Re: on formally describable universes and measures

From: George Levy <GLevy.domain.name.hidden>
Date: Wed, 31 Jan 2001 21:56:08 -0800

Jesse Mazer wrote:

>In the archive there was some discussion about what would happen if you had
>an experiment where a coin would be flipped, and if it landed heads you
>would later be duplicated, but if it landed tails you would not. The
>question there was, would your subjective probability of seeing heads be 1/2
>or 2/3? (some people also suggested that this experiment is a good argument
>against continuity of consciousness over time...maybe all that exists are
>various moments of experience, so there is a 1/2 chance of observing the
>coin landing heads but a 2/3 chance of remembering it landing heads in the
>past).

This is a great example which avoids antigonizing people by arguably increasing
measure rather than decreasing it as in Quantum suicide. The example also
illustrates beautifully the first and third person points of view. It is clear
that from a third person point of view, the probability of seeing head is 1/2.
>From a first person point of view it is 2/3.

In fact if the number of duplication is N after a head and zero after a tail
(the original is conserved), the first person probability of seeing a head would
be p(head) = N/(N+1) and p(tail) = p = 1/(N+1). In the limit as N-> infinity,
the behavior of the coin flip ceases to be random and as p(head) ->1, the
outcome of the coin flip apparently acquires the characteristics of a natural
law: it always comes up head.

An interesting variation involves making N copies at time t1 before the coin
flip, flipping the coin at time t2 and if a tail comes up, killing all the
copies at time t3 . If we consider the time interval t1-, to t3+ , the
experiment produces exactly the same results p(head) = p = N/(N+1) and p(tail)
= 1/(N+1). However, we can't make the calculation for the time interval t2 to
t3+ because the individual copies could have diverged from t1 to t2 and ceased
to be the same person and we can't talk about the perception of one single
observer. Now we could force the issue and constrain all the copies to remain
absolutely identical in the time interval t1 to t3, (by means of environmental
manipulations for example). We are then left with some questions. When we make N
absolutely identical copies which remain absolutely identical during t1 to t3,
have we really increased their measure? And then if we kill N absolutely
identical copies at t3, are we really killing N persons? What is the first
person probability of seeing head?

George Levy
Received on Wed Jan 31 2001 - 21:59:45 PST