Re: Deriving the Born Rule

[Alan Grayson]

On Monday, May 18, 2020 at 7:02:58 PM UTC-6, Bruce wrote:
>
> On Tue, May 19, 2020 at 9:59 AM Alan Grayson  > wrote:
>
>> On Monday, May 18, 2020 at 5:29:04 PM UTC-6, Bruce wrote:
>>>
>>>
>>> I am sorry if I have given the impression that I thought that objective 
>>> probabilities were possible only with frequentism. I thought I had made it 
>>> clear that frequentism fails as a basis for the meaning of probability. 
>>> There are many places where this is argued, and the consensus is that 
>>> long-run relative frequencies cannot be used as a  definition of 
>>> probability.
>>>
>>> I was appealing to the propensity interpretation, which says that 
>>> probabilities are intrinsic properties of some things.; such as decay 
>>> rates; i.e., that probability is an intrinsic property of radio-active 
>>> nuclei. But I agree with Brent, probabilities can be taken to be anything 
>>> that satisfies the basic axioms of probability theory -- such as 
>>> non-negative, normalisable, and additive. So subjective degrees of belief 
>>> can form the basis for probabilities, as can certain symmetry properties, 
>>> relative frequencies, and so on.
>>>
>>> The point is that while these things can be understood as probabilities 
>>> in ordinary usage, they don't actually define what probability is. One can 
>>> use frequency counts to estimate many of these probabilities, and one can 
>>> use Bayes's theorem to update estimates of probability based on new 
>>> evidence. But Bayes's theorem is merely an updating method -- it is not a 
>>> definition of probability. People who consider themselves to be Bayesians 
>>> usually have a basically subjective idea about probability, considering it 
>>> essentially quantifies personal degrees of belief. But that understanding 
>>> is not inherent in Bayes' theorem itself.
>>>
>>> As Brent says, these different approaches to probability have their uses 
>>> in everyday life, but most of them are not suitable for fundamental 
>>> physics. I consider objective probabilities based on intrinsic properties, 
>>> or propensities, to be essential for a proper understanding of radio-active 
>>> decay, and the probability of getting spin-up on a spin measurement, and so 
>>> on. These things are properties of the way the world is, not matters of 
>>> personal belief, or nothing more than relative frequencies. Probabilities 
>>> may well be built into the fabric of the quantum wave-function via the 
>>> amplitudes, but the probabilistic interpretation of these amplitudes has to 
>>> be imposed via the Born rule:  Just as with any mathematical theory -- one 
>>> needs correspondence rules to say how the mathematical elements relate to 
>>> physical observables. From that point of view, attempts to derive the Born 
>>> rule from within the theory are doomed to failure -- contrary to the 
>>> many-worlders' dream, the theory does not contain its own interpretation.
>>>
>>> Bruce
>>>
>>
>> "Propensity" seems pretty vague. Hard to imagine finding an objective 
>> principle underlying probabilities. What precisely does Born's rule mean? 
>> AG 
>>
>
>
> "Propensity" is just a word, the usage originates with Karl Popper, who 
> used it to convey the idea that probability may be a primitive concept, 
> like mass or charge, that is not analysable in terms of anything more 
> fundamental. So you cannot expect to explain the concept in terms of 
> anything else.
>
> The Born rule is really just the statement that quantum mechanics is a 
> theory that predicts probabilities, and those probabilities are given by 
> the mod-squared amplitudes. In other words, it is an interpretative rule, 
> connecting the theory with observation. Seen in this light, it does not 
> make sense to attempt to derive Born's rule from within the theory itself. 
> I think the analysis that I gave at the beginning of this thread is 
> probably the best that one can do -- one shows that the mod-squared 
> amplitudes play the role of probabilities, and that those are the 
> probabilities needed to connect the theory to experiment. The probabilities 
> are objective in that they are already part of the theory:  the amplitudes 
> are objective aspects of the theory.
>
> Bruce
>

I haven't followed every detail of this discussion, but enough to get this 
important point; now I have no idea what the Born's rule means.  Whereas it 
affirms something about "probabilities", it doesn't tell us what this 
means! To quote our Chief Asshole (DJT), Sad! AG  

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Re: Deriving the Born Rule

[smitra]

On 19-05-2020 03:51, Bruce Kellett wrote:

On Tue, May 19, 2020 at 11:16 AM 'Brent Meeker' via Everything List
 wrote:


On 5/18/2020 4:28 PM, Bruce Kellett wrote:


I am sorry if I have given the impression that I thought that
objective probabilities were possible only with frequentism. I
thought I had made it clear that frequentism fails as a basis for
the meaning of probability. There are many places where this is
argued, and the consensus is that long-run relative frequencies
cannot be used as a  definition of probability.

I was appealing to the propensity interpretation, which says that
probabilities are intrinsic properties of some things.; such as
decay rates; i.e., that probability is an intrinsic property of
radio-active nuclei. But I agree with Brent, probabilities can be
taken to be anything that satisfies the basic axioms of
probability theory -- such as non-negative, normalisable, and
additive. So subjective degrees of belief can form the basis for
probabilities, as can certain symmetry properties, relative
frequencies, and so on.

The point is that while these things can be understood as
probabilities in ordinary usage, they don't actually define what
probability is. One can use frequency counts to estimate many of
these probabilities, and one can use Bayes's theorem to update
estimates of probability based on new evidence. But Bayes's
theorem is merely an updating method -- it is not a definition of
probability. People who consider themselves to be Bayesians
usually have a basically subjective idea about probability,
considering it essentially quantifies personal degrees of belief.
But that understanding is not inherent in Bayes' theorem itself.

As Brent says, these different approaches to probability have
their uses in everyday life, but most of them are not suitable for
fundamental physics. I consider objective probabilities based on
intrinsic properties, or propensities, to be essential for a
proper understanding of radio-active decay, and the probability of
getting spin-up on a spin measurement, and so on. These things are
properties of the way the world is, not matters of personal
belief, or nothing more than relative frequencies. Probabilities
may well be built into the fabric of the quantum wave-function via
the amplitudes, but the probabilistic interpretation of these
amplitudes has to be imposed via the Born rule:  Just as with any
mathematical theory -- one needs correspondence rules to say how
the mathematical elements relate to physical observables. From
that point of view, attempts to derive the Born rule from within
the theory are doomed to failure -- contrary to the many-worlders'
dream, the theory does not contain its own interpretation.


But even if you're right (and I think you are) does that affect the
MWI.  In an Everett+Born theory there will still be other worlds and
the interpretation will still avoid the question, "When and where is
a measurement?"...answer "Whenever decoherence has made one state
orthogonal to all other states."   Of course we could then as the
question, "When and where has the wave function collapsed?" and give
the same answer.  Which would be CI+Zurek.


Does this analysis affect the MWI? I think it does, because if
probabilities are intrinsic, and the Born rule is merely a rule that
connects the theory with experiment;  not something that can be
derived from within the theory, then we are left with the tension that
I mentioned a while ago between many-worlds and the probability
interpretation. Everett says that every outcome happens, but separate
outcomes are in separate "relative states", or separate, orthogonal,
branches. This can only mean that the probability is given by branch
counting, and the probabilities are necessarily 50/50 for the
two-state case. Then the probability for each branch on repeated
measurements of an ensemble of N similarly prepared states is 1/2^N,
and those probabilities are independent of the amplitudes. This is
inconsistent with the analysis that gives the probability for each
branch of the repeated trials by the normal binomial probability, with
p equal to the mod-squared amplitude. (This is the analysis with which
I began this thread.) The binomial probabilities are experimentally
observed, so MWI is, on this account, inconsistent with experiment
(even if not actually incoherent).

The question of the preferred basis and the nature of measurement is
answered by decoherence, and the collapse of the wave function is
another interpretative move. On this view, the wave function is
epistemic rather that ontological. The ontology is the particles or
fields that the wave function describes, and these live on ordinary
3-space. This is not necessarily CI+Zurek, because Zurek still thinks
he can derive probabilities from within the theory, and CI does not
encompass decoherence and the quantum nature of everything. Nor is it
Qbism, since that idea does not really encompass objective
probabilities.

Bruce


It's implausible 

"Shape" of the universe

[Philip Thrift]

*Would traveling out in a "straight" line bring you back to where you 
started?*

https://www.forbes.com/sites/startswithabang/2020/05/19/would-a-long-journey-through-the-universe-bring-us-back-to-our-starting-point/#1781c2ccf6c5

In the writer's (Ethan Siegel's) *opinion*:


On a cosmic scale, there is no indication that the Universe is anything 
other than infinite and flat. There is no evidence that features in one 
region of space also appear in any other well-separated region, nor is 
there evidence of a repeating pattern in the Universe's large-scale 
structure or the Big Bang's leftover glow. The only way we know of to turn 
a freely moving object around is via gravitation slingshot, not from cosmic 
curvature.

