[KevinTryon: Jacques Mallah]

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Measure Increases or Decreases? - Was adult vs. child

by George Levy :: Rate this Message:

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Hi Jack

Nice to see you again.

The assumption that measure decreases continuously has been accepted too easily. This is, however, really the crux of the discussion.

One could argue that measure actually increases continuously and corresponds to the increase in entropy occurring in everyday life. So even if you are 90 or 100 years old you could still experience an increase in measure.

On the other hand, when you are really close to a near death event then you may argue that measure decreases.

Whether the increase compensates for the decrease is debatable.

In any case, measure is measured over a continuum and its value is infinite to begin with. So whether it increases or decreases may be a moot point.

This being said, this issue is not easily dismissed and will impact ethics and philosophy for years to come.

As I said, the increase or decrease in measure is at the crux of this problem.Your paper really did not illuminate the issue in a satisfactory manner.

George

Jack Mallah wrote:
--- On Sun, 2/8/09, Stathis Papaioannou stathisp@... wrote:
  
Suppose you differentiate into N states, then on
      
average each has 1/N of your original measure.  I guess
that's why you think the measure decreases.  But the sum
of the measures is N/N of the original.

I still find this confusing. Your argument seems to be that you won't live to 1000 because the measure of 1000 year old versions of you in the multiverse is very small - the total consciousness across the multiverse is much less for 1000 year olds than 30 year olds. But by an analogous argument, the measure of 4 year old OM's is higher than that of 30 year old OM's, since you might die between age 4 and 30.
But here you are, an adult rather than a child.
    

You might die between 4 and 30, but the chance is fairly small, let's say 10% for the sake of argument.  So, if we just consider these two ages, the effective probability of being 30 would be a little less than that of being 4 - not enough less to draw any conclusions from.

The period of adulthood is longer than that of childhood so actually you are more likely to be an adult.  How likely?  Just look at a cross section of the population.  Some children, more adults, basically no super-old folks.

  
Should you feel your consciousness more thinly spread or something?
    

No, measure affects how common an observation is, not what it feels like.




      




  


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Re: AB continuity

by Jack Mallah :: Rate this Message:

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--- On Wed, 2/11/09, Quentin Anciaux <allcolor@...> wrote:
> From a 1st perspective commonness is useless in the argument. The important is what it feels like for the experimenter.

You seem to be saying that commonness of an experience has no effect on, what for practical purposes, is whether people should expect to experience it.  That is a contradiction in terms.  It is false by definition.  If an "uncommon" experience gets experienced just as often as a "common" experience, then by definition they are equally common and have equal measure.





     


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Re: adult vs. child AB

by Brent Meeker-2 :: Rate this Message:

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Stathis Papaioannou wrote:

> 2009/2/11 Brent Meeker <meekerdb@...>:
>
>>> But the same could be said about everyday life. The person who wakes
>>> up in my bed tomorrow won't be me, he will be some guy who thinks he's
>>> me and shares my memories, personality traits, physical
>>> characteristics and so on. In other words, everyone only lives
>>> transiently, and continuity of consciousness is an illusion.
>> I think I understand your point, but I don't see that the continuity of
>> consciousness is any more an illusion than any other continuity: the continuity
>> of space, the persistence of objects, etc.  You are just generalizing Zeno's
>> paradox.  But once you look at it that way, the question becomes, "Why imagine
>> the continuity is made up of discrete elements?"  It is this conceptualization,
>> points in space, moments in time, observer moments as atoms of consciousness,
>> that creates the paradox.  So maybe we should recognize continuity as
>> fundamental.  The continuity need not be temporal, it could be a more abstract
>> property such a causal connection or perhaps what Bruno says distinguishes a
>> computation from a description of the computation.
>
> I don't think it makes a difference if life is continuous or discrete:
> it is still possible to assert that future versions of myself are
> different people who merely experience the illusion of being me.
> However, this just becomes a semantic exercise. Saying that I will
> wake up in my bed tomorrow is equivalent to saying that someone
> sufficiently similar to me will wake up in my bed tomorrow.

If continuity is fundamental then personal identity could be defined in terms of
it and there could be a real difference between you and someone with the same
memories, but without continuity to your past.

