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Feb 3, 2004, 11:17:12 PM2/3/04

to everyth...@eskimo.com

Bruno Marchal wrote:

>Thank you Jesse for your clear answer. Your comparison

>of your use of both ASSA and RSSA with Google ranking system

>has been quite useful.

>This does not mean I am totally convince because ASSA raises the

>problem of the basic frame: I don't think there is any sense to compare

>the probability of "being a human" or "being a bacteria" ..., but your

>"RSSA use of ASSA" does not *necessarily* give a meaning to such

>strong form of absolute Self Sampling Assumption, or does it?

>Thank you Jesse for your clear answer. Your comparison

>of your use of both ASSA and RSSA with Google ranking system

>has been quite useful.

>This does not mean I am totally convince because ASSA raises the

>problem of the basic frame: I don't think there is any sense to compare

>the probability of "being a human" or "being a bacteria" ..., but your

>"RSSA use of ASSA" does not *necessarily* give a meaning to such

>strong form of absolute Self Sampling Assumption, or does it?

No, I don't think it's *necessary* to think that way. Nick Bostrom gives a

good example of the use something like the "absolute self-sampling

assumption" in the FAQ of anthropic-principle.com, where two "batches" of

humans would be created, the first batch containing 3 members of one sex,

the second batch containing 5000 members of the opposite sex. If I know I am

the outcome of this experiment but I don't know which of the two batches I

am a part of, I can see that I am a male, and use Bostrom's version of the

self-sampling assumption to conclude there's a 5000:3 probability that the

larger batch is male (assuming the prior probability of either batch being

male was 50:50). One way to look at this is that if the larger batch is

male, "I" have a 5000/5003 chance of being male and a 3/5003 chance of of

being female--but presumably since you don't think it makes sense to talk

about the "probability" of being a bacteria vs. a human, you also wouldn't

think it makes sense to talk about the "probability" of being a male vs.

being a female. So, another way to think of this would just be as a sort of

abstract mathematical assumption you must make in order to calculate the

conditional probability that, when I go and ask the creators of the

experiment whether the larger batch is male or female, I will have the

experience of hearing them tell me it was male. This mathematical assumption

tells you to reason *as if* you were randomly sampled from all humans in the

experiment, but it's not strictly necessary to attach any metaphysical

significance to this assumption, it can just be considered as a step in the

calculation of probabilities that I will later learn various things about my

place in the universe.

In a similar way, one could accept both an absolute probability distribution

on observer-moments and a conditional probability distribution from each

observer-moment to any other, but one could view the absolute probability

distribution as just a sort of abstract step in the calculation of

conditional probabilities. For example, consider the two-step duplication

experiment again. Say we have an observer A who will later be copied,

resulting in two diverging observers B and C. A little later, C will be

copied again four times, while B will be left alone, so the end result will

be five observers, B, C1, C2, C3, and C4, who all remember being A in the

past. Assuming the probable future of these 5 is about the same, each one

would be likely to have about the same absolute probability. But according

to the Google-like process of assigning absolute probability I mentioned

earlier, this means that later observer-moments of C1, C2, C3 and C4 will

together "reinforce" the first observer-moment of C immediately after the

split more than later observer-moments of B will reinforce the first

observer-moment of B immediately after the split, so the first

observer-moment of C will be assigned a higher absolute probability than

that of B. This in turn means that A should expect a higher conditional

probability of becoming C than B. So again, you can say that this final

answer about A's conditional probabilities is what's really important, that

the consideration of the absolute probability of all those future

observer-moments was just a step in getting this answer, and that absolute

probabilites have no meaning apart from their role in calculating

conditional probabilities. I can't think of a way to justify the conclusion

that A is more likely to experiencing becoming C in this situation without

introducing a step like this, though.

Personally, I would prefer to assign a deeper significance to the notion of

absolute probability, since for me the fact that I find myself to be a human

rather than one of the vastly more numerous but less intelligent other

animals seems like an observation that cries out for some kind of

explanation. But I think this is more of a philosophical difference, so that

even if an ultimate TOE was discovered that gave unique absolute and

conditional probabilities to each observer-moment, people could still differ

on the interpretation of those "absolute probabilities".

>I think also that your view on RSSA is not only compatible with

>the sort of approach I have developed, but is coherent with

>"Saibal Mitra" backtracking, which, at first I have taken

>as wishful thinking.

What is the "backtracking" idea you're referring to here?