And yet, it's a legitimate possibility that the Universe may, in fact, be 
finite in extent, but larger than our observations can currently take us. 
As the Universe unfolds over the coming billions of years, more and more of 
it (about 135% more, by volume) will become visible to us. If there's any 
hint that a long-distance journey would bring us back to our starting 
point, that's the only place we'll ever find it. Our only hope for 
discovering a finite but traversible Universe lies, quite ironically, in 
our far distant future.

@philipthrift

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Re: The size of the universe

[Jason Resch]

Hi Brent,

I appreciate your comment. I've updated the article to reflect your
suggestion and credit Friedmann.

Jason

On Mon, May 18, 2020 at 11:21 PM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> Friedmann discovered the expanding universe solution to Einstein's
> equations in 1922, well before Lamaitre.  And Friedmann met with Einstein
> and proposed the expanding universe cosmology to him.  Sadly he died in
> 1925.  Lamaitre independently discovered some of the same solutions in
> 1927.  When he showed them to Einstein, Einstein showed him Friedmann's
> papers.  Lamaitre did invent the term "cosmic atom" and he connected the
> solutions to Hubble's measurements.
>
> Brent
>
> On 5/18/2020 8:20 PM, Jason Resch wrote:
>
> I recently wrote an article on the size of the universe and the scope of
> reality:
> https://alwaysasking.com/how-big-is-the-universe/
>
> It's first of what I hope will be a series of articles which are
> largely inspired by some of the conversations I've enjoyed here. It covers
> many topics including the historic discoveries, the big bang, inflation,
> string theory, and mathematical realism.
>
> Jason
> --
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> 
> .
>
>
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> 
> .
>

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Re: The size of the universe

['Brent Meeker' via Everything List]

Friedmann discovered the expanding universe solution to Einstein's 
equations in 1922, well before Lamaitre.  And Friedmann met with 
Einstein and proposed the expanding universe cosmology to him.  Sadly he 
died in 1925. Lamaitre independently discovered some of the same 
solutions in 1927.  When he showed them to Einstein, Einstein showed him 
Friedmann's papers.  Lamaitre did invent the term "cosmic atom" and he 
connected the solutions to Hubble's measurements.


Brent

On 5/18/2020 8:20 PM, Jason Resch wrote:
I recently wrote an article on the size of the universe and the scope 
of reality:

https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are 
largely inspired by some of the conversations I've enjoyed here. It 
covers many topics including the historic discoveries, the big bang, 
inflation, string theory, and mathematical realism.


Jason
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.


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The size of the universe

[Jason Resch]

I recently wrote an article on the size of the universe and the scope of
reality:
https://alwaysasking.com/how-big-is-the-universe/

It's first of what I hope will be a series of articles which are
largely inspired by some of the conversations I've enjoyed here. It covers
many topics including the historic discoveries, the big bang, inflation,
string theory, and mathematical realism.

Jason

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Re: Deriving the Born Rule

[Bruce Kellett]

On Tue, May 19, 2020 at 11:16 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> On 5/18/2020 4:28 PM, Bruce Kellett wrote:
>
>
> I am sorry if I have given the impression that I thought that objective
> probabilities were possible only with frequentism. I thought I had made it
> clear that frequentism fails as a basis for the meaning of probability.
> There are many places where this is argued, and the consensus is that
> long-run relative frequencies cannot be used as a  definition of
> probability.
>
> I was appealing to the propensity interpretation, which says that
> probabilities are intrinsic properties of some things.; such as decay
> rates; i.e., that probability is an intrinsic property of radio-active
> nuclei. But I agree with Brent, probabilities can be taken to be anything
> that satisfies the basic axioms of probability theory -- such as
> non-negative, normalisable, and additive. So subjective degrees of belief
> can form the basis for probabilities, as can certain symmetry properties,
> relative frequencies, and so on.
>
> The point is that while these things can be understood as probabilities in
> ordinary usage, they don't actually define what probability is. One can use
> frequency counts to estimate many of these probabilities, and one can use
> Bayes's theorem to update estimates of probability based on new evidence.
> But Bayes's theorem is merely an updating method -- it is not a definition
> of probability. People who consider themselves to be Bayesians usually have
> a basically subjective idea about probability, considering it essentially
> quantifies personal degrees of belief. But that understanding is not
> inherent in Bayes' theorem itself.
>
> As Brent says, these different approaches to probability have their uses
> in everyday life, but most of them are not suitable for fundamental
> physics. I consider objective probabilities based on intrinsic properties,
> or propensities, to be essential for a proper understanding of radio-active
> decay, and the probability of getting spin-up on a spin measurement, and so
> on. These things are properties of the way the world is, not matters of
> personal belief, or nothing more than relative frequencies. Probabilities
> may well be built into the fabric of the quantum wave-function via the
> amplitudes, but the probabilistic interpretation of these amplitudes has to
> be imposed via the Born rule:  Just as with any mathematical theory -- one
> needs correspondence rules to say how the mathematical elements relate to
> physical observables. From that point of view, attempts to derive the Born
> rule from within the theory are doomed to failure -- contrary to the
> many-worlders' dream, the theory does not contain its own interpretation.
>
>
> But even if you're right (and I think you are) does that affect the MWI.
> In an Everett+Born theory there will still be other worlds and the
> interpretation will still avoid the question, "When and where is a
> measurement?"...answer "Whenever decoherence has made one state orthogonal
> to all other states."   Of course we could then as the question, "When and
> where has the wave function collapsed?" and give the same answer.  Which
> would be CI+Zurek.
>


Does this analysis affect the MWI? I think it does, because if
probabilities are intrinsic, and the Born rule is merely a rule that
connects the theory with experiment;  not something that can be derived
from within the theory, then we are left with the tension that I mentioned
a while ago between many-worlds and the probability interpretation. Everett
says that every outcome happens, but separate outcomes are in separate
"relative states", or separate, orthogonal, branches. This can only mean
that the probability is given by branch counting, and the probabilities are
necessarily 50/50 for the two-state case. Then the probability for each
branch on repeated measurements of an ensemble of N similarly prepared
states is 1/2^N, and those probabilities are independent of the amplitudes.
This is inconsistent with the analysis that gives the probability for each
branch of the repeated trials by the normal binomial probability, with p
equal to the mod-squared amplitude. (This is the analysis with which I
began this thread.) The binomial probabilities are experimentally observed,
so MWI is, on this account, inconsistent with experiment (even if not
actually incoherent).

The question of the preferred basis and the nature of measurement is
answered by decoherence, and the collapse of the wave function is another
interpretative move. On this view, the wave function is epistemic rather
that ontological. The ontology is the particles or fields that the wave
function describes, and these live on ordinary 3-space. This is not
necessarily CI+Zurek, because Zurek still thinks he can derive
probabilities from within the theory, and CI does not encompass decoherence
and the quantum nature of everything. Nor is it Qbism, since

Re: Deriving the Born Rule

['Brent Meeker' via Everything List]

On 5/18/2020 4:28 PM, Bruce Kellett wrote:
On Mon, May 18, 2020 at 10:57 PM Lawrence Crowell 
> wrote:


On Monday, May 18, 2020 at 12:12:28 AM UTC-5, Brent wrote:



On 5/17/2020 6:20 PM, Lawrence Crowell wrote:

On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:

On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell
 wrote:

There is nothing wrong formally with what you argue.
I would though say this is not entirely the Born
rule. The Born rule connects eigenvalues with the
probabilities of a wave function. For quantum state
amplitudes a_i in a superposition ψ = sum_ia_iφ_i
with φ*_jφ_i = δ_{ij} the spectrum of an observable O
obeys

⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.

Your argument has a tight fit with this for O_i = ρ_{ii}.

The difficulty in part stems from the fact we keep
using standard ideas of probability to understand
quantum physics, which is more fundamentally about
amplitudes which give probabilities, but are not
probabilities. Your argument is very frequentist.



I can see why you might think this, but it is actually
not the case. My main point is to reject subjectivist
notions of probability:  probabilities in QM are clearly
objective -- there is an objective decay rate (or
half-life) for any radioactive nucleus; there is a
clearly objective probability for that spin to be
measured up rather than down in a Stern-Gerlach magnet;
and so on.


Objective probabilities are frequentism.


