### Re: Recommend this article, Even just for the Wheeler quote near the end

```

On Monday, February 25, 2019 at 9:42:01 AM UTC-6, Bruno Marchal wrote:
>
>
> On 25 Feb 2019, at 12:39, Lawrence Crowell  > wrote:
>
> On Monday, February 25, 2019 at 2:44:14 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 24 Feb 2019, at 15:24, Lawrence Crowell
>> wrote:
>>
>> On Friday, February 22, 2019 at 3:18:01 PM UTC-6, Brent wrote:
>>>
>>>
>>>
>>> On 2/22/2019 11:39 AM, Lawrence Crowell wrote:
>>>
>>> This sounds almost tautological. I have not read Masanes' paper, but he
>>> seems to be saying the Born rule is a matter of pure logic. In some ways
>>> that is what Born said.
>>>
>>> The Born rule is not hard to understand. If you have a state space with
>>> vectors |u_i> then a quantum state can be written as sum_ic_i|u_i>. For an
>>> observable O with eigenvectors o_i the expectation values for that
>>> observable is
>>>
>>>  sum_{ij} = sum_{ij} = sum_ip_io_i.
>>>
>>> So the expectations of each eigenvalue is multiple of the probability
>>> for the system to be found in that state. It is not hard to understand, but
>>> the problem is there is no general theorem and proof that the eigenvalues
>>> of an operator or observable are diagonal in the probabilities.
>>>
>>>
>> I am not sure I understand this.
>>
>>
>>
>>
>> In fact this has some subtle issues with degeneracies.
>>>
>>>
>>> Doesn't Gleason's theorem show that there is no other consistent way to
>>> assign probabilities to subspaces of a Hilbert space?
>>>
>>> Brent
>>>
>>
>> It is close. Gleason's theorem tells us that probabilities are a
>> consequence of certain measurements. So for a basis Q = {q_n} then in a
>> span in Q = P{q_n}, for P a projection operator that a measure μ(Q} is
>> given by a trace over projection operators. This is close, but it does not
>> address the issue of eigenvalues of an operator or observable. Gleason
>> tried to make this work for operators, but was ultimately not able to.
>>
>>
>> It should work for the projection operator, that this is the
>> yes-no-experiment, but that extends to the other measurement, by reducing
>> (as usual) the question “what is the value of A” into the (many) question
>> “does A measurement belong to this interval” … Gleason’s theorem assures
>> that the measure is unique (on the subspaces of H with dim bigger or equal
>> to 3), so the Born rule should be determined, at least in non degenerate
>> case (but also in the degenerate case when the degeneracy is due to tracing
>> out a subsystem from a bigger system. I will verify later as my mind
>> belongs more to the combinator and applicative algebra that QM for now.
>>
>>
>>
>>
>> Many years ago I had an idea that since the trace of a density matrix may
>> be thought of as constructed from projection operators with tr(ρ_n) = sum_n
>> |c_n|^2P_n, that observables that commute with the density matrix might
>> have a derived Born rule following Gleason. Further, maybe operators that
>> do not commute then have some dual property that still upholds Born rule. I
>> was not able to make this work.
>>
>>
>> quantum logic, and the right quantum logic is determined by the any
>> “provability” box accompanied by consistency condition (like []p & p, []p &
>> <>t, …).  The main difference to be expected, is that eventually we get a
>> “quantum credibility measure”, not really a probability. It is like
>> probability, except that credibility is between 0 and infinity (not 0 and
>> 1).
>>
>> Bruno
>>
>>
> I think I ran into the issue of why Gleason's theorem does not capture the
> Born rule. Not all operators are commutative with the density matrix. So if
> you construct the diagonal of the density matrix, or its trace elements,
> with projector operators and off diagonal elements with left and right
> acting projectors (left acting hit bra vectors and right acting hit ket
> vectors) the problem is many operators are non-commutative. In particular
> the usual situation is for the Hamiltonian to have nontrivial commutation
> with the density matrix.
>
>
>
> It seems to me that Gleason theorem takes this into account. It only means
> that the probabilities does not make the same partition of the multiverse,
> but that is not a problem for someone who use physics to see if it confirms
> or refute the “observable” available to the universal numbers/machines in
> arithmetic.
>

Gleason's theorem applies for just one set of commuting operators, and in
particular those that commute with the density matrix. The Born rule holds
for all operators, and especially the Hamiltonian that does not commute
with the density matrix.

>
> I am not completely sure. You raise a doubt, and I’m afraid it will take
> some time I come back to Gleason theorem. But I appreciate. My conversation
> with Bruce and Brent makes me think that the notion of multiverse is far
> from clear. At least with mechanism things are crystal clear! There is only
> ```

### Re: When Did Consciousness Begin?