OK you make me feel COMP could be a little less

>frightening I'm use to think.

Well, if I've spared you some sleepless nights I'm glad! ;)

>Concerning consciousness theory and its use to isolate a similarity

>relation on the computational histories---as seen from some first person

>point of view, I will try to answer asap in a common answer to

>Stephen and Stathis (and you) who asked very related questions.

>Alas I have not really the time now---I would also like to find a way to

>explain

>the consciousness theory without relying too much on mathematical logic,

>but the similarity between 1-histories *has* been derived technically in

>the part

>of the theory which is the most counter-intuitive ... mmh I will try soon

>...

Yes, I definitely hope to understand the details of your theory someday, I

think I will need to learn some more math to really follow it well though.

My current self-study project is to try to learn the basic mathematical

details of quantum computation and the many-worlds interpretation, but after

that maybe I'll try to study up a bit on mathematical logic and recursive

function theory. And even if I do, there's the little problem of my not

knowing French, but I'll cross that bridge when I come to it...

Jesse

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Feb 4, 2004, 5:00:41 AM2/4/04

to everyth...@eskimo.com

By the way, after writing my message the other day about the question of

what it means for the RSSA and ASSA to be compatible or incompatible, I

thought of another condition that should be met if you want to have both an

absolute probability distribution on observer-moments and a conditional one

from any one observer-moment to another. Suppose I pick an observer-moment B

from the set of all observer-moments according to the following procedure:

what it means for the RSSA and ASSA to be compatible or incompatible, I

thought of another condition that should be met if you want to have both an

absolute probability distribution on observer-moments and a conditional one

from any one observer-moment to another. Suppose I pick an observer-moment B

from the set of all observer-moments according to the following procedure:

1. First, randomly select an observer-moment A from the set of all

observer-moments, using the absolute probability distribution.

2. Then, select a "next" observer-moment B to follow A from the set of all

observer-moments, using the conditional probability distribution from A to

all others.

What will be the probability of getting a particular observer-moment for

your B if you use this procedure? I would say that in order for the RSSA and

ASSA to be compatible, it should always be the *same* probability as that of

getting that particular observer-moment if you just use the absolute

probability distribution alone. If this wasn't true, if the two probability

distributions differed, then I don't see how you could justify using one or

the other in the ASSA--after all, my "current" observer-moment is also just

the "next" moment from my previous observer-moment's point of view, and a

moment from now I will experience a different observer-moment which is the

successor of my current one. I shouldn't get different conclusions if I look

at a given observer-moment from different but equally valid perspectives, or

else there is something fundamentally wrong with the theory.

I think there'd be an analogy for this in statistical mechanics, in a case

where you have a probabilistic rule for deciding the path through phase

space...if the system is at equilibrium, then the probabilities of the

system being in different states should not change over time, so if I find

the probability the system will be in the state B at time t+1 by first

finding the probability of all possible states at time t and then

multiplying by the conditional probability of each one evolving to B at time

t+1, then summing all these products, I should get the same answer as if I

just looked at the probability I would find it in state B at time t. I'm not

sure what the general conditions are that need to be met in order for an

absolute probability distribution and a set of conditional probability

distributions to have this property though. In the case of absolute and

conditional probability distributions on observer-moments, hopefully this

property would just emerge naturally once you found the correct theory of

consciousness and wrote the equations for how the absolute and relative

distributions must relate to one another.

One final weird thought I had a while ago on this type of TOE. What if, in

finding the correct theory of consciousness, there turned out to a sort of

self-similarity between the way individual observer-moments work and the way

the probability distributions on the set of all observer-moments work? In

other words, perhaps the theory of consciousness would describe an

individual observer-moment in terms of some set of sub-components which are

each assigned a different absolute weight (perhaps corresponding to the

amount of 'attention' I am giving to different elements of my current

experience), along with weighted links between these elements (which could

correspond to the percieved relationships between these different elements,

like in a neural net). This kind of self-similarity might justify a sort of

pantheist interpretation of the theory, or an "absolute idealist" one maybe,

in which the multiverse as a whole could be seen as a kind of infinite

observer-moment, the only possible self-consistent one (assuming the

absolute and conditional probability distributions constrain each other in

such a way as to lead to a unique solution, as I suggested earlier). Of

course there's no reason to think a theory of consciousness will necessarily

describe observer-moments in this way, but it doesn't seem completely

implausible that it would, so it's interesting to think about.