No necessarily.  Objective probabilities may be based on
symmetries and the principle of insufficient reason.  I agree
with Bruce; just because you measure a probability with
frequency, that doesn't imply it must be based on frequentism.


That is not what I meant. Bruce does sound as if he is appealing
to an objective basis for probability based on the frequency of
occurrences of events. I am not arguing this isy wrong, but rather
that this is an interpretation of probability.



I am sorry if I have given the impression that I thought that 
objective probabilities were possible only with frequentism. I thought 
I had made it clear that frequentism fails as a basis for the meaning 
of probability. There are many places where this is argued, and the 
consensus is that long-run relative frequencies cannot be used as a 
 definition of probability.


I was appealing to the propensity interpretation, which says that 
probabilities are intrinsic properties of some things.; such as decay 
rates; i.e., that probability is an intrinsic property of radio-active 
nuclei. But I agree with Brent, probabilities can be taken to be 
anything that satisfies the basic axioms of probability theory -- such 
as non-negative, normalisable, and additive. So subjective degrees of 
belief can form the basis for probabilities, as can certain symmetry 
properties, relative frequencies, and so on.


The point is that while these things can be understood as 
probabilities in ordinary usage, they don't actually define what 
probability is. One can use frequency counts to estimate many of these 
probabilities, and one can use Bayes's theorem to update estimates of 
probability based on new evidence. But Bayes's theorem is merely an 
updating method -- it is not a definition of probability. People who 
consider themselves to be Bayesians usually have a basically 
subjective idea about probability, considering it essentially 
quantifies personal degrees of belief. But that understanding is not 
inherent in Bayes' theorem itself.


As Brent says, these different approaches to probability have their 
uses in everyday life, but most of them are not suitable for 
fundamental physics. I consider objective probabilities based on 
intrinsic properties, or propensities, to be essential for a proper 
understanding of radio-active decay, and the probability of getting 
spin-up on a spin measurement, and so on. These things are properties 
of the way the world is, not matters of personal belief, or nothing 
more than relative frequencies. Probabilities may well be built into 
the fabric of the quantum wave-function via the amplitudes, but the 
probabilistic interpretation of these amplitudes has to be imposed via 
the Born rule:  Just as with any mathematical theory -- one needs 
correspondence rules to say how the mathematical elements relate to 
physical observables. From that point of view, attempts to derive the 
Born rule from within the theory are doomed to failure -- contrary to 
the many-worlders' dream, the theory does not contain its own 
interpretation.


But even if you're right (a

Re: Deriving the Born Rule

[Bruce Kellett]

On Tue, May 19, 2020 at 9:59 AM Alan Grayson  wrote:

> On Monday, May 18, 2020 at 5:29:04 PM UTC-6, Bruce wrote:
>>
>>
>> I am sorry if I have given the impression that I thought that objective
>> probabilities were possible only with frequentism. I thought I had made it
>> clear that frequentism fails as a basis for the meaning of probability.
>> There are many places where this is argued, and the consensus is that
>> long-run relative frequencies cannot be used as a  definition of
>> probability.
>>
>> I was appealing to the propensity interpretation, which says that
>> probabilities are intrinsic properties of some things.; such as decay
>> rates; i.e., that probability is an intrinsic property of radio-active
>> nuclei. But I agree with Brent, probabilities can be taken to be anything
>> that satisfies the basic axioms of probability theory -- such as
>> non-negative, normalisable, and additive. So subjective degrees of belief
>> can form the basis for probabilities, as can certain symmetry properties,
>> relative frequencies, and so on.
>>
>> The point is that while these things can be understood as probabilities
>> in ordinary usage, they don't actually define what probability is. One can
>> use frequency counts to estimate many of these probabilities, and one can
>> use Bayes's theorem to update estimates of probability based on new
>> evidence. But Bayes's theorem is merely an updating method -- it is not a
>> definition of probability. People who consider themselves to be Bayesians
>> usually have a basically subjective idea about probability, considering it
>> essentially quantifies personal degrees of belief. But that understanding
>> is not inherent in Bayes' theorem itself.
>>
>> As Brent says, these different approaches to probability have their uses
>> in everyday life, but most of them are not suitable for fundamental
>> physics. I consider objective probabilities based on intrinsic properties,
>> or propensities, to be essential for a proper understanding of radio-active
>> decay, and the probability of getting spin-up on a spin measurement, and so
>> on. These things are properties of the way the world is, not matters of
>> personal belief, or nothing more than relative frequencies. Probabilities
>> may well be built into the fabric of the quantum wave-function via the
>> amplitudes, but the probabilistic interpretation of these amplitudes has to
>> be imposed via the Born rule:  Just as with any mathematical theory -- one
>> needs correspondence rules to say how the mathematical elements relate to
>> physical observables. From that point of view, attempts to derive the Born
>> rule from within the theory are doomed to failure -- contrary to the
>> many-worlders' dream, the theory does not contain its own interpretation.
>>
>> Bruce
>>
>
> "Propensity" seems pretty vague. Hard to imagine finding an objective
> principle underlying probabilities. What precisely does Born's rule mean?
> AG
>


"Propensity" is just a word, the usage originates with Karl Popper, who
used it to convey the idea that probability may be a primitive concept,
like mass or charge, that is not analysable in terms of anything more
fundamental. So you cannot expect to explain the concept in terms of
anything else.

The Born rule is really just the statement that quantum mechanics is a
theory that predicts probabilities, and those probabilities are given by
the mod-squared amplitudes. In other words, it is an interpretative rule,
connecting the theory with observation. Seen in this light, it does not
make sense to attempt to derive Born's rule from within the theory itself.
I think the analysis that I gave at the beginning of this thread is
probably the best that one can do -- one shows that the mod-squared
amplitudes play the role of probabilities, and that those are the
probabilities needed to connect the theory to experiment. The probabilities
are objective in that they are already part of the theory:  the amplitudes
are objective aspects of the theory.

Bruce

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Re: Deriving the Born Rule

[Alan Grayson]

On Monday, May 18, 2020 at 5:29:04 PM UTC-6, Bruce wrote:
>
> On Mon, May 18, 2020 at 10:57 PM Lawrence Crowell <
> goldenfield...@gmail.com > wrote:
>
>> On Monday, May 18, 2020 at 12:12:28 AM UTC-5, Brent wrote:
>>>
>>>
>>>
>>> On 5/17/2020 6:20 PM, Lawrence Crowell wrote:
>>>
>>> On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote: 

 On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
 goldenfield...@gmail.com> wrote:

> There is nothing wrong formally with what you argue. I would though 
> say this is not entirely the Born rule. The Born rule connects 
> eigenvalues 
> with the probabilities of a wave function. For quantum state amplitudes 
> a_i 
> in a superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of 
> an 
> observable O obeys
>
> ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.
>
> Your argument has a tight fit with this for O_i = ρ_{ii}.
>
> The difficulty in part stems from the fact we keep using standard 
> ideas of probability to understand quantum physics, which is more 
> fundamentally about amplitudes which give probabilities, but are not 
> probabilities. Your argument is very frequentist.
>


 I can see why you might think this, but it is actually not the case. My 
 main point is to reject subjectivist notions of probability:  
 probabilities 
 in QM are clearly objective -- there is an objective decay rate (or 
 half-life) for any radioactive nucleus; there is a clearly objective 
 probability for that spin to be measured up rather than down in a 
 Stern-Gerlach magnet; and so on.


