Clarifying the add vs average issue and Irreducible Cartesian Tensors

[Bryan Sanctuary]

Dear Richard,

Now that the Diether debacle has subsided, I would like to discuss and focus on the substantive issues.

I was disappointed by your recent remark suggesting gaps in my basic mathematical education and comparing me with Fred. After the prolonged ad hominem attacks from Fred, I had hoped we could now proceed in a more collegial and technical spirit. I ask that we all, and you, refrain from personal characterizations and keep the discussion focused on mathematics and physics. I have not made ad hominem remarks about anyone in this group to my knowledge, and I intend to keep it that way.

I readily acknowledge that my formal mathematical training does not match yours. That is not in dispute. My background was shaped by Bob Snider and John Coope at UBC when I was in grad school, particularly through Irreducible Cartesian tensors (ict), which Bob later summarized in his book. I attach a copy of ict.pdf for anyone who is interested in that subject: I most certainly benefited from it. That background led me naturally to geometric algebra and how I think about spin. Whether my approach is correct is, of course, a matter for technical discussion, not credentials

What concerns me in your remark is your specific phrase:

 “the(sic your) confusion about whether you can add correlations or take convex combinations of them.”

This is a key point, and I raised it in Section 2.4 of my response to Diether. There I show that reproducing the full EPR correlation requires two distinct contributions, not one. That conclusion is not my opinion but follows from a decomposition and an isotropic average. I am certain this was not lost on you.

I would very much welcome a clear, technical critique of that. If you believe Section 2.4 is mathematically incorrect, I ask you to identify precisely where the reasoning fails. If, on the other hand, you believe the calculation is correct but physically irrelevant, I ask you to state why.

You have privately shared with me that Anton asked ChatGPT to analyze parts of my work. I am not opposed to such critiques, but I would prefer that objections be stated openly here for the group, rather than by implication or dismissal. If you are willing, I suggest opening a new thread focused specifically on the add-versus-average issue in the context of EPR correlations. I will respond in good faith.

This question is not marginal but central to Bell. If the two-channel structure is valid, the implications are substantial. If not, then it should be possible to say exactly why. Either way, this seems squarely within the purpose of this group.

Bryan

[Mark Hadley]

Dear Bryan,

Yes, I thought Fred behaved just like you with the mathematical arguments, except he added in rudeness - you remain polite. It was amusing seeing you argue. A case of the kettle calling the pot black.

Your mathematical mistakes have been pointed out so many times and in so many different ways, by several people. and each time you ignore the comments or deny very simple maths.

Correlations of combined populations is high school maths. I know you can do that. I know you don't like the result. Your position in this is not scientific, it is emotional and fraudulent. I don't know why you have raised it again. You have been shown how to combine correlations in small simple detailed steps. You have been shown the structural nonsense off you equation. And you have been told how to disprove by example using a spreadsheet.

You persist in presenting new material to the group. But I won't look at it because you have destroyed your own credibility. Others are welcome to engage with you, but I would caution them not to.

Mark

[Jan-Åke Larsson]

Bryan was not polite in the end to me, when I did exactly what he is asking for: 

Show that even if the full EPR correlation requires two distinct contributions, not one, correlations are created by convex combinations. 

This is always the case, whatever the underlying distribution. With Bryan's method, the total probability is strictly larger than 1 which is nonsense, of course.

After I pointed this out to Bryan he resorted to name-calling.

I will not rejoin the group.

/Jan-Åke

--
Jan-Åke Larsson
Professor, Head of Department

Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:512 Please visit us at www.liu.se

[Richard Gill]

Chat GPT made the same analysis as I did! You are making category errors.

Of course you can express 3 as 2 + 1. You can separate terms and then use fancy words, and come up with a story about helucity and spin. But what you say about dual convex sets is just non-sense. And what you say about statistical data analysis for Bell experiments is non-sense too.

Many people asked for literature references but you gave none. My guess is that you are recycling technical words which you saw in a different context long ago, without actual mathematical understanding of the resulting sentences.

In this sense your grasp of maths is similar to Fred’s. In all other respects you are incomparable.

Sent from my iPad

On 12 Jan 2026, at 09:33, Bryan Sanctuary <bryancs...@gmail.com> wrote:



<ict.pdf>

[Bryan Sanctuary]

Jan-Åke

Please tell me what names I called you?  Please copy them to the group.

 If you recall you continually said that I failed probability 101, and ridiculed me for adding.  You simply stated I was wrong without engaging as to why. No issue if you are not interested but you have nor replied in substance.. 

I will reply to Mark soon, and I will copy you for the last time. After that it is up to you if you wish to engage or not.

Regards

Bryan

 

[Richard Gill]

Honestly Bryan,  I am sure you passed Probability 101, but I do guess it was a long time ago. And what about Statistics 201?

Sent from my iPad

On 12 Jan 2026, at 11:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Mark Hadley]

Jan did tell you why you were wrong.

Repeatedly, he put a lot of effort into helping you. As did others including myself. We gave you very detailed explanations of what you were doing wrong.

[Mark Hadley]

I personally do think Bryan can do the maths.

He made a maths error, we all do at times. But he liked the wrong result, it played to his narrative. So he refused to correct it.

Bryan's formula show a lack of integrity, not an inability at maths.

Mark

[Richard Gill]

Adding is just wrong. Bryan just does it, he does not give mathematical justification.

“Convex duality”, Minkowski sums and now Cartesian Tensors have nothing whatever to do with this.

Sent from my iPad

On 12 Jan 2026, at 11:30, Bryan Sanctuary <bryancs...@gmail.com> wrote: