Julio's periodic cone

[ERIC SCERRI]

Hola Julio,

Que tal?

I tried to post a response to your recent posting.  Did it appear?

I am asking because I did not see it and could not even find it in my “sent mail" box.  So this is a 2nd and briefer attempt.

I was saying that I very much liked your video and your way of presenting the periodic system in an abstract manner, which ignores

anomalies and specific details about the elements interpreted as ’simple substances’.

As Mendeleev emphasized, the periodic system is primarily concerned with the abstract sense of ‘element’.

On this point, I have recently co-authored an article on structural realism in the context of the periodic system which is currently under review at a philosophy of science journal.

Here is a pre-print,

[ERIC SCERRI]

<184. SR-PT-Michele.pdf>

Finally, have you built a 3-D model of your conical representation of the elements as seen in the video?

How would a conical representation look if the arrangement were not based on binods but on the usual single-period representation?

Also, you make an analogy with Kuhn’s view on anomalies and scientific revolutions.

How does your binodic approach resolve these anomalies?

regards

Eric

ERIC SCERRI PhD

UCLA

Website: http://www.ericscerri.com
PhilPeople https://philpeople.org/profiles/eric-scerri
Google Scholar https://scholar.google.com/citations?hl=en&user=8w1T5bEAAAAJ
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Editor-in-Chief of Foundations of Chemistry https://link.springer.com/journal/10698

 

ERIC SCERRI PhD

UCLA

Website: http://www.ericscerri.com
PhilPeople https://philpeople.org/profiles/eric-scerri
Google Scholar https://scholar.google.com/citations?hl=en&user=8w1T5bEAAAAJ
ResearchGate https://www.researchgate.net/profile/Eric-Scerri

Editor-in-Chief of Foundations of Chemistry https://link.springer.com/journal/10698

 

[Julio Gutiérrez Samanez]

Dear Eric and colleagues:

 

Yes, I received your initial communication, and I began translating and reading your article on structural realism in chemistry. I found it novel and fascinating that the most important thing is the "structure," which in scientific terms is always a mathematical formulation, equations, or functions, as in Physics. The article concludes that chemistry, especially the Periodic Table or the periodic system, cannot be expressed mathematically. This means that structural realism could not be applied, which would prevent a "general and complete philosophical explanation of mature science." I am currently trying to reconcile or differentiate your assertion with my own years of work searching for a function that mathematizes the periodic system, precisely to rationalize the periodic system from a mathematical foundation, apart from the phenomenological aspects of chemistry itself (furthermore, if we consider that it deals with proton relationships, we temporarily disregard what happens with the electrons). In this understanding, I have achieved some successes that may be useful, which I will send you in more detail: First, without thinking about it or intuiting it, just by testing it again and again, the two functions (2n²) (the size of the Pauli periods) and (4n²), which I call the binodic function, already known since Rydberg, which Janet probably also knew (1928), and which Hakala rediscovered (1952), turn out to be quadratic parabolas, functioning as "structural patterns."

 

I performed the (sum of the squares of n times 4) and something unexpected happened: the function turned out to be Z,  The complete series of atomic numbers! This was before 2002 and it's in my 2004 book. It struck me that it was necessary to "double the principal quantum numbers," and I had to devise another number, (N), exactly the same as the Rydberg ordinal numbers, which I was unfamiliar with. Obviously, if we consider the elements in the DIM concept (as abstract entities, stripped of their attributes as "individual entities"), my mathematical proposal (4 Summation of N squared) turns out to be that basic formula for rationalizing the periodic table and all imaginable "tables."

 

I owe these conceptions to Baca Mendoza (1965) (who was a dialectical materialist and sought to mathematize the periodic table) and to my readings of Bachelard when he says: "The science of reality is no longer satisfied with the phenomenological 'how': it seeks the mathematical 'why'" (in the introduction to his work: "The Formation of the Scientific Mind" (1948)). From there to Worrall's conception, which I am only now becoming familiar with, there is no difference whatsoever. It is natural that science is built with failed hypotheses or scaffolding; by discarding them, the finished work appears, which, later, will also be surpassed by other, more sophisticated theories and technologies. I believe that this dynamic conception is very important in science, and it comes from Haraclitus, Leucippus and Democritus, Hegel, Engels, and perhaps even Kuhn. I think that when an old building requires patches, remodeling, and shoring, it is because it is about to collapse. We must have the blueprint for the new building with a new, broader paradigmatic conception, as occurs in the metamorphoses of certain animals.

