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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)

Graduate Student / Many Worlder / Devil's Advocate

"I know what no one else knows" - 'Runaway Train', Soul Asylum

My URL: http://pages.nyu.edu/~jqm1584/

Received on Thu Jan 14 1999 - 16:08:53 PST

Date: Thu, 14 Jan 1999 19:07:01 -0500

On Mon, 11 Jan 1999, Hal Finney wrote:

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)

Graduate Student / Many Worlder / Devil's Advocate

"I know what no one else knows" - 'Runaway Train', Soul Asylum

My URL: http://pages.nyu.edu/~jqm1584/

Received on Thu Jan 14 1999 - 16:08:53 PST

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