### Re: The probability problem in Everettian quantum mechanics

```

On 17 Oct 2013, at 00:49, LizR wrote:

By the way, my son (14) asked me the other day what's the oddest
prime number?

Fortunately, I got the right answer!

I would say 2. LOL

Was it 2 that you found?  To be odd is very subjective here :)

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 15 Oct 2013, at 19:31, meekerdb wrote:

On 10/15/2013 3:54 AM, Quentin Anciaux wrote:

2013/10/15 Richard Ruquist yann...@gmail.com
Bruno: On the contrary: I assume only that my brain (or generalized
brain) is computable, then I show that basically all the rest is
not. In everything, or just in arithmetic, the computable is rare
and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno
was claiming. How does anything exist if it is not computed by
the or a machine? And I thought the generalized brain did the
computations, not that it was only computed. How does Bruno show
that all the rest which presumably includes energy and matter is
not computed. Bruno is constantly confusing me.

Energy and matter (and the universe whatever it is), is composed by
the sum

What does sum mean?  And how does is constitute a piece of matter?

of the infinity of computations going through your state as it
is defined by an infinity of computations (and not one), it is not
computed.

But that's not a definition.  It's saying the piece of matter is
*constituted* by an infinity of computations.

That is a misleading phrasing. The matter is not constituted of
anything. It is an appearance coming from the FPI on all computations.

But what associates the computations to a piece of matter that we
*define* ostensively?

The FPI.

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 15 Oct 2013, at 19:39, meekerdb wrote:

On 10/15/2013 7:49 AM, Bruno Marchal wrote:

On 15 Oct 2013, at 12:45, Richard Ruquist wrote:

Bruno: On the contrary: I assume only that my brain (or
generalized brain) is computable, then I show that basically all
the rest is not. In everything, or just in arithmetic, the
computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno
was claiming. How does anything exist if it is not computed by
the or a machine?

We assume the arithmetical truth. In particular we assume that all
closed formula written in the language of arithmetic (and thus
using logical symbol + the symbol 0, s (+1), + and *) are all
either true or false, independently of us.

From this we cannot prove that matter exists, or not, but we can
prove that the average universal numbers will (correctly) believe
in matter (but it will not know that it is correct).

That's not at all clear to me.  A universal number encodes proofs -
is that what you mean by it believes something?

Yes. (I am thinking about the Löbian universal numbers).

But how is this something identified at 'matter'?

It should follow from the step seven.

So, if you have no problem in believing propositions like there is
no biggest prime number are true independently of me and you, and
the universe, then you can understand that the proposition
asserting the existence of (infinitely many) computations in which
you believe reading my current post, is also true independently of
us.

The appearance of matter emerges from the FPI that the machines
cannot avoid in the arithmetical truth.

Arithmetical truth escapes largely the computable arithmetical
truth (by Gödel).

And I thought the generalized brain did the computations,

Only the computations associated to your mind.

not that it was only computed. How does Bruno show that all the
rest which presumably includes energy and matter is not computed.
Bruno is constantly confusing me.

I guess you missed the step seven of the UDA, and are perhaps not
aware that arithmetical truth is incredibly big, *much* bigger than
what any computer can generate or compute.

Then my, or your, mind is associated to *all* computations going
through your actual state of mind,

That sounds like an uncomputable totality.

No, by virtue of the closure of the set of partial (includes the total
functions) computable functions for diagonalization, or equivalently,
by the existence of universal machines/numbers, that totality is
computable/enumerable, and that is why we do have a UD.
What happens is that most interesting subset will be uncomputable, so
that the FPI entails a priori the non computability of *some* physical
things (which can be only the apparent collapse of the wave, but it
could be more than that too: open problem).

Bruno

Brent

and below your substitution level there are infinitely many such
computations. They all exist in arithmetic, and the FPI glues them,
in a non computable way, in possible long and deep physical
histories.

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 15 Oct 2013, at 23:04, Russell Standish wrote:

On Tue, Oct 15, 2013 at 01:02:13PM -0400, Richard Ruquist wrote:
Bruno: Arithmetical truth escapes largely the computable
arithmetical truth

(by Gödel).

Richard: I guess I am too much a physicist to believe that
uncomputible

arithmetical truth can produce the physical.
Since you read my paper you know that I think computations in this
universe
if holographic are limited to 10^120 bits (the Lloyd limit) which
is very
far from infinity. I just do not believe in infinity. In other
words, I
believe the largest prime number in this universe is less than
10^120. So I

will drop out of these discussions. My assumptions differ from yours.

Then you might well be interested in the Movie Graph Argument, which
deals directly with the case where the universe doesn't have
sufficient

resources to run the universal dovetailer.

Good point.

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```Bruno Marchal
2:47 AM (8 hours ago)
to everything-list
On 15 Oct 2013, at 19:02, Richard Ruquist wrote:

Bruno: Arithmetical truth escapes largely the computable arithmetical truth
(by Gödel).

Richard: I guess I am too much a physicist to believe that uncomputible
arithmetical truth can produce the physical.

Nobody is perfect :)
(You are not alone, physicalism is believed by almost everybody those days)

Since you read my paper you know that I think computations in this universe
if holographic are limited to 10^120 bits (the Lloyd limit) which is very
far from infinity.

Of course, I do not assume such a universe. I assume only that I am
Turing emulable.

I just do not believe in infinity. In other words, I believe the largest
prime number in this universe is less than 10^120. So I will drop out of
these discussions. My assumptions differ from yours.

OK. And then the reasoning (UDA), if you do assume some physicalism, is
that we are not Turing emulable. You are working in a non comp theory. Not
sure this solves anything, as now you can't justify matter (you assume it),
and are back to the usual mind-body problem, with an non satisfying
identity between mind and matter.

Bruno

Richard: I guess you did not read my paper afterall. The Metaverse machine
is what computes matter and its energy from the get-go. I grant you that I
assume such a Metaverse. But the universe with its limited computations are
given by known physics.

Regarding MWI vs Wave Collapse , here is some interesting data:

Measurement-induced collapse of quantum wavefunction captured in slow
motion.

On Wed, Oct 16, 2013 at 2:59 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 15 Oct 2013, at 23:04, Russell Standish wrote:

On Tue, Oct 15, 2013 at 01:02:13PM -0400, Richard Ruquist wrote:

Bruno: Arithmetical truth escapes largely the computable arithmetical
truth
(by Gödel).

Richard: I guess I am too much a physicist to believe that uncomputible
arithmetical truth can produce the physical.
Since you read my paper you know that I think computations in this
universe
if holographic are limited to 10^120 bits (the Lloyd limit) which is very
far from infinity. I just do not believe in infinity. In other words, I

believe the largest prime number in this universe is less than 10^120.
So I
will drop out of these discussions. My assumptions differ from yours.

Then you might well be interested in the Movie Graph Argument, which
deals directly with the case where the universe doesn't have sufficient
resources to run the universal dovetailer.

Good point.

Bruno

--

--**--**

Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au
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### Re: The probability problem in Everettian quantum mechanics

```On Wed, Oct 16, 2013 at 11:41:46AM -0400, Richard Ruquist wrote:

Measurement-induced collapse of quantum wavefunction captured in slow
motion.

The headline is sensationlist and misleading. What is being done is a
series of weak measurements that capturing the change from a
superposition to a non superposed state. An MWIer would say this is
capturing the process of decoherence. It is most certainly not
demonstrating wave function collapse is occurring, interesting though
the experiment is for technical reasons.

Cheers

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University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```

On 16 Oct 2013, at 17:41, Richard Ruquist wrote:

2:47 AM (8 hours ago)

to everything-list

On 15 Oct 2013, at 19:02, Richard Ruquist wrote:

Bruno: Arithmetical truth escapes largely the computable
arithmetical truth (by Gödel).

Richard: I guess I am too much a physicist to believe that
uncomputible arithmetical truth can produce the physical.

Nobody is perfect :)
(You are not alone, physicalism is believed by almost everybody
those days)

Since you read my paper you know that I think computations in this
universe if holographic are limited to 10^120 bits (the Lloyd
limit) which is very far from infinity.

Of course, I do not assume such a universe. I assume only that I
am Turing emulable.

I just do not believe in infinity. In other words, I believe the
largest prime number in this universe is less than 10^120. So I
will drop out of these discussions. My assumptions differ from yours.

OK. And then the reasoning (UDA), if you do assume some physicalism,
is that we are not Turing emulable. You are working in a non comp
theory. Not sure this solves anything, as now you can't justify
matter (you assume it), and are back to the usual mind-body problem,
with an non satisfying identity between mind and matter.

Bruno

Richard: I guess you did not read my paper afterall.

I read it, but as you said, we start from very different assumption,
and many things you say about PA seems a bit weird for a logician.

The Metaverse machine is what computes matter and its energy from
the get-go. I grant you that I assume such a Metaverse. But the
universe with its limited computations are given by known physics.

But that universe, if it exists, must be justified by using + and *
and the numbers only, if comp is assumed.

Regarding MWI vs Wave Collapse , here is some interesting data:

Measurement-induced collapse of quantum wavefunction captured in
slow motion.

A slow motion movie of the wave collapse is a slow motion movie of a
differentiating multiverse. Everett theory predicts such motions.

Bruno

On Wed, Oct 16, 2013 at 2:59 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 15 Oct 2013, at 23:04, Russell Standish wrote:

On Tue, Oct 15, 2013 at 01:02:13PM -0400, Richard Ruquist wrote:
Bruno: Arithmetical truth escapes largely the computable
arithmetical truth

(by Gödel).

Richard: I guess I am too much a physicist to believe that
uncomputible

arithmetical truth can produce the physical.
Since you read my paper you know that I think computations in this
universe
if holographic are limited to 10^120 bits (the Lloyd limit) which is
very
far from infinity. I just do not believe in infinity. In other
words, I

believe the largest prime number in this universe is less than
10^120. So I

will drop out of these discussions. My assumptions differ from yours.

Then you might well be interested in the Movie Graph Argument, which
deals directly with the case where the universe doesn't have
sufficient

resources to run the universal dovetailer.

Good point.

Bruno

--

Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```On 16 October 2013 06:02, Richard Ruquist yann...@gmail.com wrote:

Richard: I guess I am too much a physicist to believe that uncomputible
arithmetical truth can produce the physical.
Since you read my paper you know that I think computations in this
universe if holographic are limited to 10^120 bits (the Lloyd limit) which
is very far from infinity. I just do not believe in infinity. In other
words, I believe the largest prime number in this universe is less than
10^120. So I will drop out of these discussions. My assumptions differ from
yours.

So what happens if someone proves that, say, 2^200 - 1 is a prime number?

Personally I find a statements about prime numbers in this universe to be
rather odd. Would 17 remain prime in an empty universe?

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### Re: The probability problem in Everettian quantum mechanics

```By the way, my son (14) asked me the other day what's the oddest prime
number?

Fortunately, I got the right answer!

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/16/2013 3:49 PM, LizR wrote:

By the way, my son (14) asked me the other day what's the oddest prime number?

Fortunately, I got the right answer!

2, because it's the only one that's even.

Brent
There are 10 kinds of people.  Those who think in binary and those who don't.

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### Re: The probability problem in Everettian quantum mechanics

```Or the largest prime number less than 10^120, because it's the biggest
prime number...?!?!? :)

There are two secrets to success.
The first is not to give away everything you know...

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### Re: The probability problem in Everettian quantum mechanics

```

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one
another?   Do they divide into two infinite subsets on a
binary measurement, or do infinitely many come into existence
in order that some branch-counting measure produces the right
proportion?  Do you not see any problems with assigning a
measure to infinite countable subsets (are there more even
numbers that square numbers?).

And why should we prefer this model to simply saying the Born
rule derives from a Bayesian epistemic view of QM as argued
by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel

I don't understand the question.  What parallel experiences do
you refer to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one
photon interference in the two slits experiment.

?? The math predicts probabilities of events, including where a
single photon will land in a Young's slit experiment - no
superposition of observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise:
yes the quantum wave describes only psychological states, but
they concern still a *many* dreams/worlds/physical-realities,
including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the
personal subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the
real, which is a bit weird to me.

The 'interference' is a calculational event 'between' possible
futures.  Or even the result of considering all possible paths.

understand or get a bigger picture.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological,
which is not a problem for me. there are still many.

Yes, that's why I said I think his approach is consistent with
yours.  I think Fuchs view of QM is similar to what William S.
Cooper calls for at the end of his book The Evolution of Reason
- a probabilistic extension of logic. This is essentially the view
he defends at length in Interview with a Quantum Bayesian, arXiv:
1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique
(multiversal) physical reality. Neither in Everett +GR, nor in
comp.

Bayesian epistemic view is no problem, but you have to define
what is the knower, the observer, etc. If not, it falls into a
cosmic form of solipsism, and it can generate some strong

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I
think you do the same).

What? Not at all. the observer is defined by its set of beliefs,
itself define by a relative universal numbers.

Fuchs defines 'the observer' as the one who bets on the outcome of
his actions.

Comp has a pretty well defined notion of observer, with its
octalist points of view, and an whole theology including his
physics, etc.

Physicists, like Fuchs, and unlike philosophers, are generally
comfortable with not explaining everything.

Me too. but he has still to explain the terms that he is using.

What's your explanation for the existence of persons?  So far what
I've heard is that it's an inside view of arithmetic - which I
don't find very enlightening.

What do you miss in the UDA?

As I understand it the UD computes everything computable and it's
only your inference that observers (and the rest of the multiverse)
*must be in there somewhere* because you've assumed that everything
is computable.

On the contrary: I assume only that my brain (or generalized brain) is
computable, then I show that basically all the rest is not. In
everything, or just in arithmetic, the computable is rare and
exceptional.

Fuchs, correctly I think, says an 'interpretation' ```

### Re: The probability problem in Everettian quantum mechanics

```Bruno: On the contrary: I assume only that my brain (or generalized brain)
is computable, then I show that basically all the rest is not. In
everything, or just in arithmetic, the computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno was
claiming. How does anything exist if it is not computed by the or a
machine? And I thought the generalized brain did the computations, not that
it was only computed. How does Bruno show that all the rest which
presumably includes energy and matter is not computed. Bruno is constantly
confusing me.

