Triad Periodic Tables (including new variations with 100% Döbereiner-Scerri Triads)

[Scott Hutcheon]

Moving these Triadic Periodic Table variations into a separate email chain for clarity. The attached newly discovered PTs are variations of the RSPT-32 and RSPT-36 (Right Step Periodic Table) and contain Döbereiner-Scerri Triads for 100% of the elements.

A. 2025 Right-step Triadic Periodic Table (RTPT-32) Pros:

1) The RTPT-32 contains the Column of Instability (Mn–125, and related Island of Stability connection), as well as Schwarz's "backbone of the periodic table" with the connected H-Halogen Group (as per René also), the He-Octet Gases Group, and the Alkali Metals and Alkaline Earth Metals Groups; and

2) Contains the mandatory Sc-Y-La-Ac, as well as the B-Al-Sc-Y-La-Ac Group extension/relation that René has extensively researched, rehabilitated, and referenced; and

3) Contains periods of 8-8-16-16-32-32; and

4) Continues the RSPT idea of later orbital/charge density types 'pushing out' or displacing earlier orbital types, where here 4p and 5p are also displaced by 3d and 4d, and 6p and 7p are also displaced by 4f and 5f which naturally displaces 5d and 6d; and

5) As far as I'm aware, this is the only table that satisfies Eric's research on triads, René's research on the trends of the potential extended Group B-Al-Sc-Y-La-Ac, and the RSPT paper. Peace descended on the village and there was much rejoicing.

2025 Right-step Triadic Periodic Table (RTPT-32) Cons:

• This PT entirely breaks up the traditionally stacked p-block into three p-periods:This follows the mandatory breakup of the d-block into separate d-periods for any scientific (universal) periodic table in order to correctly incorporate the Column of Instability (and related Island of Stability, as well as the proper relationship for the REE elements), however, it appears too radical based on electronic/charge density periodicities; and
• Not aware of as much recent detailed work as René's on p1 B-Al-Sc-Y-La-Ac to justify these later p2- through p4-element headed Groups as sharing chemical and/or physical properties...
• Though this may be acceptable as p1- through p4-element groups of the p-block have always been an illogical and fundamentally unexplainable mixed-bag of chemically and/or physically unrelated elements, and René has provided detailed trend justifications for at least the p1-element headed Group containing B-Al-Sc-Y-La-Ac...
• Whereas p5 (Halogens) and p6 (Octet Gases) are uncontroversial Groups; and
• Comes preloaded with the obvious dismissal as the Split-p or Split-p Soup table -- though it has precedent with the 1934 VRPT-32 (Victor Romanoff Periodic Table) split-d periodic table that interests René: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=290

• 
  

B. 2025 Split Triadic Periodic Table (STPT-16):

This further variation of the RSPT and Right-step Triadic Periodic Table moves the p5 Halogens and p6 Octet Gases to the right (as per understood 'cylinder' aspect of periodic tables). Though I'm never satisfied with artificial gaps in PTs (here between the first four p-periods and their split p5 and p6 counterparts), the chemical and/or physical properties seem as near as perfect as possible for periods and groups.

C. 2025 Perfect Triadic Periodic Table (PTPT-16) aka the Maple Leaf Periodic Table (MLPT-16):

With the discovery of the RTPT-32, naturally the challenge was then to find a 'perfect' triadic table where every single element exists within perfect triads both vertically and horizontally. Per the RSPT paper and the Bell Curve Rule -- where focusing entirely on one aspect or entirely ignoring one aspect (such as triads) while ignoring chemical and/or physical properties leads to artificial tables -- the most interesting bit for me about this curiosity is that the first naturally occurring radioactive element (Bismuth) forms a group with the first unnaturally occurring element (Einsteinium). Though the expected Mn–125 Column of Instability forms with anti-rule artificial gaps in it (as Selenium and Tellurium and Iridium are not radioactive/unstable). Note: the RSPT paper predicts that the lone not-currently-considered-radioactive isotope of Mn (Manganese) will turn out to be around as unstable, at similar orders of magnitude, as the recently understood single primordial Bismuth (Bi) isotope is now known to be.

As always, commentary, critiques, and concerns are always welcome (what doesn't kill a table makes it stronger)!

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[Scott Hutcheon]

As I'm sure anyone who has or has had a long-term partner can relate, my wife took one look at the 'perfect triadic periodic table' and gleefully (with entirely too much joy and satisfaction) pointed out that two sets of elements (Chlorine 17–20 Calcium and Iodine 53–61 Promethium) do not form exactly perfect vertical triads (each part of 2/3 vertical triads instead of the required 3/3).

Changing the name of the more mathematical curiosity to the 2025 Maple Leaf Triadic Table (MLTT-16) and shelving it as it also does not contain the expected periodicities of a scientific PT.  

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[johnmarks9]

Calm down, Scott.

She´s wrong:

Each set forms perfect 18-triads:

Cl-Br-J, Ar-Kr-Xe, K-Rb-Cs, Ca-Sr-Ba, are all Döbereiner triads

Sc-Y-La, Ti-Zr-Ce, V-Nb-Bz, Cr-Mo-Ty, Mn-Tc-Pm, are all Sommerfeld triads.

Beylkin´s PT shows this clearly:

So enjoy your final glee . . .

