relevance of the real measure
Wei Dai
and B, and you know that A has measure 0.9, and B has measure 0.1. Suppose
that until time T the history of these two universes are identical. At
time T an experiment will be done in both universes. In universe A the
outcome of the experiment will be "a", and in universe B the outcome will
be "b". If before time T you were given an opportunity to bet $10 that the
outcome is "a" at 1:1 odds, so that in universe A you would gain $10, and
in universe B you would lose $10, Would you take the bet?
The standard answer is yes, you should take it because A has greater
measure. But that assumes you care more about universes that have greater
measure than universes that have less measure. But you could say that you
don't care about what happens in universe A, only about what happens in
universe B, in which case you wouldn't take the bet. So it seems that the
measure only affects your decisions if it enters into your utility
function somehow, and it's not clear that it must.
Even if you knew that only universe A is real, that is, A has measure 1,
and B has measure 0, you could still rationally not take the bet. After
all, even if universe B doesn't have "real" existence, whatever that
means, it still has some sort of platonic existence, and you can still
care more about what happens in universe B than what happens in universe
A.
If people's utilities functions could ignore the "real" measure, then what
relevance does it have? Why are we arguing about whether the real measure
is the Speed Prior or a more dominant prior?
You might argue that most people aproximately behave as if they use the
real measure. But by using the word "most" you're already presuming that
the real measure is relevant. In the above example (where universe B has
measure 0), universe B might be filled with people who ignore the real
measure and only care about universe B, and if you yourself only cared
about universe B, then you'd act as if you expected most people to ignore
the real measure.
h...@finney.org
> Suppose there are only two logically possible deterministic universes A
> and B, and you know that A has measure 0.9, and B has measure 0.1. Suppose
> that until time T the history of these two universes are identical. At
> time T an experiment will be done in both universes. In universe A the
> outcome of the experiment will be "a", and in universe B the outcome will
> be "b". If before time T you were given an opportunity to bet $10 that the
> outcome is "a" at 1:1 odds, so that in universe A you would gain $10, and
> in universe B you would lose $10, Would you take the bet?
Measure is not supposed to be just an abstract number that is attached
to a universe. It has meaning in terms of our own perceptions and
experience in that universe. The all-universe theory includes both a
model of universes which exist, and a way of relating our experiences of
consciousness to those universes. In the theory, if there is a physical
system in the multiverse which is isomorphic to our own mental state, then
the probability of experiencing subjective consequences which correspond
to changes in that system will be proportional to its measure. This is
a crucial linkage for the theory to have explanatory power, otherwise
our experiences would not need to have any connection to measure and it
would be a meaningless parameter.
> The standard answer is yes, you should take it because A has greater
> measure. But that assumes you care more about universes that have greater
> measure than universes that have less measure. But you could say that you
> don't care about what happens in universe A, only about what happens in
> universe B, in which case you wouldn't take the bet. So it seems that the
> measure only affects your decisions if it enters into your utility
> function somehow, and it's not clear that it must.
Think of a single-universe model with ordinary probability, where you
have a bet with a 90% chance of outcome A and 10% chance of outcome B.
Conventionally you should take the bet which maximizes your expectations
based on A occuring. But you could imagine someone who only cared about
what happened if outcome B happened, and bet on B so that he would do
well in that unlikely case. It's rational in a certain sense, but it
is going to lead to bad consequences in practice.
These two examples are similar in that in each case you have to face the
reality that you are likely to subjectively experience outcome A. In the
multiverse model that is part of the theory which relates subjective
experience to the physical model. You can't escape the fact that the
subjective consequences of your actions will be based on measure. So
I don't think you can ignore it or treat it as a parameter to be dealt
with as you like.
Hal
Wei Dai
> Measure is not supposed to be just an abstract number that is attached
> to a universe. It has meaning in terms of our own perceptions and
> experience in that universe. The all-universe theory includes both a
> model of universes which exist, and a way of relating our experiences of
> consciousness to those universes. In the theory, if there is a physical
> system in the multiverse which is isomorphic to our own mental state, then
> the probability of experiencing subjective consequences which correspond
> to changes in that system will be proportional to its measure.
This may be true but I don't think utility functions should be based on
subjective experiences. Otherwise everyone would endlessly re-run
simulations of their most favorable subjective experiences. Utility
functions should be based on external reality, so you'd choose actions
based on their overall effects on the multiverse. In that case it's not
clear why we should care about each universe in proportion to its measure.
This may make more practical sense if you consider the debate between
Juergen and I about Speed vs. more dominant priors. Even if I believed
that the multiverse was instantiated by a Great Programmer running the
FAST algorithm, why should I then care about each universe in proportion
to its Speed prior instead of any other arbitrary measure that I choose?
