov (robotact@mail.ru)
Date: Fri Aug 31 2007 - 11:22:44 MDT
Tuesday, August 28, 2007, Stathis Papaioannou wrote:
SP> By TM enumerator I take it you mean a program that enumerates all
SP> possible programs, like a universal dovetailer. In the sense I have
SP> described, then yes, all the other simulations are irrelevant.
SP> However, where there are multiple competing futures (as below) the
SP> weighting of each one matters. There are theories in which it is
SP> assumed that the universe is the set of all possible programs (which
SP> perhaps need only exist as Platonic objects), but I don't know if it
SP> has been successfully shown that this idea yields the known laws of
SP> physics.
It yields all laws of physics, including ours, as long as they are
computable. (It doesn't seem possible to ever prove as a result of
observations that some laws of physics are not computable. Observations
are finite. When a decision is drawn by experts, it's equivalent to
experts' minds being is a particular configuration set, which is also
a finite thing.)
>> SP> However, if there are two or more competing "next moments" then the
>> SP> number of simulations is relevant. If there are X simulations in which
>> SP> you are tortured and Y simulations in which you are not tortured in
>> SP> the next moment, then you have a X/(X+Y) chance of being tortured.
I think I found a better argument about this point. Certainly one
tries to anticipate the future, but this behaviour is grounded in
anticipation of _future experience_. And future experience itself
does not depend on number of times it's simulated.
When you use probability theory to make rational choices, you do it
only because you anticipate that they will pay off in your future
experience, in dominating bulk of possible futures. Still, you usually
sacrifice those possible futures where fate plays against you.
>> To the point of my previous message: how do you count simulations?
>> What is your solution to that counting paradox I wrote about in previous message?
>> Does a presence of 2^N simulations within a single implementation
>> somehow influence probability of you being in certain simulation?
SP> If I understand you correctly, you are suggesting that doubling the
SP> number of implementations in a recursive simulation will increase the
SP> total number of entities in that implementation not by a factor of 2,
SP> but by a factor of 2^N, with N being the number of levels. I don't see
SP> why this shouldn't also increase the weighting by 2^N for the purpose
SP> of probability calculations, although this does provide a possible
SP> experimental method to determine if we are in a recursive simulation.
That's not what I meant, but details don't really matter. This
counting issue raises just another serious problem of simulations.
What really counts as simulation of certain mathematical model of
simulated universe? Any implementation arranges matter of host
universe in certain patterns. Why some patterns are said to provide
simulations and not others? Matter of host universe has no direct
correspondence to 'matter' of simulated universe. To establish that
implementation X (particular pattern of matter in host universe) is
a simulation of universe model Y (mathematical description), one needs
an interpretation procedure F that can take X as an input, convert it to
the same mathemetical notation and compare to Y, F(X)=Y. Presence of this
procedure (which nobody needs to actually build in order to simulation
to be a genuine one) is somehow implied, if X is developed to
implement Y. But how complex is F allowed to be? If it doesn't need to
be implemented, can't it include whole simulation, so that X is nil
and F(nil)=Y?
As a simple example, say, state of simulated universe is a finite 2D binary
image, of size AxB. When is it considered simulated? If a program
stores this state in computer memory and performs computation that
modifies it every simulated tick according to simulation's laws of physics, and
outputs the image to a monitor screen, it seems to simulate that
universe. But will it cease to simulate it if I turn monitor off?
Will it simulate it twice if I install two monitors in parallel?
It's only meaningful to say that implementation provides a way to
access information about simulated universe.
I'm mainly interested in this issue because I have doubts about
uploads not being p-zombies. These handy-wavy theories of simulated
experience are full of paradoxes. I agree that one can't in principle
prove that given observed entity has conscience, but at least there
should be a consistent theory of what conscience is. In this case, I
take a universe containing a conscious observer as a consciousness
vessel, so that genuine simulation corresponds to implementation of
consciousness.
-- Vladimir Nesov mailto:robotact@mail.ru
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