On Tue, Oct 15, 2013 at 3:40 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?   Do they
divide into two infinite subsets on a binary measurement, or do infinitely
many come into existence in order that some branch-counting measure
produces the right proportion?  Do you not see any problems with assigning
a measure to infinite countable subsets (are there more even numbers that
square numbers?).

And why should we prefer this model to simply saying the Born rule derives
from a Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

I don't understand the question.  What parallel experiences do you refer
to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be contagious
on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon
interference in the two slits experiment.

?? The math predicts probabilities of events, including where a single
photon will land in a Young's slit experiment - no superposition of
observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise: yes the
quantum wave describes only psychological states, but they concern still
a *many* dreams/worlds/physical-realities, including the many
self-multiplication.

There is no many in Fuchs interpretation, there is only the personal
subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the real,
which is a bit weird to me.

The 'interference' is a calculational event 'between' possible futures.
Or even the result of considering all possible paths.

That leads to instrumentalism. That is dont ask, don't try to understand
or get a bigger picture.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological, which is not
a problem for me. there are still many.

Yes, that's why I said I think his approach is consistent with yours.  I
think Fuchs view of QM is similar to what William S. Cooper calls for at
the end of his book The Evolution of Reason - a probabilistic extension
of logic. This is essentially the view he defends at length in Interview
with a Quantum Bayesian, arXiv:1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical reality. Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is
the knower, the observer, etc. If not, it falls into a cosmic form of
solipsism, and it can generate some strong don't ask imperative.

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I think you
do the same).

What? Not at all. the observer is defined by its set of beliefs, itself
define by a relative universal numbers.

Fuchs defines 'the observer' as the one who bets on the outcome of his
actions.

Comp has a pretty well defined notion of observer, with its octalist
points of view, and an whole theology including his physics, etc.

Physicists, like Fuchs, and unlike philosophers, are generally
comfortable with not explaining everything.

Me too. but he has still to explain the terms that he is using.

What's your explanation for the existence of ```

### Re: The probability problem in Everettian quantum mechanics

```2013/10/15 Richard Ruquist yann...@gmail.com

Bruno: On the contrary: I assume only that my brain (or generalized
brain) is computable, then I show that basically all the rest is not. In
everything, or just in arithmetic, the computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno was
claiming. How does anything exist if it is not computed by the or a
machine? And I thought the generalized brain did the computations, not that
it was only computed. How does Bruno show that all the rest which
presumably includes energy and matter is not computed. Bruno is constantly
confusing me.

Energy and matter (and the universe whatever it is), is composed by the sum
of the infinity of computations going through your state as it is
defined by an infinity of computations (and not one), it is not computed.

A piece of matter (or you fwiw) below the substitution level is an infinity
of computations.

Quentin

On Tue, Oct 15, 2013 at 3:40 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?   Do they
divide into two infinite subsets on a binary measurement, or do infinitely
many come into existence in order that some branch-counting measure
produces the right proportion?  Do you not see any problems with assigning
a measure to infinite countable subsets (are there more even numbers that
square numbers?).

And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for example,
Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

I don't understand the question.  What parallel experiences do you refer
to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon
interference in the two slits experiment.

?? The math predicts probabilities of events, including where a single
photon will land in a Young's slit experiment - no superposition of
observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise: yes the
quantum wave describes only psychological states, but they concern still
a *many* dreams/worlds/physical-realities, including the many
self-multiplication.

There is no many in Fuchs interpretation, there is only the personal
subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the real,
which is a bit weird to me.

The 'interference' is a calculational event 'between' possible futures.
Or even the result of considering all possible paths.

understand or get a bigger picture.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological, which is not
a problem for me. there are still many.

Yes, that's why I said I think his approach is consistent with yours.  I
think Fuchs view of QM is similar to what William S. Cooper calls for at
the end of his book The Evolution of Reason - a probabilistic extension
of logic. This is essentially the view he defends at length in Interview
with a Quantum Bayesian, arXiv:1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical reality. Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is
the knower, the observer, etc. If not, it falls into a cosmic form of
solipsism, and it can generate some strong don't ask imperative.

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I think you
do the same).

What? Not at all. the observer is defined by its set of beliefs, itself
define by a relative universal numbers.

Fuchs defines 'the observer' as the one who bets on the outcome of his
```

### Re: The probability problem in Everettian quantum mechanics

```2013/10/15 Richard Ruquist yann...@gmail.com

-- Forwarded message --
From: Quentin Anciaux allco...@gmail.com
Date: Tue, Oct 15, 2013 at 6:54 AM
Subject: Re: The probability problem in Everettian quantum mechanics

2013/10/15 Richard Ruquist yann...@gmail.com

Bruno: On the contrary: I assume only that my brain (or generalized
brain) is computable, then I show that basically all the rest is not. In
everything, or just in arithmetic, the computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno was
claiming. How does anything exist if it is not computed by the or a
machine? And I thought the generalized brain did the computations, not that
it was only computed. How does Bruno show that all the rest which
presumably includes energy and matter is not computed. Bruno is constantly
confusing me.

Energy and matter (and the universe whatever it is), is composed by the
sum of the infinity of computations going through your state as it is
defined by an infinity of computations (and not one), it is not computed.

A piece of matter (or you fwiw) below the substitution level is an
infinity of computations.

Quentin

No I'm saying, that matter/you is not *a* computation, but the infinite set
of computations going through your current state (at every state, an
infinity of computations diverge, but there is still an infinity going
through that state and it's for every state).

Quentin

You seem to be saying that the infinity of computations are not computed.
That does not make sense.
Richard

On Tue, Oct 15, 2013 at 3:40 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?   Do they
divide into two infinite subsets on a binary measurement, or do infinitely
many come into existence in order that some branch-counting measure
produces the right proportion?  Do you not see any problems with assigning
a measure to infinite countable subsets (are there more even numbers that
square numbers?).

And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for example,
Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

I don't understand the question.  What parallel experiences do you refer
to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon
interference in the two slits experiment.

?? The math predicts probabilities of events, including where a single
photon will land in a Young's slit experiment - no superposition of
observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise: yes the
quantum wave describes only psychological states, but they concern still
a *many* dreams/worlds/physical-realities, including the many
self-multiplication.

There is no many in Fuchs interpretation, there is only the personal
subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the
real, which is a bit weird to me.

The 'interference' is a calculational event 'between' possible futures.
Or even the result of considering all possible paths.

understand or get a bigger picture.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological, which is not
a problem for me. there are still many.

Yes, that's why I said I think his approach is consistent with yours.  I
think Fuchs view of QM is similar to what William S. Cooper calls for at
the end of his book The Evolution of Reason - a probabilistic extension
of logic. This is essentially the view he defends at length in Interview
with a Quantum Bayesian, arXiv:1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical```

### Re: The probability problem in Everettian quantum mechanics

```

On 15 Oct 2013, at 12:45, Richard Ruquist wrote:

Bruno: On the contrary: I assume only that my brain (or generalized
brain) is computable, then I show that basically all the rest is
not. In everything, or just in arithmetic, the computable is rare
and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno
was claiming. How does anything exist if it is not computed by the
or a machine?

We assume the arithmetical truth. In particular we assume that all
closed formula written in the language of arithmetic (and thus using
logical symbol + the symbol 0, s (+1), + and *) are all either true or
false, independently of us.

From this we cannot prove that matter exists, or not, but we can
prove that the average universal numbers will (correctly) believe in
matter (but it will not know that it is correct).

So, if you have no problem in believing propositions like there is no
biggest prime number are true independently of me and you, and the
universe, then you can understand that the proposition asserting the
existence of (infinitely many) computations in which you believe
reading my current post, is also true independently of us.

The appearance of matter emerges from the FPI that the machines cannot
avoid in the arithmetical truth.

Arithmetical truth escapes largely the computable arithmetical truth
(by Gödel).

And I thought the generalized brain did the computations,

Only the computations associated to your mind.

not that it was only computed. How does Bruno show that all the
rest which presumably includes energy and matter is not computed.
Bruno is constantly confusing me.

I guess you missed the step seven of the UDA, and are perhaps not
aware that arithmetical truth is incredibly big, *much* bigger than
what any computer can generate or compute.

Then my, or your, mind is associated to *all* computations going
there are infinitely many such computations. They all exist in
arithmetic, and the FPI glues them, in a non computable way, in
possible long and deep physical histories.

Bruno

On Tue, Oct 15, 2013 at 3:40 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one
another?   Do they divide into two infinite subsets on a
binary measurement, or do infinitely many come into existence
in order that some branch-counting measure produces the right
proportion?  Do you not see any problems with assigning a
measure to infinite countable subsets (are there more even
numbers that square numbers?).

And why should we prefer this model to simply saying the Born
rule derives from a Bayesian epistemic view of QM as argued
by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel

I don't understand the question.  What parallel experiences do
you refer to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function -
so superpositions are just something that happens in the
mathematics.

But then I don't see how this could fit with even just the one
photon interference in the two slits experiment.

?? The math predicts probabilities of events, including where a
single photon will land in a Young's slit experiment - no
superposition of observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise:
yes the quantum wave describes only psychological states,
but they concern still a *many* dreams/worlds/physical-
realities, including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the
personal subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the
real, which is a bit weird to me.

The 'interference' is a calculational event 'between' possible
futures.  Or even the result of considering all possible paths.

understand or get a bigger picture.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes   ```

### Re: The probability problem in Everettian quantum mechanics

```

On 15 Oct 2013, at 13:21, Quentin Anciaux wrote:

2013/10/15 Richard Ruquist yann...@gmail.com

-- Forwarded message --
From: Quentin Anciaux allco...@gmail.com
Date: Tue, Oct 15, 2013 at 6:54 AM
Subject: Re: The probability problem in Everettian quantum mechanics

2013/10/15 Richard Ruquist yann...@gmail.com
Bruno: On the contrary: I assume only that my brain (or generalized
brain) is computable, then I show that basically all the rest is
not. In everything, or just in arithmetic, the computable is rare
and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno
was claiming. How does anything exist if it is not computed by the
or a machine? And I thought the generalized brain did the
computations, not that it was only computed. How does Bruno show
that all the rest which presumably includes energy and matter is
not computed. Bruno is constantly confusing me.

Energy and matter (and the universe whatever it is), is composed by
the sum of the infinity of computations going through your state
as it is defined by an infinity of computations (and not one), it is
not computed.

A piece of matter (or you fwiw) below the substitution level is an
infinity of computations.

Quentin

No I'm saying, that matter/you is not *a* computation, but the
infinite set of computations going through your current state (at
every state, an infinity of computations diverge, but there is still
an infinity going through that state and it's for every state).

Yes. It generalizes what Everett did on the universal quantum wave, on
the whole arithmetical truth (which contains the whole computer
science theoretical truth). If QM is correct, the SWE is redundant,
and a consequence of comp. Physics is one aspect of arithmetic seen by
its internal creatures (the universal or not numbers). We can
concretely extract physics from the interview of the chatty rich one
(the Löbian numbers).

Bruno

Quentin

You seem to be saying that the infinity of computations are not
computed. That does not make sense.

Richard

On Tue, Oct 15, 2013 at 3:40 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one
another?   Do they divide into two infinite subsets on a
binary measurement, or do infinitely many come into existence
in order that some branch-counting measure produces the right
proportion?  Do you not see any problems with assigning a
measure to infinite countable subsets (are there more even
numbers that square numbers?).

And why should we prefer this model to simply saying the Born
rule derives from a Bayesian epistemic view of QM as argued
by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel

I don't understand the question.  What parallel experiences do
you refer to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function -
so superpositions are just something that happens in the
mathematics.

But then I don't see how this could fit with even just the one
photon interference in the two slits experiment.

?? The math predicts probabilities of events, including where a
single photon will land in a Young's slit experiment - no
superposition of observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise:
yes the quantum wave describes only psychological states,
but they concern still a *many* dreams/worlds/physical-
realities, including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the
personal subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the
real, which is a bit weird to me.

The 'interference' is a calculational event 'between' possible
futures.  Or even the result of considering all possible paths.

understand or get a bigger picture.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological,
which```

### Re: The probability problem in Everettian quantum mechanics

```Bruno: Arithmetical truth escapes largely the computable arithmetical truth
(by Gödel).

Richard: I guess I am too much a physicist to believe that uncomputible
arithmetical truth can produce the physical.
Since you read my paper you know that I think computations in this universe
if holographic are limited to 10^120 bits (the Lloyd limit) which is very
far from infinity. I just do not believe in infinity. In other words, I
believe the largest prime number in this universe is less than 10^120. So I
will drop out of these discussions. My assumptions differ from yours.