```

On 2/28/2019 3:00 PM, Philip Thrift wrote:

On Thursday, February 28, 2019 at 4:34:54 PM UTC-6, Brent wrote:

On 2/28/2019 2:14 PM, Philip Thrift wrote:

On Thursday, February 28, 2019 at 3:48:04 PM UTC-6, Brent wrote:

On 2/28/2019 1:17 PM, Philip Thrift wrote:

The best current philosopher of (and writer about)
consciousness is *Galen Strawson*.

https://en.wikipedia.org/wiki/Galen_Strawson

https://liberalarts.utexas.edu/philosophy/faculty/profile.php?id=gs24429

There is a lot of his material (PDFs, articles, videos,
etc.) freely available online.

The main word that is synonymous with /consciousness /is
/experience/.

Which is something bacteria and plants and my thermostat
have...and ability to detect and react to the environment
based on internal states.

Brent

Galen is a (type of) micropsychist.

But the point is we don't need a philosopher to explain that level
of consciousness to us.  It's already at the level of
engineering.  If Strawson is going to provide any useful
explanations of consciousness he should study machine
learning...it's getting close to engineering consciousness at the
next higher level.

Brent

It won't be accomplished via certain types of engineering, like
"information network" approaches (IIT
[ https://en.wikipedia.org/wiki/Integrated_information_theory ]) but
potentially could with a "synthetic" approach that *combines networks
with synthetic biology*. Something along these lines is the "fusion"
idea proposed by

I don't know why IIT is even discussed.  Aaronson pretty well shot it down.

My son may get a chance to work on the Deepmind team.  What kind of
brain cells would you suggest he sprinkle on the CPUs?

Brent

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### Re: When Did Consciousness Begin?

```

On Thursday, February 28, 2019 at 4:34:54 PM UTC-6, Brent wrote:
>
>
>
> On 2/28/2019 2:14 PM, Philip Thrift wrote:
>
>
>
> On Thursday, February 28, 2019 at 3:48:04 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 2/28/2019 1:17 PM, Philip Thrift wrote:
>>
>>
>>
>> The best current philosopher of (and writer about) consciousness is *Galen
>> Strawson*.
>>
>> https://en.wikipedia.org/wiki/Galen_Strawson
>> https://liberalarts.utexas.edu/philosophy/faculty/profile.php?id=gs24429
>>
>> There is a lot of his material (PDFs, articles, videos, etc.) freely
>> available online.
>>
>> The main word that is synonymous with *consciousness *is *experience*.
>>
>>
>> Which is something bacteria and plants and my thermostat have...and
>> ability to detect and react to the environment based on internal states.
>>
>
>> Brent
>>
>
>
>
> Galen is a (type of) micropsychist.
>
>
> But the point is we don't need a philosopher to explain that level of
> consciousness to us.  It's already at the level of engineering.  If
> Strawson is going to provide any useful explanations of consciousness he
> should study machine learning...it's getting close to engineering
> consciousness at the next higher level.
>
> Brent
>

It won't be accomplished via certain types of engineering, like
"information network" approaches (IIT
[ https://en.wikipedia.org/wiki/Integrated_information_theory ]) but
potentially could with a "synthetic" approach that *combines networks with
synthetic biology*. Something along these lines is the "fusion" idea
proposed by

- Hedda Hassel Mørch
@heddamorch

https://philpapers.org/rec/MRCICI

- pt

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### Re: When Did Consciousness Begin?

```

On 2/28/2019 2:14 PM, Philip Thrift wrote:

On Thursday, February 28, 2019 at 3:48:04 PM UTC-6, Brent wrote:

On 2/28/2019 1:17 PM, Philip Thrift wrote:

The best current philosopher of (and writer about) consciousness
is *Galen Strawson*.

https://en.wikipedia.org/wiki/Galen_Strawson

https://liberalarts.utexas.edu/philosophy/faculty/profile.php?id=gs24429

There is a lot of his material (PDFs, articles, videos, etc.)
freely available online.

The main word that is synonymous with /consciousness /is
/experience/.

Which is something bacteria and plants and my thermostat
have...and ability to detect and react to the environment based on
internal states.