Jesse

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Feb 4, 2004, 8:37:04 AM2/4/04

to Jesse Mazer, everyth...@eskimo.com

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.

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.

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). Note that S' has to

contain the information that an hour ago he remembers being in state S. The

concept of the conditional probability is only an approximate one, and has

no meaning e.g. when simulating a person directly in state S' or in cases

where there are no states S' that remember being in S (e.g. S is the state

an observer is in just before certain death). Ignoring these effects, it is

easy to see that P(S')/P(S) has the properties you would expect. E.g. the

sum over all S' compatible with S yields 1.

Saibal

Feb 4, 2004, 5:32:20 PM2/4/04

to everyth...@eskimo.com

Hi Jesse,

Jesse Mazer wrote:

By the way, after writing my message the other day about the question of what it means for the RSSA and ASSA to be compatible or incompatible, I thought of another condition that should be met if you want to have both an absolute probability distribution on observer-moments and a conditional one from any one observer-moment to another. Suppose I pick an observer-moment B from the set of all observer-moments according to the following procedure:

1. First, randomly select an observer-moment A from the set of all observer-moments, using the absolute probability distribution.

You assume that you could get your hands on the absolute probability
distribution. You *must* assume when you observe a physical
system is that you are an observer. The existence of (objective)
absolute reality is another assumption that *may not be necessary*.
Assuming the existence of an absolute probability distribution is like
assuming the existence of an absolute frame of reference in space.

2. Then, select a "next" observer-moment B to follow A from the set of all observer-moments, using the conditional probability distribution from A to all others.

What will be the probability of getting a particular observer-moment for your B if you use this procedure? I would say that in order for the RSSA and ASSA to be compatible, it should always be the *same* probability as that of getting that particular observer-moment if you just use the absolute probability distribution alone. If this wasn't true, if the two probability distributions differed, then I don't see how you could justify using one or the other in the ASSA

The ASSA requires one additional assumption: the existence of an
objective reality. In my opinion the two approaches are not compatible,
but may give very similar results when the obervers are "close"
together, where distance here is measured as the amount of overlap of
life contingencies.

George

George

Feb 4, 2004, 6:25:02 PM2/4/04

to everyth...@eskimo.com

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.

>

>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.

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).

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. 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.

>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). It would work if you instead used 1/N * (P(S)/P(S')), where N

is the total number of distinct possible observer-moments, but obviously

that won't work if the number of distinct possible observer-moments is

infinite. And as I said, this condition should not *uniquely* imply a

certain set of conditional probabilities given the absolute probabilities,

so even with a finite N this wouldn't be the only way to satisfy the

condition.

Feb 4, 2004, 10:30:15 PM2/4/04

to Everything List

Jesse Mazer wrote:

George Levy wrote:

You assume that you could get your hands on the absolute probability distribution. You must assume >when you observe a physical system is that you are an observer. The existence of (objective) absolute >reality is another assumption that may not be necessary. Assuming the existence of an absolute >probability distribution is like assuming the existence of an absolute frame of reference in space.

No, I don't assume I know the absolute probability distribution to begin with. As I explained in earlier posts, I assume that there is some sort of theory that would be able to tell me the conditional probabilities *if* I already knew the absolute probability distribution, and likewise that this theory could tell me the absolute probability distribution *if* I already knew the all the conditional probabilities. But I don't know either one to begin with--the idea is that the two mutually constrain each other in such a way as to provide a unique solution to both, like solving a set of N simultaneous equations with N variables.

Or:

1. Conditional probability of observer-moment A having observer-moment B as its next experience = some function F of the form F(formal properties of A, formal properties of B, P(B))

[by 'formal properties' I am suggesting something like the 'similarity' between the two observer-moments which I talked about earlier, which is why I think this would need to be based on a theory of consciousness]

2. Absolute probability of observer-moment B = P(B) = some function G of the form G(the set of conditional probabilities between B and every other observer-moment)

The idea is that the theory of consciousness could tell me the exact form of the functions F and G, but the actual values of all the absolute probabilities and conditional probabilities are unknown. But since each function depends on the other in this way, it is conceivable they would mutually constrain each other in such a way that you could solve for all the absolute probabilities and conditional probabilities, although of course this is just my own pet theory.

You say that the values of the absolute and conditional probabilities are unknown. In my opinion, I have a very good idea of what their values are.

The ASSA requires one additional assumption: the existence of an objective reality.