Brent

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Re: AB continuity

by Quentin Anciaux-2 :: Rate this Message:

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2009/2/11 Jack Mallah <jackmallah@...>

--- On Wed, 2/11/09, Quentin Anciaux <allcolor@...> wrote:
> From a 1st perspective commonness is useless in the argument. The important is what it feels like for the experimenter.

You seem to be saying that commonness of an experience has no effect on, what for practical purposes, is whether people should expect to experience it.  That is a contradiction in terms.  It is false by definition.  If an "uncommon" experience gets experienced just as often as a "common" experience, then by definition they are equally common and have equal measure.


That's not what I said. I said however uncommon an experience is, if it exists... it exists by definition, if mwi is true, and measure is never strictly null for any particular moment to have a successor then any moment has a successor hence there exists a me moment of 1000 years old and it is garanteed to be lived by definition.

What you're saying is uncommon moment are *never* experienced (means their measure is strictly null), for the QI argument to hold it is suffisant to have at least *one* next moment for every moment.

Quentin
 











--
All those moments will be lost in time, like tears in rain.

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Re: AB continuity

by Günther Greindl :: Rate this Message:

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Jack,

> There are some people who will, but relatively few.  That is what counts for QS to be invalid.

Hmm, that does not make QS invalid (see Quentin and Jonathan's posts for
my views on the issue, they have expressed everything clearly), and in
fact you have already conceded QI (by asserting that measure never drops
to null).

It seems to me (judging from your abstract) that your real problem is
with the ethical conclusions which may or may not follow from QI.

But then the correct way is not to argue against QI but to tackle the
ethical questions head on.

Hilary Greaves would be an example (care for all your successors); or
even better, adopt a benevolent attitude toward all conscious OMs so
that you try to act to _increase_ conscious states (of all beings) in
the whole universe, and not decrease them.

I do not see a true ethical problem following from QI when people are
ethical in the first case. And if they are not, I don't think that QI
will add much incentive to be unethical.

Cheers,
Günther

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Re: Dreams and measure

by Stathis Papaioannou-2 :: Rate this Message:

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2009/2/12 Saibal Mitra <smitra@...>:
>
> Welcome back Jack Mallah!
>
> I have a different argument against QTI.
>
> I had a nice dream last night, but unfortunately it suddenly ended.
> Now, this is empirical evidence against QTI because, according to the
> QTI, the life expectancy of the version of me simulated in that dream
> should have been be infinite.

If you remember that you had a nice dream then the version of you in
the dream is continuing. And if you had forgotten it, there would be
other versions of you that didn't, as Brent suggested.


--
Stathis Papaioannou

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Re: AB continuity

by Stathis Papaioannou-2 :: Rate this Message:

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2009/2/12 Jack Mallah <jackmallah@...>:

>
> --- On Wed, 2/11/09, Stathis Papaioannou <stathisp@...> wrote:
>> I don't think it makes a difference if life is continuous or discrete: it is still possible to assert that future versions of myself are different people who merely experience the illusion of being me.
>> However, this just becomes a semantic exercise. Saying that I will wake up in my bed tomorrow is equivalent to saying that someone sufficiently similar to me will wake up in my bed tomorrow.
>
> Exactly.
>
> And if your measure were to drop off dramatically overnight, it is equivalent to saying that many _more people_ woke up in your bed today as compared to the number of people who will wake up in your bed tommorrow.
>
> Which is equivalent to saying that, for all practical purposes, you will probably die overnight.  And that is the point.

You agree that if one version of me goes to bed tonight and one
version of me wakes up tomorrow, then I should expect to wake up
tomorrow. But if extra versions of me are manufactured and run today,
then switched off when I go to sleep, then you are saying that I might
not wake up tomorrow. The extra copies of me have somehow sapped my
life strength.


--
Stathis Papaioannou

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Re: adult vs. child AB

by Stathis Papaioannou-2 :: Rate this Message:

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2009/2/12 Brent Meeker <meekerdb@...>:

> If continuity is fundamental then personal identity could be defined in terms of
> it and there could be a real difference between you and someone with the same
> memories, but without continuity to your past.

But that could lead to absurd conclusions. Suppose you discover that
you have a disease which breaks the required continuity every time you
go to sleep, and that this has been happening your whole life. Will
you worry about falling asleep tonight? Should your property be
disposed of tomorrow according to your will?


