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 » Thu Oct 22, 2020 12:40 am

gill1109 wrote:
Joy Christian wrote:Pure nonsense again. I don't care about John the Biased or any other online bullies you want to recruit to your unhealthy obsession with me. You are a complete ignoramus who knows nothing about the subject of algebra. I have refuted your argument hundreds of times on the RSOS thread of my paper since 2018, and most recently on the following PubPeer thread:https://pubpeer.com/publications/E3CC09191C99B14164303D5CAEE98D#4. The algebra in my RSOS and "octonion-like" papers does not conflict with either Hurwitz's theorem or Frobenius' theorem. But you, like John the Biased, are too ignorant to understand that. Alternatively, you can find a mistake in the calculation in my paper and prove me wrong. But you are too algebraically challenged to be able to do that. And no mathematician in the world has found a mistake in my calculation because there is none. This fact needs to go through your thick skull. The algebra in my paper is a normed division algebra whether you like it or not.

Sorry to get you so upset. Honestly, *you* don't seem interested to find the mistake which you apparently claim is present in existing proofs by famous mathematicians of a famous theorem in pure mathematics. So I doubt that any serious mathematician in the world is interested to find a mistake in your proof for you. And I'm just a statistician, so my opinion counts for nothing, so why should I take the trouble to look? But I will take a look again, next time you get this paper published. I trust you'll let us know on this forum when that happens.

Where did I claim there is a mistake in the existing proofs? Your claim again shows that you do not know what you are talking about.

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

Postby gill1109 » Thu Oct 22, 2020 2:58 am

Joy Christian wrote:
gill1109 wrote:
Joy Christian wrote:Pure nonsense again. I don't care about John the Biased or any other online bullies you want to recruit to your unhealthy obsession with me. You are a complete ignoramus who knows nothing about the subject of algebra. I have refuted your argument hundreds of times on the RSOS thread of my paper since 2018, and most recently on the following PubPeer thread:https://pubpeer.com/publications/E3CC09191C99B14164303D5CAEE98D#4. The algebra in my RSOS and "octonion-like" papers does not conflict with either Hurwitz's theorem or Frobenius' theorem. But you, like John the Biased, are too ignorant to understand that. Alternatively, you can find a mistake in the calculation in my paper and prove me wrong. But you are too algebraically challenged to be able to do that. And no mathematician in the world has found a mistake in my calculation because there is none. This fact needs to go through your thick skull. The algebra in my paper is a normed division algebra whether you like it or not.

Sorry to get you so upset. Honestly, *you* don't seem interested to find the mistake which you apparently claim is present in existing proofs by famous mathematicians of a famous theorem in pure mathematics. So I doubt that any serious mathematician in the world is interested to find a mistake in your proof for you. And I'm just a statistician, so my opinion counts for nothing, so why should I take the trouble to look? But I will take a look again, next time you get this paper published. I trust you'll let us know on this forum when that happens.

Where did I claim there is a mistake in the existing proofs? Your claim again shows that you do not know what you are talking about.

***

I said, that you *apparently claim*. You have published a theorem which contradicts existing theorems. John Baez seems to think that this is the case. He has published his own expositions of those classical results. So by implication, you are either saying that their proofs are wrong and that Baez’ published work is wrong, or you are saying that mathematics is inconsistent.
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Re: Bell's Theorem and Normed Division Algebras

Postby Heinera » Thu Oct 22, 2020 3:03 am

Joy Christian wrote:Where did I claim there is a mistake in the existing proofs? Your claim again shows that you do not know what you are talking about.

***

Why don't you show us a formulation of Hurwitz's theorem that is consistent with your claim that you have found an "eight-dimensional octonion-like but associative normed division algebra" in the retracted article? Because the formulation that everybody else seems to agree on is surely in conflict with your claim.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Thu Oct 22, 2020 3:11 am

Heinera wrote:
Joy Christian wrote:
Where did I claim there is a mistake in the existing proofs? Your claim again shows that you do not know what you are talking about.

Why don't you show us a formulation of Hurwitz's theorem that is consistent with your claim that you have found an "eight-dimensional octonion-like but associative normed division algebra" in the retracted article? Because the formulation that everybody else seems to agree on is surely in conflict with your claim.