>>> Objective probabilities are frequentism. 
>>>
>>>
>>> No necessarily.  Objective probabilities may be based on symmetries and 
>>> the principle of insufficient reason.  I agree with Bruce; just because you 
>>> measure a probability with frequency, that doesn't imply it must be based 
>>> on frequentism.
>>>
>>
>> That is not what I meant. Bruce does sound as if he is appealing to an 
>> objective basis for probability based on the frequency of occurrences of 
>> events. I am not arguing this isy wrong, but rather that this is an 
>> interpretation of probability. 
>>
>
>
> I am sorry if I have given the impression that I thought that objective 
> probabilities were possible only with frequentism. I thought I had made it 
> clear that frequentism fails as a basis for the meaning of probability. 
> There are many places where this is argued, and the consensus is that 
> long-run relative frequencies cannot be used as a  definition of 
> probability.
>
> I was appealing to the propensity interpretation, which says that 
> probabilities are intrinsic properties of some things.; such as decay 
> rates; i.e., that probability is an intrinsic property of radio-active 
> nuclei. But I agree with Brent, probabilities can be taken to be anything 
> that satisfies the basic axioms of probability theory -- such as 
> non-negative, normalisable, and additive. So subjective degrees of belief 
> can form the basis for probabilities, as can certain symmetry properties, 
> relative frequencies, and so on.
>
> The point is that while these things can be understood as probabilities in 
> ordinary usage, they don't actually define what probability is. One can use 
> frequency counts to estimate many of these probabilities, and one can use 
> Bayes's theorem to update estimates of probability based on new evidence. 
> But Bayes's theorem is merely an updating method -- it is not a definition 
> of probability. People who consider themselves to be Bayesians usually have 
> a basically subjective idea about probability, considering it essentially 
> quantifies personal degrees of belief. But that understanding is not 
> inherent in Bayes' theorem itself.
>
> As Brent says, these different approaches to probability have their uses 
> in everyday life, but most of them are not suitable for fundamental 
> physics. I consider objective probabilities based on intrinsic properties, 
> or propensities, to be essential for a proper understanding of radio-active 
> decay, and the probability of getting spin-up on a spin measurement, and so 
> on. These things are properties of the way the world is, not matters of 
> personal belief, or nothing more than relative frequencies. Probabilities 
> may well be built into the fabric of the quantum wave-function via the 
> amplitudes, but the probabilistic interpretation of these amplitudes has to 
> be imposed via the Born rule:  Just as with any mathematical theory -- one 
> needs correspondence rules to say how the mathematical elements relate to 
> physical observables. From that point of view, attempts to derive the Born 
> rule from within the theory are doomed to failure -- contrary to the 
> many-worlders' dream, the theory does not contain its own interpretation.
>
> Bruce
>

"Propensity" seems pretty vague. Hard to imagine finding an objec

Re: Deriving the Born Rule

[Bruce Kellett]

On Mon, May 18, 2020 at 10:57 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

> On Monday, May 18, 2020 at 12:12:28 AM UTC-5, Brent wrote:
>>
>>
>>
>> On 5/17/2020 6:20 PM, Lawrence Crowell wrote:
>>
>> On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:
>>>
>>> On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
>>> goldenfield...@gmail.com> wrote:
>>>
 There is nothing wrong formally with what you argue. I would though say
 this is not entirely the Born rule. The Born rule connects eigenvalues with
 the probabilities of a wave function. For quantum state amplitudes a_i in a
 superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an
 observable O obeys

 ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.

 Your argument has a tight fit with this for O_i = ρ_{ii}.

 The difficulty in part stems from the fact we keep using standard ideas
 of probability to understand quantum physics, which is more fundamentally
 about amplitudes which give probabilities, but are not probabilities. Your
 argument is very frequentist.

>>>
>>>
>>> I can see why you might think this, but it is actually not the case. My
>>> main point is to reject subjectivist notions of probability:  probabilities
>>> in QM are clearly objective -- there is an objective decay rate (or
>>> half-life) for any radioactive nucleus; there is a clearly objective
>>> probability for that spin to be measured up rather than down in a
>>> Stern-Gerlach magnet; and so on.
>>>
>>>
>> Objective probabilities are frequentism.
>>
>>
>> No necessarily.  Objective probabilities may be based on symmetries and
>> the principle of insufficient reason.  I agree with Bruce; just because you
>> measure a probability with frequency, that doesn't imply it must be based
>> on frequentism.
>>
>
> That is not what I meant. Bruce does sound as if he is appealing to an
> objective basis for probability based on the frequency of occurrences of
> events. I am not arguing this isy wrong, but rather that this is an
> interpretation of probability.
>


I am sorry if I have given the impression that I thought that objective
probabilities were possible only with frequentism. I thought I had made it
clear that frequentism fails as a basis for the meaning of probability.
There are many places where this is argued, and the consensus is that
long-run relative frequencies cannot be used as a  definition of
probability.

I was appealing to the propensity interpretation, which says that
probabilities are intrinsic properties of some things.; such as decay
rates; i.e., that probability is an intrinsic property of radio-active
nuclei. But I agree with Brent, probabilities can be taken to be anything
that satisfies the basic axioms of probability theory -- such as
non-negative, normalisable, and additive. So subjective degrees of belief
can form the basis for probabilities, as can certain symmetry properties,
relative frequencies, and so on.

The point is that while these things can be understood as probabilities in
ordinary usage, they don't actually define what probability is. One can use
frequency counts to estimate many of these probabilities, and one can use
Bayes's theorem to update estimates of probability based on new evidence.
But Bayes's theorem is merely an updating method -- it is not a definition
of probability. People who consider themselves to be Bayesians usually have
a basically subjective idea about probability, considering it essentially
quantifies personal degrees of belief. But that understanding is not
inherent in Bayes' theorem itself.

As Brent says, these different approaches to probability have their uses in
everyday life, but most of them are not suitable for fundamental physics. I
consider objective probabilities based on intrinsic properties, or
propensities, to be essential for a proper understanding of radio-active
decay, and the probability of getting spin-up on a spin measurement, and so
on. These things are properties of the way the world is, not matters of
personal belief, or nothing more than relative frequencies. Probabilities
may well be built into the fabric of the quantum wave-function via the
amplitudes, but the probabilistic interpretation of these amplitudes has to
be imposed via the Born rule:  Just as with any mathematical theory -- one
needs correspondence rules to say how the mathematical elements relate to
physical observables. From that point of view, attempts to derive the Born
rule from within the theory are doomed to failure -- contrary to the
many-worlders' dream, the theory does not contain its own interpretation.

Bruce

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Re: Vaccines

[Bruce Kellett]

On Fri, May 15, 2020 at 2:41 AM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

> I will say this about Covid-19, seeing as how I am pretty sure I have had
> this. The penultimate worst part of this is the fatigue, at least for me
> who had mild symptoms. I am having less fatigue as time goes on. Right now
> I feel pretty rested and had a good night's sleep. I am though sleeping
> about an extra hour per night. However, there is something worse that comes
> with this. You do not recover and return to what you were. I feel as if
> some neural circuitry has been rewired, I have a different feeling about
> things in general and none of this is for the better. I honestly feel a bit
> more crouchy and more easily irritated. It is as if this virus by some
> means has changed how my brain works or set points on hormonal function.
>
> I can only hope for immunity from this. If immunity is short lived and we
> are destined to get this every year, at least until a vaccine that we will
> have to take annually, this might erode us into walking ruins.
>


It seems that on-going severe fatigue after mild infections with COVIN-19
is quite common. There is a piece on the Australian ABC news site about
this:

https://www.abc.net.au/news/2020-05-19/covid-fatigue-one-of-worst-symptons-patients-say/12252602

So it might take some time for you to get over this.

Bruce

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Coordinate time vs Proper time

[Alan Grayson]

Suppose the universe is a hyper-sphere, not expanding, and an observer 
travels on a closed loop and returns to his spatial starting point. His 
elapsed or proper time will be finite, but what is his coordinate time at 
the end of the journey?  TIA, AG

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Re: Deriving the Born Rule

['Brent Meeker' via Everything List]

On 5/18/2020 4:27 AM, Lawrence Crowell wrote:
Probability and statistics are in part an empirical subject. This is 
not pure mathematics, and it is one reason why there is no single 
foundation. It would be as if linear algebra or any area of 
mathematics had two competing axiomatic foundation. There are also 
subdivisions in the frequentist and subjectivist camps, particularly 
the first of these.


Quantum mechanics computes probabilities not according to some idea of 
incomplete knowledge, but according to amplitudes. There is no lack of 
information from the perspective of the observer or analyst, but it is 
intrinsic. From what I can see this means it is irrelevant whether one 
adopts a Bayesian or frequentist perspective. The division between 
these two approaches to probability correlate somewhat with 
interpretations of QM that are ψ-ontic (aligned with frequentist) 
and ψ-epistemic (aligned with Bayesian). The divisions between the two 
camps amongst statisticians is amazingly sharp and almost hostile. I 
think the issues is somewhat irrelevant.


Probability has several different meanings and people argue over them as 
if one must settle on the real meaning.  But this is a mistake.  Just 
like “cost” or “energy”, “probability” is useful precisely because the 
same value has different interpretations. There are four interpretations 
that commonly come up.


1. It has a mathematical definition that lets us manipulate it and draw 
inferences.

2. It has a physical interpretation as a symmetry.
3. It quantifies a degree of belief that tells us whether to act on it.
4. It has an empirical meaning that lets us measure it.

The usefulness of probability is that we can start with one of these, we 
can then manipulate it mathematically, and then interpret the result in 
one of the other ways.