--
Stathis Papaioannou

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Re: adult vs. child AB

by Brent Meeker-2 :: Rate this Message:

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Stathis Papaioannou wrote:
> 2009/2/12 Brent Meeker <meekerdb@...>:
>
>> If continuity is fundamental then personal identity could be defined in terms of
>> it and there could be a real difference between you and someone with the same
>> memories, but without continuity to your past.
>
> But that could lead to absurd conclusions. Suppose you discover that
> you have a disease

Who has this disease?  :-)

>which breaks the required continuity every time you
> go to sleep, and that this has been happening your whole life. Will
> you worry about falling asleep tonight? Should your property be
> disposed of tomorrow according to your will?
>
>


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Re: Measure Increases or Decreases? - Was adult vs. child

by Jack Mallah :: Rate this Message:

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Hi George.  The everything list feels just like old times, no?  Which is nice in a way but has a big drawback - I can only take so much of arguing the same old things, and being outnumbered.  And that limit is approaching fast again.  At least I think your point here is new to the list.

--- On Wed, 2/11/09, George Levy <glevy@...> wrote:
> One could argue that measure actually increases continuously and corresponds to the increase in entropy occurring in everyday life. So even if you are 90 or 100 years old you could still experience an increase in measure.

I guess you are basing that on some kind of branch-counting idea.

If that were the case, the Born Rule would fail.  Perhaps the probability rule would be more like proportionality to norm^2 exp(entropy) instead of just norm^2.  If that was it, then for example unstable nuclei would be observed to decay a lot faster than the Born Rule predicts.

Conventional half life calculations are accurate.  So either entropy would not be a factor, or the MWI is experimentally disproven already.  Well, if it is a weak enough function of entropy then maybe it hasn't been disproven, but inclusion of free parameters like that which can always be made small enough goes against Occam's Razor.  Otherwise there'd be no end of possible correction factors.

At least your idea was testable, with none of the meaningless "first person" sloganeering.  Ideas like that, keep em' coming!

> In any case, measure is measured over a continuum and its value is infinite to begin with. So whether it increases or decreases may be a moot point.

It's not moot.  Just take density ratios.  The size of the universe may be infinite, but that didn't stop Hubble from saying it's getting bigger.

> As I said, the increase or decrease in measure is at the crux of this problem.  Your paper really did not illuminate the issue in a satisfactory manner.

It could no doubt use some tweaking, which is why I'm on the list now.  I know I'm not always a good communicator.  What should be clarified or added to it?




     


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Re: continuity - cloning

by Jack Mallah :: Rate this Message:

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--- On Wed, 2/11/09, Stathis Papaioannou <stathisp@...> wrote:
> You agree that if one version of me goes to bed tonight and one version of me wakes up tomorrow, then I should expect to wake up tomorrow. But if extra versions of me are manufactured and run today, then switched off when I go to sleep, then you are saying that I might not wake up tomorrow.

You won't know this evening if you are one of the "extra versions" or the original.  So yes, in that situation, you will probably not be around tomorrow.  Only the original will.

> The extra copies of me have somehow sapped my life strength.

Not at all.  I guess that is a joke?

Creating more copies, then getting rid of the same number, does not result in a net decrease in measure.  That is why the movie "The Prestige" bears no resemblance whatsoever to QS despite rumors to the contrary.

If you create extra copies and leave them alive, there is a net increase in measure.  That is equivalent to new people being born even if they have your memories.  This once happenned to Will Riker on Star Trek: TNG.




     


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Re: AB continuity

by Jack Mallah :: Rate this Message:

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--- On Wed, 2/11/09, Quentin Anciaux <allcolor@...> wrote:
> > > From a 1st perspective commonness is useless in
> the argument. The important is what it feels like for the experimenter.
> >
> > You seem to be saying that commonness of an experience has no effect on, what for practical purposes, is whether people should expect to experience it.  That is a contradiction in terms.  It is false by definition.  If an "uncommon" experience gets experienced just as often as a "common" experience, then by definition they are equally common and have equal measure.
> >
> That's not what I said. I said however uncommon an experience is, if it exists... it exists by definition, if mwi is true, and measure is never strictly null for any particular moment to have a successor then any moment has a successor hence there exists a me moment of 1000 years old and it is garanteed to be lived by definition.

It will be experienced - but not by most of "you".  For all practical purposes it might as well not exist.