 

Chemistry is the science of matter that presents itself as a fluid; it is "diffusional processes" that we see throughout the cosmos, physics, and biology.

 

If you carefully observe my video on the telluric helix over a cone, you can clearly see that there are three "relational patterns" of matter: A pattern of division of the binodes or segments of the cone that determine the quantitative growth (2n²) = 2, 8, 18, 32, 50... Each binode contains two spirals of different sizes, but with the same number of elements (doubling of periods), that is: (n, n) (which is why I propose the fifth quantum Tau, which can be seen in my "Genome of Matter" published by Mark in 2016). The other pattern is (4n²) = 4, 16, 36, 64, 100... is what determines the size of the binodes or pairs of symmetric periods.

 

Finally, the third pattern is that of the summation that links and concatenates everything, by defining Z as a function of the number N or the order number of the binode. Therein lies the very simple and straightforward mathematics that underlies the Periodic Table, necessary for its "realistic" structural rationalization. DIM's genius was that, a century and a half ago, he glimpsed this ordering and gave it predictive use even before it had been revealed or discovered to him.

 

But it doesn't end there. In another graph I sent you earlier, I proposed a cone whose generatrix Z contains the series of atomic numbers colored with the colors proposed by H. Bent to identify the chemical properties of the elements (strictly speaking, "some" of the chemical properties, as G. Restrepo pointed out). These colored spiral functions show growth. and the expansion of "chemical space," periodic, binodic repetition, and generation of new quantum azimuthals, with complete accuracy and without exception, as a limit of some cosmological constant (which would be the standard predictions). Furthermore, if we develop these lines or strings using the "Baca Mendoza oblique line," we can find the other limit of this cosmological growth constant: the one that determines the actual and effective appearance of the azimuthals, d, f, g... (Baca Mendoza's predictions): (In the fourth binode, the appearance of "f" orbitals shifts from the pair (57La, 89Ac) to the pair (58Ce, 90Yh); (and the prediction of the appearance of "g" orbitals in the fifth binode shifts from the pair (121, 171) to the pair (123, 173)),

we can no longer consider them as "anomalies or peripheral or superficial exceptions" but as a contraction, shift, or necessary adjustment that matter makes (in the "colored strings or lines"). To balance the "strain" or distortion effect inherent in atomic topology, the screening effect, spin-orbital coupling, relativistic and non-relativistic effects, etc., which has led to approximations (Hartree-Fock), relativistic Dirac corrections, treatment of electron correlation, etc. (as Pekka-Pikko pointed out to me in a personal communication about my 2020 Foch article). Undoubtedly, this will generate paradigm shifts in aspects of the philosophy of chemistry, wave functions, the concept of islands of instability, etc., and a "binodic" Schrödinger equation will have to be formulated—topics that exceed my modest abilities.

Have a wonderful holiday season.

Regards.

 Julio

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1221

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=946

www.academia.edu/144611039/HARMONIC_PERIODICITY_OF_THE_CHEMICAL_PROPERTIES_OF_THE_CHEMICAL_ELEMENTS_2025_

[Julio gutierrez samanez]

Julio Antonio Gutiérrez Samanez

TALLER INCA Escuela de Cerámica y Arte.

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[René]

On 22 Dec 2025, at 06:43, ERIC SCERRI <sce...@g.ucla.edu> wrote:

As Mendeleev emphasized, the periodic system is primarily concerned with the abstract sense of ‘element’.

Dear Eric

As I understand it, there is more to what Mendeleev emphasised than the abstract sense of an element.

He wrote that atomic weight served as the departure point for the discovery of the periodic law, and that the law expressed a relationship between variables: atomic weight as the first variable, and chemical and physical properties as the second. As he put it:

"It is not only in the forms of the compounds that we observe a regular dependency when the elements are arranged according to...atomic weights but also in their other chemical and physical properties.

It would be more correct to call my system ‘periodic’ because it springs from a periodic law, which may be expressed as: "The measurable chemical and physical properties of the elements and their compounds are...[an approximate] periodic function of the atomic weight of the elements." (Mendeleev 1871, 1871a, in Jensen 2005, pp. 45, 116).

It seems, then, that the periodic system is concerned just as much with the measurable chemical and physical properties of elements (including as simple substances) as it is with their abstract sense, from which a semi-periodic repetition of properties is observed.