On Tue, Oct 15, 2013 at 10:53 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 15 Oct 2013, at 13:21, Quentin Anciaux wrote:

2013/10/15 Richard Ruquist yann...@gmail.com

-- Forwarded message --
From: Quentin Anciaux allco...@gmail.com
Date: Tue, Oct 15, 2013 at 6:54 AM
Subject: Re: The probability problem in Everettian quantum mechanics

2013/10/15 Richard Ruquist yann...@gmail.com

Bruno: On the contrary: I assume only that my brain (or generalized
brain) is computable, then I show that basically all the rest is not. In
everything, or just in arithmetic, the computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno was
claiming. How does anything exist if it is not computed by the or a
machine? And I thought the generalized brain did the computations, not that
it was only computed. How does Bruno show that all the rest which
presumably includes energy and matter is not computed. Bruno is constantly
confusing me.

Energy and matter (and the universe whatever it is), is composed by the
sum of the infinity of computations going through your state as it is
defined by an infinity of computations (and not one), it is not computed.

A piece of matter (or you fwiw) below the substitution level is an
infinity of computations.

Quentin

No I'm saying, that matter/you is not *a* computation, but the infinite
set of computations going through your current state (at every state, an
infinity of computations diverge, but there is still an infinity going
through that state and it's for every state).

Yes. It generalizes what Everett did on the universal quantum wave, on the
whole arithmetical truth (which contains the whole computer science
theoretical truth). If QM is correct, the SWE is redundant, and a
consequence of comp. Physics is one aspect of arithmetic seen by its
internal creatures (the universal or not numbers). We can concretely
extract physics from the interview of the chatty rich one (the Löbian
numbers).

Bruno

Quentin

You seem to be saying that the infinity of computations are not computed.
That does not make sense.
Richard

On Tue, Oct 15, 2013 at 3:40 AM, Bruno Marchal marc...@ulb.ac.bewrote:

On 14 Oct 2013, at 21:30, meekerdb wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?   Do they
divide into two infinite subsets on a binary measurement, or do infinitely
many come into existence in order that some branch-counting measure
produces the right proportion?  Do you not see any problems with assigning
a measure to infinite countable subsets (are there more even numbers that
square numbers?).

And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for example,
Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

I don't understand the question.  What parallel experiences do you
refer to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon
interference in the two slits experiment.

?? The math predicts probabilities of events, including where a single
photon will land in a Young's slit experiment - no superposition of
observer required.

But it illustrates that superposition is physical/real, not purely
mathematical. Then linearity expands it to us.

When I read Fuchs I thought this: Comp suggest a compromise: yes the
quantum wave describes only psychological states, but they concern still
a *many* dreams/worlds/physical-realities, including the many
self-multiplication.

There is no many in Fuchs interpretation, there is only the personal
subjective```

### Re: The probability problem in Everettian quantum mechanics

```
On 10/15/2013 3:54 AM, Quentin Anciaux wrote:

2013/10/15 Richard Ruquist yann...@gmail.com mailto:yann...@gmail.com

Bruno: On the contrary: I assume only that my brain (or generalized brain)
is
computable, then I show that basically all the rest is not. In everything,
or just
in arithmetic, the computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno was
claiming. How
does anything exist if it is not computed by the or a machine? And I
thought the
generalized brain did the computations, not that it was only computed. How
does
Bruno show that all the rest which presumably includes energy and matter
is not
computed. Bruno is constantly confusing me.

Energy and matter (and the universe whatever it is), is composed by the sum

What does sum mean?  And how does is constitute a piece of matter?

of the infinity of computations going through your state as it is defined by an
infinity of computations (and not one), it is not computed.

But that's not a definition.  It's saying the piece of matter is *constituted* by an
infinity of computations.  But what associates the computations to a piece of matter that
we *define* ostensively?

Brent

A piece of matter (or you fwiw) below the substitution level is an infinity of
computations.

Quentin

--
You received this message because you are subscribed to the Google Groups
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To post to this group, send email to everything-list@googlegroups.com.

```

### Re: The probability problem in Everettian quantum mechanics

```
On 10/15/2013 7:49 AM, Bruno Marchal wrote:

On 15 Oct 2013, at 12:45, Richard Ruquist wrote:

Bruno: On the contrary: I assume only that my brain (or generalized brain) is
computable, then I show that basically all the rest is not. In everything, or just in
arithmetic, the computable is rare and exceptional.

Richard: Wow. This contradicts everything I have ever though Bruno was claiming. How
does anything exist if it is not computed by the or a machine?

We assume the arithmetical truth. In particular we assume that all closed formula
written in the language of arithmetic (and thus using logical symbol + the symbol 0, s
(+1), + and *) are all either true or false, independently of us.

From this we cannot prove that matter exists, or not, but we can prove that the average
universal numbers will (correctly) believe in matter (but it will not know that it is
correct).

That's not at all clear to me.  A universal number encodes proofs - is that what you mean
by it believes something?  But how is this something identified at 'matter'?

So, if you have no problem in believing propositions like there is no biggest prime
number are true independently of me and you, and the universe, then you can understand
that the proposition asserting the existence of (infinitely many) computations in which
you believe reading my current post, is also true independently of us.

The appearance of matter emerges from the FPI that the machines cannot avoid in the
arithmetical truth.

Arithmetical truth escapes largely the computable arithmetical truth (by Gödel).

And I thought the generalized brain did the computations,

Only the computations associated to your mind.

not that it was only computed. How does Bruno show that all the rest which presumably
includes energy and matter is not computed. Bruno is constantly confusing me.

I guess you missed the step seven of the UDA, and are perhaps not aware that
arithmetical truth is incredibly big, *much* bigger than what any computer can generate
or compute.

Then my, or your, mind is associated to *all* computations going through your actual
state of mind,

That sounds like an uncomputable totality.

Brent

and below your substitution level there are infinitely many such computations. They all
exist in arithmetic, and the FPI glues them, in a non computable way, in possible long
and deep physical histories.

Bruno

--
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Everything List group.
To unsubscribe from this group and stop receiving emails from it, send an email
To post to this group, send email to everything-list@googlegroups.com.

```

### Re: The probability problem in Everettian quantum mechanics

```On Tue, Oct 15, 2013 at 01:02:13PM -0400, Richard Ruquist wrote:
Bruno: Arithmetical truth escapes largely the computable arithmetical truth
(by Gödel).

Richard: I guess I am too much a physicist to believe that uncomputible
arithmetical truth can produce the physical.
Since you read my paper you know that I think computations in this universe
if holographic are limited to 10^120 bits (the Lloyd limit) which is very
far from infinity. I just do not believe in infinity. In other words, I
believe the largest prime number in this universe is less than 10^120. So I
will drop out of these discussions. My assumptions differ from yours.

Then you might well be interested in the Movie Graph Argument, which
deals directly with the case where the universe doesn't have sufficient
resources to run the universal dovetailer.

--

Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

--
You received this message because you are subscribed to the Google Groups
Everything List group.
To unsubscribe from this group and stop receiving emails from it, send an email
To post to this group, send email to everything-list@googlegroups.com.

```

### Re: The probability problem in Everettian quantum mechanics

```

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one
another?   Do they divide into two infinite subsets on a binary
measurement, or do infinitely many come into existence in order
that some branch-counting measure produces the right
proportion?  Do you not see any problems with assigning a
measure to infinite countable subsets (are there more even
numbers that square numbers?).

And why should we prefer this model to simply saying the Born
rule derives from a Bayesian epistemic view of QM as argued by,
for example, Chris Fuchs?

If you can explain to me how this makes the parallel

I don't understand the question.  What parallel experiences do you
refer to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon
interference in the two slits experiment.

When I read Fuchs I thought this: Comp suggest a compromise: yes
the quantum wave describes only psychological states, but they
concern still a *many* dreams/worlds/physical-realities,
including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the
personal subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the
real, which is a bit weird to me.

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological, which
is not a problem for me. there are still many.

Yes, that's why I said I think his approach is consistent with
yours.  I think Fuchs view of QM is similar to what William S.
Cooper calls for at the end of his book The Evolution of Reason -
a probabilistic extension of logic. This is essentially the view he
defends at length in Interview with a Quantum Bayesian, arXiv:
1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical reality. Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define
what is the knower, the observer, etc. If not, it falls into a
cosmic form of solipsism, and it can generate some strong don't

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I
think you do the same).

What? Not at all. the observer is defined by its set of beliefs,
itself define by a relative universal numbers. Comp has a pretty well
defined notion of observer, with its octalist points of view, and an
whole theology including his physics, etc.

Physicists, like Fuchs, and unlike philosophers, are generally
comfortable with not explaining everything.

Me too. but he has still to explain the terms that he is using.

What's your explanation for the existence of persons?  So far what
I've heard is that it's an inside view of arithmetic - which I don't
find very enlightening.

What do you miss in the UDA?

Fuchs, correctly I think, says an 'interpretation' of a theory, the
story that goes along with the mathematics, is important insofar as
it gives you insight into how to apply the mathematics and to extend
your theories.  He is critical of Everett's MWI for not doing that,
or at least not doing it well.

Well, perhaps Fuchs is a bit out of topic, once you agree that it is
only Everett in a psychological version. That is close to comp. But
comp leads, by UDA, that the theory of everuthing is just elementary
arithmetic (or Turing equivalent, like colmbinatirs, ...). Then
everything is defined in a very precise way in that theory.
And this explains both 100% matter and 99,999... % of consciousness.
The explanation might be false, of course, but is testable.

Bruno

Brent

Bruno

Brent
I mistrust all systematizers and avoid them. The will to a system
is a lack of integrity.

--- Fredrick Nietzsche, Twilight of the Idols

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a measurement.  How are
these universes distinct from one another?   Do they divide into two infinite
subsets on a binary measurement, or do infinitely many come into existence in order
that some branch-counting measure produces the right proportion?  Do you not see
any problems with assigning a measure to infinite countable subsets (are there more
even numbers that square numbers?).

And why should we prefer this model to simply saying the Born rule derives from a
Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences, (then),

I don't understand the question.  What parallel experiences do you refer to?  And

The question is how does Fuchs prevent a superposition to be contagious on the
observer

I think he takes an instrumentalist view of the wave function - so superpositions are
just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon interference in
the two slits experiment.

?? The math predicts probabilities of events, including where a single photon will land in
a Young's slit experiment - no superposition of observer required.

When I read Fuchs I thought this: Comp suggest a compromise: yes the quantum wave
describes only psychological states, but they concern still a *many*
dreams/worlds/physical-realities, including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the personal subjective
probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the real, which is a bit
weird to me.

The 'interference' is a calculational event 'between' possible futures.  Or even the
result of considering all possible paths.

I know Fuchs criticize Everett, but I don't see how he makes the superposition
disappearing. he only makes them psychological, which is not a problem for me. there
are still many.

Yes, that's why I said I think his approach is consistent with yours.  I think Fuchs
view of QM is similar to what William S. Cooper calls for at the end of his book The
Evolution of Reason - a probabilistic extension of logic. This is essentially the view
he defends at length in Interview with a Quantum Bayesian, arXiv:1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal) physical reality.
Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is the knower,
the observer, etc. If not, it falls into a cosmic form of solipsism, and it can
generate some strong don't ask imperative.

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I think you do
the same).

What? Not at all. the observer is defined by its set of beliefs, itself define by a
relative universal numbers.

Fuchs defines 'the observer' as the one who bets on the outcome of his actions.

Comp has a pretty well defined notion of observer, with its octalist points of view, and
an whole theology including his physics, etc.

Physicists, like Fuchs, and unlike philosophers, are generally comfortable with not
explaining everything.

Me too. but he has still to explain the terms that he is using.

What's your explanation for the existence of persons?  So far what I've heard is that
it's an inside view of arithmetic - which I don't find very enlightening.

What do you miss in the UDA?

As I understand it the UD computes everything computable and it's only your inference that
observers (and the rest of the multiverse) *must be in there somewhere* because you've
assumed that everything is computable.

Fuchs, correctly I think, says an 'interpretation' of a theory, the story that goes
along with the mathematics, is important insofar as it gives you insight into how to
apply the mathematics and to extend your theories.  He is critical of Everett's MWI for
not doing that, or at least not doing it well.

Well, perhaps Fuchs is a bit out of topic, once you agree that it is only Everett in a
psychological version.

It's kinda funny to see only...psychological from a guy who wants to show that
everything is a shared dream.

That is close to comp. But comp leads, by UDA, that the theory of ```

### Re: The probability problem in Everettian quantum mechanics

```On Mon, Oct 14, 2013 at 2:30 PM, meekerdb meeke...@verizon.net wrote:

On 10/14/2013 1:29 AM, Bruno Marchal wrote:

On 13 Oct 2013, at 22:11, meekerdb wrote:

On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?   Do they
divide into two infinite subsets on a binary measurement, or do infinitely
many come into existence in order that some branch-counting measure
produces the right proportion?  Do you not see any problems with assigning
a measure to infinite countable subsets (are there more even numbers that
square numbers?).

And why should we prefer this model to simply saying the Born rule derives
from a Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

I don't understand the question.  What parallel experiences do you refer
to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be contagious
on the observer

I think he takes an instrumentalist view of the wave function - so
superpositions are just something that happens in the mathematics.

But then I don't see how this could fit with even just the one photon
interference in the two slits experiment.

?? The math predicts probabilities of events, including where a single
photon will land in a Young's slit experiment - no superposition of
observer required.

When I read Fuchs I thought this: Comp suggest a compromise: yes the
quantum wave describes only psychological states, but they concern still
a *many* dreams/worlds/physical-realities, including the many
self-multiplication.