> What you're saying is uncommon moment are *never* experienced (means their measure is strictly null), for the QI argument to hold it is suffisant to have at least *one* next moment for every moment.

No and no.




     


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Re: continuity - cloning

by daddycaylor :: Rate this Message:

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The effects of have clones is interesting, though, regardless of the
"sapping strength" notion.  You would have reason to worry about being
killed if there were clones and then a "shell game" was played with
you being mixed up with the clones, and then all of the "yous" were
killed except one.  All of the "yous" would have reason to worry.
This has implications on ethics of cloning and killing clones.
As far as measure, it seems that having a clone of you and killing one
of you while you were asleep would be equivalent (w.r.t how much you
should worry at least) to not having any clones and someone saying
they were going to roll a die and if it came up odd they would kill
you.

Tom

On Feb 11, 8:44 pm, Jack Mallah <jackmal...@...> wrote:

> --- On Wed, 2/11/09, Stathis Papaioannou <stath...@...> wrote:
>
> > You agree that if one version of me goes to bed tonight and one version of me wakes up tomorrow, then I should expect to wake up tomorrow. But if extra versions of me are manufactured and run today, then switched off when I go to sleep, then you are saying that I might not wake up tomorrow.
>
> You won't know this evening if you are one of the "extra versions" or the original.  So yes, in that situation, you will probably not be around tomorrow.  Only the original will.
>
> > The extra copies of me have somehow sapped my life strength.
>
> Not at all.  I guess that is a joke?
>
> Creating more copies, then getting rid of the same number, does not result in a net decrease in measure.  That is why the movie "The Prestige" bears no resemblance whatsoever to QS despite rumors to the contrary.
>
> If you create extra copies and leave them alive, there is a net increase in measure.  That is equivalent to new people being born even if they have your memories.  This once happenned to Will Riker on Star Trek: TNG.
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Re: continuity - cloning

by daddycaylor :: Rate this Message:

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But of course you would worry just as much if the clone were replaced
by a zombie...  I guess that gets back to the distinction between
first person and third person.

On Feb 11, 9:05 pm, Tom Caylor <daddycay...@...> wrote:

> The effects of have clones is interesting, though, regardless of the
> "sapping strength" notion.  You would have reason to worry about being
> killed if there were clones and then a "shell game" was played with
> you being mixed up with the clones, and then all of the "yous" were
> killed except one.  All of the "yous" would have reason to worry.
> This has implications on ethics of cloning and killing clones.
> As far as measure, it seems that having a clone of you and killing one
> of you while you were asleep would be equivalent (w.r.t how much you
> should worry at least) to not having any clones and someone saying
> they were going to roll a die and if it came up odd they would kill
> you.
>
> Tom
>
> On Feb 11, 8:44 pm, Jack Mallah <jackmal...@...> wrote:
>
>
>
> > --- On Wed, 2/11/09, Stathis Papaioannou <stath...@...> wrote:
>
> > > You agree that if one version of me goes to bed tonight and one version of me wakes up tomorrow, then I should expect to wake up tomorrow. But if extra versions of me are manufactured and run today, then switched off when I go to sleep, then you are saying that I might not wake up tomorrow.
>
> > You won't know this evening if you are one of the "extra versions" or the original.  So yes, in that situation, you will probably not be around tomorrow.  Only the original will.
>
> > > The extra copies of me have somehow sapped my life strength.
>
> > Not at all.  I guess that is a joke?
>
> > Creating more copies, then getting rid of the same number, does not result in a net decrease in measure.  That is why the movie "The Prestige" bears no resemblance whatsoever to QS despite rumors to the contrary.
>
> > If you create extra copies and leave them alive, there is a net increase in measure.  That is equivalent to new people being born even if they have your memories.  This once happenned to Will Riker on Star Trek: TNG.- Hide quoted text -
>
> - Show quoted text -
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Re: continuity - cloning

by Stathis Papaioannou-2 :: Rate this Message:

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2009/2/12 Jack Mallah <jackmallah@...>:
>
> --- On Wed, 2/11/09, Stathis Papaioannou <stathisp@...> wrote:
>> You agree that if one version of me goes to bed tonight and one version of me wakes up tomorrow, then I should expect to wake up tomorrow. But if extra versions of me are manufactured and run today, then switched off when I go to sleep, then you are saying that I might not wake up tomorrow.
>
> You won't know this evening if you are one of the "extra versions" or the original.  So yes, in that situation, you will probably not be around tomorrow.  Only the original will.