John

[Scott Hutcheon]

After reviewing hundreds of related PTs, it's beginning to look more and more that Right-Step formulations are mandatory for scientific/universal PTs (which will be added to the RSPT paper Periodic Table Rules). This right handedness is necessary to include 100% of elements in Döbereiner-Scerri Triads, the Vernon Group 3 Sc-Y-La-Ac or extended B-Al-Sc-Y-La-Ac, the Schwarz backbone of the connected Halogens-Octets-Alkalis-Alkalines (and the related Vernon H-Halogens and He-Octets), and the Column of Instability (Mn, Tc, Pm, Np, 125).

Though humans have chased symmetry for thousands of years, we now know that reality is entirely asymmetrical at all levels and directly connected to handedness (or there wouldn't be a universe, physics, chemistry, or biology including us), and it seems therefore logical that a certain handed PT would necessarily be more scientifically-realistically-observationally-experimentally correct and less religious-philosophical-mathematical-theoretical.

What follows are examples and notes:

The 1953 Mendoza Right-Step PT (1953 MRPT-33) has 33 columns as the author searches to find a way to keep H naturally separate from the rest of the elements, contains the Vernon rehabilitated B-Al-Sc-Y-La-Ac, the Column on Instability, and has no artificial gaps, but breaks apart the Schwarz backbone connected (and Vernon) He-Octets and Alkalis and Alkalines from the Halogens and does not contain 100% Döbereiner-Scerri Triads .

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=407

The near ideal example of the primacy of handedness for scientific (universal) PTs is the 2002 Gutierrez-Samanez Right-step Periodic Table System A (2002 GSRPT-32A), by Julio, whose mathematical orientation in the Right-Step variant (see bottom image on linked page) includes the Vernon B-Al-Sc-Y-La-Ac, the Column of Instability (Mn-Tc-Pm-Np-125) and connected Island of Instability, has no artificial gaps between elements (correctly includes the Van den Broek-Moseley sequential atomic numbering breakthrough), but does not include the complete Schwarz PT backbone with the connected Halogens and Octet Gases by instead placing H over the Alkalis and He over the Alkaline Earths. The 2002 GSRPT-32B entirely breaks up the Schwarz backbone but keeps the Vernon B-Al-Sc-Y-La-Ac (as part of H-Li) and the Column of Instability (as part of F-Cl).

Conversely, the related 2002 Gutierrez-Samanez Left-Step Periodic Table (2002 GSLPT-32A) contains the Schwarz backbone and Vernon H-Halogens and the He-Octet Gases but does not contain the connected Alkali Metals or Alkaline Earths. The 2002 GSLPT-32B replicates Janet's Left Step Periodic Table (LSPT-32). They do not contain 100% Döbereiner-Scerri Triads:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1100
https://www.monografias.com/trabajos-pdf/tabla-periodica-nuevo-modelo/tabla-periodica-nuevo-modelo.pdf

Shared by René, the 2020 Gutierrez-Samanez Right-Step Periodic Table (GSRPT-32) version contains the Vernon B-Al-Sc-Y-La-Ac and the Column of Instability (but extended with F and Cl) and no artificial gaps, but also e over H and n over Ne (where, according to the RSPT paper, 0s would contain the Free Proton over H and the Alpha Particle over He):

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1303

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=313

Shared by René, the 2003 Rich Right-Step Periodic Table (2005 RRPT-23) contains the complete and connected Schwarz backbone (including René's H-Halogens and He-Octets), but contains the artificial f-periods gap and does not contain either 100% Döbereiner-Scerri Triads or the Column of Instability:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1242

Introduced by René, the closest to a scientific (universal) symmetrical PT is the 2018 Beylkin Symmetrical PT (BSPT-32), who commits the outsider blasphemy of correctly placing the d-periods (but only halfway due to a mathematical focus on symmetry) over the f- periods. This leads to a better PT with the mandatory Mn-Tc-Pm-Np-125 Column of Instability, the Schwarz PT backbone with the connected Halogens, Octets, Alkalis, and Alkalines, but without 100% Döbereiner-Scerri Triads, with the lesser B-Al-Ga-In-Tl (per Vernon's work on the stronger trending B-Al-Sc-Y-La-Ac Group extension), and with artificial gaps between elements (ignoring the Van den Broek-Moseley sequential atomic numbering breakthrough):

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1202

Again, while 20/20 hindsight makes the Column of Instability seem blindingly obvious (per the attribution to Arthur Schopenhauer “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.”), there have been no known previous proposals or references to such a self-evident Column of Instability and only halfhearted QM attempts to explain the seemingly random positions of Tc and Pm in the current unscientific standard table (SPT-18 and SPT-32).

While it's unbelievable that it took nearly 80 years for the Column (especially after the 1913 breakthroughs regarding atomic number and radioactivity) to be understood as a fundamental pillar for any scientific PT, it was simply a case of being unable to see the forces for the decision trees, as obviously the iconic standard table's Mn-Tc-Re-Bh-artificial gap-Pm-Np seemingly obvious 'column' is nowhere near the same as the Beylkin and Right-Step Tables Mn-Tc-Pm-Np (and extended Mn–125). Further, no such column exists with the SPT-32 (the standard periodic table in its proper 32-column form), and would continue to be missed with an extended SPT-50 (the standard periodic table in its proper extended 50-column form) if g-period elements are added (and the connection to the element 125 Island of Instability would still remain hidden).