Brent

Galen is a (type of) micropsychist.

But the point is we don't need a philosopher to explain that level of
consciousness to us.  It's already at the level of engineering. If
Strawson is going to provide any useful explanations of consciousness he
should study machine learning...it's getting close to engineering
consciousness at the next higher level.

Brent

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### Re: When Did Consciousness Begin?

```

On Thursday, February 28, 2019 at 3:48:04 PM UTC-6, Brent wrote:
>
>
>
> On 2/28/2019 1:17 PM, Philip Thrift wrote:
>
>
>
> The best current philosopher of (and writer about) consciousness is *Galen
> Strawson*.
>
> https://en.wikipedia.org/wiki/Galen_Strawson
> https://liberalarts.utexas.edu/philosophy/faculty/profile.php?id=gs24429
>
> There is a lot of his material (PDFs, articles, videos, etc.) freely
> available online.
>
> The main word that is synonymous with *consciousness *is *experience*.
>
>
> Which is something bacteria and plants and my thermostat have...and
> ability to detect and react to the environment based on internal states.
>

> Brent
>

Galen is a (type of) micropsychist.

- pt

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### Re: When Did Consciousness Begin?

```

On 2/28/2019 1:17 PM, Philip Thrift wrote:

The best current philosopher of (and writer about) consciousness is
*Galen Strawson*.

https://en.wikipedia.org/wiki/Galen_Strawson
https://liberalarts.utexas.edu/philosophy/faculty/profile.php?id=gs24429

There is a lot of his material (PDFs, articles, videos, etc.) freely
available online.

The main word that is synonymous with /consciousness /is /experience/.

Which is something bacteria and plants and my thermostat have...and
ability to detect and react to the environment based on internal states.

Brent

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### Re: When Did Consciousness Begin?

```

The best current philosopher of (and writer about) consciousness is *Galen
Strawson*.

https://en.wikipedia.org/wiki/Galen_Strawson
https://liberalarts.utexas.edu/philosophy/faculty/profile.php?id=gs24429

There is a lot of his material (PDFs, articles, videos, etc.) freely
available online.

The main word that is synonymous with *consciousness *is *experience*.

- pt

On Thursday, February 28, 2019 at 2:14:58 PM UTC-6, Azutmai wrote:
>
> Brent . . . it might be helpful to equate the word ‘consciousness’ and
> ‘awareness.’ If we are conscious or aware of something . . . then it
> pertains to our viewpoint and lifestyle. Memory is a secondary feature to
> allow the individual to retain over time . . . otherwise we would have to
> learn the same thing over and over and over again . . . which we still
> somewhat do anyway. Observe someone’s interests, passions, habits, etc . .
> . and one can get a very good idea of their general level or state of
> consciousness. It is consciousness where we all differ . . . one from the
> other. We might all be the same . . . we might all be One . . . but
> individual consciousness differentiates each of us from the other . . . no
> matter how great or minute the differences are.
>
> On Sunday, February 10, 2019 at 4:24:45 PM UTC-8, Brent wrote:
>>
>>
>>
>> On 2/10/2019 3:34 PM, Philip Thrift wrote:
>> >
>> >
>> > Two recent books:
>> >
>> > The First Minds: Caterpillars, Karyotes, and Consciousness
>> > Arthur S. Reber
>> >
>> >
>> > Brain-Mind: From Neurons to Consciousness and Creativity
>> > Paul Thagard
>> >
>> > via
>> > When Did Consciousness Begin?
>> > Paul Thagard
>> >
>> https://www.psychologytoday.com/intl/blog/hot-thought/201901/when-did-consciousness-begin
>>
>> >
>> > Thagard's 10 hypotheses:
>> >
>> > 1. Consciousness has always existed, because God is conscious and
>> eternal.
>> >
>> > 2. Consciousness began when the universe formed, around 13.7 billion
>> > years ago.
>> >
>> > 3. Consciousness began with single-celled life, around 3.7 billion
>> > years ago (Reber).
>> >
>> > 4. Consciousness began with multicellular plants, around 850 million
>> > years ago.
>> >
>> > 5. Consciousness began when animals such as jellyfish got thousands of
>> > neurons, around 580 million years ago.
>> >
>> > 6. Consciousness began when insects and fish developed larger brains
>> > with about a million neurons (honeybees) or 10 million neurons
>> > (zebrafish) around 560 million years ago.
>> >
>> > 7. Consciousness began when animals such as birds and mammals
>> > developed much larger brains with hundreds of millions neurons, around
>> > 200 million years ago. [Thagard]
>> >
>> > 8. Consciousness began with humans, homo sapiens, around 200,000 years
>> > ago.
>> >
>> > 9. Consciousness began when human culture became advanced, around 3000
>> > years ago (Julian Jaynes).
>> >
>> > 10. Consciousness does not exist, as it is just a scientific mistake
>> > (behaviorism} or a “user illusion” (Daniel Dennett).
>>
>> A good exposition, but I wish he had taken some time to consider what is
>> consciousness.  I think he recognizes that there are different kinds and
>> levels of consciousness, but he doesn't make it clear what they are; how
>> are they related to memory and communication and planning.  It seems
>> clear to me that different kinds and levels of consciousness appeared at
>> different times.
>>
>> Brent
>>
>

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### Re: When Did Consciousness Begin?