> Think of a single-universe model with ordinary probability, where you
> have a bet with a 90% chance of outcome A and 10% chance of outcome B.
> Conventionally you should take the bet which maximizes your expectations
> based on A occuring. But you could imagine someone who only cared about
> what happened if outcome B happened, and bet on B so that he would do
> well in that unlikely case. It's rational in a certain sense, but it
> is going to lead to bad consequences in practice.
I think there is a significant difference in that in the single-universe
model someone like that wouldn't survive very long and therefore evolution
would eliminate this kind of utility functions. But in the multiverse
model, this person would continue to survive in the universes that he
cares about and actually he would do very well in those universes, whereas
you would do poorly in those universes but do well in the universes you
cared more about. So there is a symmetry between him and you that doesn't
exist in the single-universe model.
h...@finney.org
> On Fri, Dec 21, 2001 at 12:12:41AM -0800, h...@finney.org wrote:
> > Measure is not supposed to be just an abstract number that is attached
> > to a universe. It has meaning in terms of our own perceptions and
> > experience in that universe.
>
> subjective experiences. Otherwise everyone would endlessly re-run
> simulations of their most favorable subjective experiences. Utility
> functions should be based on external reality, so you'd choose actions
> based on their overall effects on the multiverse. In that case it's not
> clear why we should care about each universe in proportion to its measure.
There may be subjective reasons not to re-run favorable experiences,
such as that it makes you vulnerable to unexpected threats. In any case,
we can't rule out a priori that making yourself happy in this way is
the best course of action.
> This may make more practical sense if you consider the debate between
> Juergen and I about Speed vs. more dominant priors. Even if I believed
> that the multiverse was instantiated by a Great Programmer running the
> FAST algorithm, why should I then care about each universe in proportion
> to its Speed prior instead of any other arbitrary measure that I choose?
I'm not sure why it is inadequate to say that you care because you live
in the universe and its reality affects you. You can't just choose
whatever reality you like.
> > Think of a single-universe model with ordinary probability, where you
> > have a bet with a 90% chance of outcome A and 10% chance of outcome B.
> > Conventionally you should take the bet which maximizes your expectations
> > based on A occuring. But you could imagine someone who only cared about
> > what happened if outcome B happened, and bet on B so that he would do
> > well in that unlikely case. It's rational in a certain sense, but it
> > is going to lead to bad consequences in practice.
>
> I think there is a significant difference in that in the single-universe
> model someone like that wouldn't survive very long and therefore evolution
> would eliminate this kind of utility functions. But in the multiverse
> model, this person would continue to survive in the universes that he
> cares about and actually he would do very well in those universes, whereas
> you would do poorly in those universes but do well in the universes you
> cared more about. So there is a symmetry between him and you that doesn't
> exist in the single-universe model.
That is true; in the multiverse, people in high-measure worlds will come
to expect and predict high-measure (high-likelihood) events, while those
in low-measure worlds may come to predict low-measure events. So there is
some symmetry here. However again I would break the symmetry by saying
that each of us is more likely to encounter the high-measure worlds and
people, because that is what measure means. We are effectively unable
to observe the low-measure worlds. So the universe that we are able to
perceive and predict will have the same properties as if there were only
a single world.
Imagine that we create computer simulations of two worlds with conscious
inhabitants. We can't just add a measure parameter and set it arbitarily
to say that the first world has measure .9 and the second .1. When we
tweak our measure parameter it will not affect the subjective lives
of the people in the simulation. Measure does not work that way.
Somehow it does relate to subjective probabilities.
You can get this in one way by relating it to duplicate instantiations,
such that worlds of measure .9 have 9 times as many duplicates as worlds
of measure .1. I don't personally find this to be helpful because
it requires assumptions which to my mind are equally as arbitrary as
directly requiring measure to have the required properties of subjective
probability. But in the simple case where we are running simulations
on a computer that would probably work. Run one 9 times as often and
you could plausibly suppose that the inhabitants will be more likely to
experience that world.
However you get to it, you have to think of measure as more than a label
attached to a universe, devoid of other meaning. That is the only way
to get predictions from the multiverse model.
Hal
Wei Dai
all possible universes exist and some objectively true measure exists on
the set of universes.
Instead, let's just say that all possible universes exist, period. There
is no objective measure. Instead, measure enters into the utility function
as a way of specifying how much one cares about each universe. The measure
is therefore an arbitrary and subjective choice.
The goal of the theory of everything then, is to tell us if how we should
behave given the utility function (and measure) that we do adopt. For
example one thing it might tell us is that if we adopted the Speed prior
for our utility function, then we should act as if we expect large
scale quantum computation to be impossible.