As well, when it comes to arguments against breaking the d-block into properly related d-periods and f-periods, it is widely accepted that two rows don't a Group make (which is the excuse given for removing and dropping the f-periods below the standard table) and therefore confusing that so many authors have supplied the Sloppy Sandwich Suggestion of somehow proving all d-periods should remain in an artificially stacked d-block by showing that less than half of the artificially grouped 4d- and 5d-elements (the sandwich filling) show related trends which reduces to near zero related chemical and/or physical property trends down the artificial d-block when including the same vertically grouped 3d- and 6d-elements (the sandwich bread slices) in the artificial d-columns. Just as with the artificially isolated f-periods in the standard table, two rows of elements (here 4d and 5d) cannot be considered Groups with trends.

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[René]

On 13 Nov 2025, at 08:10, Scott Hutcheon <scotth...@gmail.com> wrote:

Hi Scott

Thanks for bringing so much energy to our list.

After reviewing hundreds of related PTs, it's beginning to look more and more that Right-Step formulations are mandatory for scientific/universal PTs (which will be added to the RSPT paper Periodic Table Rules). This right handedness is necessary to include 100% of elements in Döbereiner-Scerri Triads, the Vernon Group 3 Sc-Y-La-Ac or extended B-Al-Sc-Y-La-Ac, the Schwarz backbone of the connected Halogens-Octets-Alkalis-Alkalines (and the related Vernon H-Halogens and He-Octets), and the Column of Instability (Mn, Tc, Pm, Np, 125).

I don’t understand the relevance of triads. Could you explain it to me?

As Philip Stewart said, "Triads are a consequence of the structure of the system, and a consequence cannot determine a structure."

https://www.chemistryviews.org/details/ezine/1247399/At_Last_A_Definitive_Periodic_Table/?utm_source=chatgpt.com

Eric has noted that the LSPT features a certain regularity of triads however no element in period 1 (H, He) of that table is part of a triad whereas this is not the case for all periods thereafter. In contrast, all periods of the traditional table have at least one element that is part of a triad.

Though humans have chased symmetry for thousands of years, we now know that reality is entirely asymmetrical at all levels and directly connected to handedness (or there wouldn't be a universe, physics, chemistry, or biology including us), and it seems therefore logical that a certain handed PT would necessarily be more scientifically-realistically-observationally-experimentally correct and less religious-philosophical-mathematical-theoretical.

I am not sure about the merits of a right step periodic table in terms of asymmetry compared to the conventional periodic table, which is also asymmetric in appearance.

[trim]

Again, while 20/20 hindsight makes the Column of Instability seem blindingly obvious (per the attribution to Arthur Schopenhauer “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.”), there have been no known previous proposals or references to such a self-evident Column of Instability and only halfhearted QM attempts to explain the seemingly random positions of Tc and Pm in the current unscientific standard table (SPT-18 and SPT-32). 

While it's unbelievable that it took nearly 80 years for the Column (especially after the 1913 breakthroughs regarding atomic number and radioactivity) to be understood as a fundamental pillar for any scientific PT, it was simply a case of being unable to see the forces for the decision trees, as obviously the iconic standard table's Mn-Tc-Re-Bh-artificial gap-Pm-Np seemingly obvious 'column' is nowhere near the same as the Beylkin and Right-Step Tables Mn-Tc-Pm-Np (and extended Mn–125). Further, no such column exists with the SPT-32 (the standard periodic table in its proper 32-column form), and would continue to be missed with an extended SPT-50 (the standard periodic table in its proper extended 50-column form) if g-period elements are added (and the connection to the element 125 Island of Instability would still remain hidden).

In the Column of Instability, bohrium seems to let the concept down. There does not seem to be anything out of the ordinary or notable as far as Bh goes.

As well, when it comes to arguments against breaking the d-block into properly related d-periods and f-periods, it is widely accepted that two rows don't a Group make (which is the excuse given for removing and dropping the f-periods below the standard table)...

The two rows of the f-block are dropped below the main body of the table for space-saving reasons, rather than because two rows don’t make a group.

...and therefore confusing that so many authors have supplied the Sloppy Sandwich Suggestion of somehow proving all d-periods should remain in an artificially stacked d-block by showing that less than half of the artificially grouped 4d- and 5d-elements (the sandwich filling) show related trends which reduces to near zero related chemical and/or physical property trends down the artificial d-block when including the same vertically grouped 3d- and 6d-elements (the sandwich bread slices) in the artificial d-columns. Just as with the artificially isolated f-periods in the standard table, two rows of elements (here 4d and 5d) cannot be considered Groups with trends.

In the d-block, the 5d row is impacted by the lanthanide contraction and the 6d row is expected to be impacted by the actinide contraction. That is why the groups making up the 4d, 5d and 6d rows have, or are expected to have, comparable atomic and ionic radii and hence similar chemical behavior. The 3d row can be thought of as an example of a first-row anomaly.

René

[Larry T.]

I don't understand relevance of triads either. They played important role in the beginning of 19th century, but we are well past those times.

As it was demonstrated long time ago on this list, any tabulated sequence of natural numbers will generated triads.

Larry.

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[johnmarks9]

Dear René,

That´s a fascinating discussion you posted concerning the comments following David Bradley´s article "At last a definitive PT" back in 2011.

At something like the sixtieth comment, Eric asks Bernard Schaeffer why He behaves like an inert gas if it´s an alkaline earth metal in disguise?

