Triads, symmetry etc.

[ERIC SCERRI]

I have resisted chiming in on this discussion even though I have been named.

This is partly because I am too busy teaching two courses at UCLA.

The first is philosophy of science, offered jointly through the chemistry and philosophy departments, for which the primary scientific example is the development of the periodic table.  The second is a general chemistry class of 350 students.

Rene, in particular, has commented several times, and for many years before, that we should place greater emphasis on chemical properties than on underlying symmetry.

This is an opinion, not an incontestable ‘axiom’.  

Of course, individual and specific properties of elements are of huge importance, and I have much respect for individuals like Rene who have the bandwidth to delve into specifics.  

But many among us beg to differ.  For example, many important discoveries in physics have come about as a result of making symmetry a primary consideration (Dirac’s prediction of antimatter, Gell-Mann’s prediction of the omega minus particle, more recent developments in gauge theories, etc. etc.)

Another such area is the attempts to understand why the first period length in the periodic table does not repeat (An ongoing research program in group theory), or why it should perhaps repeat (a la Janet ) 

See Pieter Thyssen’s book on “Shattered Symmetry” and my article in the 150th anniversary of the periodic table book edited by Carmen Giunta et al.

[Scott Hutcheon]

Thanks for sharing Eric, devoured these papers, and honest apologies if what follows is just a nonsensical thought experiment based on/triggered by them.

It's easy to negate atomic numbering and the mathematically related horizontal triads as now blindingly obvious (see 20/20 hindsight and Schopenhauer quote) if not reminded that the 1913 fundamental elements/periodic table paradigm-shifting confirmation -- from atomic weights without perfect horizontal triads to atomic numbers with -- required one of the greatest physicist minds in history (Moseley) whose early/senseless death in battle was a tragedy for science.

Placing all elements in horizontal triads is trivial now for a natural periodic table containing sequential atomic numbering (Z), but placing all elements in horizontal and vertical triads while also maintaining physical and chemical periodicity is not. 

The previously shared Right-step Triadic (RTPT-32) and it's cousin the cylinder wraparound version Split Triadic (STPT-32, which maintains 2-8-8-18-18-32-32 periods), are the only known scientific (universal) periodic tables that contain 100% Döbereiner-Scerri vertical triads.

However, Eric's shared papers here remind of a train of thought that was derailed as too mathematically convenient regarding the Right-Step (RSPT-32) while trying to find 100% vertical triads -- as the RSPT-32 was previously shared as the closest known with only 4 elements not also in vertical triads.

Coming from a physics-astronomy-cosmology background, the thought had been back in 2021 --following that evolution in an Emergent Universe began with and continues through Information → Physics → Chemistry → Biology (without the need for any Catholic Priest religious belief "proof of God" singularity) -- that the periodic table straightforwardly represents the Chemistry level of elemental evolution (with its exponential increase in complexity through an added layer of electronic/charge density relationships).

Per Eric's mention of using triads to find element placement and periodic table solutions (and other related ideas in the papers), the 16.4 diagram of Gell-Mann’s eight-fold way recalled this discarded RSPT variation (the -3, -2, -1, and 0 were originally part of an extended staircase including Hydrogen and Helium):

While the Free Proton as 0 here made no sense, as atomic numbering is based on protons, the thought was three pre-element (pre-Chemistry) generations (per the Standard Model) -3, -2, and -1 leading up to 0 and then 1s1 (Hydrogen, with its proton and electron).

This led to the idea that perhaps quarks (considering protons and neutrons, as well as isotopes, etc.) could be more fundamental than current atomic numbering -- revisiting atomic mass, but with total quarks/types instead as the driver-causation for an element's chemical and/or physical properties that cannot currently be predicted by atomic weight and or atomic numbering (knowing isotones still maintain parent element properties though their total quark types are different).

