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From: Saibal Mitra <smitra.domain.name.hidden>

Date: Sat, 7 Feb 2004 14:41:28 +0100

Eric's comments made me think about these two articles:

http://arxiv.org/abs/math-ph/0008018

Change, time and information geometry

Authors: Ariel Caticha

''Dynamics, the study of change, is normally the subject of mechanics.

Whether

the chosen mechanics is ``fundamental'' and deterministic or

``phenomenological'' and stochastic, all changes are described relative to

an external time. Here we show that once we define what we are talking

about, namely, the system, its states and a criterion to distinguish among

them, there is a single, unique, and natural dynamical law for irreversible

processes that is compatible with the principle of maximum entropy. In this

alternative dynamics changes are described relative to an internal,

``intrinsic'' time which is a derived, statistical concept defined and

measured by change itself. Time is quantified change.''

And:

http://arxiv.org/abs/gr-qc/0109068

Entropic Dynamics

Authors: Ariel Caticha

''I explore the possibility that the laws of physics might be laws of

inference rather than laws of nature. What sort of dynamics can one derive

from well-established rules of inference? Specifically, I ask: Given

relevant information codified in the initial and the final states, what

trajectory is the system expected to follow? The answer follows from a

principle of inference, the principle of maximum entropy, and not from a

principle of physics. The entropic dynamics derived this way exhibits some

remarkable formal similarities with other generally covariant theories such

as general relativity.''

Instead of identifying an observer moment with the exact information stored

in the ''brain'' of an observer, one could identify it with a probability

distribution over such precisely defined states. This seems more realistic

to me. No observer can be aware of all the information stored in his brain.

When I think about who I am, I am actually performing a measurement of some

average of the state my brain is in. After this measurement the probability

distribution will be updated. To apply Caticha's ideas, one has to identify

the measurements with taking averages over an ensemble of observers

described by the same probability distribution. In general this cannot be

true, but like in statistical mechanics, under certain conditions one is

allowed to replace actual averages involving only one system with averages

over a (hypothetical) ensemble.

Saibal

----- Original Message -----

From: Eric Hawthorne

To: everything-list.domain.name.hidden

Sent: Saturday, February 07, 2004 5:26 AM

Subject: Re: measure and observer moments

Given temporal proximity of two states (e.g. observer-moments),

increasing difference between the states will lead to dramatically lower

measure/probability

for the co-occurrence as observer-moments of the same observer (or

co-occurrence in the

same universe, is that maybe equivalent?) .

When I say two states S1, S4 are more different from each other whereas

states S1,S2 are less different

from each other, I mean that a complete (and yet fully abstracted i.e. fully

informationally compressed) informational

representation of the state (e.g. RS1) shares more identical (equivalent)

information with RS2 than it does with RS4.

This tells us something about what time IS. It's a dimension in which more

(non-time) difference between

co-universe-inhabiting states can occur with a particular probability

(absolute measure) as the states

get further from each other in the time of their occurrence. Things (states)

which were (nearly) the same can only

become more different from each other (or their follow-on most-similar

states can anyway) with the passage

of time (OR with lower probability in a shorter time.)

Maybe?

Eric

Saibal Mitra wrote:

----- Original Message -----

From: Jesse Mazer <lasermazer.domain.name.hidden>

To: <everything-list.domain.name.hidden>

Sent: Thursday, February 05, 2004 12:19 AM

Subject: Re: Request for a glossary of acronyms

Saibal Mitra wrote:

This means that the relative measure is completely fixed by the absolute

measure. Also the relative measure is no longer defined when

probabilities

are not conserved (e.g. when the observer may not survive an experiment

as

in quantum suicide). I don't see why you need a theory of consciousness.

The theory of consciousness is needed because I think the conditional

probability of observer-moment A experiencing observer-moment B next

should

be based on something like the "similarity" of the two, along with the

absolute probability of B. This would provide reason to expect that my

next

moment will probably have most of the same memories, personality, etc. as

my

current one, instead of having my subjective experience flit about between

radically different observer-moments.

