Re: Request for a glossary of acronyms

6 views
Skip to first unread message

Jesse Mazer

unread,
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?

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

_________________________________________________________________
Scope out the new MSN Plus Internet Software — optimizes dial-up to the max!
http://join.msn.com/?pgmarket=en-us&page=byoa/plus&ST=1

Jesse Mazer

unread,
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:

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

_________________________________________________________________
Let the new MSN Premium Internet Software make the most of your high-speed
experience. http://join.msn.com/?pgmarket=en-us&page=byoa/prem&ST=1

Saibal Mitra

unread,
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.

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

Jesse Mazer

unread,
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


Jesse Mazer

unread,
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.

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.

George Levy

unread,
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 absolute probability of any given observer moment is infinitesimal given the extremely large, possibly infinite, number of observer moments states in the plenitude, and also given the much larger non-observer moment states in the plenitude. Non-conscious observers states greatly outnumber conscious observer states. The only way to talk meaningfully about absolute probability is to "normalize" it, effectively converting it to a conditional probability.

The conditional probability of any given observer moment A transitioning to observer moment B given that he is in observer B  is one.

The conditional probability of any given observer moment A transitioning to observer moment B given that he is in observer A  is infinitesimal. There are  many more ways for our physical state to transition (randomly decay) into a non-conscious  observer moments than to transition to a conscious observer moment. Any state in the plenitude could be a target of this transition.


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

Bruno Marchal

unread,
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

Saibal Mitra

unread,
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

Eric Hawthorne

unread,
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
 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

unread,
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

Jesse Mazer

unread,
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

Jesse Mazer

unread,
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/

Bruno Marchal

unread,
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

Reply all
Reply to author
Forward
0 new messages