Bell's Theorem and Normed Division Algebras

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Sun Dec 20, 2020 1:52 am

:lol:
gill1109 wrote:

You obviously have to have sufficient mathematical background to be able to check what's written in specialist mathematical articles on Wikipedia. Good articles contain references to every asserted fact. Those two particular articles are pretty good. The split bi-quaternions have been known since Clifford wrote about them in 1873 (he called them "elliptic biquaternions"). He classified all the geometric algebras in 1882. The hypercomplex numbers have similarly been intensively studied for a long time now.

:lol:
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Sun Dec 20, 2020 4:09 am

Joy Christian wrote::lol:
gill1109 wrote:

You obviously have to have sufficient mathematical background to be able to check what's written in specialist mathematical articles on Wikipedia. Good articles contain references to every asserted fact. Those two particular articles are pretty good. The split bi-quaternions have been known since Clifford wrote about them in 1873 (he called them "elliptic biquaternions"). He classified all the geometric algebras in 1882. The hypercomplex numbers have similarly been intensively studied for a long time now.

:lol:

:lol: indeed. Happy Christmas, all the best for the New Year! Take care. The Netherlands is stopping travel from the UK because of your new Covid-19 variant...
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Mon Dec 21, 2020 11:04 pm

Joy Christian wrote:.
A professor of Engineering and Computer Science from a well-known Canadian University has taken an active interest in my "octonian-like" paper that Gill had campaigned to have retracted from the journal Communications in Algebra. Here is the abstract of the professor's paper, which he has written with one of his Ph.D. students:

Using elementary linear algebra, this paper clarifies and proves some concepts about the previously introduced octonion-like associative division algebra (pseudo-octonion algebra). For a specific seminorm described in the paper (which differs from the norm used in the original paper), it is shown that the pseudo-octonion algebra is a semi-normed algebra, which does not contradict Hurwitz’s theorem. Moreover, additional results related to the computation of inverse numbers in the pseudo-octonion algebra are introduced in the paper, confirming that the pseudo-octonion algebra is a division algebra with no zero divisors using the seminorm. The elementary linear algebra descriptions also allow straightforward software implementations of the pseudo-octonion algebra.

I have read his paper, but it is not yet available online. I will post a link here when it becomes available. My original paper is available on the arXiv: https://arxiv.org/pdf/1908.06172.pdf.

I have posted Gill's retraction saga (involving John C. Baez) on PubPeer for the future historians and sociologists of science: https://pubpeer.com/publications/E3CC09 ... 5CAEE98D#5.

The paper has now appeared online: https://arxiv.org/ftp/arxiv/papers/2012/2012.11359.pdf.
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Tue Dec 22, 2020 12:21 am

Joy Christian wrote:
Joy Christian wrote:.
A professor of Engineering and Computer Science from a well-known Canadian University has taken an active interest in my "octonian-like" paper that Gill had campaigned to have retracted from the journal Communications in Algebra. Here is the abstract of the professor's paper, which he has written with one of his Ph.D. students:

Using elementary linear algebra, this paper clarifies and proves some concepts about the previously introduced octonion-like associative division algebra (pseudo-octonion algebra). For a specific seminorm described in the paper (which differs from the norm used in the original paper), it is shown that the pseudo-octonion algebra is a semi-normed algebra, which does not contradict Hurwitz’s theorem. Moreover, additional results related to the computation of inverse numbers in the pseudo-octonion algebra are introduced in the paper, confirming that the pseudo-octonion algebra is a division algebra with no zero divisors using the seminorm. The elementary linear algebra descriptions also allow straightforward software implementations of the pseudo-octonion algebra.

I have read his paper, but it is not yet available online. I will post a link here when it becomes available. My original paper is available on the arXiv: https://arxiv.org/pdf/1908.06172.pdf.

I have posted Gill's retraction saga (involving John C. Baez) on PubPeer for the future historians and sociologists of science: https://pubpeer.com/publications/E3CC09 ... 5CAEE98D#5.

The paper has now appeared online: https://arxiv.org/ftp/arxiv/papers/2012/2012.11359.pdf.
.