Such questions can also be addressed using only an absolute measure. So, why

doesn't my subjective experience ''flit about between radically different

observer-moments''? Could I tell if it did? No! All I can know about are

memories stored in my brain about my ''previous'' experiences. Those

memories of ''previous'' experiences are part of the current experience. An

observer-moment thus contains other ''previous'' observer moments that are

consistent with it. Therefore all one needs to show is that the absolute

measure assigns a low probability to observer-moments that contain

inconsistent observer-moments.

As for probabilities not being conserved, what do you mean by that? I am

assuming that the sum of all the conditional probabilities between A and

all

possible "next" observer-moments is 1, which is based on the quantum

immortality idea that my experience will never completely end, that I will

always have some kind of next experience (although there is some small

probability it will be very different from my current one).

I don't believe in the quantum immortality idea. In fact, this idea arises

if one assumes a fundamental conditional probability. I believe that

everything should follow from an absolute measure. From this quantity one

should derive an effective conditional probability. This probability will no

longer be well defined in some extreme cases, like in case of quantum

suicide experiments. By probabilities being conserved, I mean your condition

that ''the sum of all the conditional probabilities between A and all

possible "next" observer-moments is 1'' should hold for the effective

conditional probability. In case of quantum suicide or amnesia (see below)

this does not hold.

Finally, as for your statement that "the relative measure is completely

fixed by the absolute measure" I think you're wrong on that, or maybe you

were misunderstanding the condition I was describing in that post.

I agree with you. I was wrong to say that it is completely fixed. There is

some freedom left to define it. However, in a theory in which everything

follows from the absolute measure, I would say that it can't be anything

else than P(S'|S)=P(S')/P(S)

Imagine

the multiverse contained only three distinct possible observer-moments, A,

B, and C. Let's represent the absolute probability of A as P(A), and the

conditional probability of A's next experience being B as P(B|A). In that

case, the condition I was describing would amount to the following:

P(A|A)*P(A) + P(A|B)*P(B) + P(A|C)*P(C) = P(A)

P(B|A)*P(A) + P(B|B)*P(B) + P(B|C)*P(C) = P(B)

P(C|A)*P(A) + P(C|B)*P(B) + P(C|C)*P(C) = P(C)

And of course, since these are supposed to be probabilities we should also

have the condition P(A) + P(B) + P(C) = 1, P(A|A) + P(B|A) + P(C|A) = 1 (A

must have *some* next experience with probability 1), P(A|B) + P(B|B) +

P(C|B) = 1 (same goes for B), P(A|C) + P(B|C) + P(C|C) = 1 (same goes for

C). These last 3 conditions allow you to reduce the number of unknown

conditional probabilities (for example, P(A|A) can be replaced by (1 -

P(B|A) - P(C|A)), but you're still left with only three equations and six

distinct conditional probabilities which are unknown, so knowing the

values

of the absolute probabilities should not uniquely determine the

conditional

probabilities.

Agreed. The reverse is true. From the above equations, interpreting the

conditional probabilities P(i|j) as a matrix, the absolute probability is

the right eigenvector corresponding to eigenvalue 1.

Let P(S) denote the probability that an observer finds itself in state S.

Now S has to contain everything that the observer knows, including who he

is

and all previous observations he remembers making. The ''conditional''

probability that ''this'' observer will finds himself in state S' given

that

he was in state S an hour ago is simply P(S')/P(S).

This won't work--plugging into the first equation above, you'd get

(P(A)/P(A)) * P(A) + (P(B)/P(A)) * P(B) + P(P(C)/P(A)) * P(C), which is

not

equal to P(A).

You meant to say:

''P(A)/P(A)) * P(A) + (P(A)/P(B)) * P(B) + P(A)/P(C) * P(C), which is not

equal to P(A).''

This shows that in general, the conditional probability cannot be defined in

this way. In P(S')/P(S), S' should be consistent with only one S. Otherwise

you are considering the effects of amnesia. In such cases, you would expect

the probability to increase.