Had discarded this as a cheating workaround to get 100% triads for the RSPT-32 (going on to find the RTPT-32/STPT-32 instead), though the staircase up variations for -3, -2, -1, and 0 had considered three generations, quarks, quark components (leading up to quarks being the 0), as well as information energy-dark energy-dark matter-quark or information-bosons-fermions-hadrons or gravity-weak nuclear force-strong nuclear force-electromagnetism as the four steps.

Also, unclear as to where the 0s Free Proton and Alpha Particles (no electron shells) would fit in here, or even if they needed to. 

Obviously, it would be quite the paradigm-shifting breakthrough if the Periodic Table (Chemistry) and the Standard Model (Physics) could necessarily be sequentially joined/combined through the symmetry breaking required by evolution (understanding energy/mass interconversion).

Any suggestions by anyone for what else -3, -2, -1, and 0 could be are welcome!

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Secondly, from a philosophical perspective, there are many thinkers, including Mendeleev, who put more emphasis on underlying structure than on individual and specific properties.  I have written about this in many places, including most recently in a paper I am enclosing below on structural realism.

The general idea is that we should assign more realism to the underlying structure than to the scientific entities.  There is a large literature on structural realism in many areas of science, especially in physics, where realism is attributed to the underlying mathematical structure rather than the ever-changing list of supposedly fundamental particles.  I refer to some of that literature in the paper.

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Finally, I disagree strongly with my late friend, Philip Stewart, saying,

 "Triads are a consequence of the structure of the system, and a consequence cannot determine a structure."

Triads are a consequence of chemical periodicity, not just of the system!

And given that they successfully track chemical periodicity, it is legitimate to turn the argument around and use structure to determine periodicity when the latter is ambiguous, in cases such as H or He, or both.  

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

 

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[Mario Rodriguez]

To address your last question, I think the only way that negative Z can make sense is if you consider antimatter, where you have an antiproton with negative charge. However, you wouldn´t have only until -3, but all the way down until -118 or beyond. Bringing an excerpt of this paper about Janet (https://www.researchgate.net/publication/225545084_Charles_Janet_Unrecognized_genius_of_the_periodic_system)

"Janet introduces element zero because ‘its existence is necessary to complete the series of atomic numbers in the alkaline earth column’. He explains that its nucleus would consist of two protons and two ‘nuclear electrons’—in effect a dineutron. He makes the astounding suggestion that this might be the bridge between the periodic system we know and a periodic system above it with negative atomic numbers, ‘but for the moment we shall not dwell on this possibility, which would disturb the perfect arithmetic and consequently chemical regularity’ of the system (Janet 1930,pp. 28–29). In fact, as we now know, there would be an ‘element minus-zero’, with anti-neutrons as ‘atoms’, so there would be two periods of one element linking the matter and antimatter systems, maintaining the symmetry of pairs of periods. Anyway, working in parallel with Dirac, Weyl and Oppenheimer, Janet invented anti-matter."

In summary, a Left Step table of matter, the link Z=0 (neutron or neutronium) + Z=-0 (antineutron) and a "Right Step table of antimatter".

Mario RP

https://groups.google.com/d/msgid/PT-L/CANbBqwg0VsmSoR4FX54PQM8n5wX4A-Y%2BHNumivOQkoGQ8PnkOA%40mail.gmail.com

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[Julio Gutiérrez Samanez]

“Conclusion

Attempts to explain the periodic table have been a major driving force for physicists throughout the 20th and 21st centuries. Although quantum mechanics provides an ab initio explanation for the length of periods, it has not yet explained the phenomenon of period doubling or the Madelung rule, which governs how atoms are constructed as one moves across the periodic table. Beginning in 1970, but drawing on earlier work dating back to classical two-body mechanics, group theorists have gone beyond quantum mechanics to search for the symmetry underlying the periodic system. Although considerable progress has been made, such as the recognition of the symmetry group underlying the periodic table, this project has not yet been fully successful. What remains to be done is to discover precisely how the underlying SO(4,2) symmetry is broken to produce the well-known features of the table, the first version of which was published by Mendeleev just over 150 years ago.” (Eric Scerri)

Dear colleagues. This is what Eric Scerri writes as a conclusion to the interesting article he shared with us. Although I don't yet fully understand the issue of breaking the "SO(4,2) symmetry," it's logical that there is an underlying symmetry to the periodic table. In fact, in my modest work, invisible to theorists until now, I have derived certain functional relationships from the work of Rydberg, Janet, Baca Mendoza, and Bent, which seek to highlight the aforementioned symmetry.