There is no many in Fuchs interpretation, there is only the personal
subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

OK. But apparently object of contemplation can interfere with the real,
which is a bit weird to me.

The 'interference' is a calculational event 'between' possible futures.
Or even the result of considering all possible paths.

According to Fuchs, who does the consideration have to be made by?
Obviously no person (nor any practical classical computer) could
contemplate all possible paths of a large quantum computation.  So whose
contemplation reifies or interferes with the product of that computation?

Jason

I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological, which is not
a problem for me. there are still many.

Yes, that's why I said I think his approach is consistent with yours.  I
think Fuchs view of QM is similar to what William S. Cooper calls for at
the end of his book The Evolution of Reason - a probabilistic extension
of logic. This is essentially the view he defends at length in Interview
with a Quantum Bayesian, arXiv:1207.2141v1

OK.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical reality. Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is
the knower, the observer, etc. If not, it falls into a cosmic form of
solipsism, and it can generate some strong don't ask imperative.

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I think you
do the same).

What? Not at all. the observer is defined by its set of beliefs, itself
define by a relative universal numbers.

Fuchs defines 'the observer' as the one who bets on the outcome of his
actions.

Comp has a pretty well defined notion of observer, with its octalist
points of view, and an whole theology including his physics, etc.

Physicists, like Fuchs, and unlike philosophers, are generally
comfortable with not explaining everything.

Me too. but he has still to explain the terms that he is using.

What's your explanation for the existence of persons?  So far what I've
heard is that it's an inside view of arithmetic - which I don't find very
enlightening.

What do you miss in the UDA?

As I understand it the UD computes everything computable and it's only
your inference that observers (and the rest of the multiverse) *must be in
there somewhere* because you've assumed that everything is computable.

Fuchs, correctly I think, says an 'interpretation' of a theory, the
story that goes along with the mathematics, is important insofar as it
gives you insight into how to apply the mathematics ```

### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement,
or do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).

And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for
example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

I don't understand the question.  What parallel experiences do you
refer to?  And you're asking why they disappeared?

The question is how does Fuchs prevent a superposition to be
contagious on the observer

When I read Fuchs I thought this: Comp suggest a compromise: yes
the quantum wave describes only psychological states, but they
concern still a *many* dreams/worlds/physical-realities, including
the many self-multiplication.

There is no many in Fuchs interpretation, there is only the
personal subjective probabilities of contemplated futures.

I notice the plural of futures. Are those not many?
I know Fuchs criticize Everett, but I don't see how he makes the
superposition disappearing. he only makes them psychological, which is
not a problem for me. there are still many.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical reality. Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what
is the knower, the observer, etc. If not, it falls into a cosmic
form of solipsism, and it can generate some strong don't ask
imperative.

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

Physicists, like Fuchs, and unlike philosophers, are generally
comfortable with not explaining everything.

Me too. but he has still to explain the terms that he is using.

Bruno

Brent
I mistrust all systematizers and avoid them. The will to a system
is a lack of integrity.

--- Fredrick Nietzsche, Twilight of the Idols

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/13/2013 1:48 AM, Bruno Marchal wrote:

On 12 Oct 2013, at 22:53, meekerdb wrote:

On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a measurement. How are
these universes distinct from one another?   Do they divide into two infinite subsets
on a binary measurement, or do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not see any problems
with assigning a measure to infinite countable subsets (are there more even numbers
that square numbers?).

And why should we prefer this model to simply saying the Born rule derives from a
Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences, (then),

I don't understand the question.  What parallel experiences do you refer to?  And

The question is how does Fuchs prevent a superposition to be contagious on the
observer

I think he takes an instrumentalist view of the wave function - so superpositions are just
something that happens in the mathematics.

When I read Fuchs I thought this: Comp suggest a compromise: yes the quantum wave
describes only psychological states, but they concern still a *many*
dreams/worlds/physical-realities, including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the personal subjective
probabilities of contemplated futures.

I notice the plural of futures. Are those not many?

Sure, but they are contemplated, not reified.

I know Fuchs criticize Everett, but I don't see how he makes the superposition
disappearing. he only makes them psychological, which is not a problem for me. there are
still many.

Yes, that's why I said I think his approach is consistent with yours.  I think Fuchs view
of QM is similar to what William S. Cooper calls for at the end of his book The Evolution
of Reason - a probabilistic extension of logic. This is essentially the view he defends
at length in Interview with a Quantum Bayesian, arXiv:1207.2141v1

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal) physical reality.
Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is the knower, the
observer, etc. If not, it falls into a cosmic form of solipsism, and it can generate

You assume that if others are not explained they must be rejected.

I just ask for an explanation of the terms that they introduce.

I think he takes the observer as primitive and undefined (and I think you do
the same).

Physicists, like Fuchs, and unlike philosophers, are generally comfortable with not
explaining everything.

Me too. but he has still to explain the terms that he is using.

What's your explanation for the existence of persons?  So far what I've heard is that it's
an inside view of arithmetic - which I don't find very enlightening.  Fuchs, correctly I
think, says an 'interpretation' of a theory, the story that goes along with the
mathematics, is important insofar as it gives you insight into how to apply the
mathematics and to extend your theories.  He is critical of Everett's MWI for not doing
that, or at least not doing it well.

Brent

Bruno

Brent
I mistrust all systematizers and avoid them. The will to a system is a lack of
integrity.
--- Fredrick Nietzsche, Twilight of the Idols

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### Re: The probability problem in Everettian quantum mechanics

```

On 11 Oct 2013, at 17:00, Jason Resch wrote:

On Oct 11, 2013, at 9:06 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 11 Oct 2013, at 13:16, Pierz wrote:

And just to follow up on that, there are still an infinite number
of irrational numbers between 0 and 0.1. But not as large an
infinity as those between 0.1 and 1.

It is the same cardinal (2^aleph_zero). But cardinality is not what
count when searching a measure.

So extrapolating to universes, the very low probability, white
rabbit universes also occur an infinite number of times, but that
does not make them equally as likely as the universes which behave
as we would classically expect.

That is what remain to be seen. But if comp is true, we know the
measure has to exist, and the math gives some clues that it is
indeed the case, from machines' (consistent and/or true) points of
view.

Bruno,

Could the matter of the countably infinite number of programs be
irrelevant from the first person perspective because any given mind
contains/is aware of only a finite amount of information?

Say some mind contains a million bits of information. Then there is
a finite number (2^100) of distinct combinations of content for
that mind. These differations are all that matter from the first
person view, and some may be more probable than others.

(But deciding the measures for each of those finite number of
possibilities depends on infinite computations, and so would they be
real numbers?)

Even if the 3-mind (my current 3-state) is finite, the FPI will bear
on non enumerable continuations. I will be able to distinguish only
finite numbers of cluster of histories in that infinity of
continuations, but the measure will bear (like in QM) on the
distinguishable in-principle continuation, so the relative
indeterminacy might depends on them all, and so it is consistent that
real numbers will be at play. Now, the real measure takes the fusion-
amnesia-backtracking into account, and the real picture is beyond our
intuition, and has to be extracted from the semantics of the (q)Hm. (q
for quantification in the logician sense, and Hm is for the relevant
material hypostases (Bp  Dt, Bp  Dt  p, but also on Bp  p, as it
gives a quantization (in the physicist sense) when p is in the UD (p
is sigma_1).

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 11 Oct 2013, at 19:07, meekerdb wrote:

On 10/11/2013 2:28 AM, Russell Standish wrote:

On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).
But infinite subsets in question will contain an uncountable number
of

elements.

I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

There is necessarily a continuum in comp, because the UD is so dumb as
making interacting all programs (rich enough) with a dovetailing on
the real, complex, quanternions, octonions, etc.

Very plausibly, the winning universal numbers exploit this, with the
algbraic measure structure (imposed by self-reference constraints)  to
multiply enough the first person views.

I would not have believe myself in this without the QM empirical
evidences. Without QM, I would probably not find comp plausible at all.

Bruno

Brent

That is why I'm not sure that problems with assigning
measures to countably infinite sets (such as your example above re
even and square numbers) are really such a problem.

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### Re: The probability problem in Everettian quantum mechanics

```

On 11 Oct 2013, at 23:46, Russell Standish wrote:

On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:

On 10/11/2013 2:28 AM, Russell Standish wrote:

On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement,
or

do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).
But infinite subsets in question will contain an uncountable
number of

elements.

I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT.

From the first person views statistics.

It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n},
where n is

the number of leading bits in common between x and y).

That would  be a sort of measure on infinite programs, not so much on
the computations, which will need a sort of measure on experiences,
which needs the definition of experiences and thus of the knower
logic and semantics, and for this I use the (counter-intuitive)
arithmetic of self-reference.

Bruno

ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

Cheers

--

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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 00:12, LizR wrote:

On 12 October 2013 10:46, Russell Standish li...@hpcoders.com.au
wrote:

On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n},
where n is

the number of leading bits in common between x and y). ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

I always assumed the UD output bits - i.e. not a continuum, but a
countable infinity of symbols - but maybe I'm missing something?

The first/third person distinction. I might add explanation later. It
looks like even those who grasp the FPI forget to apply it. The
invariance of UD-steps-delay plays a crucial role here. It entails
that the consciousness differentiation on the UD* takes zero second,
and that is why we are confronted with continua.

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 00:14, LizR wrote:

On 12 October 2013 11:12, LizR lizj...@gmail.com wrote:
On 12 October 2013 10:46, Russell Standish li...@hpcoders.com.au
wrote:

On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n},
where n is

the number of leading bits in common between x and y). ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

I always assumed the UD output bits - i.e. not a continuum, but a
countable infinity of symbols - but maybe I'm missing something?

Am I missing diagonalisation? i.e. Can the UD output be diagonalised?

It cannot. For the same reason that the partial computabe functions is
immune to diagonlaization. That is why it is universal.
But as I said, you forget to take into account the 1p/3p distinction.
You are forgetting step 7.

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 01:04, LizR wrote:

On 12 October 2013 11:35, Russell Standish li...@hpcoders.com.au
wrote:

The UD doesn't output anything. If it did, then certainly, the output
could not be an uncountable set due to the diagonalisation argument.

Yes, I wasn't speaking very precisely. Obviously there is no output,
because where would it go? I meant the trace, which I assume is a
record of its operation, which itself exists in arithmetic (I think?)

Yes. In different ways, but that would be technical to describe.
Shortly: arithmetic contains only finite pieces of computations, but
the first person indeterminacy (and thus the consciousness
differentiation) will glue them all.

Bruno

Rather UD* is like the internal view of the operation of the
dovetailer, like the sum of all possible experiences of the Helsinki
man being duplicated to Washington and Moscow that is being discussed
rather a lot lately.

Ah! Should read to the end :)
Thanks.

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 01:05, Pierz wrote:

On Saturday, October 12, 2013 5:42:06 AM UTC+11, Brent wrote:
On 10/11/2013 4:16 AM, Pierz wrote:
And just to follow up on that, there are still an infinite number
of irrational numbers between 0 and 0.1. But not as large an
infinity as those between 0.1 and 1.

No, the two are exactly the same uncountable infinity, because there
is a 1-to-1 mapping between them.

My mathematical terminology may not be up to scratch. The measure is
different.

So extrapolating to universes, the very low probability, white
rabbit universes also occur an infinite number of times, but that
does not make them equally as likely as the universes which behave
as we would classically expect.

But computationalism only produces rational numbers.

We were talking MWI, where a measure is permitted because of the
underlying physical continuum. It does seem that the measure problem
is an open one for comp, as far as I can tell from Bruno's
responses, but he seems confident it's not insurmountable. I'm not
competent to judge.

The comp measure problem *is* the same problem as deriving physics
from comp. It is *the* problem.
The apparition of a quantum-like quantization in the material
hypostases gives much hopes indeed.

Bruno

Brent

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:
If you subdivide a continuum, I assume you can do so in a way that
gives the required probabilities. For example if the part of the
multiverse that is involved in performing a quantum measurement
with a 50-50 chance of either outcome is represented by the numbers
0 to 1, you can divide those into 0-0.5 and 0.5 to 1. Doesn't David
do something like this in FOR? (Or is this too plistic?)

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 01:08, meekerdb wrote:

On 10/11/2013 3:44 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 03:08:30PM -0700, meekerdb wrote:
UD* (trace of the universal dovetailer) is a continuum, AFAICT.
It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-
n}, where n is

the number of leading bits in common between x and y).
Hmm? So 1000 is the same distance from 10 and 111?  What's the
measure on this space?

1000... and 101... are 0.25 apart. 1000.. and 111... are 0.5
apart. (the ... refers to an infinite number of bits that are not
relevant to the computation). So the answer to your question is that
these these three strings are not the same distance from each other.

The measure over a set of these things would be something like the
supremum over the distance between any two pairs drawn from the
set. Of course, that assumes that only sets defined by finite length
prefixes, and countable unions and intersections thereof are
considered. My maths chops aren't quite up to generalising this for
arbitrary sets of binary strings.

Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Imagine a universal (and thus finite) game of life pattern. Then you
can look at UD* as the infinite cone obtained by adding all the planes
describing its evolution. That gives a static view of UD* as a
discrete infinite 3D conic object.

It is, as Russell and Liz said, the trace of the programs which runs
all computations in that parallel -dovetailing manner.

But physics and theology are emerging from the internal relative
machines points of views, and that gives a richer structure, relying
on the continuum. The 1/3 distinction has a key role here.