Well, this seems to be the real point of disagreement between you and
the pro-QI people. If I am one of the extra versions and die
overnight, but the original survives, then I have survived. This is
why there can be a many to one relationship between earlier and later
copies. If you don't agree with this then you should make explicit
your theory of personal identity.


--
Stathis Papaioannou

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Re: continuity - cloning

by Stathis Papaioannou-2 :: Rate this Message:

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2009/2/12 Tom Caylor <daddycaylor@...>:

>
> The effects of have clones is interesting, though, regardless of the
> "sapping strength" notion.  You would have reason to worry about being
> killed if there were clones and then a "shell game" was played with
> you being mixed up with the clones, and then all of the "yous" were
> killed except one.  All of the "yous" would have reason to worry.
> This has implications on ethics of cloning and killing clones.
> As far as measure, it seems that having a clone of you and killing one
> of you while you were asleep would be equivalent (w.r.t how much you
> should worry at least) to not having any clones and someone saying
> they were going to roll a die and if it came up odd they would kill
> you.

I wouldn't worry if the clones were all kept in perfect lockstep. If
one of my clones survived, I would survive. It doesn't matter that the
clones are made up of different matter, as long as this matter is in a
configuration such that it could be a future version of myself. For
this is what happens in ordinary life: the matter comprising my body
is almost all replaced over the course of months or years, but I still
feel that I'm me. Whatever you want to call the important part of me -
mind, consciousness, soul - is preserved if the pattern making up my
brain is preserved.


--
Stathis Papaioannou

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Re: Measure Increases or Decreases? - Was adult vs. child

by George Levy :: Rate this Message:

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Jack Mallah wrote:
Hi George.  The everything list feels just like old times, no?  Which is nice in a way but has a big drawback - I can only take so much of arguing the same old things, and being outnumbered.  And that limit is approaching fast again.  At least I think your point here is new to the list.
  
I have also been overwhelmed by the volume on this list. The idea is not to take more than you can chew.
--- On Wed, 2/11/09, George Levy glevy@... wrote:
  
One could argue that measure actually increases continuously and corresponds to the increase in entropy occurring in everyday life. So even if you are 90 or 100 years old you could still experience an increase in measure.
    

I guess you are basing that on some kind of branch-counting idea.

If that were the case, the Born Rule would fail.  Perhaps the probability rule would be more like proportionality to norm^2 exp(entropy) instead of just norm^2.  If that was it, then for example unstable nuclei would be observed to decay a lot faster than the Born Rule predicts.
  

Yes I am linking the entropy to MW branching. So if you start with a low entropy state such as the Big Bang or having $1 million after a QS your entropy is going to increase. (There are many ways I could spend that million). The number of possible states you can reach increases, hence your entropy increases.

You say that the Born Rule would fail if measure increases. Here is a counterexample:
Using your own argument I could say that the Born rule would fail if measure decreases according to function f(t). For example it could be norm^2 f(t) . So using your own argument since the Born rule is only  norm^2 therefore measure stays constant?
I do not understand why you say that the Born rule would fail.

Linking entropy with measure may bring some interesting insights. Let's see how far we can go with this.

George


      




  


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Re: AB continuity

by Quentin Anciaux-2 :: Rate this Message:

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2009/2/12 Jack Mallah <jackmallah@...>

--- On Wed, 2/11/09, Quentin Anciaux <allcolor@...> wrote:
> > > From a 1st perspective commonness is useless in
> the argument. The important is what it feels like for the experimenter.
> >
> > You seem to be saying that commonness of an experience has no effect on, what for practical purposes, is whether people should expect to experience it.  That is a contradiction in terms.  It is false by definition.  If an "uncommon" experience gets experienced just as often as a "common" experience, then by definition they are equally common and have equal measure.
> >
> That's not what I said. I said however uncommon an experience is, if it exists... it exists by definition, if mwi is true, and measure is never strictly null for any particular moment to have a successor then any moment has a successor hence there exists a me moment of 1000 years old and it is garanteed to be lived by definition.

It will be experienced - but not by most of "you".  For all practical purposes it might as well not exist.