Brent

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Re: Deriving the Born Rule

['Brent Meeker' via Everything List]

On 5/18/2020 3:29 AM, Bruno Marchal wrote:


On 17 May 2020, at 20:59, 'Brent Meeker' via Everything List 
> wrote:




On 5/17/2020 3:31 AM, Bruno Marchal wrote:


On 17 May 2020, at 11:39, 'scerir' via Everything List 
> wrote:


I vaguely remember that von Weizsaecker wrote (in 'Zeit und 
Wissen') that probability is 'the expectation value of the relative 
frequency'.





That is the frequency approach to probability. Strictly speaking it 
is false, as it gives the wrong results for the “non normal history” 
(normal in the sense of Gauss). But it works retire well in the 
normal world (sorry for being tautological).


At its antipode, there is the bayesian “subjective probabilities”, 
which makes sense when complete information is available . So it 
does not make sense in many practical situation.


Remark: the expression “subjective probabilities” is used 
technically for this Bayesian approach, and is quite different from 
the first person indeterminacy that Everett call “subjective 
probabilities”. The “subjective probabilities” of Everett are 
“objective probabilities”, and can be defined trough a frequency 
operator in the limit.


That's questionable.  For the frequencies to be correct the splitting 
must the uneven.  But there's nothing in the Schoedinger evolution to 
produce this.  If there are two eigenvalues and the Born 
probabilities are 0.5 and 0.5 then it works fine.  But it the Born 
probabilities are 0.501 and 0.499 then there must be a thousand new 
worlds, yet the Schroedinger equation still only predicts two outcomes.


The SWE predicts two fist person outcomes, OK. But the “number” of 
worlds, or of histories, depends on the metaphysical assumptions.


With mechanism it is a bit hard to not see the physical multiverse


Nobody sees the physical multiverse.  It's as much a theoretical 
construct as arithmetic is.


Brent

as a confirmation of the many-computations (many = 2^aleph_0 at 
least!) theorem in (meta)-arithmetic (that is not an interpretation).


Bruno




Brent

The same occur in arithmetic, where the subjective (first person) 
probabilities are objective (they obey objective, sharable, laws).


Naïve many-worlds view are not sustainable, but there is no problem 
with consistent histories, and 0 worlds.


Bruno






Bruce wrote:

It is this subjectivity, and appeal to Bayesianism, that I reject 
for QM. I consider probabilities to be intrinsic properties -- not 
further analysable. In other words, I favour a propensity 
interpretation. Relative frequencies are the way we generally 
measure probabilities, but they do not define them.







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Re: Universe as a simulated strange loop

['Brent Meeker' via Everything List]

On 5/18/2020 3:03 AM, Bruno Marchal wrote:


On 18 May 2020, at 00:45, 'Brent Meeker' via Everything List 
> wrote:




On 5/17/2020 6:29 AM, Bruno Marchal wrote:
the appearance of matter as they are explained by the mechanist 
consciousness flux in arithmetic (itself explained by G and G* and 
their difference).


You frequently say this,


Yes, it is the PhD content.
1) UDA = the constructive reduction of the mind-body problem to the 
necessity of deriving he physical laws from arithmetic.

2) AUDA = the derivation itself.


but I have not seen this explanation except in vague hand waving.


Hand waving?

Your remark does look like hand waving, I would say.

Come on Brent, I am the guy who gives 8 precise mathematical theories, 
three of them being concerned with the appearance of matter in 
arithmetic, and so are testable, and indeed confirmed by all 
experiences until now.


They do not show the appearance of matter, the persistence of objects, 
the shared reality.  You merely assume that they must...since otherwise 
your theory doesn't work.






I refer you to my two last papers(*), which contains also some 
difficult open problems.

You might try to ask specific questions.

/*Marchal B. The computationalist reformulation of the mind-body 
problem. Prog Biophys Mol Biol; 2013 Sep;113(1):127-40

https://www.ncbi.nlm.nih.gov/pubmed/23567157
*/


A good example.  It's behind a paywall, but even the abstract shows that 
it all aspirational.  Nothing is proven about matter except that "If I'm 
right it must be provable."


" We will explain that*once we adopt the computationalist hypothesis*, 
which is a form of mechanist assumption, *we have to derive from it how 
our belief in the physical laws can emerge from *only* arithmetic* and 
classical computer science. In that sense we reduce the mind-body 
problem to a body problem appearance in computer science, or in 
arithmeticThe main point is that the derivation is constructive, and 
it provides the technical*means *to derive physics from arithmetic, and 
this*will make* the computationalist hypothesis empirically testable, 
and thus scientific in the Popperian analysis of science."




/*
Marchal B. The Universal Numbers. From Biology to Physics, Progress in 
Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.

https://www.ncbi.nlm.nih.gov/pubmed/26140993*/

Now, if you read carefully the second part of my Sane04(*) or my 
“Plotinus paper" (larger public) talk, then, if you have read some 
introduction to G and G*, like Smullyan “Forever Undecided” of better” 
Boolos 1979” or even better “Boolos 1993”, you have all the ingredient 
to proceed, and certainly to ask precise and specific question.


OK.  What's your definition of matter?

Brent



/*B. Marchal. The Origin of Physical Laws and Sensations. In 4th 
International System Administration and Network Engineering 
Conference, SANE 2004, Amsterdam, 2004.

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 
(sane04)

Marchal B. A Purely Arithmetical, yet Empirically Falsifiable, 
Interpretation of Plotinus’ Theory of Matter. In Barry Cooper S. Löwe 
B., Kent T. F. and Sorbi A., editors, Computation and Logic in the 
Real World, Third Conference on Computability in Europe June 18-23, 
pages 263–273. Universita degli studi di Sienna, Dipartimento 
di Roberto Magari, 2007.

http://iridia.ulb.ac.be/~marchal/publications/CiE2007/SIENA.pdf*/

Bruno





Brent

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Re: Wolfram Models as Set Substitution Systems

[Philip Thrift]

On Monday, May 18, 2020 at 6:52:30 AM UTC-5, Bruno Marchal wrote:
>
>
> On 15 May 2020, at 21:12, Philip Thrift > 
> wrote:
>
>
>
> On Friday, May 15, 2020 at 11:08:44 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 14 May 2020, at 12:09, Philip Thrift  wrote:
>>
>> This is true!
>>
>> https://en.wikipedia.org/wiki/The_Laundry_Files
>>
>>  "Magic " is described 
>> as being a branch of applied computation (mathematics), therefore computers 
>> and equations are just as useful, and perhaps more potent, than classic 
>> spellbooks, pentagrams, and sigils for the purpose of influencing ancient 
>> powers and opening gates to other dimensions. 
>>
>>
>>
>>
>> I don’t believe in “real magic”. If time travel was possible and a 
>> time-traveller comes back with a documentary showing Jesus making water 
>> into wine, I would still consider that the most plausible explanation would 
>> be that Jesus is a good prestidigitator. 
>>
>> Why? Just by considering the degree of credulity of the humans, and their 
>> craft in prestidigitation. 
>>
>> Similarly, I find far more reasonable, even “Occam-reasonable” that the 
>> appearance of a physical universe is due to number’s prestidigitation, 
>> because incompleteness shows the numbers being both terribly naïve, but 
>> also incredibly gifted in the art of making their fellow number believing 
>> almost everything. Gödel’s theorem warned us; if we are consistent, it is 
>> even consistent that we are inconsistent (<>t -> <>[]f).
>>
>> Computationalism is Prestidigitalism. Lol. 
>>
>> Wolfram is correct about “[]p”, but forget completely []p & p (and thus 
>> missed physics, theology, etc.)
>>
>> At least Penrose is aware of the abyssal difference between “[]p” and 
>> “[]p & p”, but literally confusse them in its use of Gödel’s incompleteness 
>> against Mechanism.
>>
>> So, with respect to metaphysics and to the Mind-Body problem in the frame 
>> of Descartes-Darwin Mechanism, we can say that Penrose is less wrong than 
>> Wolfram, and more interestingly-wrong.
>>
>> I am not claiming that Penrose or Wolfram are wrong. I am just comparing 
>> them with the canonical theology of the universal machine, that is, with 
>> the 8 modes of self-truth/belief/knowledge/observation/sensation of the 
>> universal machine having enough induction beliefs/axioms, in any hard or 
>> soft relative implementation.
>>
>> Those modes can be motivated through Mechanist thought experiments and/or 
>> through the Theaetetus of Plato.
>>
>> Bruno
>>
>>
>>
>>
>>
>
> Wolfram thinks that his H*ypergraphic Universe Modeling (HUM) language* 
> can lead to a unified QM+GR theory.
>
> Do you think consciousness is needed for this unification?
>
>
> Not necessarily, in the sense that it is still possible to conceive a 
> theory of "everything physical” which would be logically independent of a 
> theory of consciousness, as far as we are interested in predicting first 
> person plural observation.
>
> But such a theory would be cut from reality, as it would not be able to 
> explain why our consciousness satisfies those prediction, so it would not 
> be a theory of everything.
>
> To get that theory of everything including mind and consciousness, there 
> are two options: a mechanist theory of mind, or a non mechanist theory of 
> mind. With a mechanist theory, you will need to derive the “theory of 
> everything-physical” from arithmetic. I don’t see any other way to get a 
> theory of consciousness adequate with the physical observation.
> With a non-mechanist theory of mind, everything remains open, if only 
> because such a theory of mind does not exist (except in faith tales).
>
> Bruno
>
>
The get a theory of consciousness (or experience), one starts with a 
"sixth" force/field, allowing for the other five -  
https://en.wikipedia.org/wiki/Fifth_force- around now.