One could equally ask why Be isn´t an inert gas in disguise? The argument is usually that the s-p energy gap is low enough that 2s no longer behaves like a full shell, i.e. all the electrons in the L-shell become "hybridized". But it could be argued that this phenomenon continues into the M-shell and that Zn isn´t an inert gas for a similar reason. This is why Scerri´s Sommerfeld triads have predictive periodic properties similar to Döbereiner´s triads. Chemical phenomenology justifies the original ´A´ and ´B´ subgroups.

Further in the debate, Martin Channon makes the point that, like all dynamic systems, the atom is 4-D: three in space plus one in time. Therefore 3-D and even more 2-D representations inevitably fall short. The Dewey decimal system works quite well for libraries despite the innumerable degrees of freedom in the subject matter of books. He links this to a more general problem of epistemology and seems to think there´s an ideal epistemology, which I didn´t find convincing. Stowe´s model shows the disposition of shells rather than periods. Tsimmerman´s formulation of Madelung is intriguing.

On Scott´s Column of Instability, I for one would be grateful, Scott, if you could spell out to dumbos like me its "blindingly obvious" nature, let alone significance. What are you getting at?
John

[René]

On 14 Nov 2025, at 06:11, johnmarks9 <johnm...@hotmail.com> wrote:

On Scott´s Column of Instability, I for one would be grateful, Scott, if you could spell out to dumbos like me its "blindingly obvious" nature, let alone significance. What are you getting at?

John

Hi John, and Scott

Here’s my understanding, bearing in mind Scott that you’ve focussed on Tc, Pm and Np and Ubp. It seems that the picture is broader than that. Thanks Scott (and John) for prompting a closer look at this subject.

The Column (or Axis) of Instability

The Axis of Instability refers to a sequence of unusual or anomalous behaviours that appear when moving down Group 7 and its two f-block shadows, Pm and Np.

In Group 7

Mn—crystallises in a highly complex and radical cubic structure with 58 atoms per unit cell. Four distinct coordination environments occur in α-Mn, each with a different effective atomic radius. This structure is unique among the metals.

Tc—radioactive despite lying among stable neighbours; none of its isotopes are stable, making it the lightest element for which this is true.

Re—the most radioactive of the naturally occurring elements that have a stable isotope. Only 37.4% of natural rhenium is stable (^185Re); the remaining 62.6% is ^187Re with a half-life of 4.16 × 10^10 years.

Bh—too poorly characterised for any firm conclusion.

The f-block shadows

Pm—radioactive despite being flanked on both sides by lanthanides with fully stable isotopic compositions.

Np—the first of the transuranium elements, marking the onset of deliberate artificial synthesis, although later detected in trace natural amounts.

Ubp (Z = 125)

After element 120, the 6f, 7d, and 8p orbitals are expected to lie so close in energy—and to be so strongly affected by relativistic shifts—that no stable orbital-ordering sequence would exist. That said, around Z = 125 (Ubp), the 5g orbital is expected to collapse sufficiently in energy to permit the first appearance of an associated electron.

It is striking that, after the familiar period-opening sequence (each period beginning with an s-block pair—119 and 120 in this case), a naïve extension of that sequence would place element 125 in a position corresponding to Group 7.

General pattern

With one exception, the effect is limited to the d- and f-blocks. The exception is in the p-block, where (unstable) white P crystallises in the alpha-Mn structure, with 58 vibrating P4 tetrahedra. Here, P (15) and Mn (25) are linked by a Z+10 relationship.

All the elements involved have odd-Z and show either:

• half-filled subshells (P: p^3; Mn, Tc, Re, Bh: d^5); or
• a total of seven outer (fs, fds or gds) electrons (Pm, Np, Ubp via a presumed 8s2 7d4 5g1).

The pattern is absent or weak in the s- and p-blocks, and stronger in the other blocks.

Given the existence of nuclear “magic numbers”, one might reasonably ask whether there are mid-shell or “antimagic” numbers where nuclei tend to be less stable. The relevant Z values here are 15 (P), 25 (Mn), 43 (Tc), 61 (Pm), 75 (Re), 93 (Np), and 125 (Ubp).

I don’t know if this pattern has any connection with the unusually complex crystal structure of Mn. It may be coincidence—yet it may hint at a deeper periodicity that extends beyond electronic structure into nuclear structure.

In summary, we are dealing with…

• odd-Z mid-shell instability;
• anomalous crystal structures;
• nuclear-stability irregularities;
• abrupt changes in orbital energetics;
• possible “antimagic” Z-values;
• a delayed 5g collapse; and
• a numerical coincidence placing Z = 125 in the Group-7 slot.

Taken together, the constellation of coincidence and anomalies is truly remarkable—an esoteric manifestation of the periodic law anyone?

Re, "there have been no known previous proposals or references to such a self-evident Column of Instability" I mentioned the Axis of Instability, in 2019, here https://groups.google.com/g/pt-l/c/kATkE6AOCLs/m/Z7tdYjbwAAAJ and in 2013, here https://en.wikipedia.org/w/index.php?title=User%3ASandbh&diff=prev&oldid=556572291

René

[Scott Hutcheon]

Off-thread preface: While many enjoy breaking out the popcorn and watching the show (I'm often guilty of this too), have also received a couple of direct emails over the civility of some responses or comments (which apparently has some history for this group). As replied to those, thanks, but there are no concerns for me as my background is over thirty years in studying cosmology, astronomy, information, physics, and the history and philosophy of science (primarily physics) and this is expected per the Schopenhauer attribution.