Why don't you show us where the claimed "conflict" is? You can't. Because there is no conflict. The conflict is only in the sick mind of a clinically obsessed statistician.

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

Postby Heinera » Thu Oct 22, 2020 3:29 am

Joy Christian wrote:Why don't you show us where the claimed "conflict" is?

***

The accepted formulation states that "Hurwitz’s theorem says that there are only 4 normed division algebras over the real numbers, up to isomorphism: the real numbers, the complex numbers, the quaternions, and the octonions."

The conflict is that your eight-dimensional algebra is not isomorphic to the octonions.

Now it's your turn.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Thu Oct 22, 2020 3:30 am

***
Here are the words of an expert on normed division algebras who recently replied to my email. I cannot name the person publicly, because I do not have their permission to do so.

An expert wrote:
No, I wasn't particularly surprised [ by your result ] --- once I had figured out what you were doing. The Hurwitz theorem, as usually stated, assumes that the underlying coefficient algebra is real; for you, it is the split complex numbers. ... The key point is that your coefficients are *not* real, so you don't satisfy the requirements of the theorem. The key point is that, as you note in your email message, conjugation does *not* affect your coefficients.

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

Postby gill1109 » Thu Oct 22, 2020 7:00 am

Joy Christian wrote:Here are the words of an expert on normed division algebras who recently replied to my email. I cannot name the person publicly, because I do not have their permission to do so.
An expert wrote:No, I wasn't particularly surprised [ by your result ] --- once I had figured out what you were doing. The Hurwitz theorem, as usually stated, assumes that the underlying coefficient algebra is real; for you, it is the split complex numbers. ... The key point is that your coefficients are *not* real, so you don't satisfy the requirements of the theorem. The key point is that, as you note in your email message, conjugation does *not* affect your coefficients.


Brilliant! Reading through the RSOS paper, or the Communications in Algebra paper, the author nowhere explicitly mentions that he is working with the split complex numbers as scalars. Silly me. I got the impression he worked over the reals. For instance, he says in the RSOS paper "the corresponding algebraic representation space (2.31) is nothing but the eight-dimensional even sub-algebra of the 2^4 = 16-dimensional Clifford algebra Cl(4,0)." This result is very well known for real Clifford algebras. The dimensionality referred to is the dimensionality as *real* vector spaces. Norms are defined as sums of squares, not sums of squares of absolute values. I think the author needs to submit a correction note to RSOS. And thoroughly revise the Communications in Algebra paper before re-submitting elsewhere.

The GA Viewer program also becomes useless, now.

I do hope you can convince your expert to go public.

The modulus of a split-complex number is not a norm, and the split-complex numbers are not a field. Wow. You are in very deep water here where very few people can help you. No wonder you can hardly find an expert to support your result. https://en.wikipedia.org/wiki/Split-complex_number.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Thu Oct 22, 2020 7:13 am

gill1109 wrote:
Joy Christian wrote:Here are the words of an expert on normed division algebras who recently replied to my email. I cannot name the person publicly, because I do not have their permission to do so.
An expert wrote:No, I wasn't particularly surprised [ by your result ] --- once I had figured out what you were doing. The Hurwitz theorem, as usually stated, assumes that the underlying coefficient algebra is real; for you, it is the split complex numbers. ... The key point is that your coefficients are *not* real, so you don't satisfy the requirements of the theorem. The key point is that, as you note in your email message, conjugation does *not* affect your coefficients.


Brilliant! Reading through the RSOS paper, or the Communications in Algebra paper, the author nowhere explicitly mentions that he is working with the split complex numbers as scalars. Silly me. I got the impression he worked over the reals. For instance, he says in the RSOS paper "the corresponding algebraic representation space (2.31) is nothing but the eight-dimensional even sub-algebra of the 2^4 = 16-dimensional Clifford algebra Cl(4,0)." This result is very well known for real Clifford algebras. The dimensionality referred to is the dimensionality as *real* vector spaces. Norms are defined as sums of squares, not sums of squares of absolute values. I think the author needs to submit a correction note to RSOS. And thoroughly revise the Communications in Algebra paper before re-submitting elsewhere.