The ostensible counter-example given at p. 8 of the preprint is, in my view, less than successful. It says that:

"...the halogen elements (fluorine, chlorine, bromine, and iodine) appear to be very different from each other if one focuses on the simple substances, since they consist of two gases, a liquid, and a solid, respectively."

However, if one plots Z against melting point for the four halogens, the result is a smooth trend with a second-order polynomial fit of R² = 0.977. A corresponding plot for boiling point is likewise smooth (0.962). Thus, despite their mixed macroscopic appearances, the halogens are closely related, in a periodic system sense, even as simple substances.

I have a few other concerns about the preprint, which I intend to post separately.

best regards,

René

• Jensen, W. B. (ed.): Mendeleev on the Periodic Law: Selected writings, 1869–1905, Dover Publications, Mineola, New York (2005)
• Mendeleev, D.: On the periodic regularity of the chemical elements, Annalen der Chemie und Pharmacie, 6 (Supplmentband) 133–229 (1871) in Jensen (2005)
• Mendeleev, D.: On the question concerning the system of elements, Berichte der Deuthschen Chemishcen Gesellschaft, 4, 348–352 (1871a) in Jensen (2005)

[Julio gutierrez samanez]

Dear colleagues, dear Eric,

I am sharing my latest experiences working with Artificial Intelligence platforms, which I have used to analyze some of my texts and my postgraduate thesis on the application of the binomial periodic system in teaching the chemical periodic table. I look forward to your expert opinions. I believe that AI is a valuable and useful tool for scientific research.

https://www.academia.edu/145664523/THE_BINODIC_PERIODIC_SYSTEM_THE_ENCOUNTER_BETWEEN_NATURAL_AND_ARTIFICIAL_INTELLIGENCE

Happy New Year!

Warm regards

 Julio

[Brian Gregory]

I asked Google’s Gemini “what is the quantum fold periodic table” and it gave a beautifully accurate and detailed description. I asked the exact same question to chatGPT and it said, to paraphrase, "pseudoscience not recognized in legitimate research”. Wow!

-Brian

Happy New Year

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[ERIC SCERRI]

Don’t worry about it Brian. I too have been getting some bizarre responses from chatGPT. 

HAPPY NEW YEAR TO ALL FELLOW PERIODIC TABLE FANS. 

Eric Scerri

On Dec 30, 2025, at 3:09 PM, Brian Gregory <brian.g...@gmail.com> wrote:

I asked Google’s Gemini “what is the quantum fold periodic table” and it gave a beautifully accurate and detailed description. I asked the exact same question to chatGPT and it said, to paraphrase, "pseudoscience not recognized in legitimate research”. Wow!

[Julio Gutiérrez Samanez]

This is what happened to me at first; the AI knew nothing about what I was asking it to do. But I kept feeding it information, requesting articles, books, authors who addressed the topic, etc., and it still gave incorrect answers. I persisted, pointed out the errors, and the AI corrected them, agreeing with me, so the collaborative work proved to be improvable. Afterward, I asked it to synthesize the conversation and the questions and submitted the result to both AIs. The result was admirable; it produced critical and self-critical assessments. The second AI highlighted the qualities the first one had seen and apologized for not having seen them, revising its previous verdict—something that can't be done in peer review. Furthermore, the AI doesn't harbor emotional or personal biases, prejudices, suspicions, complicity, or preference for any particular paradigm, etc. It is, after all, a machine; its reasoning is direct, impartial, objective, schematic, and concise. But they can be wrong, due to the "bias of the dominant paradigm" with which they have been trained. They acknowledge their limitations, although, because of the volume of information they handle, they find unexpected interrelationships and rebel against what they recognize as "academic silence," which they say can be more harmful than criticism because it blocks all innovation.

Topics such as the ontological and epistemological status of a theory, the heuristic evaluation of research, are not beyond their reach, as they might be for the "natural intelligence" of the researcher.

 

Dear colleagues, this year was almost fatal for me; I had serious health problems. I hope that next year will be even better. That is what I wish for all the wise members of this website, many of whom have already left us, such as: Philip Stewart, Henry Bend, Rubén Darío Osorio, Ray Hefferlin, N. Ymyanitov, and Gary Katz. We will always carry them in our memories.

Many thanks to all.