Additionally, I have rhino skin as a result of being personally and publicly attacked (face-to-face in classrooms and studios) for seven years at a college and two universities over incredibly intimate and personal creations -- while also knowing that sociopathy cannot be tested until the early/mid twenties as we're nearly all necessarily antisocial at younger ages to allow for intellectual/belief separation and societal/cultural evolution (meaning it required continually defending myself against still-sociopathic students back when pure toxicity was normalized and even expected/encouraged by professors).

Obviously, being accused of naivety, of merely luckily finding coincidence, misdirecting energy, facing assumptions about levels of education-experience-understanding-knowledge, or that reading the RSPT paper is beneath or a waste of time (even if it would have prevented so many repetitive replies in these threads), is minor and trivial compared to Experts viciously criticizing Boltzmann into suicide (for correctly proposing statistical mechanics and the kinetic thoery of gases) or Semmelweis into an asylum and death (for correctly suggesting the paradigm shift of washing your hands before surgery or childbirth). Not that I'm remotely in their league, but they are cautionary tales.

I'm actually instead saddened about the ongoing reality in the sciences of most Experts being unable to adapt to a new paradigm, per German physicist Planck and his "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." It's an unnecessary hangover from attempts to force religious beliefs as eternal truths onto everyone else. Instead, knowing the science behind the 10,000-hour rule, it's much more tragic that so much life and work and energy and time can (even if just partially) be spent within an incorrect/unscientific paradigm after a more scientifically evolved one is proposed but then only briefly skimmed and rejected outright to defend turf rather than be closely examined, fully understood, and then pondered for its consequences.

Obviously not all proposed paradigm shifts can be completely considered as science would quickly mire under the sheer numbers and weight, resulting in non-evolutionary inertia. Experts are fundamentally necessary to both find and share the very evidence that leads to and triggers paradigm shifts, while also acting as funnelling screens to sort out potential shifts. However, believing in only evolution at every level (as a core belief, not a tacked-on educated one) -- and especially completely accepting that there are no eternal truths and only unpredictable universal evolutionary change -- is still not the normal worldwide culture and past-and-present religious beliefs continue to infect, degrade, and undermine scientific advancement (with anti-science, anti-intellectualism, and anti-education beliefs unhappily a growing concern these days).

And, truly, any mild or slight criticisms/shadings here are loving compliments compared to what I'm about to endure after even daring to show Physicists that their science primacy (including lifetime work, legacy, career, stature, and power structure) is being displaced by Information and Cosmologists/Astronomers that they've mostly wasted their intellectual lives, and almost exactly a century of dead-ended/delayed/stalled field progress considering observational and theoretical paradoxes, due to somehow actually believing in the embarrassing paradigm of the Catholic Priest singularity → evolution (Catholic Priest singularity → Physics → Chemistry → Biology) instead of the blindingly obvious, as always with 20/20 hindsight per Schopenhauer's attribution, actually scientific paradigm where evolution began with and continues through the increasing complexity phase transitions of Information → Physics → Chemistry → Biology.

Real scientist English astronomer Fred Hoyle will have his revenge served cold regarding the secularized religious belief hot expansion.

Back to the thread: Thanks René, and I mean this sincerely and honestly due to my deep understanding of and agreement with the 10,000-hour rule, as always your deep expertise around chemical/physical properties of elements and their placements regarding the periodic table is very welcome.

As your Axis of Instability was not peer-reviewed and published, I hadn't known of it. It's interesting and not a coincidence that we arrived at similar names for the relationship coming from completely different interests and backgrounds. Mine in relation to physics/cosmology and the Z ≥126 Island of Stability, while also necessarily including (from first principles) 125 -- which, just like the Column, was hidden in plain sight behind the non-obvious Ubp naming convention.

Since I do not subscribe to shadow property/dotted-line relationships or any concept of recovering both Mn-Tc-Re-Bh and Mn-Tc-Pm-Np within simultaneous bifurcated relationships (similar to the misunderstanding of the cat being in a superposition of both dead and alive), while only accepting Mn-Tc-Pm-Np-125 from first principles as the Column of Instability and it's relation to the Island of Stability, let's revisit the RSPT paper -- which also, in direct relation, addresses the artificial bifurcated simultaneous relationship of Sc-Y-La-Ac and Sc-Y-Lu-Lr.

1. Any Periodic Table that is symmetrical (bilaterally symmetrical) should now be regarded as non-science/nonsense. From Physics, with its recently agreed paradigm shift (that certainly wasn't the case when I was in school) that perceived symmetry is actually impossible within physical, chemical, or biological reality -- asymmetrical gravity, asymmetrical time, asymmetrical baryon matter-antimatter, asymmetrical charges, asymmetrical spins, asymmetrical orbits/orbitals/charge densities, asymmetrical handedness, asymmetrical chirality, etc. -- the use of band-aid/secondary line connections to claim multiple/shadow chemical and/or physical property relationships in order to salvage/rescue symmetrical tables is straightforward evidence of an artificial workaround to sidestep/avoid proof from first principles.