Bruno

Brent

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 01:16, meekerdb wrote:

On 10/11/2013 4:05 PM, Pierz wrote:
It does seem that the measure problem is an open one for comp, as
far as I can tell from Bruno's responses, but he  seems
confident it's not insurmountable.

Bruno's so confident that he argues that there must be a measure
(because he's assumed comp is true and his argument from comp is
valid).  :-)

Haha! Yes, that's a good point. IF COMP is true that measure must
exist, even if it took a billions years for humans to extract it. But
the apparently universal machine get quickly a quantized structure
(thanks to the p - []p appearing at the right places). So hope can
exist that such problem is not that insurmountable.

Bruno

Brent

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 01:36, Russell Standish wrote:

On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:

Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and Liz did
also, this morning) a few years ago. I'm not sure anyone has a clear,
crisp mathematical explanation of what UD* is - I certainly don't.

To do that needs the phi_i, or the W_i. It is the sequence

phi_0(0)^0, phi_0(0)^1, etc.

With the three numbers (i, j, k) going through all element of NxNxN, and
phi_i(j)^k = the kth state /step of the computation of machine/number
i, on input j.

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 04:52, Russell Standish wrote:

On Fri, Oct 11, 2013 at 05:46:57PM -0700, meekerdb wrote:

On 10/11/2013 4:36 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:

Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and Liz
did
also, this morning) a few years ago. I'm not sure anyone has a
clear,

crisp mathematical explanation of what UD* is - I certainly don't.

Even if we have the complete record of everything the UD has done up
to some point I don't see how we can define the kind of measure we
need over that, because the measure has to be over all threads of
computation corresponding to a particular classical state.

And these correspond to a countable union of sets of strings sharing
the same prefix, which is just the Solomonoff-Levin measure.

I think this might play some role in the thermodynamic, but the
quantum and the very existence of physics needs the measure on the
points of view (which I handle with the self-reference logics).

Bruno

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### Re: The probability problem in Everettian quantum mechanics

```

On 12 Oct 2013, at 05:15, meekerdb wrote:

On 10/11/2013 7:52 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 05:46:57PM -0700, meekerdb wrote:

On 10/11/2013 4:36 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:
Maybe I'm not clear on what UD* means.  I took it to be, at a
given

state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and
Liz did
also, this morning) a few years ago. I'm not sure anyone has a
clear,

crisp mathematical explanation of what UD* is - I certainly don't.

Even if we have the complete record of everything the UD has done up
to some point I don't see how we can define the kind of measure we
need over that, because the measure has to be over all threads of
computation corresponding to a particular classical state.

And these correspond to a countable union of sets of strings sharing
the same prefix, which is just the Solomonoff-Levin measure.

But there are infinitely more threads going thru (near) this state
which have not yet been computed.  So the threads counted up to some
point are of zero measure. ?

But the arithmetical truth is time independent, and all computations
are computed, like in a block universe. The FPI do the rest.
Then you are right, all finite portion of UD* have no role, and the
thread counted up to some point have zero measure. The 1-p exploits
the neighborhood of omega, not zero.

Bruno

Brent

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### Re: The probability problem in Everettian quantum mechanics

```

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some branch-
counting measure produces the right proportion?  Do you not see any
problems with assigning a measure to infinite countable subsets (are
there more even numbers that square numbers?).

And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for
example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences,

When I read Fuchs I thought this: Comp suggest a compromise: yes the
quantum wave describes only psychological states, but they concern
still a *many* dreams/worlds/physical-realities, including the many
self-multiplication.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal)
physical reality. Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is
the knower, the observer, etc. If not, it falls into a cosmic form of
solipsism, and it can generate some strong don't ask imperative.

Bruno

Brent

On 10/10/2013 6:11 PM, Pierz wrote:
I'm puzzled by the controversy over this issue - although given
that I'm not a physicist and my understanding comes from popular
renditions of MWI by Deutsch and others, it may be me who's missing
the point. But in my understanding of Deutsch's version of  MWI,
the reason for Born probabilities lies in the fact that there is no
such thing as a single branch. Every branch of the multiverse
contains an infinity of identical, fungible universes. When a
quantum event occurs, that set of infinite universes divides
proportionally according to Schroedinger's equation. The appearance
of probability arises, as in Bruno's comp, from multiplication of
the observer in those infinite branches. Why is this problematic?

On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:
quantum mechanics persists. British Jour. Philosophy of Science
IN PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]).
The possible outcomes of measurement as per ‘orthodox’ quantum
mechanics are, in EQM, all instantiated. Given this metaphysics,
Everettians face the ‘probability problem’—how to make sense
of probabilities, and recover the Born Rule. To solve the
probability problem, Wallace, following Deutsch ([1999]), has
derived a quantum representation theorem. I argue that Wallace’s
solution to the probability problem is unsuccessful, as follows.
First, I examine one of the axioms of rationality used to derive
the theorem, Branching Indifference (BI). I argue that Wallace is
not successful in showing that BI is rational. While I think it is
correct to put the burden of proof on Wallace to motivate BI as an
axiom of rationality, it does not follow from his failing to do so
that BI is not rational. Thus, second, I show that there is an
alternative strategy for setting one’s credences in the face of
branching which is rational, and which violates BI. This is Branch
Counting (BC). Wallace is aware of BC, and has proffered various
arguments against it. However, third, I argue that Wallace’s
arguments against BC are unpersuasive. I conclude that the
probability problem in EQM persists.

Publications (a Ph.D. in Philosophy, London School of Economics,
May 2012)
‘The Probability Problem in Everettian Quantum Mechanics
Persists’, British Journal for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science,
2011 78(5): 976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73:
393-412, (with R. Frigg and S. Hartmann)
‘Conﬁrmation and Reduction: A Bayesian Account’, Synthese,
2011 179(2): 321-338, (with R. Frigg and S. Hartmann)

His paper may be an interesting read once it comes out. Also
available in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas
(eds): Recent Progress in Philosophy of Science: Perspectives and
Foundational Problems, 2013, (The Third European Philosophy of
Science Association Proceedings), Dordrecht: Springer

I think this list needs another discussion of the possible MWI
probability problem although it has been covered here and elsewhere
by members of this list. Previous discussions have not been
personally convincing.

Richard
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### Re: The probability problem in Everettian quantum mechanics

```
On 10/12/2013 10:55 AM, Bruno Marchal wrote:

On 11 Oct 2013, at 03:25, meekerdb wrote:

So there are infinitely many identical universes preceding a measurement.  How are
these universes distinct from one another?   Do they divide into two infinite subsets
on a binary measurement, or do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not see any problems
with assigning a measure to infinite countable subsets (are there more even numbers
that square numbers?).

And why should we prefer this model to simply saying the Born rule derives from a
Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

If you can explain to me how this makes the parallel experiences, (then),

I don't understand the question.  What parallel experiences do you refer to?  And you're

When I read Fuchs I thought this: Comp suggest a compromise: yes the quantum wave
describes only psychological states, but they concern still a *many*
dreams/worlds/physical-realities, including the many self-multiplication.

There is no many in Fuchs interpretation, there is only the personal subjective
probabilities of contemplated futures.

It is still Everett wave as seen from inside.

We just don't know if the dreams defined an unique (multiversal) physical reality.
Neither in Everett +GR, nor in comp.

Bayesian epistemic view is no problem, but you have to define what is the knower, the
observer, etc. If not, it falls into a cosmic form of solipsism, and it can generate

You assume that if others are not explained they must be rejected. Physicists, like Fuchs,
and unlike philosophers, are generally comfortable with not explaining everything.

Brent
I mistrust all systematizers and avoid them. The will to a system is a lack of
integrity.
--- Fredrick Nietzsche, Twilight of the Idols

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### Re: The probability problem in Everettian quantum mechanics

```On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:
So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).

But infinite subsets in question will contain an uncountable number of
elements. That is why I'm not sure that problems with assigning
measures to countably infinite sets (such as your example above re
even and square numbers) are really such a problem.

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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```If you subdivide a continuum, I assume you can do so in a way that gives
the required probabilities. For example if the part of the multiverse that
is involved in performing a quantum measurement with a 50-50 chance of
either outcome is represented by the numbers 0 to 1, you can divide those
into 0-0.5 and 0.5 to 1. Doesn't David do something like this in FOR? (Or
is this too simplistic?)

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### Re: The probability problem in Everettian quantum mechanics

```

On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?

They aren't 'distinct'. The hypothesis is that every universe branch
contains an *uncountable* infinity of fungible (identical and
interchangeable) universes. While this seems extravagant, it actually kind
of makes more sense than the idea of a universe splitting into two (where
did the second universe come from?). Instead, uncountable infinities of
universes are differentiated from one another. Quantum interference
patterns arise because of the possibility of universes merging back into
one another again.

Do they divide into two infinite subsets on a binary measurement, or do
infinitely many come into existence in order that some branch-counting
measure produces the right proportion?  Do you not see any problems with
assigning a measure to infinite countable subsets (are there more even
numbers that square numbers?).

The former. Deutsch goes into the problem of infinite countable sets in
great detail and shows how this is *not* a problem for these uncountable
infinities (as Russell points out)), whereas it may be a problem for
Bruno's computations - a point I've tried to argue with Bruno, but he
bamboozles my sophomoric maths with his replies. To me it seems you can't
count computations that go through a state, because for every function f
that computes a certain function, there is also some function f1 that also
computes f such that f1 = f + 1 - 1. But maybe that can be solved by
counting only the functions with the least number of steps (?).

And why should we prefer this model to simply saying the Born rule derives
from a Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

I don't know about Chris Fuchs, although isn't that just Copenhagen? It's
clear that one would need strong reasons to favour MWI with its crazy
proliferation of entities, which at first blush seems to run against
Occam's razor. However Deutsch makes a damn good fist of explaining why we
in fact have those reasons. For instance, when a quantum computer
calculates a function based on a superposition of states, MWI can explain
where these calculations are occurring - in other universes. The computer
is exploiting the possibility of massive parallelism inherent in that
infinity of universes. It is entirely unclear how these calculations occur
in the standard interpretation. MWI also solves the problem of what happens
to non-realized measurement states once a system decoheres. And of course
it gets around the intractable difficulties of non-computable wave
collapse. So it's a case of choose your poison: infinite universes or
conceptual incoherence. I'll take the former, even though in some ways I'd
like the universe (or the multiverse) better if it wasn't that way.

Max Born was my great grandfather. I wonder what he would have made of
Everett if he'd been a bit younger. When he died in 1970, it was still
probably too out there for him to have seriously considered.

Brent

On 10/10/2013 6:11 PM, Pierz wrote:

I'm puzzled by the controversy over this issue - although given that I'm
not a physicist and my understanding comes from popular renditions of MWI
by Deutsch and others, it may be me who's missing the point. But in my
understanding of Deutsch's version of  MWI, the reason for Born
probabilities lies in the fact that there is no such thing as a single
branch. Every branch of the multiverse contains an infinity of identical,
fungible universes. When a quantum event occurs, that set of infinite
universes divides proportionally according to Schroedinger's equation. The
appearance of probability arises, as in Bruno's comp, from multiplication
of the observer in those infinite branches. Why is this problematic?

On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:

mechanics persists. British Jour. Philosophy of Science   IN PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]). The
possible outcomes of measurement as per ‘orthodox’ quantum mechanics are,
in EQM, all instantiated. Given this metaphysics, Everettians face the
‘probability problem’—how to make sense of probabilities, and recover the
Born Rule. To solve the probability problem, Wallace, following Deutsch
([1999]), has derived a quantum representation theorem. I argue that
Wallace’s solution to the probability problem is unsuccessful, as follows.
First, I examine one of the axioms of rationality used to derive the
theorem, Branching Indifference (BI). I argue that Wallace is not
successful in showing that BI is rational. While I think it is correct to
put the burden of proof on Wallace to ```

### Re: The probability problem in Everettian quantum mechanics

```That is pretty much exactly my understanding. It does puzzle me that this
argument about the supposed probability problem with MWI is still live,
when that explanation seems perfectly coherent.

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:

If you subdivide a continuum, I assume you can do so in a way that gives
the required probabilities. For example if the part of the multiverse that
is involved in performing a quantum measurement with a 50-50 chance of
either outcome is represented by the numbers 0 to 1, you can divide those
into 0-0.5 and 0.5 to 1. Doesn't David do something like this in FOR? (Or
is this too simplistic?)

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### Re: The probability problem in Everettian quantum mechanics

```And just to follow up on that, there are still an infinite number of
irrational numbers between 0 and 0.1. But not as large an infinity as
those between 0.1 and 1. So extrapolating to universes, the very low
probability, white rabbit universes also occur an infinite number of times,
but that does not make them equally as likely as the universes which behave
as we would classically expect.

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:

If you subdivide a continuum, I assume you can do so in a way that gives
the required probabilities. For example if the part of the multiverse that
is involved in performing a quantum measurement with a 50-50 chance of
either outcome is represented by the numbers 0 to 1, you can divide those
into 0-0.5 and 0.5 to 1. Doesn't David do something like this in FOR? (Or
is this too simplistic?)

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### Re: The probability problem in Everettian quantum mechanics

```

On 11 Oct 2013, at 13:09, Pierz wrote:

On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote:
So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?

They aren't 'distinct'. The hypothesis is that every universe branch
contains an *uncountable* infinity of fungible (identical and
interchangeable) universes. While this seems extravagant, it
actually kind of makes more sense than the idea of a universe
splitting into two (where did the second universe come from?).
Instead, uncountable infinities of universes are differentiated from
one another. Quantum interference patterns arise because of the
possibility of universes merging back into one another again.