It's nature would be "localized" in a way different from the other five (or 
four).

And no one knows what gravity - for example - really is either, aside from 
some mathematical formulas - we invented - matching its "behavior".

@philipthrift


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Re: Deriving the Born Rule

['scerir' via Everything List]

<>

“One may call these uncertainties [i.e. the Born probabilities] objective, in 
that they are simply a consequence of the fact that we describe the experiment 
in terms of classical physics; they do not depend in detail on the observer. 
One may call them subjective, in that they reflect our incomplete knowledge of 
the world.” (Heisenberg)


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Re: Deriving the Born Rule

[Lawrence Crowell]

On Monday, May 18, 2020 at 12:12:28 AM UTC-5, Brent wrote:
>
>
>
> On 5/17/2020 6:20 PM, Lawrence Crowell wrote:
>
> On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote: 
>>
>> On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>>> There is nothing wrong formally with what you argue. I would though say 
>>> this is not entirely the Born rule. The Born rule connects eigenvalues with 
>>> the probabilities of a wave function. For quantum state amplitudes a_i in a 
>>> superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an 
>>> observable O obeys
>>>
>>> ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.
>>>
>>> Your argument has a tight fit with this for O_i = ρ_{ii}.
>>>
>>> The difficulty in part stems from the fact we keep using standard ideas 
>>> of probability to understand quantum physics, which is more fundamentally 
>>> about amplitudes which give probabilities, but are not probabilities. Your 
>>> argument is very frequentist.
>>>
>>
>>
>> I can see why you might think this, but it is actually not the case. My 
>> main point is to reject subjectivist notions of probability:  probabilities 
>> in QM are clearly objective -- there is an objective decay rate (or 
>> half-life) for any radioactive nucleus; there is a clearly objective 
>> probability for that spin to be measured up rather than down in a 
>> Stern-Gerlach magnet; and so on.
>>
>>
> Objective probabilities are frequentism. 
>
>
> No necessarily.  Objective probabilities may be based on symmetries and 
> the principle of insufficient reason.  I agree with Bruce; just because you 
> measure a probability with frequency, that doesn't imply it must be based 
> on frequentism.
>

That is not what I meant. Bruce does sound as if he is appealing to an 
objective basis for probability based on the frequency of occurrences of 
events. I am not arguing this isy wrong, but rather that this is an 
interpretation of probability. 

LC
 

>
> The idea from a probability perspective is that one has a sample space 
> with a known distribution. Your argument, which I agree was my first 
> impression when I encountered the Bayesian approach to QM by Fuchs and 
> Schack, who I have had occasions to talk to. My impression right way was 
> entirely the same; we have operators with outcomes and they have a 
> distribution etc according to Born rule. However, we have a bit of a 
> sticking point; is Born's rule really provable? We most often think in a 
> sample space frequentist manner with regards to the Born rule. However, it 
> is at least plausible to think of the problem from a Bayesian perspective, 
> and where the probabilities have become known is when the Bayesian updates 
> have become very precise. 
>
> However, all this talk of probability theory may itself be wrong. Quantum 
> mechanics derives probabilities or distributions or spectra, but it really 
> is a theory of amplitudes or the density matrix. The probabilities come 
> with modulus square or the trace over the density matrix. Framing QM around 
> an interpretation of probability may be wrong headed to begin with.
>
>
> But if it's not just mathematics, there has to be some way to make contact 
> with experiment...which for probabilistic predictions usually means 
> frequencies.
>
> Brent
>
>  
>
>>
>> The argument by Carroll and Sebens, using a concept of the wave function 
>>> as an update mechanism, is somewhat Bayesian.
>>>
>>
>>
>> It is this subjectivity, and appeal to Bayesianism, that I reject for QM. 
>> I consider probabilities to be intrinsic properties -- not further 
>> analysable. In other words, I favour a propensity interpretation. Relative 
>> frequencies are the way we generally measure probabilities, but they do not 
>> define them.
>>
>>
> I could I suppose talk to Fuchs about this. He regards QM as having this 
> uncertainty principle, which we can only infer probabilities with a large 
> number of experiments where upon we update Bayesian priors. Of course a 
> frequentists, or a system based on relative frequencies, would say we just 
> make lots of measurements and use that as a sample space. In the end either 
> way works because QM appears to be a pure system that derives 
> probabilities. In other words, since outcome occur acausally or 
> spontaneously there are not meddlesome issues of incomplete knowledge. 
> Because of this, and I have pointed it out, the two perspective end up 
> being largely equivalent.
>  
>
>>
>> This is curious since Fuchs developed QuBism as a sort of 
>>> ultra-ψ-epistemic interpretation, and Carroll and Sebens are appealing to 
>>> the wave function as a similar device for a ψ-ontological interpretation.
>>>
>>> I do though agree if there is a proof for the Born rule that is may not 
>>> depend on some particular quantum interpretation. If the Born rule is some 
>>> unprovable postulate then it would seem plausible that any sufficiently 
>>> strong quantum interpretation may prove the Bo

Re: Deriving the Born Rule

[Philip Thrift]

On Monday, May 18, 2020 at 6:27:34 AM UTC-5, Lawrence Crowell wrote:
>
>
>
>>
> Probability and statistics are in part an empirical subject. This is not 
> pure mathematics, and it is one reason why there is no single foundation. 
> It would be as if linear algebra or any area of mathematics had two 
> competing axiomatic foundation. There are also subdivisions in the 
> frequentist and subjectivist camps, particularly the first of these. 
>
> Quantum mechanics computes probabilities not according to some idea of 
> incomplete knowledge, but according to amplitudes. There is no lack of 
> information from the perspective of the observer or analyst, but it is 
> intrinsic. From what I can see this means it is irrelevant whether one 
> adopts a Bayesian or frequentist perspective. The division between these 
> two approaches to probability correlate somewhat with interpretations of QM 
> that are ψ-ontic (aligned with frequentist) and ψ-epistemic (aligned with 
> Bayesian). 
> The divisions between the two camps amongst statisticians is amazingly 
> sharp and almost hostile. I think the issues is somewhat irrelevant. 
>
> LC
>  
>
>>
>>
All of this is an opinion, and its painful to read.

Probability Theory  can be just as much a subject of Pure mathematics as 
Group Theory or Real Analysis.

Quantum mechanics computes probabilities not according to some idea of 
incomplete knowledge

That some physicists think this is their problem.