```

On 2/28/2019 10:35 AM, Azutmai wrote:

Brent . . . it might be helpful to equate the word ‘consciousness’ and
‘awareness.’ If we are conscious or aware of something . . . then it
pertains to our viewpoint and lifestyle.

I take awareness to be consciousness without reflection or evaluation; a
minimal level of consciousness.

Memory is a secondary feature to allow the individual to retain over
time . . . otherwise we would have to learn the same thing over and
over and over again . . . which we still somewhat do anyway.

Without memory we couldn't even learn something the first time. Without
even short term memory one is reduced to the level of aware=>react; the
level at which my thermostat is conscious.

Observe someone’s interests, passions, habits, etc . . . and one can
get a very good idea of their general level or state of consciousness.

One can only observe someone's actions.  The rest is inference from
assuming they have an inner life similar to your own. That's a good bet
with other humans, and even many animals.  But does it apply to an
octopus?  To an artificially intelligent Mars rover?   If two Mars
rovers use a single AI via an RF link are they two consicousness because
they have two different viewpoints?  Or are they just one consciousness
that uses two viewpoints to create a worldview?

Brent

It is consciousness where we all differ . . . one from the other. We
might all be the same . . . we might all be One . . . but individual
consciousness differentiates each of us from the other . . . no matter
how great or minute the differences are.

On Sunday, February 10, 2019 at 4:24:45 PM UTC-8, Brent wrote:

On 2/10/2019 3:34 PM, Philip Thrift wrote:
>
>
> Two recent books:
>
> The First Minds: Caterpillars, Karyotes, and Consciousness
> Arthur S. Reber
>

>
> Brain-Mind: From Neurons to Consciousness and Creativity
> Paul Thagard
>

>
> via
> When Did Consciousness Begin?
> Paul Thagard
>

https://www.psychologytoday.com/intl/blog/hot-thought/201901/when-did-consciousness-begin

>
> Thagard's 10 hypotheses:
>
> 1. Consciousness has always existed, because God is conscious
and eternal.
>
> 2. Consciousness began when the universe formed, around 13.7
billion
> years ago.
>
> 3. Consciousness began with single-celled life, around 3.7 billion
> years ago (Reber).
>
> 4. Consciousness began with multicellular plants, around 850
million
> years ago.
>
> 5. Consciousness began when animals such as jellyfish got
thousands of
> neurons, around 580 million years ago.
>
> 6. Consciousness began when insects and fish developed larger
brains
> with about a million neurons (honeybees) or 10 million neurons
> (zebrafish) around 560 million years ago.
>
> 7. Consciousness began when animals such as birds and mammals
> developed much larger brains with hundreds of millions neurons,
around
> 200 million years ago. [Thagard]
>
> 8. Consciousness began with humans, homo sapiens, around 200,000
years
> ago.
>
> 9. Consciousness began when human culture became advanced,
around 3000
> years ago (Julian Jaynes).
>
> 10. Consciousness does not exist, as it is just a scientific
mistake
> (behaviorism} or a “user illusion” (Daniel Dennett).

A good exposition, but I wish he had taken some time to consider
what is
consciousness.  I think he recognizes that there are different
kinds and
levels of consciousness, but he doesn't make it clear what they
are; how
are they related to memory and communication and planning.  It seems
clear to me that different kinds and levels of consciousness
appeared at
different times.

Brent

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.
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.