Saibal

Received on Sat Feb 07 2004 - 08:48:26 PST

Date: Sat, 7 Feb 2004 14:41:28 +0100

Eric's comments made me think about these two articles:

http://arxiv.org/abs/math-ph/0008018

Change, time and information geometry

Authors: Ariel Caticha

''Dynamics, the study of change, is normally the subject of mechanics.

Whether

the chosen mechanics is ``fundamental'' and deterministic or

``phenomenological'' and stochastic, all changes are described relative to

an external time. Here we show that once we define what we are talking

about, namely, the system, its states and a criterion to distinguish among

them, there is a single, unique, and natural dynamical law for irreversible

processes that is compatible with the principle of maximum entropy. In this

alternative dynamics changes are described relative to an internal,

``intrinsic'' time which is a derived, statistical concept defined and

measured by change itself. Time is quantified change.''

And:

http://arxiv.org/abs/gr-qc/0109068

Entropic Dynamics

Authors: Ariel Caticha

''I explore the possibility that the laws of physics might be laws of

inference rather than laws of nature. What sort of dynamics can one derive

from well-established rules of inference? Specifically, I ask: Given

relevant information codified in the initial and the final states, what

trajectory is the system expected to follow? The answer follows from a

principle of inference, the principle of maximum entropy, and not from a

principle of physics. The entropic dynamics derived this way exhibits some

remarkable formal similarities with other generally covariant theories such

as general relativity.''

Instead of identifying an observer moment with the exact information stored

in the ''brain'' of an observer, one could identify it with a probability

distribution over such precisely defined states. This seems more realistic

to me. No observer can be aware of all the information stored in his brain.

When I think about who I am, I am actually performing a measurement of some

average of the state my brain is in. After this measurement the probability

distribution will be updated. To apply Caticha's ideas, one has to identify

the measurements with taking averages over an ensemble of observers

described by the same probability distribution. In general this cannot be

true, but like in statistical mechanics, under certain conditions one is

allowed to replace actual averages involving only one system with averages

over a (hypothetical) ensemble.

Saibal

----- Original Message -----

From: Eric Hawthorne

To: everything-list.domain.name.hidden

Sent: Saturday, February 07, 2004 5:26 AM

Subject: Re: measure and observer moments

Given temporal proximity of two states (e.g. observer-moments),

increasing difference between the states will lead to dramatically lower

measure/probability

for the co-occurrence as observer-moments of the same observer (or

co-occurrence in the

same universe, is that maybe equivalent?) .

When I say two states S1, S4 are more different from each other whereas

states S1,S2 are less different

from each other, I mean that a complete (and yet fully abstracted i.e. fully

informationally compressed) informational

representation of the state (e.g. RS1) shares more identical (equivalent)

information with RS2 than it does with RS4.

This tells us something about what time IS. It's a dimension in which more

(non-time) difference between

co-universe-inhabiting states can occur with a particular probability

(absolute measure) as the states

get further from each other in the time of their occurrence. Things (states)

which were (nearly) the same can only

become more different from each other (or their follow-on most-similar

states can anyway) with the passage

of time (OR with lower probability in a shorter time.)

Maybe?

Eric

Saibal Mitra wrote:

----- Original Message -----

From: Jesse Mazer <lasermazer.domain.name.hidden>

To: <everything-list.domain.name.hidden>

Sent: Thursday, February 05, 2004 12:19 AM

Subject: Re: Request for a glossary of acronyms

Saibal Mitra wrote:

This means that the relative measure is completely fixed by the absolute

measure. Also the relative measure is no longer defined when

probabilities

are not conserved (e.g. when the observer may not survive an experiment

as

in quantum suicide). I don't see why you need a theory of consciousness.

The theory of consciousness is needed because I think the conditional

probability of observer-moment A experiencing observer-moment B next

should

be based on something like the "similarity" of the two, along with the

absolute probability of B. This would provide reason to expect that my

next

moment will probably have most of the same memories, personality, etc. as

my

current one, instead of having my subjective experience flit about between

radically different observer-moments.

