# Measure again

From: Jacques M Mallah <jqm1584.domain.name.hidden>
Date: Thu, 14 Jan 1999 19:07:01 -0500

On Mon, 11 Jan 1999, Hal Finney wrote:
> It seems that there are two ways to increase the measure of copies
> and near-copies of yourself which have favorable experiences. [...]
> The other method is by killing yourself when things go wrong. [...]
> By doing so they are increasing the
> fraction of their near-copies which have good experiences.

Like your fellow death-worshipers on this list, you have a very
mixed-up understanding of measure. So once again I will take you guys to
school. The class is RM 102 - Remedial Measure Theory.

RM102 Syllabus:
1. Historical background
2. Effective probabilities
3. Actual or 'unnormalized' measure
4. The infinite universe model
5. Application to quantum suicide
6. Final Exam

1. The term comes from the mathematical theory of measures, of which
probability theory is a subset. A probability is treated as a measure on
a set of events with the additional properties that the sum of the
probabilities is 1 and that they are nonnegative.
The first use of the term 'measure' in the sense of this class,
related to effective probabilities, was in the 1957 thesis of Everett.
This simple concept is a prerequisite for understanding the basic concepts
of the MWI.

2. An effective probability is just what it sounds like, and replaces
the stochastic concept of probability found in single-world interpretations.
A typical observer should expect his observations to be as though they
were drawn from a probability distribution of observations equal to the
effective probability distribution.
By definition, the effective probability of an observation is
proportional to its measure. Effective probability is fractional measure,
normalized so that the sum is 1.

3. Actual or 'unnormalized' measure is the actual amount of an
certain observation present in a model. Only measure ratios affect
effective probabilities, but actual measure is also important. In a
computationalist interpretation, actual measure of a computation is equal
to the number of implementations of a computation.
By definition, if two people agree on the measure distribution for
a model, they agree both on all predictions (given by the effective
probabilities) and on how much consciousness is present in that model.

4. An infinite universe with a single-world interpretation is a
useful model, because it is easy to follow what is happening, and because
by (3.) only the measure distribution of a model is relevant to any
analysis of behavior relating to consciousness.

5. When an individual U chooses to commit suicide at time t, assume
he has an effective chance p of succeeding, as measured by an external
observer. As usual, assume that the measure of an observation is
proportional to the number of observers in that branch of the
wavefunction, times the squared amplitude of that branch.
What are the effects of the suicide, as opposed to what would
happen if U never attempted it?
- The effective probability of an observation being one of those
associated with U is decreased.
- The conditional effective probability, given an observation
associated with U, that it is after time t is decreased.
- The total measure in the universe is decreased, and all of the
decrease is in the total measure of U's observations. In sum, it is a
costly act for U.

6. Final Exam. Are the circumstances under which it is a good idea
to commit suicide the same in the MWI as they would be in a single world
interpretation? (Hint: you can use the infinite universe, single world
model for the MWI.)

- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)