Well either the measure is strictly null and then I agree it does not exist or it is not null and therefore it exists (by MWI). This all boils down to:

- If there always exists a moment after any given moment then from 1st person perspective you will be one of the available next moment whatever it is (and whatever low absolute measure it could have, but with the most probable expectation given by the highest measure next moment where you exist).
- If there isn't then OK, QI is false.

But here you're not clear at all, if the measure never drop to null, your conclusion is erroneous.
 


> What you're saying is uncommon moment are *never* experienced (means their measure is strictly null), for the QI argument to hold it is suffisant to have at least *one* next moment for every moment.

No and no.


Yes and yes or I don't understand what you're talking about.

Regards,
Quentin
 










--
All those moments will be lost in time, like tears in rain.

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Re: AB continuity

by Quentin Anciaux-2 :: Rate this Message:

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And could you explicit the "not by you", if the "me" of 1000 years old has all my memories up to now (+ his own from now on to 1000 years old)... It is me, if you disagree what is personnal identity for you ? What is the magical "I" you're talking about ?

Quentin

2009/2/12 Quentin Anciaux <allcolor@...>


2009/2/12 Jack Mallah <jackmallah@...>


--- On Wed, 2/11/09, Quentin Anciaux <allcolor@...> wrote:
> > > From a 1st perspective commonness is useless in
> the argument. The important is what it feels like for the experimenter.
> >
> > You seem to be saying that commonness of an experience has no effect on, what for practical purposes, is whether people should expect to experience it.  That is a contradiction in terms.  It is false by definition.  If an "uncommon" experience gets experienced just as often as a "common" experience, then by definition they are equally common and have equal measure.
> >
> That's not what I said. I said however uncommon an experience is, if it exists... it exists by definition, if mwi is true, and measure is never strictly null for any particular moment to have a successor then any moment has a successor hence there exists a me moment of 1000 years old and it is garanteed to be lived by definition.

It will be experienced - but not by most of "you".  For all practical purposes it might as well not exist.

Well either the measure is strictly null and then I agree it does not exist or it is not null and therefore it exists (by MWI). This all boils down to:

- If there always exists a moment after any given moment then from 1st person perspective you will be one of the available next moment whatever it is (and whatever low absolute measure it could have, but with the most probable expectation given by the highest measure next moment where you exist).
- If there isn't then OK, QI is false.

But here you're not clear at all, if the measure never drop to null, your conclusion is erroneous.
 


> What you're saying is uncommon moment are *never* experienced (means their measure is strictly null), for the QI argument to hold it is suffisant to have at least *one* next moment for every moment.

No and no.


Yes and yes or I don't understand what you're talking about.

Regards,
Quentin
 










--
All those moments will be lost in time, like tears in rain.



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Re: continuity - cloning

by Günther Greindl :: Rate this Message:

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Jack,

As Stathis and Quentin wrote, we have approached the core of the
disagreement.

You (Jack) seem to have a very "quaint" idea of personal identity - some
kind of essentialism. Strange that you hold that theory and call talk of
1st person/3rd person distinction "sloganeering".

It seems, perhaps, that the sloganeers have a much more scientific
concept of personal identity than you do?

Cheers,
Günther



Jack Mallah wrote:

> --- On Wed, 2/11/09, Stathis Papaioannou <stathisp@...> wrote:
>> You agree that if one version of me goes to bed tonight and one version of me wakes up tomorrow, then I should expect to wake up tomorrow. But if extra versions of me are manufactured and run today, then switched off when I go to sleep, then you are saying that I might not wake up tomorrow.
>
> You won't know this evening if you are one of the "extra versions" or the original.  So yes, in that situation, you will probably not be around tomorrow.  Only the original will.
>
>> The extra copies of me have somehow sapped my life strength.
>
> Not at all.  I guess that is a joke?
>
> Creating more copies, then getting rid of the same number, does not result in a net decrease in measure.  That is why the movie "The Prestige" bears no resemblance whatsoever to QS despite rumors to the contrary.
>
> If you create extra copies and leave them alive, there is a net increase in measure.  That is equivalent to new people being born even if they have your memories.  This once happenned to Will Riker on Star Trek: TNG.
>
>
>
>
>      
>
>
> >
>

--
Günther Greindl
Department of Philosophy of Science
University of Vienna
guenther.greindl@...

Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/


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