Such questions can also be addressed using only an absolute measure. So, why

doesn't my subjective experience ''flit about between radically different

observer-moments''? Could I tell if it did? No! All I can know about are

memories stored in my brain about my ''previous'' experiences. Those

memories of ''previous'' experiences are part of the current experience. An

observer-moment thus contains other ''previous'' observer moments that are

consistent with it. Therefore all one needs to show is that the absolute

measure assigns a low probability to observer-moments that contain

inconsistent observer-moments.

As for probabilities not being conserved, what do you mean by that? I am

assuming that the sum of all the conditional probabilities between A and

all

possible "next" observer-moments is 1, which is based on the quantum

immortality idea that my experience will never completely end, that I will

always have some kind of next experience (although there is some small

probability it will be very different from my current one).

I don't believe in the quantum immortality idea. In fact, this idea arises

if one assumes a fundamental conditional probability. I believe that

everything should follow from an absolute measure. From this quantity one

should derive an effective conditional probability. This probability will no

longer be well defined in some extreme cases, like in case of quantum

suicide experiments. By probabilities being conserved, I mean your condition

that ''the sum of all the conditional probabilities between A and all

possible "next" observer-moments is 1'' should hold for the effective

conditional probability. In case of quantum suicide or amnesia (see below)

this does not hold.

Finally, as for your statement that "the relative measure is completely

fixed by the absolute measure" I think you're wrong on that, or maybe you

were misunderstanding the condition I was describing in that post.

I agree with you. I was wrong to say that it is completely fixed. There is

some freedom left to define it. However, in a theory in which everything

follows from the absolute measure, I would say that it can't be anything

else than P(S'|S)=P(S')/P(S)

Imagine

the multiverse contained only three distinct possible observer-moments, A,

B, and C. Let's represent the absolute probability of A as P(A), and the

conditional probability of A's next experience being B as P(B|A). In that

case, the condition I was describing would amount to the following:

P(A|A)*P(A) + P(A|B)*P(B) + P(A|C)*P(C) = P(A)

P(B|A)*P(A) + P(B|B)*P(B) + P(B|C)*P(C) = P(B)

P(C|A)*P(A) + P(C|B)*P(B) + P(C|C)*P(C) = P(C)

And of course, since these are supposed to be probabilities we should also

have the condition P(A) + P(B) + P(C) = 1, P(A|A) + P(B|A) + P(C|A) = 1 (A

must have *some* next experience with probability 1), P(A|B) + P(B|B) +

P(C|B) = 1 (same goes for B), P(A|C) + P(B|C) + P(C|C) = 1 (same goes for

C). These last 3 conditions allow you to reduce the number of unknown

conditional probabilities (for example, P(A|A) can be replaced by (1 -

P(B|A) - P(C|A)), but you're still left with only three equations and six

distinct conditional probabilities which are unknown, so knowing the

values

of the absolute probabilities should not uniquely determine the

conditional

probabilities.

Agreed. The reverse is true. From the above equations, interpreting the

conditional probabilities P(i|j) as a matrix, the absolute probability is

the right eigenvector corresponding to eigenvalue 1.

Let P(S) denote the probability that an observer finds itself in state S.

Now S has to contain everything that the observer knows, including who he

is

and all previous observations he remembers making. The ''conditional''

probability that ''this'' observer will finds himself in state S' given

that

he was in state S an hour ago is simply P(S')/P(S).

This won't work--plugging into the first equation above, you'd get

(P(A)/P(A)) * P(A) + (P(B)/P(A)) * P(B) + P(P(C)/P(A)) * P(C), which is

not

equal to P(A).

You meant to say:

''P(A)/P(A)) * P(A) + (P(A)/P(B)) * P(B) + P(A)/P(C) * P(C), which is not

equal to P(A).''

This shows that in general, the conditional probability cannot be defined in

this way. In P(S')/P(S), S' should be consistent with only one S. Otherwise

you are considering the effects of amnesia. In such cases, you would expect

the probability to increase.

Saibal

Received on Sat Feb 07 2004 - 08:48:26 PST

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