@philipthrift

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Re: Wolfram Models as Set Substitution Systems

[Bruno Marchal]

> On 15 May 2020, at 21:12, Philip Thrift  wrote:
> 
> 
> 
> On Friday, May 15, 2020 at 11:08:44 AM UTC-5, Bruno Marchal wrote:
> 
>> On 14 May 2020, at 12:09, Philip Thrift > 
>> wrote:
>> 
>> This is true!
>> 
>> https://en.wikipedia.org/wiki/The_Laundry_Files 
>> 
>> 
>>  "Magic " is described as 
>> being a branch of applied computation (mathematics), therefore computers and 
>> equations are just as useful, and perhaps more potent, than classic 
>> spellbooks, pentagrams, and sigils for the purpose of influencing ancient 
>> powers and opening gates to other dimensions. 
> 
> 
> 
> I don’t believe in “real magic”. If time travel was possible and a 
> time-traveller comes back with a documentary showing Jesus making water into 
> wine, I would still consider that the most plausible explanation would be 
> that Jesus is a good prestidigitator. 
> 
> Why? Just by considering the degree of credulity of the humans, and their 
> craft in prestidigitation. 
> 
> Similarly, I find far more reasonable, even “Occam-reasonable” that the 
> appearance of a physical universe is due to number’s prestidigitation, 
> because incompleteness shows the numbers being both terribly naïve, but also 
> incredibly gifted in the art of making their fellow number believing almost 
> everything. Gödel’s theorem warned us; if we are consistent, it is even 
> consistent that we are inconsistent (<>t -> <>[]f).
> 
> Computationalism is Prestidigitalism. Lol. 
> 
> Wolfram is correct about “[]p”, but forget completely []p & p (and thus 
> missed physics, theology, etc.)
> 
> At least Penrose is aware of the abyssal difference between “[]p” and “[]p & 
> p”, but literally confusse them in its use of Gödel’s incompleteness against 
> Mechanism.
> 
> So, with respect to metaphysics and to the Mind-Body problem in the frame of 
> Descartes-Darwin Mechanism, we can say that Penrose is less wrong than 
> Wolfram, and more interestingly-wrong.
> 
> I am not claiming that Penrose or Wolfram are wrong. I am just comparing them 
> with the canonical theology of the universal machine, that is, with the 8 
> modes of self-truth/belief/knowledge/observation/sensation of the universal 
> machine having enough induction beliefs/axioms, in any hard or soft relative 
> implementation.
> 
> Those modes can be motivated through Mechanist thought experiments and/or 
> through the Theaetetus of Plato.
> 
> Bruno
> 
> 
> 
> 
> 
> 
> Wolfram thinks that his Hypergraphic Universe Modeling (HUM) language can 
> lead to a unified QM+GR theory.
> 
> Do you think consciousness is needed for this unification?

Not necessarily, in the sense that it is still possible to conceive a theory of 
"everything physical” which would be logically independent of a theory of 
consciousness, as far as we are interested in predicting first person plural 
observation.

But such a theory would be cut from reality, as it would not be able to explain 
why our consciousness satisfies those prediction, so it would not be a theory 
of everything.

To get that theory of everything including mind and consciousness, there are 
two options: a mechanist theory of mind, or a non mechanist theory of mind. 
With a mechanist theory, you will need to derive the “theory of 
everything-physical” from arithmetic. I don’t see any other way to get a theory 
of consciousness adequate with the physical observation.
With a non-mechanist theory of mind, everything remains open, if only because 
such a theory of mind does not exist (except in faith tales).

Bruno


> 
> That would be bizarre.






> 
> @philipthrift
> 
> 
> 
> 
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Re: Deriving the Born Rule

[Bruce Kellett]

On Mon, May 18, 2020 at 9:27 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

> On Sunday, May 17, 2020 at 9:06:12 PM UTC-5, Bruce wrote:
>>
>> On Mon, May 18, 2020 at 11:20 AM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>>>
>>> Objective probabilities are frequentism.
>>>
>>
>>
>> Rubbish. Popper's original propensity ideas may have had frequentist
>> overtones, but we can certainly move beyond Popper's outdated thinking. An
>> objective probability is one that is an intrinsic property of an object,
>> such as a radio-active nucleus. One can use relative frequencies or
>> Bayesian updating to estimate these intrinsic probabilities experimentally.
>> But neither relative frequencies nor Bayesian updating of subjective
>> beliefs actually define what the probabilities are in quantum mechanics.
>>
>>
> Probability and statistics are in part an empirical subject. This is not
> pure mathematics, and it is one reason why there is no single foundation.
> It would be as if linear algebra or any area of mathematics had two
> competing axiomatic foundation. There are also subdivisions in the
> frequentist and subjectivist camps, particularly the first of these.
>
> Quantum mechanics computes probabilities not according to some idea of
> incomplete knowledge, but according to amplitudes. There is no lack of
> information from the perspective of the observer or analyst, but it is
> intrinsic. From what I can see this means it is irrelevant whether one
> adopts a Bayesian or frequentist perspective. The division between these
> two approaches to probability correlate somewhat with interpretations of QM
> that are ψ-ontic (aligned with frequentist) and ψ-epistemic (aligned with 
> Bayesian).
> The divisions between the two camps amongst statisticians is amazingly
> sharp and almost hostile. I think the issues is somewhat irrelevant.
>


OK. So stick with instrumentalism then.

Bruce

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Re: Deriving the Born Rule

[Lawrence Crowell]

On Sunday, May 17, 2020 at 9:06:12 PM UTC-5, Bruce wrote:
>
> On Mon, May 18, 2020 at 11:20 AM Lawrence Crowell <
> goldenfield...@gmail.com > wrote:
>
>> On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:
>>>
>>> On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
>>> goldenfield...@gmail.com> wrote:
>>>
 There is nothing wrong formally with what you argue. I would though say 
 this is not entirely the Born rule. The Born rule connects eigenvalues 
 with 
 the probabilities of a wave function. For quantum state amplitudes a_i in 
 a 
 superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an 
 observable O obeys

 ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.

 Your argument has a tight fit with this for O_i = ρ_{ii}.

 The difficulty in part stems from the fact we keep using standard ideas 
 of probability to understand quantum physics, which is more fundamentally 
 about amplitudes which give probabilities, but are not probabilities. Your 
 argument is very frequentist.

>>>
>>>
>>> I can see why you might think this, but it is actually not the case. My 
>>> main point is to reject subjectivist notions of probability:  probabilities 
>>> in QM are clearly objective -- there is an objective decay rate (or 
>>> half-life) for any radioactive nucleus; there is a clearly objective 
>>> probability for that spin to be measured up rather than down in a 
>>> Stern-Gerlach magnet; and so on.
>>>
>>>
>> Objective probabilities are frequentism.
>>
>
>
> Rubbish. Popper's original propensity ideas may have had frequentist 
> overtones, but we can certainly move beyond Popper's outdated thinking. An 
> objective probability is one that is an intrinsic property of an object, 
> such as a radio-active nucleus. One can use relative frequencies or 
> Bayesian updating to estimate these intrinsic probabilities experimentally. 
> But neither relative frequencies nor Bayesian updating of subjective 
> beliefs actually define what the probabilities are in quantum mechanics.
>
>
Probability and statistics are in part an empirical subject. This is not 
pure mathematics, and it is one reason why there is no single foundation. 
It would be as if linear algebra or any area of mathematics had two 
competing axiomatic foundation. There are also subdivisions in the 
frequentist and subjectivist camps, particularly the first of these. 

Quantum mechanics computes probabilities not according to some idea of 
incomplete knowledge, but according to amplitudes. There is no lack of 
information from the perspective of the observer or analyst, but it is 
intrinsic. From what I can see this means it is irrelevant whether one 
adopts a Bayesian or frequentist perspective. The division between these 
two approaches to probability correlate somewhat with interpretations of QM 
that are ψ-ontic (aligned with frequentist) and ψ-epistemic (aligned with 
Bayesian). 
The divisions between the two camps amongst statisticians is amazingly 
sharp and almost hostile. I think the issues is somewhat irrelevant. 

LC
 

>
> The idea from a probability perspective is that one has a sample space 
>> with a known distribution.
>>
>
> These are consequences of the existence of probabilities -- not a 
> definition of them.
>
> Your argument, which I agree was my first impression when I encountered 
>> the Bayesian approach to QM by Fuchs and Schack, who I have had occasions 
>> to talk to. My impression right way was entirely the same; we have 
>> operators with outcomes and they have a distribution etc according to Born 
>> rule. However, we have a bit of a sticking point; is Born's rule really 
>> provable? We most often think in a sample space frequentist manner with 
>> regards to the Born rule. However, it is at least plausible to think of the 
>> problem from a Bayesian perspective, and where the probabilities have 
>> become known is when the Bayesian updates have become very precise. 
>>
>
> Again, you are confusing measuring or estimating the probabilities with 
> their definition. Propensities are intrinsic properties, not further 
> analysable. Whether or not the Born rule can be derived from simpler 
> principles is far from clear. I don't think the attempts based on decision 
> theory (Deutsch, Wallace, etc) succeed, and attempts based on self-location 
> (Carroll, Zurek) are far from convincing, since they are probably 
> intrinsically dualist.
>
> However, all this talk of probability theory may itself be wrong. Quantum 
>> mechanics derives probabilities or distributions or spectra, but it really 
>> is a theory of amplitudes or the density matrix. The probabilities come 
>> with modulus square or the trace over the density matrix. Framing QM around 
>> an interpretation of probability may be wrong headed to begin with.
>>
>
>
>
> The basic feature of quantum mechanics is that it predicts probabilities. 
> You confuse the way this is expressed in the theory with t

Re: Deriving the Born Rule

[Bruno Marchal]