2a. Any salvaging of the current standard periodic table by claiming multiple or shadow or secondary connections for Sc-Y-La-Ac and/or the Mn-Tc-Pm-Np/Mn–125 Column of Instability is belied from first principles:

2b. Any rescuing of the Left-Step (or any left-step) periodic table by claiming multiple or shadow or secondary connections for Sc-Y-La-Ac and/or the Mn-Tc-Pm-Np/Mn–125 Column of Instability is belied from first principles:

2c. Even though it's obscured/hidden by the 18-column's more symmetrically attractive form, it should be clear by now from the 32-column forms that the current standard iconic periodic table is a modified left-step table (cylinder wraparound interconversion/equivalency for chemical and/or physical property relationships) -- and 100% universally wrong for all the same reasons.

3. As historically expected, only outsiders would dare commit the blasphemy (aka paradigm shift) of breaking apart the sacred artificial idol d-block into scientifically correct d- and f-period pieces/relationships -- where, from first principles, there is no possibility of Mn-Tc-Re-Bh and of only Mn-Tc-Pm-Np-125 (and where nothing needs to be recovered or fudged):

While, per the paper, the RSPT may not be the final 'one' of the right-steps -- as it was accidentally realized while solving for H and He Eddington numbers and chemical/physical properties in relation to all other elements, addressing missing Mass 5 and 8, and the underrepresented masses of 2 and 3 as well as Lithium and Beryllium, while also simultaneously finding a way to keep the traditional p-Groups -- it naturally contains, from first principles, the Column of Instability.

As does every scientific right-step:

Right-Step Mendoza: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=407

Right-Step Gutierrez-Samanez: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1100
Right-Step Vernon/Gutierrez-Samanez: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1303

These right-steps necessarily contain correct relationships -- Sc-Y-La-Ac and/or B-Al-Sc-Y-La-Ac, as well as Mn-Tc-Pm-Np-125 -- as an inherent feature from simply following first principles of Van den Broek-Moseley sequential atomic numbering and the Madelung Rule (with corroborating support from the 1913 breakthrough of radioactive periodicity).

Mathematics at the Information level obviously contains symmetries, whereas Physics and Chemistry are asymmetrical, so while the Beylkin and its artificial gaps is halfway correct with five proper d- and f-period relationships, that started with the one proper relationship with Romanoff and its artificial gaps (https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?textfield=Romanoff), only right-step tables fully resolve.

This is supported by the Döbereiner-Scerri triads, where only proper alignment of d- and f-periods allows for full d- and f-element vertical triads (equally one correct for Romanoff, five/half for Beylkin, and 10/complete for right-steps). As stated in another chain, horizontal triads are now trivially obvious after the monumental paradigm shift from atomic weights to Van den Broek-Moseley sequential atomic numbering. But only after the paradigm shift, within the incorrect paradigm Experts blindly hashed out atomic weight anomalies where Mendeleev prevailed by recognizing/intuiting an unverifiable/unfalsifiable (for that paradigm) underlying Information-level triadic relationships.

While similarly, group theories, algebras, and simple vertical triad math relationships may seem (rightfully) ridiculous as entities at the Physics or Chemistry level if you're trapped in the Catholic Priest singularity → Physics → Chemistry → Biology paradigm, they are very real as actual self-organizing emergent Information-level entities in the Information → Physics → Chemistry → Biology paradigm that drives and informs the underlying level from which the spontaneous-symmetry-broken asymmetric relationships and properties we experience as real at the level of Physics and Chemistry arise (including the periodic table).

4a. Unless I'm missing something obvious (always likely), it seems self-defeating/illogical to continue defending the outdated/superseded paradigm of the artificial d-block and arguing against the more scientific/evolved d- and f-period orientations within the right-step periodic table forms, considering they are also the only from-first-principle non-fudge-factored variants that support all the investigatory and research work towards Sc-Y-La-Ac as a better trend fit versus Sc-Y-Lu-Lr as well as the Rang-Vernon B-Al-Sc-Y-La-Ac extended Group as a better trend fit versus B-Al-Ga-In-Tl-Nh.

4b. I'm never interested in winning, or proving I'm right, simply because of the hard-earned realization there is no eternal win, no permanent 'right' -- only permanent wrong (i.e., disproven beliefs). Think of biologic evolution, there is no winning, merely continuing to survive and adapt, versus permanent extinction (wrong for the changing environment). Fundamental evolution means there are never eternal truths, every scientific fact is necessarily incorrect/incomplete, just like the paradigm it was formed within, and will either be discarded as wrong or superseded/made more complete/more evolved by a more fundamental understanding. 

Since ever discovering completely objective reality is not realizable, it's instead the fruitful journey towards the impossible destination. 

[johnmarks9]

Another delightful philosophical deep-dive!

Yes, the cosmos just is.

Physics deals basically with events in space and time - and electromagnetism. 

Chemistry deals with the subset of physics which concerns that quantum phenomenon, the atom.

Biology deals with that subset of chemistry which concerns a phenomenon nicknamed "Maxwell´s demon", demonstrated by the thermodynamic phenomenon known as a "Markov blanket" and realized in the biological unit known as a cell, which nevertheless follows the laws of physics and chemistry, yet grows into humans via that other homœostatic phenomenon, Darwinian evolution.

John

PS "Since ever discovering completely objective reality is not realizable": Well, you may be able to discover it, but can´t ever know that you have! - Popper.