Yes, but in a way doesn't a belief in an "objective" truth about conditional probabilities assume this too? A truly subjective approach would be one like Wei Dai's, where observers can make any assumptions about probabilities that they like.

Who says truth has to be objective? or even if there is such a thing an objective truth? And I don't agree with Wei. Ultimately the assumptions that an observer makes about probabilities must be grounded in his own status as observer. Assuming the observer is the only assumption that needs to be made.

Imho there can be an emergent reality purely based on the observer states without the need for any objective entity.

The observer himself is an emergent phenomenon reflected on / reflecting the observer himself.

George

Feb 6, 2004, 8:28:32 AM2/6/04

to everyth...@eskimo.com

At 20:17 03/02/04 -0500, Jesse Mazer wrote:

>Personally, I would prefer to assign a deeper significance to the notion

>of absolute probability, since for me the fact that I find myself to be a

>human rather than one of the vastly more numerous but less intelligent

>other animals seems like an observation that cries out for some kind of

>explanation.

I am not sure about that. Suppose a teacher has 10^1000 students. Today

he says to the students that he will, tomorrow, interrogate one student of the

class and he will chooses it randomly. Each student thinks that there is only

1/(10^1000) chance that he will be interrogated. That's quite negligible, and

(assuming that all student are lazy) none of the students prepare the

interrogation.

But then the day after the teacher says: "Smith, come on to the board, I will

interrogate you".

I hope you agree there has been no miracle here, even if for the student, being

the one interrogated is a sort of (1-person) miracle. No doubt that this

student

could cry out for an explanation, but we know there is no explanations...

Suppose the teacher and the student are immortal and the teacher interrogates

one student each day. Eternity is very long, and there will be arbitrarily

large

period where poor student Smith will be interrogated each days of that period.

Obviously Smith will believe that the teacher has something special against

him/her.

But still we know it is not the case ...

So I don't think apparent low probability forces us to search for an

explanation

especially in an everything context, only the relative probability of

continuation

could make sense, or "ab initio" absolute probabilities could perhaps be

given for the

entire histories.

>But I think this is more of a philosophical difference, so that even if an

>ultimate TOE was discovered that gave unique absolute and conditional

>probabilities to each observer-moment, people could still differ on the

>interpretation of those "absolute probabilities".

I am not yet sure I can make sense of them.

>>I think also that your view on RSSA is not only compatible with

>>the sort of approach I have developed, but is coherent with

>>"Saibal Mitra" backtracking, which, at first I have taken

>>as wishful thinking.

>

>What is the "backtracking" idea you're referring to here?

That if you put the probabilities on the infinite stories, any finite

story will be of measure null, so that if an accident happens to you,

and make you dead (in some absolute sense), you will never live that accident,

nor the events leading to that accident: from a 3-person pov it is like

there has been some backtracking, but it's seems linear from a 1-pov.

(pov = point of view)

>OK you make me feel COMP could be a little less

>>frightening I'm use to think.

>

>Well, if I've spared you some sleepless nights I'm glad! ;)

Thanks.

>>Concerning consciousness theory and its use to isolate a similarity

>>relation on the computational histories---as seen from some first person

>>point of view, I will try to answer asap in a common answer to

>>Stephen and Stathis (and you) who asked very related questions.

>>Alas I have not really the time now---I would also like to find a way to

>>explain

>>the consciousness theory without relying too much on mathematical logic,

>>but the similarity between 1-histories *has* been derived technically in

>>the part

>>of the theory which is the most counter-intuitive ... mmh I will try

>>soon ...

>

>Yes, I definitely hope to understand the details of your theory someday, I

>think I will need to learn some more math to really follow it well though.

>My current self-study project is to try to learn the basic mathematical

>details of quantum computation and the many-worlds interpretation,

It seems a good plan.

>but after that maybe I'll try to study up a bit on mathematical logic and

>recursive function theory. And even if I do, there's the little problem of

>my not knowing French, but I'll cross that bridge when I come to it...

Nice, you will be able to read the long version of my thesis ... It's

almost self-contained.

In logic it is only the beginning which is hard, really. Nevertheless I

will try to explain the

consciousness theory and the minimal amount of logic needed. The fact is

that it is easy

to be wrong with self-applied probability, and using logic, it is possible

to derive the logic

of [probability one] quasi-directly from the (counter-intuitive) godelian

logic of self-reference.