> On 17 May 2020, at 20:59, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 5/17/2020 3:31 AM, Bruno Marchal wrote:
>> 
>>> On 17 May 2020, at 11:39, 'scerir' via Everything List 
>>> >> > wrote:
>>> 
>>> I vaguely remember that von Weizsaecker wrote (in 'Zeit und Wissen') that 
>>> probability is 'the expectation value of the relative frequency'.
>>> 
>>> 
>> 
>> That is the frequency approach to probability. Strictly speaking it is 
>> false, as it gives the wrong results for the “non normal history” (normal in 
>> the sense of Gauss). But it works retire well in the normal world (sorry for 
>> being tautological).
>> 
>> At its antipode, there is the bayesian “subjective probabilities”, which 
>> makes sense when complete information is available . So it does not make 
>> sense in many practical situation.
>> 
>> Remark: the expression “subjective probabilities” is used technically for 
>> this Bayesian approach, and is quite different from the first person 
>> indeterminacy that Everett call “subjective probabilities”. The “subjective 
>> probabilities” of Everett are “objective probabilities”, and can be defined 
>> trough a frequency operator in the limit.
> 
> That's questionable.  For the frequencies to be correct the splitting must 
> the uneven.  But there's nothing in the Schoedinger evolution to produce 
> this.  If there are two eigenvalues and the Born probabilities are 0.5 and 
> 0.5 then it works fine.  But it the Born probabilities are 0.501 and 0.499 
> then there must be a thousand new worlds,  yet the Schroedinger equation 
> still only predicts two outcomes.

The SWE predicts two fist person outcomes, OK. But the “number” of worlds, or 
of histories, depends on the metaphysical assumptions.

With mechanism it is a bit hard to not see the physical multiverse as a 
confirmation of the many-computations (many = 2^aleph_0 at least!) theorem in 
(meta)-arithmetic (that is not an interpretation). 

Bruno


> 
> Brent
> 
>> The same occur in arithmetic, where the subjective (first person) 
>> probabilities are objective (they obey objective, sharable, laws).
>> 
>> Naïve many-worlds view are not sustainable, but there is no problem with 
>> consistent histories, and 0 worlds.
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> 
 Bruce wrote: 
 
 It is this subjectivity, and appeal to Bayesianism, that I reject for QM. 
 I consider probabilities to be intrinsic properties -- not further 
 analysable. In other words, I favour a propensity interpretation. Relative 
 frequencies are the way we generally measure probabilities, but they do 
 not define them.
 
 
 
>>> 
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Re: Universe as a simulated strange loop

[Bruno Marchal]

> On 18 May 2020, at 00:45, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 5/17/2020 6:29 AM, Bruno Marchal wrote:
>> the appearance of matter as they are explained by the mechanist 
>> consciousness flux in arithmetic (itself explained by G and G* and their 
>> difference).
> 
> You frequently say this,

Yes, it is the PhD content. 
1) UDA = the constructive reduction of the mind-body problem to the necessity 
of deriving he physical laws from arithmetic. 
2) AUDA = the derivation itself.

> but I have not seen this explanation except in vague hand waving.

Hand waving?

Your remark does look like hand waving, I would say.

Come on Brent, I am the guy who gives 8 precise mathematical theories, three of 
them being concerned with the appearance of matter in arithmetic, and so are 
testable, and indeed confirmed by all experiences until now.

I refer you to my two last papers(*), which contains also some difficult open 
problems.
You might try to ask specific questions.

Marchal B. The computationalist reformulation of the mind-body problem. Prog 
Biophys Mol Biol; 2013 Sep;113(1):127-40
https://www.ncbi.nlm.nih.gov/pubmed/23567157

Marchal B. The Universal Numbers. From Biology to Physics, Progress in 
Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.
https://www.ncbi.nlm.nih.gov/pubmed/26140993

Now, if you read carefully the second part of my Sane04(*) or my “Plotinus 
paper" (larger public) talk, then, if you have read some introduction to G and 
G*, like Smullyan “Forever Undecided” of better” Boolos 1979” or even better 
“Boolos 1993”, you have all the ingredient to proceed, and certainly to ask 
precise and specific question.

B. Marchal. The Origin of Physical Laws and Sensations. In 4th International 
System Administration and Network Engineering Conference, SANE 2004, Amsterdam, 
2004.
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 
(sane04)

Marchal B. A Purely Arithmetical, yet Empirically Falsifiable, Interpretation of 
Plotinus’ Theory of Matter. In Barry Cooper S. Löwe B., Kent T. F. and Sorbi 
A., editors, Computation and Logic in the Real World, Third Conference on 
Computability in Europe June 18-23, pages 263–273. Universita degli studi di 
Sienna, Dipartimento di Roberto Magari, 2007.
http://iridia.ulb.ac.be/~marchal/publications/CiE2007/SIENA.pdf

Bruno



> 
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Re: Deriving the Born Rule

[Philip Thrift]

On Sunday, May 17, 2020 at 8:20:01 PM UTC-5, Lawrence Crowell wrote:
>
>
>
> However, all this talk of probability theory may itself be wrong. Quantum 
> mechanics derives probabilities or distributions or spectra, but it really 
> is a theory of amplitudes or the density matrix. The probabilities come 
> with modulus square or the trace over the density matrix. Framing QM around 
> an interpretation of probability may be wrong headed to begin with.
>  
> LC
>

Physicists *frequently*  talk as if QM was defined by God writing its 
formulation into stone in front of Moses, like religious fundamentalists 
talk.

There are measure/probability theoretic formulations of QM  that do not 
come from any "density matrix" or Hilbert space but from their 
measure/probability spaces.

@philipthift






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Re: Deriving the Born Rule

[Alan Grayson]

On Sunday, May 17, 2020 at 4:32:13 PM UTC-6, Bruce wrote:
>
> On Mon, May 18, 2020 at 5:18 AM smitra > 
> wrote:
>
>>
>> Deriving the Born rule within the context of QM seems to me a rather 
>> futile effort as you still have the formalism of QM itself that is then 
>> unexplained. So, I think one has to tackle QM itself. It seems t me 
>> quite plausible that QM gives an approximate description of a multiverse 
>> of algorithms. So, we are then members of such a multiverse, this then 
>> includes alternative versions of us who found different results in 
>> experiments, but the global structure of this multiverse is something 
>> that QM does not describe adequately.
>>
>> QM then gives a local approximation of this multiverse that's valid in 
>> the neighborhood of a given algorithm, That algorithm can be an observer 
>> who has found some experimental result, and the local approximation 
>> gives a description of the "nearby algorithms" that are processing 
>> alternative measurement results. The formalism of QM can then arise due 
>> to having to sum over all algorithms that fall within the criterion of 
>> being close to the particular algorithm that is processing some 
>> particular data. This is then a constrained summation over all possible 
>> algorithms. One can then replace such a constrained summation by an 
>> unrestricted summation and implement the constraint by including phase 
>> factors of the form exp(i u constraint function) where constraint 
>> function = 0 for the terms of the original constrained summation. One 
>> can then write the original summation as an integral over u.
>>
>
> And that is all hopelessly ad hoc, without a shred of evidence.
>
> Bruce
>

We don't need no stinkin' evidence. AG 

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Re: Deriving the Born Rule

[smitra]

On 18-05-2020 00:31, Bruce Kellett wrote:

On Mon, May 18, 2020 at 5:18 AM smitra  wrote:


Deriving the Born rule within the context of QM seems to me a rather

futile effort as you still have the formalism of QM itself that is
then
unexplained. So, I think one has to tackle QM itself. It seems t me
quite plausible that QM gives an approximate description of a
multiverse
of algorithms. So, we are then members of such a multiverse, this
then
includes alternative versions of us who found different results in
experiments, but the global structure of this multiverse is
something
that QM does not describe adequately.

QM then gives a local approximation of this multiverse that's valid
in
the neighborhood of a given algorithm, That algorithm can be an
observer
who has found some experimental result, and the local approximation
gives a description of the "nearby algorithms" that are processing
alternative measurement results. The formalism of QM can then arise
due
to having to sum over all algorithms that fall within the criterion
of
being close to the particular algorithm that is processing some
particular data. This is then a constrained summation over all
possible
algorithms. One can then replace such a constrained summation by an
unrestricted summation and implement the constraint by including
phase
factors of the form exp(i u constraint function) where constraint
function = 0 for the terms of the original constrained summation.
One
can then write the original summation as an integral over u.


And that is all hopelessly ad hoc, without a shred of evidence.

Bruce


That's true for everything that has ever been said about this subject. 
If there were evidence then the matter would have been settled already.


Saibal

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