Julio

[ERIC SCERRI]

On Dec 31, 2025, at 10:30 AM, Julio Gutiérrez Samanez <kut...@gmail.com> wrote:

This is what happened to me at first; the AI knew nothing about what I was asking it to do. But I kept feeding it information, requesting articles, books, authors who addressed the topic, etc., and it still gave incorrect answers. I persisted, pointed out the errors, and the AI corrected them, agreeing with me, so the collaborative work proved to be improvable. Afterward, I asked it to synthesize the conversation and the questions and submitted the result to both AIs. The result was admirable; it produced critical and self-critical assessments. The second AI highlighted the qualities the first one had seen and apologized for not having seen them, revising its previous verdict—something that can't be done in peer review. Furthermore, the AI doesn't harbor emotional or personal biases, prejudices, suspicions, complicity, or preference for any particular paradigm, etc. It is, after all, a machine; its reasoning is direct, impartial, objective, schematic, and concise. But they can be wrong, due to the "bias of the dominant paradigm" with which they have been trained. They acknowledge their limitations, although, because of the volume of information they handle, they find unexpected interrelationships and rebel against what they recognize as "academic silence," which they say can be more harmful than criticism because it blocks all innovation.

Topics such as the ontological and epistemological status of a theory, the heuristic evaluation of research, are not beyond their reach, as they might be for the "natural intelligence" of the researcher.

 

Dear colleagues, this year was almost fatal for me; I had serious health problems. I hope that next year will be even better. That is what I wish for all the wise members of this website, many of whom have already left us, such as: Philip Stewart, Henry Bend, Rubén Darío Osorio, Ray Hefferlin, N. Ymyanitov, and Gary Katz. We will always carry them in our memories.

Many thanks to all.

Julio

Dear Julio,

I am very happy to hear that you have recovered from your illness.  

Your dedication to the study of the periodoc table is an example for all of us.  I still remember very fondly the 3rd International Conference on the Periodic Table which you so ably organized in your home town of Cusco, Peru in 2012, where Ruben and Ray presented papers.  

Thank you for remembering the colleagues you mention, all of whom I knew.

What I did not know was that Gary Katz had passed away.  It was his article in “The Chemical Educator” which first turned my attention to Janet’s left-step periodic table.  

Here is the article,

[René]

Presumably, different AI models can yield different responses depending on how a question is framed and how cautiously each model interprets unfamiliar or non-canonical terminology.

I expect the same goes for humans.

René

[Mark Leach]

Hi All,

As reported by Chemistry World, this periodic table was generated by Microsoft’s Co-Pilot AI:

Yup, it's in the database!  https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1344

Mark Leach

meta-synthesis

[Mario Rodriguez]

This is an example of an “AI hallucination”. This phenomenon can occur in a lot of fields, and it can be mitigated within the same AI with more training.

For this reason, it is always important to include the exact prompt used, since different prompts can lead to different results, even with the same version of an AI. An AI principle, referred to as “shit in, shit out”, states that the quality of the output depends on the quality of the input prompt. 

In other words, it cannot be described simply as the Copilot Periodic Table, but rather as a Periodic Table generated by Copilot in 2025 using a specific prompt. A different prompt can produce a different table, and over time Copilot may improve its ability to generate these representations. It may even eventually consider drawing the periodic table as a spiral :)

Mario RP

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[Larry T.]

Yeah! Quite a contraption! H/He is very telling. Both start with the same letters.

On Fri, Jan 2, 2026 at 12:44 PM Mark Leach <ma...@meta-synthesis.com> wrote:

Hi All,

As reported by Chemistry World, this periodic table was generated by Microsoft’s Co-Pilot AI:

Yup, it's in the database!  https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1344

Mark Leach

meta-synthesis

meta-synthesis.com.

[René]

There’s nothing to see here.

AI is a tool in one’s toolbox. Anyone who uses a tool presumably checks the outcome of that use.

The Chemistry World article...

https://www.chemistryworld.com/news/the-chemistry-community-should-ban-drawing-chemical-structures-with-generative-ai-chemists-warn/4022242.article

...also included a ChatGPT image:

The legend is in the wrong place; the lower half of the actinides are missing. While the rest is accurate the image is obviously unusable in its current form. Disappointing. That aside, so what?

René

On 3 Jan 2026, at 04:44, Mark Leach <ma...@meta-synthesis.com> wrote:

Hi All,

As reported by Chemistry World, this periodic table was generated by Microsoft’s Co-Pilot AI:

[René]

Nice call Larry. I missed H/He the first time I looked at the image.

Perhaps Copilot had in mind my H over He paper:

Or see:

https://chemrxiv.org/engage/api-gateway/chemrxiv/assets/orp/resource/item/6370605c80c9bf76689515a5/original/hydrogen-over-helium-a-philosophical-position.pdf