With comp too, it is best to see one consciousness differentiating
than actual splitting of universes.

Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some branch-
counting measure produces the right proportion?  Do you not see any
problems with assigning a measure to infinite countable subsets (are
there more even numbers that square numbers?).

The former. Deutsch goes into the problem of infinite countable sets
in great detail and shows how this is *not* a problem for these
uncountable infinities (as Russell points out)), whereas it may be a
problem for Bruno's computations - a point I've tried to argue with
Bruno, but he bamboozles my sophomoric maths with his replies. To me
it seems you can't count computations that go through a state,
because for every function f that computes a certain function, there
is also some function f1 that also computes f such that f1 = f + 1 -
1. But maybe that can be solved by counting only the functions with
the least number of steps (?).

You have to take all the programs, and all computations. Your relative
1-indeterminacy bears on all computations going through your state.

Using little programs would beg the 1-p/3-p problem.
There is an uncountable set of such computations, as they dovetail on
the reals. Just keep in mind that the UD is enough dumb to implement
the infinite iterated self-duplication, which leads to uncountably
many histories.

(Having said that, there are many ways to put probability and measure
on any set, finite, enumerable, non enumerable, etc. Sometimes people
just relinquish the sigma-additivity condition, and still get
something very close to a measure).

And why should we prefer this model to simply saying the Born rule
derives from a Bayesian epistemic view of QM as argued by, for
example, Chris Fuchs?

I don't know about Chris Fuchs, although isn't that just Copenhagen?
It's clear that one would need strong reasons to favour MWI with its
crazy proliferation of entities, which at first blush seems to run
against Occam's razor. However Deutsch makes a damn good fist of
explaining why we in fact have those reasons. For instance, when a
quantum computer calculates a function based on a superposition of
states, MWI can explain where these calculations are occurring - in
other universes. The computer is exploiting the possibility of
massive parallelism inherent in that infinity of universes. It is
entirely unclear how these calculations occur in the standard
interpretation. MWI also solves the problem of what happens to non-
realized measurement states once a system decoheres. And of course
it gets around the intractable difficulties of non-computable wave
collapse. So it's a case of choose your poison: infinite universes
or conceptual incoherence. I'll take the former, even though in some
ways I'd like the universe (or the multiverse) better if it wasn't
that way.

Max Born was my great grandfather. I wonder what he would have made
of Everett if he'd been a bit younger. When he died in 1970, it was
still probably too out there for him to have seriously considered.

That would have been nice to know. I really love the correspondence
between Max Born and Albert Einstein. I think both would have accepted
Everett, even if with some grimaces, like François Englert and many
quantum cosmologists.

I disagree with the idea that Everett propose a new interpretation of
QM. Everett proposes a new theory, which is just Copenhagen without
the collapse.  Everett himself talk about a new formulation of QM, not
a new interpretation. that is not so important, except when we begin
to use logic, which forces to be precise on what is a theory, and what
is an interpretation of a theory.

And Everett QM obeys Occam in the sense that he used less hypotheses.

Bruno

Brent

On 10/10/2013 6:11 PM, Pierz wrote:
I'm puzzled by the controversy over this issue - although given
that I'm not a physicist and my understanding comes from popular
renditions of MWI by Deutsch and others, it may be me who's missing
the point. But in my ```

### Re: The probability problem in Everettian quantum mechanics

```Pierz: Every branch of the multiverse contains an infinity of identical,
fungible universes.
Richard: How do you know this? Who said so?
Besides the branches must contain a finite number of identical universes
for probabilities to be realized.
Dividing infinity by any number results in an infinity.

On Thu, Oct 10, 2013 at 9:11 PM, Pierz pier...@gmail.com wrote:

I'm puzzled by the controversy over this issue - although given that I'm
not a physicist and my understanding comes from popular renditions of MWI
by Deutsch and others, it may be me who's missing the point. But in my
understanding of Deutsch's version of  MWI, the reason for Born
probabilities lies in the fact that there is no such thing as a single
branch. Every branch of the multiverse contains an infinity of identical,
fungible universes. When a quantum event occurs, that set of infinite
universes divides proportionally according to Schroedinger's equation. The
appearance of probability arises, as in Bruno's comp, from multiplication
of the observer in those infinite branches. Why is this problematic?

On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:

mechanics persists. British Jour. Philosophy of Science   IN PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]). The
possible outcomes of measurement as per ‘orthodox’ quantum mechanics are,
in EQM, all instantiated. Given this metaphysics, Everettians face the
‘probability problem’—how to make sense of probabilities, and recover the
Born Rule. To solve the probability problem, Wallace, following Deutsch
([1999]), has derived a quantum representation theorem. I argue that
Wallace’s solution to the probability problem is unsuccessful, as follows.
First, I examine one of the axioms of rationality used to derive the
theorem, Branching Indifference (BI). I argue that Wallace is not
successful in showing that BI is rational. While I think it is correct to
put the burden of proof on Wallace to motivate BI as an axiom of
rationality, it does not follow from his failing to do so that BI is not
rational. Thus, second, I show that there is an alternative strategy for
setting one’s credences in the face of branching which is rational, and
which violates BI. This is Branch Counting (BC). Wallace is aware of BC,
and has proffered various arguments against it. However, third, I argue
that Wallace’s arguments against BC are unpersuasive. I conclude that the
probability problem in EQM persists.

Publications (a Ph.D. in Philosophy, London School of Economics, May 2012)
‘The Probability Problem in Everettian Quantum Mechanics Persists’,
British Journal for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science, 2011
78(5): 976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73: 393-412,
(with R. Frigg and S. Hartmann)
‘Conﬁrmation and Reduction: A Bayesian Account’, Synthese, 2011 179(2):
321-338, (with R. Frigg and S. Hartmann)

His paper may be an interesting read once it comes out. Also available in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas (eds): Recent
Progress in Philosophy of Science: Perspectives and Foundational Problems,
2013, (The Third European Philosophy of Science Association Proceedings),
Dordrecht: Springer

I think this list needs another discussion of the possible MWI
probability problem although it has been covered here and elsewhere by
members of this list. Previous discussions have not been personally
convincing.

Richard

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### Re: The probability problem in Everettian quantum mechanics

```Opps. I replied before reading the entire discussion

On Fri, Oct 11, 2013 at 9:08 AM, Richard Ruquist yann...@gmail.com wrote:

Pierz: Every branch of the multiverse contains an infinity of identical,
fungible universes.
Richard: How do you know this? Who said so?
Besides the branches must contain a finite number of identical universes
for probabilities to be realized.
Dividing infinity by any number results in an infinity.

On Thu, Oct 10, 2013 at 9:11 PM, Pierz pier...@gmail.com wrote:

I'm puzzled by the controversy over this issue - although given that I'm
not a physicist and my understanding comes from popular renditions of MWI
by Deutsch and others, it may be me who's missing the point. But in my
understanding of Deutsch's version of  MWI, the reason for Born
probabilities lies in the fact that there is no such thing as a single
branch. Every branch of the multiverse contains an infinity of identical,
fungible universes. When a quantum event occurs, that set of infinite
universes divides proportionally according to Schroedinger's equation. The
appearance of probability arises, as in Bruno's comp, from multiplication
of the observer in those infinite branches. Why is this problematic?

On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:

quantum mechanics persists. British Jour. Philosophy of Science   IN
PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]). The
possible outcomes of measurement as per ‘orthodox’ quantum mechanics are,
in EQM, all instantiated. Given this metaphysics, Everettians face the
‘probability problem’—how to make sense of probabilities, and recover the
Born Rule. To solve the probability problem, Wallace, following Deutsch
([1999]), has derived a quantum representation theorem. I argue that
Wallace’s solution to the probability problem is unsuccessful, as follows.
First, I examine one of the axioms of rationality used to derive the
theorem, Branching Indifference (BI). I argue that Wallace is not
successful in showing that BI is rational. While I think it is correct to
put the burden of proof on Wallace to motivate BI as an axiom of
rationality, it does not follow from his failing to do so that BI is not
rational. Thus, second, I show that there is an alternative strategy for
setting one’s credences in the face of branching which is rational, and
which violates BI. This is Branch Counting (BC). Wallace is aware of BC,
and has proffered various arguments against it. However, third, I argue
that Wallace’s arguments against BC are unpersuasive. I conclude that the
probability problem in EQM persists.

Publications (a Ph.D. in Philosophy, London School of Economics, May
2012)
‘The Probability Problem in Everettian Quantum Mechanics Persists’,
British Journal for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science, 2011
78(5): 976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73: 393-412,
(with R. Frigg and S. Hartmann)
‘Conﬁrmation and Reduction: A Bayesian Account’, Synthese, 2011 179(2):
321-338, (with R. Frigg and S. Hartmann)

His paper may be an interesting read once it comes out. Also available
in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas (eds):
Recent Progress in Philosophy of Science: Perspectives and Foundational
Problems, 2013, (The Third European Philosophy of Science Association
Proceedings), Dordrecht: Springer

I think this list needs another discussion of the possible MWI
probability problem although it has been covered here and elsewhere by
members of this list. Previous discussions have not been personally
convincing.

Richard

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### Re: The probability problem in Everettian quantum mechanics

```

On Oct 11, 2013, at 9:06 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 11 Oct 2013, at 13:16, Pierz wrote:

And just to follow up on that, there are still an infinite number
of irrational numbers between 0 and 0.1. But not as large an
infinity as those between 0.1 and 1.

It is the same cardinal (2^aleph_zero). But cardinality is not what
count when searching a measure.

So extrapolating to universes, the very low probability, white
rabbit universes also occur an infinite number of times, but that
does not make them equally as likely as the universes which behave
as we would classically expect.

That is what remain to be seen. But if comp is true, we know the
measure has to exist, and the math gives some clues that it is
indeed the case, from machines' (consistent and/or true) points of
view.

Bruno,

Could the matter of the countably infinite number of programs be
irrelevant from the first person perspective because any given mind
contains/is aware of only a finite amount of information?

Say some mind contains a million bits of information. Then there is a
finite number (2^100) of distinct combinations of content for that
mind. These differations are all that matter from the first person
view, and some may be more probable than others.

(But deciding the measures for each of those finite number of
possibilities depends on infinite computations, and so would they be
real numbers?)

Jason

Bruno

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:
If you subdivide a continuum, I assume you can do so in a way that
gives the required probabilities. For example if the part of the
multiverse that is involved in performing a quantum measurement
with a 50-50 chance of either outcome is represented by the numbers
0 to 1, you can divide those into 0-0.5 and 0.5 to 1. Doesn't David
do something like this in FOR? (Or is this too simplistic?)

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 2:28 AM, Russell Standish wrote:

On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).

But infinite subsets in question will contain an uncountable number of
elements.

I don't think being uncountable makes it any easier unless they form a continuum, which I
don't think they do.  I QM an underlying continuum (spacetime) is assumed, but not in
Bruno's theory.

Brent

That is why I'm not sure that problems with assigning
measures to countably infinite sets (such as your example above re
even and square numbers) are really such a problem.

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 4:09 AM, Pierz wrote:

On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote:

So there are infinitely many identical universes preceding a measurement.
How are
these universes distinct from one another?

They aren't 'distinct'. The hypothesis is that every universe branch contains an
*uncountable* infinity of fungible (identical and interchangeable) universes. While this
seems extravagant, it actually kind of makes more sense than the idea of a universe
splitting into two (where did the second universe come from?). Instead, uncountable
infinities of universes are differentiated from one another. Quantum interference
patterns arise because of the possibility of universes merging back into one another again.

Do they divide into two infinite subsets on a binary measurement, or do
infinitely
many come into existence in order that some branch-counting measure
produces the
right proportion?  Do you not see any problems with assigning a measure to
infinite
countable subsets (are there more even numbers that square numbers?).

The former. Deutsch goes into the problem of infinite countable sets in great detail and
shows how this is *not* a problem for these uncountable infinities (as Russell points
out)), whereas it may be a problem for Bruno's computations - a point I've tried to
argue with Bruno, but he bamboozles my sophomoric maths with his replies. To me it seems
you can't count computations that go through a state, because for every function f that
computes a certain function, there is also some function f1 that also computes f such
that f1 = f + 1 - 1. But maybe that can be solved by counting only the functions with
the least number of steps (?).

And why should we prefer this model to simply saying the Born rule derives
from a
Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

I don't know about Chris Fuchs, although isn't that just Copenhagen?

No, it's an interpretation of QM as personal probabilities, i.e. quantum Bayesianism.  It
reifies information, not quantum states, c.f. http://arxiv.org/pdf/1207.2141.pdf or
http://arxiv.org/pdf/1301.3274.pdf  It's might be compatible with Bruno's ideas where
Copenhagen certainly isn't.

It's clear that one would need strong reasons to favour MWI with its crazy proliferation
of entities, which at first blush seems to run against Occam's razor. However Deutsch
makes a damn good fist of explaining why we in fact have those reasons. For instance,
when a quantum computer calculates a function based on a superposition of states, MWI
can explain where these calculations are occurring - in other universes. The computer is
exploiting the possibility of massive parallelism inherent in that infinity of
universes. It is entirely unclear how these calculations occur in the standard
interpretation. MWI also solves the problem of what happens to non-realized measurement
states once a system decoheres. And of course it gets around the intractable
difficulties of non-computable wave collapse. So it's a case of choose your poison:
infinite universes or conceptual incoherence. I'll take the former, even though in some
ways I'd like the universe (or the multiverse) better if it wasn't that way.

If you just read this list you have the impression that MWI is the consensus true
interpretation of QM; but it's still controversial (as are all other intepretations).  I
highly recommend reading Scott Aaronson's arXiv:1108.1791v3  Why Philosophers Should Care
About Computational Complexity.  Section 8 is his discussion of Deutsch's argument based
on computation.  He gives several reasons why Deutsch's argument, if not actually wrong,
may not mean what people think it means.  Here's the concluding part:

=

One can sharpen the point as follows: if one took the parallel-universes
explanation of how a
quantum computer works too seriously (as many popular writers do!), then it would be
natural to

make further inferences about quantum computing that are flat-out wrong. For
example:

“Using only a thousand quantum bits (or qubits), a quantum computer could store
21000
classical bits.”

This is true only for a bizarre definition of the word “store”! The fundamental problem is
that,

when you measure a quantum computer’s state, you see only one of the possible
outcomes; the
rest disappear. Indeed, a celebrated result called Holevo’s Theorem [74] says that, using
n qubits,
there is no way to store more than n classical bits so that the bits can be reliably
retrieved later.
In other words: for at least one natural definition of “information-carrying capacity,”
qubits have

exactly the same capacity as bits.

To take another example:

“Unlike a classical computer, which can only factor numbers by trying the
divisors one
by one, a quantum computer could try all possible divisors in parallel.”

If quantum computers can harness vast numbers of ```

### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 4:16 AM, Pierz wrote:
And just to follow up on that, there are still an infinite number of irrational numbers
between 0 and 0.1. But not as large an infinity as those between 0.1 and 1.

No, the two are exactly the same uncountable infinity, because there is a 1-to-1 mapping
between them.

So extrapolating to universes, the very low probability, white rabbit universes also
occur an infinite number of times, but that does not make them equally as likely as the
universes which behave as we would classically expect.

But computationalism only produces rational numbers.

Brent

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:

If you subdivide a continuum, I assume you can do so in a way that gives the
required probabilities. For example if the part of the multiverse that is
involved
in performing a quantum measurement with a 50-50 chance of either outcome is
represented by the numbers 0 to 1, you can divide those into 0-0.5 and 0.5
to 1.
Doesn't David do something like this in FOR? (Or is this too plistic?)

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### Re: The probability problem in Everettian quantum mechanics