The GA Viewer program also becomes useless, now.

I do hope you can convince your expert to go public.

The modulus of a split-complex number is not a norm, and the split-complex numbers are not a field. Wow. You are in very deep water here where very few people can help you. No wonder you can hardly find an expert to support your result. https://en.wikipedia.org/wiki/Split-complex_number.

More garbage from Gill, in addition to factually incorrect statements.

But I did not expect anything but a garbage reaction from Gill in any case.

I have no idea how Gill exposing his stupidity can land me in "deep water."

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

Postby Heinera » Thu Oct 22, 2020 7:29 am

Joy Christian wrote:***
Here are the words of an expert on normed division algebras who recently replied to my email. I cannot name the person publicly, because I do not have their permission to do so.

An expert wrote:
No, I wasn't particularly surprised [ by your result ] --- once I had figured out what you were doing. The Hurwitz theorem, as usually stated, assumes that the underlying coefficient algebra is real; for you, it is the split complex numbers. ... The key point is that your coefficients are *not* real, so you don't satisfy the requirements of the theorem. The key point is that, as you note in your email message, conjugation does *not* affect your coefficients.

***

Well, that was certainly a jaw dropping twist.

But nowhere in your paper do you mention that the coefficients are actually split complex numbers (which are certainly very different from the reals). So at best the paper needs a complete rewrite, where this alleged property needs a prominent place.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Thu Oct 22, 2020 7:35 am

Heinera wrote:
Joy Christian wrote:***
Here are the words of an expert on normed division algebras who recently replied to my email. I cannot name the person publicly, because I do not have their permission to do so.

An expert wrote:
No, I wasn't particularly surprised [ by your result ] --- once I had figured out what you were doing. The Hurwitz theorem, as usually stated, assumes that the underlying coefficient algebra is real; for you, it is the split complex numbers. ... The key point is that your coefficients are *not* real, so you don't satisfy the requirements of the theorem. The key point is that, as you note in your email message, conjugation does *not* affect your coefficients.

***

Well, that was certainly a jaw dropping twist.

But nowhere in your paper do you mention that the coefficients are actually split complex numbers (which are certainly very different from the reals). So at best the paper needs a complete rewrite, where this alleged property needs a prominent place.

So, like Gill, and not surprisingly, you haven't read my paper either: https://arxiv.org/pdf/1908.06172.pdf.

But, for that matter, neither has John the Biased or the editors of Communications in Algebra.

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

Postby Heinera » Thu Oct 22, 2020 7:59 am

Joy Christian wrote:
Heinera wrote:Well, that was certainly a jaw dropping twist.

But nowhere in your paper do you mention that the coefficients are actually split complex numbers (which are certainly very different from the reals). So at best the paper needs a complete rewrite, where this alleged property needs a prominent place.

So, like Gill, and not surprisingly, you haven't read my paper either: https://arxiv.org/pdf/1908.06172.pdf.

***

Are you referring to the fact that four days ago, you edited the arxiv-version to include a tiny little mention of split complex numbers in the appendix?
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Thu Oct 22, 2020 8:04 am

Heinera wrote:
Joy Christian wrote:
Heinera wrote:Well, that was certainly a jaw dropping twist.

But nowhere in your paper do you mention that the coefficients are actually split complex numbers (which are certainly very different from the reals). So at best the paper needs a complete rewrite, where this alleged property needs a prominent place.

So, like Gill, and not surprisingly, you haven't read my paper either: https://arxiv.org/pdf/1908.06172.pdf.

***

Are you referring to the fact that four days ago, you edited the arxiv-version to include a tiny little mention of split complex numbers in the appendix?

No. I am referring to the fact that QQ* is a sum of a scalar and a pseudoscalar, which is the same as a split complex number to those not familiar with the language of Geometric Algebra.