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### Re: When Did Consciousness Begin?

```

Brent . . . it might be helpful to equate the word ‘consciousness’ and
‘awareness.’ If we are conscious or aware of something . . . then it
pertains to our viewpoint and lifestyle. Memory is a secondary feature to
allow the individual to retain over time . . . otherwise we would have to
learn the same thing over and over and over again . . . which we still
somewhat do anyway. Observe someone’s interests, passions, habits, etc . .
. and one can get a very good idea of their general level or state of
consciousness. It is consciousness where we all differ . . . one from the
other. We might all be the same . . . we might all be One . . . but
individual consciousness differentiates each of us from the other . . . no
matter how great or minute the differences are.

On Sunday, February 10, 2019 at 4:24:45 PM UTC-8, Brent wrote:
>
>
>
> On 2/10/2019 3:34 PM, Philip Thrift wrote:
> >
> >
> > Two recent books:
> >
> > The First Minds: Caterpillars, Karyotes, and Consciousness
> > Arthur S. Reber
> >
> >
> > Brain-Mind: From Neurons to Consciousness and Creativity
> > Paul Thagard
> >
> > via
> > When Did Consciousness Begin?
> > Paul Thagard
> >
> https://www.psychologytoday.com/intl/blog/hot-thought/201901/when-did-consciousness-begin
>
> >
> > Thagard's 10 hypotheses:
> >
> > 1. Consciousness has always existed, because God is conscious and
> eternal.
> >
> > 2. Consciousness began when the universe formed, around 13.7 billion
> > years ago.
> >
> > 3. Consciousness began with single-celled life, around 3.7 billion
> > years ago (Reber).
> >
> > 4. Consciousness began with multicellular plants, around 850 million
> > years ago.
> >
> > 5. Consciousness began when animals such as jellyfish got thousands of
> > neurons, around 580 million years ago.
> >
> > 6. Consciousness began when insects and fish developed larger brains
> > with about a million neurons (honeybees) or 10 million neurons
> > (zebrafish) around 560 million years ago.
> >
> > 7. Consciousness began when animals such as birds and mammals
> > developed much larger brains with hundreds of millions neurons, around
> > 200 million years ago. [Thagard]
> >
> > 8. Consciousness began with humans, homo sapiens, around 200,000 years
> > ago.
> >
> > 9. Consciousness began when human culture became advanced, around 3000
> > years ago (Julian Jaynes).
> >
> > 10. Consciousness does not exist, as it is just a scientific mistake
> > (behaviorism} or a “user illusion” (Daniel Dennett).
>
> A good exposition, but I wish he had taken some time to consider what is
> consciousness.  I think he recognizes that there are different kinds and
> levels of consciousness, but he doesn't make it clear what they are; how
> are they related to memory and communication and planning.  It seems
> clear to me that different kinds and levels of consciousness appeared at
> different times.
>
> Brent
>

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### Re: The halting problem

```

A program may not halt, but it could rot.

https://en.wikipedia.org/wiki/Software_rot

- pt

On Thursday, February 28, 2019 at 12:53:23 PM UTC-6, Brent wrote:
>
>

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### Re: Are there real numbers that cannot be defined?

```

On Thursday, February 28, 2019 at 10:54:28 AM UTC-6, Bruno Marchal wrote:
>
>
> On 27 Feb 2019, at 19:18, Philip Thrift >
> wrote:
>
>
>
> On Wednesday, February 27, 2019 at 11:25:06 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 26 Feb 2019, at 19:41, Philip Thrift  wrote:
>>
>>
>>
>> There is another approach vs. the JD Hamkins / set theory & mathematical
>> logic (math dept.) approach. the one of Martin Escardo / type & programming
>> language theory (computer science dept.).
>>
>> Martin Escardo
>> http://www.cs.bham.ac.uk/~mhe/
>>
>> *higher-type computation = *
>>
>> *sets that can be exhaustively searched by an algorithm, in the sense of
>> Turing, in finite time, as those that are topologically compact*
>>
>>
>> ?
>>
>> If it is an algorithm in the sense of Turing, and if the search is
>> required to be finite, then the set is finite.
>>
>
>
>
> In any case, there is programming he has written
>
> M.H. Escardo. *Infinite sets that admit fast exhaustive search*.
>
>
> In that sense, there is no problem. The universal dovetailer exhaust all
> computations with all oracles in that sense.
>
>
>
>
> In LICS'2007, IEEE, pages 443-452, Poland, Wroclaw, July.
>
> pdf  (paper), hs
> program extracted from the paper
>
> from   https://www.cs.bham.ac.uk/~mhe/papers/
>
>
> One could say: *There is nothing outside the code.*
>
> (The program stands on its own.)
>
>
>
>
> Programs can’t do that when becoming inputs to universal programs. You
> can’t escape truth so easily, even if you can’t define it. All Gödel-Löbian
> machines know that. There is definitely something outside the code, if
> there is a code. And that is the many universal codes which gives the
> behaviour and the experience to the person attached to their infinitely
> many codes in arithmetic. But the laws of physics must be derived from
> this, and by using the self-reference logics of Gödel-Löb-Solovay (G*), we
> get the qualia as supplementary gifts, in the form of immediate “volume”
> type of truth that we cannot prove, nor define, yet indubitably known.
>
> Bruno
>

We have only scratched the surface of the subject of *Semantic*s (of code)
in PLT.

*PLT: A path to enlightenment in Programming Language Theory*
https://steshaw.org/plt/

- pt

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### Re: Recommend this article, Even just for the Wheeler quote near the end