[René]

On 20 Nov 2025, at 09:27, Scott Hutcheon <scotth...@gmail.com> wrote:

1. Any Periodic Table that is symmetrical (bilaterally symmetrical) should now be regarded as non-science/nonsense.

Hi Scott

The attached periodic table has four axes of symmetry; its shape; four block types in each half; metals and nonmetals in each half; and a subatomic particle in each half.

Should it now be regarded as non-science?

René

[Mark Leach]

And, such periodic tables have an honourable history:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1039

Mark Leach

meta-synthesis

<PastedGraphic-1.png>

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[ERIC SCERRI]

Or the original version due to Thomsen who taught chemistry to Bohr. 

It was also Bohr’s preferred format. 

Eric Scerri PhD

On Nov 24, 2025, at 7:36 AM, Mark Leach <ma...@meta-synthesis.com> wrote:

And, such periodic tables have an honourable history:

To view this discussion visit https://groups.google.com/d/msgid/PT-L/7E087276-85E8-49F3-8F1E-428DF84D014C%40meta-synthesis.com.

[Scott Hutcheon]

Like Periodic Table periods, can only repeat so many times before there's not enough energy available to continue...

Went back and am copying-and-pasting a few parts from a previous thread's fuller reply:

"The step-pyramid periodic table is a bilaterally near visually symmetrical attractive artificial construct that has been rehashed since at least its invention in 1882 by Bayley (true science is built on discoveries that lead to falsifiable theories not beliefs that lead to unfalsifiable invented works of art): https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=66"

"2. Per the RSPT paper, this form claims the electron (e) and the Neutron (N) as Period 0, despite any 0s or Period 0 being the Free Proton and Alpha Particle based on the universal reality of Chemistry (starting at 1s) evolving from Physics"

"5d. Rather than further going into gruelling detail pointing out how forcing artificial bilateral symmetry onto a periodic table can only reinforce a biologically pleasing yet physically shallow understanding of true symmetry, it might be better to show here how little actual symmetry there is between periods, blocks, primary, and secondary (dotted line) relationships (a picture speaks a thousand words and all that):

"

There is no actual (bilateral or otherwise) symmetry in chemical reality. It looks like basic gross generic bilateral symmetry if orientations are visually manipulated to match organizationalist desires (per the RSPT paper), but it's not possible for symmetry to exist at an asymmetrical level like Chemistry. 

Would also strongly recommend not using period blocks as they obscure relationships within periods (between metalloids and other metals for example):

This is the same table as the capstone step-pyramid, just in a more scientific/evolved paradigm format. Favourite scientific (universal) right-steps such as Working Chemist would be interconverted variations of this.

[René]

On 25 Nov 2025, at 06:17, Scott Hutcheon <scotth...@gmail.com> wrote:

There is no actual (bilateral or otherwise) symmetry in chemical reality.

Well, yes there is: in terms of chemical reality, there are metals and nonmetals in each half. The context here is that the metal-nonmetal dichotomy is one of the great foundational aspects of chemistry, well known in terms of the general saying that metals are on the left and nonmetals on the right.

Too, there are four block types in each half. For the chemical reality of blocks, consider the following:

The division into blocks is justified by their distinctive nature: s is characterized, except in H and He, by highly electropositive metals; p by a range of very distinctive metals and non-metals, many of them essential to life; d by metals with multiple oxidation states; f by metals so similar that their separation is problematic. Useful statements about the elements can be made on the basis of the block they belong to and their position in it, for example highest oxidation state, density, melting point ... Electronegativity is rather systematically distributed across and between blocks.

P. J. Stewart

In Foundations of Chemistry, 2017

Would also strongly recommend not using period blocks as they obscure relationships within periods (between metalloids and other metals for example):

I see no basis for such a negative recommendation.

Thus, the diagonal transition from p-block metals to metalloids in the p-block is a beautiful illustration of the culmination of metallic-to-nonmetallic trends across each period, considering that metalloids have a predominately nonmetallic chemistry.

How do you see this now?

René

Stewart, P. J. (7 November 2017). "Tetrahedral and spherical representations of the periodic system". Foundations of Chemistry. 20 (2): 111–120. doi:10.1007/s10698-017-9299-y

[Scott Hutcheon]

Physics Versus Chemistry History of the Periodic Table:

As mentioned before, where it's vital for chemists to continually adapt to more evolved paradigms and standards if they want to be taken as seriously as physicists, Eric's note about Bohr inspired:

1a. Physics culture, once trapped in the religious-philosophical belief/paradigm that symmetry is somehow possible in scientific physical reality, meant even the great physicist Bohr (a personal hero) grew up in, was educated in, and worked within the artificial and incorrect paradigm of symmetry. 

• Even genius Bohr preferred the artificially symmetrical-appearing capstone step-pyramid table via his teacher Thomsen.

1b. Physics culture realizes religious-philosophical symmetry is never possible in scientific physical reality -- after baryon asymmetry becomes a known fundamental problem, etc.

• Physicists paradigm shift away from needlessly wasting space even showing the Standard Model diagram in its full mirrored/bilaterally symmetrical (anti-particles, etc.) form, knowing there's no point as informational symmetry cannot survive emergence into asymmetric physical reality. 
• Physicists start being drawn to the previously not-widely-known asymmetrical 32-column Left-Step Periodic Table -- which is a more asymmetrical modified/interconvertible version of the standard table.
• Physicists create the entirely asymmetrical chemical elements radioactivity nuclides chart.