```I know I shouldn't be flattered to hear that Max Born's great grandson
endorses my view of quantum probability, but.

:D  :D  :D

On 12 October 2013 00:11, Pierz pier...@gmail.com wrote:

That is pretty much exactly my understanding. It does puzzle me that this
argument about the supposed probability problem with MWI is still live,
when that explanation seems perfectly coherent.

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:

If you subdivide a continuum, I assume you can do so in a way that gives
the required probabilities. For example if the part of the multiverse that
is involved in performing a quantum measurement with a 50-50 chance of
either outcome is represented by the numbers 0 to 1, you can divide those
into 0-0.5 and 0.5 to 1. Doesn't David do something like this in FOR? (Or
is this too simplistic?)

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### Re: The probability problem in Everettian quantum mechanics

```On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
On 10/11/2013 2:28 AM, Russell Standish wrote:
On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:
So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).
But infinite subsets in question will contain an uncountable number of
elements.

I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n}, where n is
the number of leading bits in common between x and y). ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

Cheers

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### Re: The probability problem in Everettian quantum mechanics

```On Fri, Oct 11, 2013 at 04:09:20AM -0700, Pierz wrote:
The former. Deutsch goes into the problem of infinite countable sets in
great detail and shows how this is *not* a problem for these uncountable
infinities (as Russell points out)), whereas it may be a problem for

Interesting. I wasn't aware that Deutsch had done that. I was aware of
his critiques of measuring countable sets (such as in the infinity
hotel chapter of BoI), but not that he showed there was no such
problems with uncountable sets. Do you have a reference?

Of course, I take the position that it will be alright on the night,
and give a plausible account of it in my solution of the White Rabbit
problem in my paper Why Occams razor, but that has been criticised,
particularly by Bruno, that the measure issue is not so simple. I
don't feel confident enough in the maths of measure theory to say that
it isn't a problem, just that I can't see a problem in using
Solomonoff's measure. Hence my interest in Deutsch's take.

Cheers

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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 2:46 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:

On 10/11/2013 2:28 AM, Russell Standish wrote:

On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:

So there are infinitely many identical universes preceding a
measurement.  How are these universes distinct from one another?
Do they divide into two infinite subsets on a binary measurement, or
do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not
see any problems with assigning a measure to infinite countable
subsets (are there more even numbers that square numbers?).

But infinite subsets in question will contain an uncountable number of
elements.

I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n}, where n is
the number of leading bits in common between x and y).

Hmm? So 1000 is the same distance from 10 and 111?  What's the measure on this
space?

Brent

ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

Cheers

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### Re: The probability problem in Everettian quantum mechanics

```On 12 October 2013 11:12, LizR lizj...@gmail.com wrote:

On 12 October 2013 10:46, Russell Standish li...@hpcoders.com.au wrote:

On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n},
where n is
the number of leading bits in common between x and y). ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

I always assumed the UD output bits - i.e. not a continuum, but a
countable infinity of symbols - but maybe I'm missing something?

Am I missing diagonalisation? i.e. Can the UD output be diagonalised?

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### Re: The probability problem in Everettian quantum mechanics

```On Sat, Oct 12, 2013 at 11:14:32AM +1300, LizR wrote:
On 12 October 2013 11:12, LizR lizj...@gmail.com wrote:

On 12 October 2013 10:46, Russell Standish li...@hpcoders.com.au wrote:

On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
I don't think being uncountable makes it any easier unless they form
a continuum, which I don't think they do.  I QM an underlying
continuum (spacetime) is assumed, but not in Bruno's theory.

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n},
where n is
the number of leading bits in common between x and y). ISTM, this
metric induces a natural measure over sets of program executions that
is rather continuum like - but maybe I'm missing something?

I always assumed the UD output bits - i.e. not a continuum, but a
countable infinity of symbols - but maybe I'm missing something?

Am I missing diagonalisation? i.e. Can the UD output be diagonalised?

The UD doesn't output anything. If it did, then certainly, the output
could not be an uncountable set due to the diagonalisation argument.

Rather UD* is like the internal view of the operation of the
dovetailer, like the sum of all possible experiences of the Helsinki
man being duplicated to Washington and Moscow that is being discussed
rather a lot lately.

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Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```On Fri, Oct 11, 2013 at 03:08:30PM -0700, meekerdb wrote:
UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n}, where n
is
the number of leading bits in common between x and y).

Hmm? So 1000 is the same distance from 10 and 111?  What's the measure on
this space?

1000... and 101... are 0.25 apart. 1000.. and 111... are 0.5
apart. (the ... refers to an infinite number of bits that are not
relevant to the computation). So the answer to your question is that
these these three strings are not the same distance from each other.

The measure over a set of these things would be something like the
supremum over the distance between any two pairs drawn from the
set. Of course, that assumes that only sets defined by finite length
prefixes, and countable unions and intersections thereof are
considered. My maths chops aren't quite up to generalising this for
arbitrary sets of binary strings.

--

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Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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### Re: The probability problem in Everettian quantum mechanics

```On 12 October 2013 11:35, Russell Standish li...@hpcoders.com.au wrote:

The UD doesn't output anything. If it did, then certainly, the output
could not be an uncountable set due to the diagonalisation argument.

Yes, I wasn't speaking very precisely. Obviously there is no output,
because where would it go? I meant the trace, which I assume is a record of
its operation, which itself exists in arithmetic (I think?)

Rather UD* is like the internal view of the operation of the
dovetailer, like the sum of all possible experiences of the Helsinki
man being duplicated to Washington and Moscow that is being discussed
rather a lot lately.

Ah! Should read to the end :)
Thanks.

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### Re: The probability problem in Everettian quantum mechanics

```

On Saturday, October 12, 2013 5:42:06 AM UTC+11, Brent wrote:

On 10/11/2013 4:16 AM, Pierz wrote:

And just to follow up on that, there are still an infinite number of
irrational numbers between 0 and 0.1. But not as large an infinity as
those between 0.1 and 1.

No, the two are exactly the same uncountable infinity, because there is a
1-to-1 mapping between them.

My mathematical terminology may not be up to scratch. The measure is
different.

So extrapolating to universes, the very low probability, white rabbit
universes also occur an infinite number of times, but that does not make
them equally as likely as the universes which behave as we would
classically expect.

But computationalism only produces rational numbers.

We were talking MWI, where a measure is permitted because of the underlying
physical continuum. It does seem that the measure problem is an open one
for comp, as far as I can tell from Bruno's responses, but he seems
confident it's not insurmountable. I'm not competent to judge.

Brent

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:

If you subdivide a continuum, I assume you can do so in a way that gives
the required probabilities. For example if the part of the multiverse that
is involved in performing a quantum measurement with a 50-50 chance of
either outcome is represented by the numbers 0 to 1, you can divide those
into 0-0.5 and 0.5 to 1. Doesn't David do something like this in FOR? (Or
is this too plistic?)

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### Re: The probability problem in Everettian quantum mechanics

```Haha. The flattery may be undone by learning that your view of quantum
probability is also endorsed by Olivia Newton-John's nephew! :)

On Saturday, October 12, 2013 8:26:23 AM UTC+11, Liz R wrote:

I know I shouldn't be flattered to hear that Max Born's great grandson
endorses my view of quantum probability, but.

:D  :D  :D

On 12 October 2013 00:11, Pierz pie...@gmail.com javascript: wrote:

That is pretty much exactly my understanding. It does puzzle me that this
argument about the supposed probability problem with MWI is still live,
when that explanation seems perfectly coherent.

On Friday, October 11, 2013 10:04:40 PM UTC+11, Liz R wrote:

If you subdivide a continuum, I assume you can do so in a way that gives
the required probabilities. For example if the part of the multiverse that
is involved in performing a quantum measurement with a 50-50 chance of
either outcome is represented by the numbers 0 to 1, you can divide those
into 0-0.5 and 0.5 to 1. Doesn't David do something like this in FOR? (Or
is this too simplistic?)

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 3:44 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 03:08:30PM -0700, meekerdb wrote:

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n}, where n is
the number of leading bits in common between x and y).

Hmm? So 1000 is the same distance from 10 and 111?  What's the measure on this
space?

1000... and 101... are 0.25 apart. 1000.. and 111... are 0.5
apart. (the ... refers to an infinite number of bits that are not
relevant to the computation). So the answer to your question is that
these these three strings are not the same distance from each other.

The measure over a set of these things would be something like the
supremum over the distance between any two pairs drawn from the
set. Of course, that assumes that only sets defined by finite length
prefixes, and countable unions and intersections thereof are
considered. My maths chops aren't quite up to generalising this for
arbitrary sets of binary strings.

Maybe I'm not clear on what UD* means.  I took it to be, at a given state of the UD, the
last bit output by the 1st prog, the last bit output by the 2nd program,...up to the last
prog that the UD has started.  Right?

Brent

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 4:05 PM, Pierz wrote:
It does seem that the measure problem is an open one for comp, as far as I can tell from
Bruno's responses, but he seems confident it's not insurmountable.

Bruno's so confident that he argues that there must be a measure (because he's assumed
comp is true and his argument from comp is valid).  :-)

Brent

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### Re: The probability problem in Everettian quantum mechanics

```On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:

Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and Liz did
also, this morning) a few years ago. I'm not sure anyone has a clear,
crisp mathematical explanation of what UD* is - I certainly don't.

Cheers

--

Prof Russell Standish  Phone 0425 253119 (mobile)
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Visiting Professor of Mathematics  hpco...@hpcoders.com.au
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### Re: The probability problem in Everettian quantum mechanics

```

On Saturday, October 12, 2013 9:07:57 AM UTC+11, Russell Standish wrote:

On Fri, Oct 11, 2013 at 04:09:20AM -0700, Pierz wrote:
The former. Deutsch goes into the problem of infinite countable sets
in
great detail and shows how this is *not* a problem for these uncountable
infinities (as Russell points out)), whereas it may be a problem for

Interesting. I wasn't aware that Deutsch had done that. I was aware of
his critiques of measuring countable sets (such as in the infinity
hotel chapter of BoI), but not that he showed there was no such
problems with uncountable sets. Do you have a reference?

Of course, I take the position that it will be alright on the night,
and give a plausible account of it in my solution of the White Rabbit
problem in my paper Why Occams razor, but that has been criticised,
particularly by Bruno, that the measure issue is not so simple. I
don't feel confident enough in the maths of measure theory to say that
it isn't a problem, just that I can't see a problem in using
Solomonoff's measure. Hence my interest in Deutsch's take.

Cheers

Sorry to disappoint you. I was referring rather to his arguments in BoI
that the measure problem is not an issue for MWI because of the underlying
relationships between the universes (on page 179-180 for instance). It
wasn't actually about uncountable infinities versus countable ones :(

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### Re: The probability problem in Everettian quantum mechanics

```

On Saturday, October 12, 2013 10:08:05 AM UTC+11, Brent wrote:

On 10/11/2013 3:44 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 03:08:30PM -0700, meekerdb wrote:

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n}, where n
is
the number of leading bits in common between x and y).

Hmm? So 1000 is the same distance from 10 and 111?  What's the measure on
this space?