```

On Thursday, February 28, 2019 at 11:13:07 AM UTC-6, Bruno Marchal wrote:
>
>
> On 28 Feb 2019, at 02:01, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, February 13, 2019 at 9:40:32 PM UTC-7, cdemorsella wrote:
>>
>> Two fascinating (and very different) approaches are presented to derive
>> Quantim Mechanics main practical tool (e.g. Born's rule). Wonder what some
>>
>> I find the argument that no laws is the fundamental law... and that the
>> universe and its laws are emergent guided by subtle mathematical
>> statistical phenomena, at the same time both alluring and annoying it
>> is somehow unsatisfactory like being served a quite empty plate with
>> nice garnish for dinner.
>>
>> One example of emergence from chaotic conditions is how traffic jams (aka
>> density waves) can emerge from chaotic initial conditions, becoming self
>> re-enforcing within local domains of influence... for those unlucky to be
>> stuck in them. Density wave emergence is seen across scale, for example the
>> spiral arms of galaxies can be explained as giant gravitational pile ups
>> with some fundamentally similar parallels to say a rush hour traffic jam,
>> except on vastly different scales of course and due to other different
>> factors, in the galactic case the emergent effects of a vast number of
>> gravitational inter-actions as stars migrate through these arms on their
>> grand voyages around the galactic core.
>>
>> This paired with the corollary argument that any attempt to discover a
>> fundamental law seems doomed to the infinite regression of then needing to
>> explain what this foundation itself rests upon leading to the "it's
>> turtles all the way down" hall of mirrors carnival house... head-banger.
>>
>> Perhaps, as Wheeler argued, the world is a self-synthesizing system, and
>> the seeming order we observe, is emergent... a law without law.
>>
>> Here is the link to the article:
>>
>>
>>
>> The Born Rule Has Been Derived From Simple Physical Principles | Quanta
>> Magazine
>>
>> The Born Rule Has Been Derived From Simple Physical Principles | Quanta
>> Magazine
>>
>> The new work promises to give researchers a better grip on the core
>> mystery of quantum mechanics.
>>
>>
>>
>>
>>
>
>> *Is there consensus that Born's rule can be, and has been derived from
>> physical principles, and/or the other postulates of QM? TIA, AG*
>>
>
>
> I would say no. Just many interesting hints though. Then with mechanism,
> you need to derive the wave/matrix as well, and the symmetries, from any
> universal machinery phi_i. All the rest is given by Gauge invariance and
> our breaking of the symmetries.
>
> I am (re)reading what Weinberg says about all this, but his conclusion is
> that quantum mechanics could be simply wrong, and just a symptom of a
> deeper theory, which it should with Indexical Digital Mechanism.
>
> Bruno
>
>
>
>
As for the beginning with the *Feynman postulates* (listed here):

http://muchomas.lassp.cornell.edu/8.04/Lecs/lec_FeynmanDiagrams/node3.html

it seems thatsome form of the Born rule should be derivable, but I don't
know.