Now that the group is investigating triads and the system of 32 elements arranged in right-step rows, Baca Mendoza's work comes to mind. In the table presented by Scott Hutcheon, the first “dyad” or “binode” of bold composition, with “elements” or “subatomic particles” (-3, -2, -1, 0, 1, 2, 3, 4), forms the dyad (8, 8) with its pair. Obviously, this is followed by the subsequent dyads: (18, 18); (32, 32)... The same occurs with Baca Mendoza's proposal (1953) (which Mark published on his website) in which, in the first dyad or binode, hydrogen is superfluous. Therefore, to preserve the pair (8, 8), hydrogen is removed from the table as a “bridging element between matter and antimatter.”
Thus, without hydrogen, the series (8, 8); (18, 18) holds true; (32, 32)…, which result from the relation: 2(n^2), 2(n^2), where n is greater than 1. However, following Rydberg and Janet, this duality with n = 1, 2, 3, 4, …., generates the complete pairs: (2, 2), (8, 8), (18, 18), (32, 32)… without resorting to particles or hypothetical negative elements, since, placed horizontally, the binodes reproduce the series: 4, 16, 36, 64… which are the squares of the even integers. These same numbers, added one by one, reproduce the series: 4, 20, 56, 120… a series that seems to show the periodicity in its entirety, since, plotted on a parabolic curve, it contains, on the Y-axis, all the atomic numbers Z, as a function of the number corresponding to the binode or dyad. Where Z arises from mathematically operating on the quadruple of the sum of the squares of the binode number. This new sequence does indeed "explain the phenomenon of period doubling," so dear to our friend Scerri. In reality, chemical periodicity does not occur between periods but between "double periods," and to understand this requires another quantum number (N) (different from (n)) or binode number, which appears or changes after two periods (n) of equal size of elements. This coincides with the appearance of a new azimuthal quantum number (s, p, d, f...). This identifies the binode and is fundamental to understanding periodicity because it defines the "symmetry underlying the periodic system." Therefore, triads and other ways of revealing periodicity are derivatives or consequences that—although I regret that Eric does not admit it—cannot determine the system. However, I could be wrong.

Likewise, it is evident that the periodicity is not monotonous but increasing and progressive, as Dr. Baca Mendoza opined. And this growth occurs in pairs of periods, not in individual periods. Understanding this, it would not be necessary to go "beyond quantum mechanics," since we only need to admit a new concept to give a new order to the puzzle of the periodic system, even though the standard table in use remains unchanged.

I hope to see in my lifetime the moment when someone else joins these ideas that, modestly, without being a university professor, a doctorate, or a PhD, I have dared to offer to science with no other hope than to have contributed some truth.

A hug to all.
JAGS

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[johnmarks9]

Dear Mario,

Yes, it was a fascinating paper. Of course, as Kant noted back in 1781, we construct our world from the tools of our bodies and the calculations of our brains. Naturally, since humans have evolved perceiving four degrees of freedom (3 of space and one of time), we are inclined to interpret the world through this a priori 4-D prism. But light appears to ignore time: in its own frame of reference it takes no time to get anywhere: time doesn´t exist for it. And Feynman´s QED suggests that it is equally contemptuous of space.  Electromagnetism seems to be independent of our 4-D, so Gunnar Nordström, in his gravitational theory of 1914, simply extended Maxwell´s equations to 5-D to accommodate electromagnetism. Maybe a suggestion for periodic table mathematicians?