1000... and 101... are 0.25 apart. 1000.. and 111... are 0.5
apart. (the ... refers to an infinite number of bits that are not
relevant to the computation). So the answer to your question is that
these these three strings are not the same distance from each other.

The measure over a set of these things would be something like the
supremum over the distance between any two pairs drawn from the
set. Of course, that assumes that only sets defined by finite length
prefixes, and countable unions and intersections thereof are
considered. My maths chops aren't quite up to generalising this for
arbitrary sets of binary strings.

Maybe I'm not clear on what UD* means.  I took it to be, at a given state
of the UD, the last bit output by the 1st prog, the last bit output by the
2nd program,...up to the last prog that the UD has started.  Right?

Brent

But Russell just said there *is* no output. There are only machine states
(computation X is at step Y and so on). I thought the UD* was the entire
history of computational states the the UD passes through from the moment
it starts up to ... well, forever.

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### Re: The probability problem in Everettian quantum mechanics

```On 12 October 2013 12:06, Pierz pier...@gmail.com wrote:

Haha. The flattery may be undone by learning that your view of quantum
probability is also endorsed by Olivia Newton-John's nephew! :)

OMG!!!

:D :D :D

It's electrifying!

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 4:45 PM, Pierz wrote:

On Saturday, October 12, 2013 10:08:05 AM UTC+11, Brent wrote:

On 10/11/2013 3:44 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 03:08:30PM -0700, meekerdb wrote:

UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n}, where
n is
the number of leading bits in common between x and y).

Hmm? So 1000 is the same distance from 10 and 111?  What's the measure on
this space?

1000... and 101... are 0.25 apart. 1000.. and 111... are 0.5
apart. (the ... refers to an infinite number of bits that are not
relevant to the computation). So the answer to your question is that
these these three strings are not the same distance from each other.

The measure over a set of these things would be something like the
supremum over the distance between any two pairs drawn from the
set. Of course, that assumes that only sets defined by finite length
prefixes, and countable unions and intersections thereof are
considered. My maths chops aren't quite up to generalising this for
arbitrary sets of binary strings.

Maybe I'm not clear on what UD* means.  I took it to be, at a given state
of the UD,
the last bit output by the 1st prog, the last bit output by the 2nd
program,...up to
the last prog that the UD has started.  Right?

Brent

But Russell just said there *is* no output.

I just meant last printed onto the tape.

Brent

There are only machine states (computation X is at step Y and so on). I thought the UD*
was the entire history of computational states the the UD passes through from the moment
it starts up to ... well, forever.

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 4:36 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:

Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and Liz did
also, this morning) a few years ago. I'm not sure anyone has a clear,
crisp mathematical explanation of what UD* is - I certainly don't.

Even if we have the complete record of everything the UD has done up to some point I don't
see how we can define the kind of measure we need over that, because the measure has to be
over all threads of computation corresponding to a particular classical state.

Brent

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### Re: The probability problem in Everettian quantum mechanics

```On Fri, Oct 11, 2013 at 05:46:57PM -0700, meekerdb wrote:
On 10/11/2013 4:36 PM, Russell Standish wrote:
On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:
Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and Liz did
also, this morning) a few years ago. I'm not sure anyone has a clear,
crisp mathematical explanation of what UD* is - I certainly don't.

Even if we have the complete record of everything the UD has done up
to some point I don't see how we can define the kind of measure we
need over that, because the measure has to be over all threads of
computation corresponding to a particular classical state.

And these correspond to a countable union of sets of strings sharing
the same prefix, which is just the Solomonoff-Levin measure.

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### Re: The probability problem in Everettian quantum mechanics

```
On 10/11/2013 7:52 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 05:46:57PM -0700, meekerdb wrote:

On 10/11/2013 4:36 PM, Russell Standish wrote:

On Fri, Oct 11, 2013 at 04:08:05PM -0700, meekerdb wrote:

Maybe I'm not clear on what UD* means.  I took it to be, at a given
state of the UD, the last bit output by the 1st prog, the last bit
output by the 2nd program,...up to the last prog that the UD has
started.  Right?

Its not the output, because the UD doesn't actually output
anything. Rather its an internal view of the states the machines
emulated by the UD pass through, rather like what the Helsinki man
experiences when being duplicated to Moscow and Washington.

Its a subtle point, and I fell into the same trap you did (and Liz did
also, this morning) a few years ago. I'm not sure anyone has a clear,
crisp mathematical explanation of what UD* is - I certainly don't.

Even if we have the complete record of everything the UD has done up
to some point I don't see how we can define the kind of measure we
need over that, because the measure has to be over all threads of
computation corresponding to a particular classical state.

And these correspond to a countable union of sets of strings sharing
the same prefix, which is just the Solomonoff-Levin measure.

But there are infinitely more threads going thru (near) this state which have not yet been
computed.  So the threads counted up to some point are of zero measure. ?

Brent

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### Re: The probability problem in Everettian quantum mechanics

```I'm puzzled by the controversy over this issue - although given that I'm
not a physicist and my understanding comes from popular renditions of MWI
by Deutsch and others, it may be me who's missing the point. But in my
understanding of Deutsch's version of  MWI, the reason for Born
probabilities lies in the fact that there is no such thing as a single
branch. Every branch of the multiverse contains an infinity of identical,
fungible universes. When a quantum event occurs, that set of infinite
universes divides proportionally according to Schroedinger's equation. The
appearance of probability arises, as in Bruno's comp, from multiplication
of the observer in those infinite branches. Why is this problematic?

On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:

mechanics persists. British Jour. Philosophy of Science   IN PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]). The
possible outcomes of measurement as per ‘orthodox’ quantum mechanics are,
in EQM, all instantiated. Given this metaphysics, Everettians face the
‘probability problem’—how to make sense of probabilities, and recover the
Born Rule. To solve the probability problem, Wallace, following Deutsch
([1999]), has derived a quantum representation theorem. I argue that
Wallace’s solution to the probability problem is unsuccessful, as follows.
First, I examine one of the axioms of rationality used to derive the
theorem, Branching Indifference (BI). I argue that Wallace is not
successful in showing that BI is rational. While I think it is correct to
put the burden of proof on Wallace to motivate BI as an axiom of
rationality, it does not follow from his failing to do so that BI is not
rational. Thus, second, I show that there is an alternative strategy for
setting one’s credences in the face of branching which is rational, and
which violates BI. This is Branch Counting (BC). Wallace is aware of BC,
and has proffered various arguments against it. However, third, I argue
that Wallace’s arguments against BC are unpersuasive. I conclude that the
probability problem in EQM persists.

Publications (a Ph.D. in Philosophy, London School of Economics, May 2012)
‘The Probability Problem in Everettian Quantum Mechanics Persists’,
British Journal for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science, 2011
78(5): 976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73: 393-412,
(with R. Frigg and S. Hartmann)
‘Conﬁrmation and Reduction: A Bayesian Account’, Synthese, 2011 179(2):
321-338, (with R. Frigg and S. Hartmann)

His paper may be an interesting read once it comes out. Also available in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas (eds):
Recent Progress in Philosophy of Science: Perspectives and Foundational
Problems, 2013, (The Third European Philosophy of Science Association
Proceedings), Dordrecht: Springer

I think this list needs another discussion of the possible MWI probability
problem although it has been covered here and elsewhere by members of this
list. Previous discussions have not been personally convincing.

Richard

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### Re: The probability problem in Everettian quantum mechanics

```So there are infinitely many identical universes preceding a measurement.  How are these
universes distinct from one another?   Do they divide into two infinite subsets on a
binary measurement, or do infinitely many come into existence in order that some
branch-counting measure produces the right proportion?  Do you not see any problems with
assigning a measure to infinite countable subsets (are there more even numbers that square
numbers?).

And why should we prefer this model to simply saying the Born rule derives from a Bayesian
epistemic view of QM as argued by, for example, Chris Fuchs?

Brent

On 10/10/2013 6:11 PM, Pierz wrote:
I'm puzzled by the controversy over this issue - although given that I'm not a physicist
and my understanding comes from popular renditions of MWI by Deutsch and others, it may
be me who's missing the point. But in my understanding of Deutsch's version of  MWI, the
reason for Born probabilities lies in the fact that there is no such thing as a single
branch. Every branch of the multiverse contains an infinity of identical, fungible
universes. When a quantum event occurs, that set of infinite universes divides
proportionally according to Schroedinger's equation. The appearance of probability
arises, as in Bruno's comp, from multiplication of the observer in those infinite
branches. Why is this problematic?

On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:

mechanics
persists. British Jour. Philosophy of Science   IN PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple, emergent,
branching quasi-classical realities’ (Wallace [2012]). The possible
outcomes of
measurement as per ‘orthodox’ quantum mechanics are, in EQM, all
instantiated. Given
this metaphysics, Everettians face the ‘probability problem’—how to make
sense of
probabilities, and recover the Born Rule. To solve the probability problem,
Wallace,
following Deutsch ([1999]), has derived a quantum representation theorem. I
argue
that Wallace’s solution to the probability problem is unsuccessful, as
follows.
First, I examine one of the axioms of rationality used to derive the
theorem,
Branching Indifference (BI). I argue that Wallace is not successful in
showing that
BI is rational. While I think it is correct to put the burden of proof on
Wallace to
motivate BI as an axiom of rationality, it does not follow from his failing
to do so
that BI is not rational. Thus, second, I show that there is an alternative
strategy
for setting one’s credences in the face of branching which is rational, and
which
violates BI. This is Branch Counting (BC). Wallace is aware of BC, and has
proffered
various arguments against it. However, third, I argue that Wallace’s
arguments
against BC are unpersuasive. I conclude that the probability problem in EQM
persists.

Publications (a Ph.D. in Philosophy, London School of Economics, May 2012)
‘The Probability Problem in Everettian Quantum Mechanics Persists’, British
Journal
for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science, 2011 78(5):
976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73: 393-412, (with
R. Frigg
and S. Hartmann)
‘Conﬁrmation and Reduction: A Bayesian Account’, Synthese, 2011 179(2):
321-338,
(with R. Frigg and S. Hartmann)

His paper may be an interesting read once it comes out. Also available in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas (eds): Recent
Progress
in Philosophy of Science: Perspectives and Foundational Problems, 2013,
(The Third
European Philosophy of Science Association Proceedings), Dordrecht: Springer

I think this list needs another discussion of the possible MWI probability
problem
although it has been covered here and elsewhere by members of this list.
Previous
discussions have not been personally convincing.

Richard

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### Re: The probability problem in Everettian quantum mechanics

```

On 04 Oct 2013, at 23:30, John Mikes wrote:

Richard:
I grew into denying probability in cases where not - ALL -
circumstances are known.

I agree with this. That is why there are many other attempt to study
ignorance and beliefs (like believability theories, which is like
probability, except they can sum and go above 1).
Now I am not sure Dizadji-Bahmani is successful on his critics on
branching indifference, which of ourse can be seen as part of the
first person indeterminacy in the (more general) comp or arithmetical
duplication situations.

Bruno

Since we know only part of the infinite complexity of the WORLD, we
buy in for a mistake if fixing anything like 'probability'.
The same goes for statistical: push the borderlines abit further
away and the COUNT of the studied item (= statistical value) will
change. Also the above argument for probability is valid for results
as 'statistical' values.

JM

On Fri, Oct 4, 2013 at 12:27 PM, Richard Ruquist yann...@gmail.com
wrote:
quantum mechanics persists. British Jour. Philosophy of Science   IN
PRESS.

ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple,
emergent, branching quasi-classical realities’ (Wallace [2012]).
The possible outcomes of measurement as per ‘orthodox’ quantum
mechanics are, in EQM, all instantiated. Given this metaphysics,
Everettians face the ‘probability problem’—how to make sense of
probabilities, and recover the Born Rule. To solve the probability
problem, Wallace, following Deutsch ([1999]), has derived a quantum
representation theorem. I argue that Wallace’s solution to the
probability problem is unsuccessful, as follows. First, I examine
one of the axioms of rationality used to derive the theorem,
Branching Indifference (BI). I argue that Wallace is not successful
in showing that BI is rational. While I think it is correct to put
the burden of proof on Wallace to motivate BI as an axiom of
rationality, it does not follow from his failing to do so that BI is
not rational. Thus, second, I show that there is an alternative
strategy for setting one’s credences in the face of branching which
is rational, and which violates BI. This is Branch Counting (BC).
Wallace is aware of BC, and has proffered various arguments against
it. However, third, I argue that Wallace’s arguments against BC are
unpersuasive. I conclude that the probability problem in EQM persists.

Publications (a Ph.D. in Philosophy, London School of Economics, May
2012)
‘The Probability Problem in Everettian Quantum Mechanics
Persists’, British Journal for Philosophy of Science, forthcoming
‘The Aharanov Approach to Equilibrium’, Philosophy of Science,
2011 78(5): 976-988
‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73:
393-412, (with R. Frigg and S. Hartmann)
‘Conﬁrmation and Reduction: A Bayesian Account’, Synthese, 2011
179(2): 321-338, (with R. Frigg and S. Hartmann)

His paper may be an interesting read once it comes out. Also
available in:
‘Why I am not an Everettian’, in D. Dieks and V. Karakostas
(eds): Recent Progress in Philosophy of Science: Perspectives and
Foundational Problems, 2013, (The Third European Philosophy of
Science Association Proceedings), Dordrecht: Springer

I think this list needs another discussion of the possible MWI
probability problem although it has been covered here and elsewhere
by members of this list. Previous discussions have not been
personally convincing.

Richard

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