There are already evidence that we get sort of quantum logic for those

probability one.

I'm really searching how to justify the wavy aspect of nature.

Bruno

Feb 6, 2004, 8:45:19 AM2/6/04

to Jesse Mazer, everyth...@eskimo.com

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

From: Jesse Mazer <laser...@hotmail.com>

To: <everyth...@eskimo.com>

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

Feb 6, 2004, 11:32:19 PM2/6/04

to everyth...@eskimo.com

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

increasing difference between the states will lead to dramatically lower measure/probability

Â 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) asÂ 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

Feb 7, 2004, 8:48:25 AM2/7/04

to Eric Hawthorne, everyth...@eskimo.com

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

Feb 9, 2004, 5:10:17 AM2/9/04

to everyth...@eskimo.com

But I would expect this consistency to be a matter of degree, because

sharing "memories" with other observer-moments also seems to be a matter of

degree. Normally we use the word "memories" to refer to discrete episodic

memories, but this is actually a fairly restricted use of the term, episodic

memories are based on particular specialized brain structures (like the

hippocampus, which if damaged can produce an inability to form new episodic

memories like the main character in the movie 'Memento') and it is possible

to imagine conscious beings which don't have them. The more general kind of

memory is the kind we see in a basic neural network, basically just

conditioned associations. So if a theory of consciousness determined

"similarity" of observer-moments in terms of a very general notion of memory

like this, there'd be a small degree to which my memories match those of any

other person on earth, so I'd expect a nonzero (but hopefully tiny)

probability of my next experience being that of a totally different person.

>Therefore all one needs to show is that the absolute

>measure assigns a low probability to observer-moments that contain

>inconsistent observer-moments.

But if observer-moments don't "contain" past ones in discrete way, but just

have some sort of fuzzy "degree of similarity" with possible past

observer-moments, then you could only talk about some sort of probability

distribution on possible pasts, one which might be concentrated on

observer-moments a lot like my current one but assign some tiny but nonzero

probability to very different ones.

In any case, surely my current observer-moment is not complex enough to

contain every bit of information about all observer-moments I've experienced

in the past, right? If you agree, then what do you mean when you say my

current one "contains" past ones?

> >

> > 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.

Yes, it depends on whether one believes there is some theory that would give

an objective truth about first-person conditional probabilities. But even if

one does assume such an objective truth about conditional probabilities,

quantum immortality need not *necessarily* be true--perhaps for a given

observer-moment, this theory would assign probabilities to various possible

future observer-moments, but would also include a nonzero probability that

this observer-moment would be a "terminal" one, with no successors. However,

I do have some arguments for why an objective conditional probability

distribution would at least strongly suggest the quantum immortality idea,

which I outlined in a post at

http://www.escribe.com/science/theory/m4805.html

>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.

I'm not sure what you mean by "effective conditional probability"...is it

just the P(S'|S) = P(S')/P(S) idea you suggested earlier? This equation

would seem to suggest that the degree of similarity between two

observer-moments is irrelevant when deciding the conditional probability of

experiencing the second after the first, that if an observer-moment of

Charlie Chaplin's brain in 1925 has the same absolute probability as an

observer-moment of my brain 1 second from now, I should expect the same

probability of either one as my next experience. But from your other

comments I guess you're also adding that if an observer-moment S' doesn't

"contain" my current one S then there's 0 probability I will experience it

next.

>

> >

> > 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)

Only if you also impose the condition that each observer-moment has a unique

past, that there can be no "merging". If merging is possible, the

conditional measure could still follow from the absolute measure (my

suggestion is that the two measures mutually determine each other), but the

probabilities would be different.

Yes, that occurred to me after I had posted this. But I don't remember

enough linear algebra to say what conditions have to be met for a

nonnegative matrix to have a unique eigenvector for a given eigenvalue, and

the situation is complicated by the fact that I'm really imagining an

infinite number of distinct possible observer-moments and thus the matrix

would have an infinite number of components (but the sum of each row and

each column would be finite).

I also thought of a possible simplification: I said earlier that I thought

the function for the conditional probability between A and B would involve

both the absolute probability of B, P(B), and 'formal properties' of A and B

that, like the vague notion of 'similarity' I have been talking about, which

would have to be quantified by a theory of consciousness. But it seems like

there's a good argument for saying something a bit more specific, namely

that the function would involve the *product* of P(B) with the 'similarity'

(or whatever you call it) between A and B. Think of a duplication experiment

where the initial difference between the two duplicates is very small, like

they initially have identical brainstates but then diverge as one sees he's

in a room with green walls and the other sees he's in a room with red walls.