On Fri, Dec 21, 2001 at 03:21:49PM -0800, h...@finney.org wrote:
> There may be subjective reasons not to re-run favorable experiences,
> such as that it makes you vulnerable to unexpected threats.
But still, the only reason to do anything would be to increase the number
of times you can re-run favorable experiences.
> In any case,
> we can't rule out a priori that making yourself happy in this way is
> the best course of action.
I'm not saying that it can't be the best course of action for *anyone*,
I'm saying that it can't be the best course of action for *everyone*.
> I'm not sure why it is inadequate to say that you care because you live
> in the universe and its reality affects you. You can't just choose
> whatever reality you like.
Suppose I live in the FAST multiverse. Why should its reality affect me in
this particular way, so that I care about each universe in proportion to
its Speed prior?
> That is true; in the multiverse, people in high-measure worlds will come
> to expect and predict high-measure (high-likelihood) events, while those
> in low-measure worlds may come to predict low-measure events. So there is
> some symmetry here. However again I would break the symmetry by saying
> that each of us is more likely to encounter the high-measure worlds and
> people, because that is what measure means. We are effectively unable
> to observe the low-measure worlds. So the universe that we are able to
> perceive and predict will have the same properties as if there were only
> a single world.
Just because you won't observe something, doesn't mean you shouldn't care
about it. For example some people put significant effort into writing
wills and setting up foundations which they will never see the effects of.
> Imagine that we create computer simulations of two worlds with conscious
> inhabitants. We can't just add a measure parameter and set it arbitarily
> to say that the first world has measure .9 and the second .1. When we
> tweak our measure parameter it will not affect the subjective lives
> of the people in the simulation. Measure does not work that way.
> Somehow it does relate to subjective probabilities.
>
> You can get this in one way by relating it to duplicate instantiations,
> such that worlds of measure .9 have 9 times as many duplicates as worlds
> of measure .1. I don't personally find this to be helpful because
> it requires assumptions which to my mind are equally as arbitrary as
> directly requiring measure to have the required properties of subjective
> probability. But in the simple case where we are running simulations
> on a computer that would probably work. Run one 9 times as often and
> you could plausibly suppose that the inhabitants will be more likely to
> experience that world.
When you run it 9 times as often, it still doesn't change the subjective
lives of the people in the simulations. They won't notice any difference.
And it's still not obvious why the people in the simulations should care
about one world 9 times more just because it has been run 9 times as
often.
> However you get to it, you have to think of measure as more than a label
> attached to a universe, devoid of other meaning. That is the only way
> to get predictions from the multiverse model.
The thing is, we need a decision theory, otherwise it's not clear what
predictions mean. To be cute about it, I could say that without a decision
theory, a prediction is no more than a number (probability) attached to a
statement, devoid of other meaning. Once you think in terms of decision
theory, it seems that measure only has meaning if you give it meaning by
making it part of your utility function.
George Levy
Wei Dai wrote:
>
>
> The thing is, we need a decision theory, otherwise it's not clear what
> predictions mean. To be cute about it, I could say that without a decision
> theory, a prediction is no more than a number (probability) attached to a
> statement, devoid of other meaning. Once you think in terms of decision
> theory, it seems that measure only has meaning if you give it meaning by
> making it part of your utility function.
Wei, you have been asking about a decision theory for a long time.
It seems to me that if utility function is defined as your own
probability (or possibly measure) of existence then all decision process
becomes based on conditional probability given your own existence. Your
decision theory is just based on conditional probabilities. Most of the
time you assume that the probability of the continuation of your own
existence is one. In these cases the conditional probability approach
reverts to plain probability.
Thus if you consider your own measure only, the probability that (you
continue living AND that (you shoot yourself if you don't win the
lottery) given that (you continue living) is one... and leading a life
of leisure and quantum suicide are justified; working overtime is not.
On the other hand, if you consider the measure of, and utility to your
family, the probability that (their measure and utility is not
decreased) AND that (you shoot yourself if you don't win the lottery) is
definitely smaller than one... and you should buy a life insurance and
work overtime to make the payments. Leading a life of leisure is not
justified. So depending on the point of view you reach different and
sometimes opposite results.
I have been superficially following your discussion with Juergens, Hal
and Russell. I assume that by "prior" you mean prior probability
distribution of universal states as defined by some universal algorithm
or machine. It seems to me that such distributions are totally
irrelevent because what actually matters TO AN OBSERVER is the specific
subsets of disconnected state vectors necessary to make that OBSERVER
conscious. The state vector in that subset could be widely separated and
therefore not at all related or ordered according to the originating
prior. Their ordering and/or relationship to each other depends on the
physical and mental processes governing that OBSERVER consciousness. The
linkage from state vector to state vector that gives rise to
consciousness is purely subjective in a relativistic way to the
observer.
George