- pt

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```

### Re: Questions about the Equivalence Principle (EP) and GR

```

On 2/28/2019 4:07 AM, agrayson2...@gmail.com wrote:

On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:

On 2/27/2019 4:58 PM, agrays...@gmail.com  wrote:

*Are you assuming uniqueness to tensors; that only tensors can
produce covariance in 4-space? Is that established or a
mathematical speculation? TIA, AG *

That's looking at it the wrong way around.  Anything that
transforms as an object in space, must be representable by
tensors. The informal definition of a tensor is something that
transforms like an object, i.e. in three space it's something that
has a location and an orientation and three extensions.  Something
that doesn't transform as a tensor under coordinate system changes
is something that depends on the arbitrary choice of coordinate
system and so cannot be a fundamental physical object.

Brent

1) Is it correct to say that tensors in E's field equations can be
represented as 4x4 matrices which have different representations
depending on the coordinate system being used, but represent the same
object?

That's right as far as it goes.   Tensors can be of any order.  The
curvature tensor is 4x4x4x4.

2) In SR we use the LT to transform from one*non-accelerating* frame
to another. In GR, what is the transformation for going from one
*accelerating* frame to another?

The Lorentz transform, but only in a local patch.

Brent

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### Re: Recommend this article, Even just for the Wheeler quote near the end

```
> On 28 Feb 2019, at 02:01, agrayson2...@gmail.com wrote:
>
>
>
> On Wednesday, February 13, 2019 at 9:40:32 PM UTC-7, cdemorsella wrote:
> Two fascinating (and very different) approaches are presented to derive
> Quantim Mechanics main practical tool (e.g. Born's rule). Wonder what some of
>
> I find the argument that no laws is the fundamental law... and that the
> universe and its laws are emergent guided by subtle mathematical statistical
> phenomena, at the same time both alluring and annoying it is somehow
> unsatisfactory like being served a quite empty plate with nice garnish
> for dinner.
>
> One example of emergence from chaotic conditions is how traffic jams (aka
> density waves) can emerge from chaotic initial conditions, becoming self
> re-enforcing within local domains of influence... for those unlucky to be
> stuck in them. Density wave emergence is seen across scale, for example the
> spiral arms of galaxies can be explained as giant gravitational pile ups with
> some fundamentally similar parallels to say a rush hour traffic jam, except
> on vastly different scales of course and due to other different factors, in
> the galactic case the emergent effects of a vast number of gravitational
> inter-actions as stars migrate through these arms on their grand voyages
> around the galactic core.
>
> This paired with the corollary argument that any attempt to discover a
> fundamental law seems doomed to the infinite regression of then needing to
> explain what this foundation itself rests upon leading to the "it's
> turtles all the way down" hall of mirrors carnival house... head-banger.
>
> Perhaps, as Wheeler argued, the world is a self-synthesizing system, and the
> seeming order we observe, is emergent... a law without law.
>
> Here is the link to the article:
>
>
>
> The Born Rule Has Been Derived From Simple Physical Principles | Quanta
> Magazine
>
>
> The Born Rule Has Been Derived From Simple Physical Principles | Quanta
> Magazine
> The new work promises to give researchers a better grip on the core mystery
> of quantum mechanics.
>
>
>
>
> Is there consensus that Born's rule can be, and has been derived from
> physical principles, and/or the other postulates of QM? TIA, AG

I would say no. Just many interesting hints though. Then with mechanism, you
need to derive the wave/matrix as well, and the symmetries, from any universal
machinery phi_i. All the rest is given by Gauge invariance and our breaking of
the symmetries.

I am (re)reading what Weinberg says about all this, but his conclusion is that
quantum mechanics could be simply wrong, and just a symptom of a deeper theory,
which it should with Indexical Digital Mechanism.