Presumably any quantity based on a comparison of formal properties between

two observer-moments, such as 'similarity', would be basically the same

whether you compared my current observer-moment with the one in the green

room or the one in the red room, so if the observer-moment in the green room

had twice the absolute probability as the one in the red room (say, because

the one in the green room was scheduled to be duplicated again later while

the one in the red room was not), it makes intuitive sense that my

conditional probability of becoming the one in the green room would also be

twice as large.

Obviously this isn't a watertight argument, but if it's true then we could

say P(B|A) = P(B)*Sab, where Sab is the 'similarity' between A and B (Don't

take the term 'similarity' too literally since this function might be quite

different from the ordinary sense of the term...for example, ordinarily we

think of the word similarity as something symmetrical, so the similarity of

A to B is the same as that of B to A, but the subjective directionality of

time and memory suggests this probably shouldn't be true for whatever

function is used here, because I'd expect to have a much higher conditional

probability of my next experience being that of my brain 1 second from now

than he should have of his next experience being my current one.) So the

equations would look like this:

P(A)*Saa*P(A) + P(A)*Sab*P(B) + P(A)*Sac*P(C) = P(A)

P(B)*Sba*P(A) + P(B)*Sbb*P(B) + P(B)*Sbc*P(C) = P(B)

P(C)*Sca*P(A) + P(C)*Scb*P(B) + P(C)*Scc*P(C) = P(C)

Which simplifies to:

Saa*P(A) + Sab*P(B) + Sac*P(C) = 1

Sba*P(A) + Sbb*P(B) + Sbc*P(C) = 1

Sca*P(A) + Scb*P(B) + Scc*P(C) = 1

Which would mean the "similarity matrix" operating on the

absolute-probability vector equals the unit vector, so as long as the

similarity matrix has an inverse, this inverse operating on the unit vector

would give the vector of absolute probabilities. Again though, I don't know

much about how linear algebra works for infinite matrices, or whether they'd

have inverses.

>

> >

> > >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).''

Actually I just got confused about whether S' or S was the current state,

but yeah, that's what I should have written. Anyway, as I said, for

something like this to be true in general you'd need a 1/N factor, where N

is the total number of possible observer-moments. But from your comments

about amnesia below I take it you're saying that S' has a unique previous

state S, so if B's unique past state was A, then P(B|A) = P(B)/P(A) while

P(B|C) = 0 and P(B|B) = 0, so the condition P(B|A)*P(A) + P(B|B)*P(B) +

P(B|C)*P(C) = P(B) would be satisfied. But does this also mean that each

observer-moment has a unique future? Consider the matrix of conditional

probabilities:

P(A|A) P(A|B) P(A|C)

P(B|A) P(B|B) P(B|C)

P(C|A) P(C|B) P(C|C)

You're saying that only one entry in each row can be nonzero. But this means

either that each column has exactly one entry that's nonzero (every

observer-moment has a unique future), or that some columns have multiple

nonzero entries while others have all zero entries--maybe these might

correspond to "terminal" observer-moments where death is certain? Anyway, I

guess this conclusion wouldn't hold for a matrix whose rows and columns

contained an infinite number of components, where you could have something

like this:

.5 0 0 0 0 0 . . .

.5 0 0 0 0 0

0 .5 0 0 0 0

0 .5 0 0 0 0

0 0 .5 0 0 0

0 0 .5 0 0 0

. .

. .

. .

>

>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.

By "amnesia", you're talking about the idea that streams of consciousness

can merge as well as split, correct? That a given observer-moment can be

compatible with multiple pasts? If so, then yes, I would assume something

like that is possible, if splitting is possible.

Jesse

_________________________________________________________________

Click here for a FREE online computer virus scan from McAfee.

http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963

Feb 9, 2004, 4:30:43 PM2/9/04

to everyth...@eskimo.com

But your example assumes we already know the probabilities. If Smith has two

different hypotheses that a priori both seem subjectively plausible to

him--for example, "the teacher will pick fairly, therefore my probability of

being picked is 1 in 10^1000" vs. "I know my father is the teacher's

arch-nemesis, therefore to punish my family I expect he will fake the random

draw and unfairly single me out with probability 1", then if Smith actually

is picked, he can use Bayesian reasoning to now conclude the second

hypothesis is more likely (unless he considered its a priori subjective

likelihood to be less than 10^-1000 that of the first hypothesis).

