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From: Wei Dai <weidai.domain.name.hidden>

Date: Tue, 9 Jun 1998 15:12:03 -0700

I put off considering possibilities for the theory of identity, F.

Although it is philosophically interesting and necessary for computing

probabilities for "I will observer X", these probabilities are not

actually predictions since they are not testable. I don't have and can't

possibly get any empirical information about whether or not I actually

will observe X. I only have information about what I currently experience

and what I remember.

So here are some possibilities for I (the set of all observer-instants)

and Q (the probability measure over I).

1. I is the set of all finite binary strings that represent

observer-instants. Q(i) is proportional to UP(i) where UP is the universal

prior.

2. I is the set of all infinite binary inputs for some universal prefix

machine that produce encodings of observer-instants as outputs. Q(J) is

defined iff J is the set of all infinite binary strings that share a

common prefix, in which case Q(J) is proportional to 2^-l, where l is the

length of that prefix.

3. I is the set of all observer-instants in worlds that can be encoded as

binary strings. Q(i), where i=<w,j> for some world w and index j, is

proportional to UP(w).

4. I is the set of all observer-instants in worlds that can be encoded as

binary strings. Q(i), where i=<w,j> for some world w and index j, is

proportional to UP(w)/N(w) where N(w) is the number of observer-instants

in w.

Some observations: (1) and (2) produces the same probabilities for "I

currently observe X", but it might be easier to construct a theory of

identity for (2) that leads to intuitive probabilities for "I will observe

X, given I currently observe Y." Both (3) and (4) are ill-defined unless

we restrict to worlds that contain finite numbers of observer-instants.

(3) can be discarded immediately, because Q would be dominated by counting

worlds that contain very many observer-instants and have high universal

priors. (1) and (2) have the advantage over (4) that they are less

sensitive to how we define what counts as observers, but it might be

easier to find an intuitive interpretation for (4).

Received on Tue Jun 09 1998 - 15:27:01 PDT

Date: Tue, 9 Jun 1998 15:12:03 -0700

I put off considering possibilities for the theory of identity, F.

Although it is philosophically interesting and necessary for computing

probabilities for "I will observer X", these probabilities are not

actually predictions since they are not testable. I don't have and can't

possibly get any empirical information about whether or not I actually

will observe X. I only have information about what I currently experience

and what I remember.

So here are some possibilities for I (the set of all observer-instants)

and Q (the probability measure over I).

1. I is the set of all finite binary strings that represent

observer-instants. Q(i) is proportional to UP(i) where UP is the universal

prior.

2. I is the set of all infinite binary inputs for some universal prefix

machine that produce encodings of observer-instants as outputs. Q(J) is

defined iff J is the set of all infinite binary strings that share a

common prefix, in which case Q(J) is proportional to 2^-l, where l is the

length of that prefix.

3. I is the set of all observer-instants in worlds that can be encoded as

binary strings. Q(i), where i=<w,j> for some world w and index j, is

proportional to UP(w).

4. I is the set of all observer-instants in worlds that can be encoded as

binary strings. Q(i), where i=<w,j> for some world w and index j, is

proportional to UP(w)/N(w) where N(w) is the number of observer-instants

in w.

Some observations: (1) and (2) produces the same probabilities for "I

currently observe X", but it might be easier to construct a theory of

identity for (2) that leads to intuitive probabilities for "I will observe

X, given I currently observe Y." Both (3) and (4) are ill-defined unless

we restrict to worlds that contain finite numbers of observer-instants.

(3) can be discarded immediately, because Q would be dominated by counting

worlds that contain very many observer-instants and have high universal

priors. (1) and (2) have the advantage over (4) that they are less

sensitive to how we define what counts as observers, but it might be

easier to find an intuitive interpretation for (4).

Received on Tue Jun 09 1998 - 15:27:01 PDT

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