Bruno

>
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### Re: Are there real numbers that cannot be defined?

```
> On 27 Feb 2019, at 19:18, Philip Thrift  wrote:
>
>
>
> On Wednesday, February 27, 2019 at 11:25:06 AM UTC-6, Bruno Marchal wrote:
>
>> On 26 Feb 2019, at 19:41, Philip Thrift >
>> wrote:
>>
>>
>>
>> On Tuesday, February 26, 2019 at 5:07:38 AM UTC-6, Bruno Marchal wrote:
>>
>>> On 25 Feb 2019, at 20:35, Philip Thrift > wrote:
>>>
>>> via
>>>
>>>
>>> Joel David Hamkins   @JDHamkins
>>>
>>> Must there be numbers we cannot describe or define? Definability in
>>> mathematics and the Math Tea argument
>>> Pure Mathematics Research Seminar at the University of East Anglia in
>>> Norwich on Monday, 25 February, 2019.
>>>
>>>
>>> Abstract:
>>>
>>> An old argument, heard perhaps at a good math tea, proceeds: “there must be
>>> some real numbers that we can neither describe nor define, since there are
>>> uncountably many real numbers, but only countably many definitions.
>>
>>
>> But that argument is rather weak, as the notion of cardinality is a relative
>> notion, depending of the model (not the theory) that we might use. There are
>> countable models of Cantor’s theory of set and the transfinite (cf the
>> paradox of Skolem). If you agree o identify a real number with a total
>> computable function (from N to N), as Turing did originally, then you can
>> prove the existence of specific non definable real number, in any rich
>> enough extension of any essentially undecidable theory.
>>
>> It is very simple, any theory reich enough to define a universal
>> machine/number, is automatically essentially undecidable. It is a generator
>> of infinitely many surprises for *any* machines and super-marching, etc. We
>> know now that we know basically nothing, with such “rich” theories.
>> Elementary arithmetic is already essentially undecidable.
>>
>> You can change the logic, and will get quite different view on the real
>> numbers. In brouwer’s intuitionistic logic, and in the effective topos
>> (which generalises Kleene’s realisability notion, and is based on the
>> category of partial combinatory algebra): we have that all real number are
>> computable, and all functions are continuous. I am not sure if we get that
>> all real numbers will be definable, though. They might be not-not-definable
>> ...
>>
>>
>>
>>> ” Does it withstand scrutiny? In this talk, I will discuss the phenomenon
>>> of pointwise definable structures in mathematics, structures in which every
>>> object has a property that only it exhibits. A mathematical structure is
>>> Leibnizian, in contrast, if any pair of distinct objects in it exhibit
>>> different properties.
>>
>> x ≠ y ->. Ax ≠ Ay, that is Ax = Ay ->. x = y. That is the axiom of
>> extensionality (in Combinators, lama calculus, set theories).
>>
>> I have used it in the elimination of variables in the combinations. It is a
>> god’s gift, as it leads to simple efficacious combinators. It is, with the
>> combinators, equivalent to [x](Ax) = A, when A has no free occurence of x.
>> Not to be confuse with ([x]A)x = A (which is always true, and just defines
>> what elimination of x means).
>>
>>
>>
>>> Is there a Leibnizian structure with no definable elements?
>>
>> Yes. The classical reals, or the classical set of total computable functions.
>>
>>
>>
>>> Must indiscernible elements in a mathematical structure be automorphic
>>> images of one another?
>>
>> No. If we cannot discern them, we cannot build a morphism between them. I
>> would say.
>>
>>
>>> We shall discuss many elementary yet interesting examples, eventually
>>> working up to the proof that every countable model of set theory has a
>>> pointwise definable extension, in which every mathematical object is
>>> definable.
>>>
>>> http://jdh.hamkins.org/must-there-be-number-we-cannot-define-norwich-february-2019/
>>>
>>>
>>>
>>> Lecture notes:
>>>
>>>
>> I will take a look, but that does not make much sense, unless the logic is
>> weakemed in some way. In some intuitionist set theory with choice, it might
>> make sense.
>>
>> Bruno
>>
>>
>>
>>
>> There is another approach vs. the JD Hamkins / set theory & mathematical
>> logic (math dept.) approach. the one of Martin Escardo / type & programming
>> language theory (computer science dept.).
>>
>> Martin Escardo
>> http://www.cs.bham.ac.uk/~mhe/
>>
>> higher-type computation =
>>
>> sets that can be exhaustively searched by an algorithm, in the sense of
>> Turing, in finite time, as those that are topologically compact
>
> ?
>
> If it is an ```

### Re: Questions about the Equivalence Principle (EP) and GR

```

On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:
>
>
>
> On 2/27/2019 4:58 PM, agrays...@gmail.com  wrote:
>
> *Are you assuming uniqueness to tensors; that only tensors can produce
> covariance in 4-space? Is that established or a mathematical speculation?
> TIA, AG *
>
>
> That's looking at it the wrong way around.  Anything that transforms as an
> object in space, must be representable by tensors. The informal definition
> of a tensor is something that transforms like an object, i.e. in three
> space it's something that has a location and an orientation and three
> extensions.  Something that doesn't transform as a tensor under coordinate
> system changes is something that depends on the arbitrary choice of
> coordinate system and so cannot be a fundamental physical object.
>
> Brent
>

1) Is it correct to say that tensors in E's field equations can be
represented as 4x4 matrices which have different representations depending
on the coordinate system being used, but represent the same object?
2) In SR we use the LT to transform from one* non-accelerating* frame to
another. In GR, what is the transformation for going from one *accelerating*
frame to another?
AG

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