This is a better analogy to the situation of finding myself to be a human

and not one of the much larger number of other conscious animals (even if we

restrict ourselves to mammals and birds, who most would agree are genuinely

conscious, the number of mammals/birds that have ever lived is surely much

larger than the number of humans that have ever lived--just think of how

many rodents have been born throughout the last 65 million years!) Even if I

a priori favor the idea that I should consider any observer-moment equally

likely, unless I am virtually certain that the probabilities are not biased

in favor of observer-moments with human-level complexity, then finding

myself to actually be experiencing such an observer-moment should lead me to

shift my subjective probability estimate in favor of this second sort of

hypothesis. Of course, both hypotheses assume it is meaningful to talk about

the absolute probability of being different observer-moments, an assumption

you may not share (but in that case the Smith/teacher analogy should not be

a good one from your perspective).

Another possible argument I thought of for having absolute probabilities as

well as conditional probabilities. If one had a theory that only involved

conditional probabilities, this might in some way be able to explain why I

see the laws of physics work a certain way from one moment to the next, by

describing it in terms of the probability that my next experience will be Y

if my current one is X. But how would it explain why, when I examine records

of events that happened in the past, even records of events before my

subjective stream of consciousness began, I still see that everything obeyed

those same laws back then as well? Could you explain that without talking

about the absolute probability of what type of "universe" a typical

observer-moment is likely to percieve himself being in, including memories

and external records of the past?

Jesse

_________________________________________________________________

Create your own personal Web page with the info you use most, at My MSN.

http://click.atdmt.com/AVE/go/onm00200364ave/direct/01/

Feb 20, 2004, 9:00:50 AM2/20/04

to everyth...@eskimo.com, Fabric-o...@yahoogroups.com

Hi All,

I have put "Conscience & Mecanisme" in my web page, along

with other stuffs. (And some others will arrive). It could be of some

interest to you.

"Conscience et Mecanisme" is the 1995 Brussels thesis (which

has neither been defended, ... nor attacked ....).

Beside the "Introduction", "Recapitulation" etc., there are mainly

9 sections (from 1.1 to 3.3). The first seven are the theory of

consciousness derived from the computationalist hypothesis.

The last two give the application of that theory of consciousness

for isolating an arithmetical formulation of the mind body problem.

It contains the physico/psycho-reversal.

Basically the Lille's PhD thesis is just a concise presentation

of the section 3.2 and 3.3 of Brussels thesis.

This is possible by the trick consisting in *defining* machine's

psychology/theology by the self-referentially correct Loebian

machine's discourse (but that is what *is* explained in detail

in the first seven sections of C&M).

To 'consolate' those who doesn't read french I have made accessible

my older "Mechanism, and Personal Identity", and "Amoeba, Planaria,

and Dreaming Machine". So old that the modal box did not survive!

That is, a modal formula like <>[]p -> -[][]p is transformed

into <>,p -> -,,p in AP&DM, and into <>,,p -> -,, ,,p in M&PI.

That is the box [] is transformed into one comma in AP&DM, and

two commas in M&PI. Sorry.

This makes things a little less readable, but as logical symbol, it does

not change anything if you read the paper from the beginning.

Note that all "symbols" in C&M have survived (but then there are typo

errors, ....).

I will also put "Le secret de l'amibe" on the web page. It is the story of

the thesis, and a lot of readers of preliminary version told me it helps

a lot for understanding the work. I have finished it in 2001, and it should

have been published since, but I'm still waiting (without any explanations).

I have also been kindly proposed for an invited talk at the international

SANE'2004 in Amsterdam.

http://www.nluug.nl/events/sane2004/CfP-2004.html

Title: The Origin of Physical Laws and Sensations.

Abstract: I first sum up a non constructive argument showing that the

mechanist hypothesis in the cognitive science gives

enough constraints to decide what a "physical reality"

can possibly consist in.

Then I explain how computer science together with logic

make it possible to extract a constructive version of the

argument by interviewing a Modest (Loebian) Universal Machine.

Reversing von Neumann probabilistic interpretation of

quantum logic on those provided by the Loebian Machine

provides a kind of explanation of how both sharable physical

laws and un-sharable physical knowledge arise from number

theoretical relations.

Bruno

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