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

Postby Heinera » Thu Oct 22, 2020 8:47 am

Joy Christian wrote:No. I am referring to the fact that QQ* is a sum of a scalar and a pseudoscalar, which is the same as a split complex number to those not familiar with the language of Geometric Algebra.
***

A scientific paper should not read like a mystery novel. On the contrary, everything should be clearly laid out in the beginning, so the reader knows exactly what to expect. It is clear that everyone (with the exception of Tevian Dray) read this paper as describing an algebra over the reals. And I suspect that this "everyone" included yourself. If it is an algebra over the split complex numbers, it must be said so in the abstract.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Thu Oct 22, 2020 9:08 am

Heinera wrote:
Joy Christian wrote:No. I am referring to the fact that QQ* is a sum of a scalar and a pseudoscalar, which is the same as a split complex number to those not familiar with the language of Geometric Algebra.
***

A scientific paper should not read like a mystery novel. On the contrary, everything should be clearly laid out in the beginning, so the reader knows exactly what to expect. It is clear that everyone (with the exception of Tevian Dray) read this paper as describing an algebra over the reals. And I suspect that this "everyone" included yourself. If it is an algebra over the split complex numbers, it must be said so in the abstract.

I often wonder where your smugness stems from. You, a bot, trying to advise me on how to write a scientific paper? Go look into your mirror and see who you are. Then check out my scientific background and pedigree to realize who I am.

In any case, the algebra itself is not over the split complex numbers. But I am not obliged to explain to you what the algebra is all about. It is all there explicitly spelled out in the paper.

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

Postby Joy Christian » Fri Oct 23, 2020 10:33 am

***
RetractionWatch has been slow to pick up the story this time around: https://retractionwatch.com/2020/10/22/ ... thematics/

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

Postby gill1109 » Sat Oct 24, 2020 9:47 am

Joy Christian wrote:RetractionWatch has been slow to pick up the story this time around: https://retractionwatch.com/2020/10/22/ ... thematics/

I just submitted to RSOS, and to arXiv, a comment on Joy's RSOS paper. The RSOS paper depends on the material in the Algebra paper. I named Joy as a person who should definitely be asked to referee my paper, and I named Derek Abbott as my preferred editor. I was urged by Andrew Dunn, managing editor, to take this step. I do not want the paper retracted, but I do want the errors in the paper, if they indeed are errors, exposed.

RSOS does not want to retract the paper, either, they do want the critics of the paper to submit "commentaries".

If anyone wants to see my draft before Tuesday morning when I can (I hope) post the arXiv reference, please just send me an email or a PM on this forum. I don't say anything new which I haven't said in public before, so Joy will have no difficulties in shooting my contribution down.

If Joy wants to suggest further referees he can tell me privately and I'll pass on their coordinates to RSOS.

I'm not even a real mathematician, I'm just a statistician, and I've been retired for so many years that I am no longer allowed even to have PhD students. Nobody needs to believe me.
Last edited by FrediFizzx on Sat Oct 24, 2020 10:12 am, edited 1 time in total.
Reason: Personal attack deleted.
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Re: Bell's Theorem and Normed Division Algebras

Postby local » Sat Oct 24, 2020 10:32 am

gill1109 wrote: Nobody needs to believe me.

Not to worry, we don't.
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Sat Oct 24, 2020 10:33 am

local wrote:
gill1109 wrote: Nobody needs to believe me.

Not to worry, we don't.

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

Postby gill1109 » Sat Oct 24, 2020 11:22 am

Joy Christian wrote:
local wrote:
gill1109 wrote: Nobody needs to believe me.

Not to worry, we don't.

:lol:

I'm not worrying! I'm having a lot of fun; and I hope that that also holds for "local" and for Joy! :mrgreen:
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Re: Bell's Theorem and Normed Division Algebras

Postby Joy Christian » Sun Oct 25, 2020 9:57 am

gill1109 wrote:
I just submitted to RSOS, and to arXiv, a comment on Joy's RSOS paper. The RSOS paper depends on the material in the Algebra paper. I named Joy as a person who should definitely be asked to referee my paper... I do not want the paper retracted, but I do want the errors in the paper ... exposed.

If Gill's paper is indeed submitted to RSOS, and if RSOS takes his paper seriously, and if I am asked to review it, then I will certainly recommend his paper for publication out of self-interest.

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