Notice that they do not use Christian’s norm, but introduce a *semi-norm*, in other words, non-zero elements can have norm zero. If one now follows the usual mathematical procedure of forming equivalence classes of all elements at zero distance to one another, the result will be a collapse of dimension. The space with this “norm” reduces to the quaternions. After all, it’s an associative normed division algebra, and the Hurwitz theorem says it must be R, C or H. It’s overparametrised. It’s actually only 4 dimensional.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Tue Dec 22, 2020 3:23 am

.
More nonsense from Gill continues. I would advise him to stick with statistics. Don't try to be a jack of all trades.
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Tue Dec 22, 2020 4:45 am

Joy Christian wrote:.
More nonsense from Gill continues. I would advise him to stick with statistics. Don't try to be a jack of all trades.
.

:lol:
Wise advice. I have a degree in mathematics from the University of Cambridge (UK).
:lol:
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Tue Dec 22, 2020 5:01 am

gill1109 wrote:
I have a degree in mathematics from the University of Cambridge (UK).

That does not make you a mathematician. You are a retired statistician, and that is about it.
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Wed Dec 23, 2020 12:18 am

Joy Christian wrote:
gill1109 wrote:I have a degree in mathematics from the University of Cambridge (UK).

That does not make you a mathematician. You are a retired statistician, and that is about it.

And proud of it, too! Retired member of the Royal Dutch Academy of Sciences; past president of the Dutch society for statistics and O.R.; elected member of the Institute of Physics, and of FQXi; ... now enjoying my retirement.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Wed Dec 23, 2020 1:56 am

gill1109 wrote:
Joy Christian wrote:
gill1109 wrote:I have a degree in mathematics from the University of Cambridge (UK).

That does not make you a mathematician. You are a retired statistician, and that is about it.

And proud of it, too! Retired member of the Royal Dutch Academy of Sciences; past president of the Dutch society for statistics and O.R.; elected member of the Institute of Physics, and of FQXi; ... now enjoying my retirement.

And continuing to make extremely elementary mathematical mistakes over and over again, as I have exposed here: https://www.academia.edu/38423874/Refut ... ls_Theorem.

Bravo!
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Wed Dec 23, 2020 5:12 am

Joy Christian wrote:
gill1109 wrote:
Joy Christian wrote:
gill1109 wrote:I have a degree in mathematics from the University of Cambridge (UK).

That does not make you a mathematician. You are a retired statistician, and that is about it.

And proud of it, too! Retired member of the Royal Dutch Academy of Sciences; past president of the Dutch society for statistics and O.R.; elected member of the Institute of Physics, and of FQXi; ... now enjoying my retirement.

And continuing to make extremely elementary mathematical mistakes over and over again, as I have exposed here: https://www.academia.edu/38423874/Refut ... ls_Theorem.

Bravo!
.

Thank you! Please keep on publishing. All the best wishes for 2021.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Fri Jan 15, 2021 12:21 pm

.
For what it's worth, my Collaboration Distance from Einstein seems to be 4: https://mathscinet.ams.org/mathscinet/c ... rce=309696.

Image

And from John S. Bell it seems to be 2:https://mathscinet.ams.org/mathscinet/collaborationDistance.html?group_source=309696.

Image
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Fri Jan 15, 2021 9:28 pm

Our distance is 3: Richard Gill - Anton Zeilinger - Abner Shimony - Joy Christian
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Re: Bell's Theorem and Normed Division Algebras

Postby FrediFizzx » Sat Jan 16, 2021 8:50 am

LOL! I guess I'm then 5 from Einstein and 3 from Bell. And 4 from Gill. Ugh! :mrgreen:
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Sat Jan 16, 2021 9:36 pm

FrediFizzx wrote:LOL! I guess I'm then 5 from Einstein and 3 from Bell. And 4 from Gill. Ugh! :mrgreen:
.

Sorry Fred, you are not on MathSciNet. :lol:
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Re: Bell's Theorem and Normed Division Algebras

Postby FrediFizzx » Sun Jan 17, 2021 9:06 am

gill1109 wrote:
FrediFizzx wrote:LOL! I guess I'm then 5 from Einstein and 3 from Bell. And 4 from Gill. Ugh! :mrgreen:
.

Sorry Fred, you are not on MathSciNet.

Does this look like a face that cares whether or not I'm on MathSciNet? :mrgreen: :lol:
.
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Re: Bell's Theorem and Normed Division Algebras

Postby gill1109 » Sun Jan 17, 2021 12:37 pm

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:LOL! I guess I'm then 5 from Einstein and 3 from Bell. And 4 from Gill. Ugh! :mrgreen:
.

Sorry Fred, you are not on MathSciNet.

Does this look like a face that cares whether or not I'm on MathSciNet? :mrgreen: :lol:

Of course not! :D :P
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