Re: Are we simulated by some massive computer?

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Mon, 26 Apr 2004 18:41:11 +0200

----- Oorspronkelijk bericht -----
Van: "Kory Heath" <kory.heath.domain.name.hidden>
Aan: <everything-list.domain.name.hidden>
Verzonden: Monday, April 26, 2004 03:00 AM
Onderwerp: Re: Are we simulated by some massive computer?


> At 10:48 AM 4/25/04, Saibal Mitra wrote:
> >This is the ''white rabbit'' problem which was discussed on this list a
few
> >years ago. This can be solved by assuming that there exists a measure
over
> >the set of al universes, favoring simpler ones.
>
> I don't believe there are any grounds for assuming that, so the problem
> isn't solved for me.

This can be motivated in a number of ways. I think Hall Finney made this
argument some time ago, and it is my favorite argument. Suppose you identify
a universe with the program specifying it. The probability that you find
yourself in a universe X will be proportional to the priori probability of X
multiplied by the number of times you will be computed in X. It is possible
to define universes Y_{n} that are defined by executing X n times. The
probability that you find yourself in Y_{n} is thus proportional to the
prior probability of Y_{n} times n. To have a well normalizable probability
distribution Y_{n} has to go to zero faster than 1/n. Now, the size of
program Y_{n} depends linearly on Log(n) (because you have to specify the
number n in the program). So, asuming that the prior probability only
depends on program size, it must decay (at least) exponentially as a
function of program size.


>
> >Once you
> >consider the whole of Platonia all you have is a probability distribution
> >over the set of all possible states you can be in (because you can't
define
> >time in a normal way anymore).
>
> I don't agree with this. I can imagine an infinite 2D lattice of cells,
> seeded with the binary digits of pi, and ask the following question: if
the
> rules of Conway's Life were applied to this lattice, what would it look
> like after a million ticks of the clock? There's an objective answer to
> this question, and that answer exists in Platonia. I believe that this
> implies that the universe I just described (and all other possible CA
> universes, and much more) exists in Platonia. I define "time" as the
> "ticking of the clock" in such computational worlds, so I believe time
> exists in Platonia. (Of course, in another sense, Platonia exists in a
> timeless "all at once". This is similar to the way that time exists in the
> "block universe" of relativity theory.)
>

I agree. I was refering to the whole of Platonia which is timeless.


> >There is no conditional probability for your
> >next experience given what you have experienced now. A valid question is:
> >What is the probability that you will be in a state P that contains the
> >memory that you have been in a state P'.
>
> I find this way of looking at things very confusing. What do you mean by
> "you" in this formulation? Is "you" a thing that jumps from state to
state?
> If so, then we have some form of time. If not, what is this "you"?
> Obviously it is something that can be said to be "in a state P"
(otherwise,
> you wouldn't consider your above question valid). But what does it mean
for
> "you to be in a state P"? If it's true that "you are in a state P", are
you
> just timelessly in state P, or what? How can you even talk about something
> "being" without talking about time?


It's confusing, but it has a big advantage over the more intuitive point of
view. This is how I see it (I know that others on thius list disagee with
me):

Clearly there exists a program that represents me. If you know exactly how
my brain works, you can run me on a computer. I thus have to identify myself
with that program. Note that if you run this program it will change itself
(I would have a notion of time even if simulated without any external
environment). So, by program I mean the program plus the exact computational
state it is in.

Then, I like to get rid of the concept of personal identity. The idea that
Saibal yesterday is the same as Saibal today cannot be made precise. You can
try to identify programs p and p' by saying that they represent the same
person if by running p you eventually obtain p'. But what about external
influences changing a person? There are other reasons too (see my input in
the the quantum suicide debate).

To see how it works (in principle) consider Saibal doing an experiment. Let
S1 denote the program specifying me just before I start the experiment and
S2 the program after I observe the result (taking seriously what I wrote
above, I couldn't write the sentence like this...). Suppose that there are
many possible outcomes, and I want to know the probability that I will
observe a particular outcome. According to the intuitive view there exists a
conditional probability that you are in state S2 given that you were in
state S1, and that is what you should try to compute using some theory.
However, since S2 and S1 are strictly speaking different persons this is
difficult, as I wrote above. Instead, one should compute quantities that
refer to single persons (programs) only. In this case I could, using a prior
probability over all possible universes, compute the probability
distribution over the set of all programs that remember being in S1 and have
observed the outcome of the experiment. This strictly refers to single
programs and is thus well defined. Note that this remains well defined in
cases where a particular experimental outcome would kill you (so-called
(quantum) suicide experiments).


Saibal
Received on Mon Apr 26 2004 - 12:54:05 PDT