1c. Physics culture, trapped in the secularized religious-philosophical belief/paradigm of a Catholic Priest (God) singularity → Physics, eventually shifts to the scientific evolutionary Emergent Universe where Information → Physics.

• Physicists start being drawn to the previously not-widely-known right-step or even more asymmetric periodic table formats and eventually realize 'the one.'

2a. Chemistry culture, once trapped in the religious-philosophical belief/paradigm that symmetry is somehow possible in chemical reality, created thousands of artificially symmetric-looking periodic tables.

• The logical implications for periodic tables regarding the 1913 chemical elements radioactive periodicity breakthrough are ignored -- i.e, the Column of Instability.
• Chemists preferred symmetrical tables to the point of obscuring the asymmetry of the modified/interconvertible left-step 32-column standard iconic table in an 18-column format that artificially appears even more bilaterally symmetrical.

2b. Chemistry culture, still trapped in the religious-philosophical belief that symmetry is somehow possible in scientific chemical reality, continues attempting to create, defend, and advocate for...

2c. ...

[johnmarks9]

See my explanation at Mark Leach´s database, PT = 1279.

[René]

Hi Scott

The right-step variation you posted earlier (marked-up copy attached) is interesting, but what stood out to me is that the primary periodic relationships have to be restored by way of sloped connecting lines. In other words, the geometry of the diagram doesn't itself encode periodicity; three supplementary sets of lines are doing the work that the layout would normally do.

By comparison:

• In triangular formats, sloped connections are expected because this format is explicitly designed to display both primary and secondary relationships in multidirectional pathways.
• In the long-form 18-column table, no such connectors are needed at all—the primary relationships are the Groups themselves.

All of this gets to the issue of representational economy. Michael Laing captured it well:

“A useful periodic table must contain in the minimum area, using the least printer’s ink, the largest number of patterns and thus the maximum amount of information in an easily readable format, and so give the viewer the greatest number of ideas in the shortest time.”

—Laing (2004), South African Journal of Science, 100(3):198–204.

I suggest that when primary periodicity has to be reinstated by drawn lines because the spatial geometry has displaced it, the table becomes more diagram than classification tool. The viewer must now interpret a mapping superimposed on the layout rather than a logic embodied in the layout.

However the triangular system shows a consistent internal logic: its slope is intentional, and the sloped connections express a structured hierarchy of primary and secondary relationships. The right-step version in question, however, uses slopes merely to repair the consequences of its geometry, which is a different matter.

On Laing’s criterion—maximum patterns, minimum ink, highest semantic compression—the conventional medium-long form table still outperforms these alternatives. That does not make the alternatives useless, but simply highlights that the medium-long form preserves primary periodicity intrinsically, without requiring annotations to restore it.

René

[Scott Hutcheon]

Fully agree on representational economy, and the capstone step-pyramid is one of (if not) the least economical formats:

The capstone step-pyramid has no vertical/column/Groups and has to use right sloping connecting lines to show primary p-period relationships. Just like the previous/above right-step variation had to use the same right sloping lines to show primary p-period relationships.

The capstone further wastes space by having to have three additional rows of Group numbers to artificially claim symmetry is somehow possible in chemical reality.

Upright capstone step-pyramids use right sloping lines to connect p-period primary relationships in addition to sloping lines for secondary relationships -- which makes relationships less obvious just to artificially manufacture a symmetry that is not possible with sequential atomic numbering and 2-8-8-18-18-32-32 periods -- making this format with it's additional space-wasting artificial gaps between rows one of the least economical formats.

Especially because those secondary (and even primary) shared relationships are not agreed upon (for example, the non-consensual H-s1 Alkalis Group, He-s2 Alkaline Earths Group, H 1s1-p5 Halogens Group, He 1s2-p6 octet gases Group, 4d-5d Sloppy Sandwich Solution, B-Al-Sc-Y-La-Ac versus B-Al-Ga-In-Tl-Nh, etc.).

Here are other right-steps that show primary p-period relationships as traditional vertical/column Groups (the second one with sloping lines to the right for primary p-period connections just like the capstone pyramid and the previous contracted-symmetry variant) along with some of the secondary relationships that don't have consensus:

This last one is simply the corrected standard table and is easy to create in the proper corrected 18-column format.

Following atomic sequential numbering and periods of 2-8-8-18-18-32-32 in a two-dimensional matrix left-to-right Western standard writing format, the periods are displaced to the right:

• First there is one s-period (2), 
• then two p-periods are displaced to the right by two s-periods (8-8), 
• then two p-periods are displaced to the right by two d-periods which are displaced to the right by two s-periods (18-18), 
• then two p-periods are displaced to the right by two d-periods which are displaced to the right by two f-periods which are displaced to the right by two s-periods (32-32). 
• The g-period also displaces the f-period to the right and naturally contains the 125 element as part of the Column of Instability.

In the capstone step-pyramid graphic:

• yellow (containing later, higher-numbered elements) is displaced to the right by red (containing earlier, lower-numbered elements), 
• then yellow is displaced to the right by blue and red, 
• then yellow is displaced to the right by blue and green and red.

Which is why primary p-period connections in the center-step pyramid also have to be restored by sloping lines to the right (just not as far to the right as in the two right-steps with the same sloping lines to the right to maintain primary p-period relationships).

The only other claim would be that, for example, a later yellow (p-block) displaces an earlier red (s-block) to the left -- which is completely illogical as it would require later period orbitals/shells to displace earlier period orbitals/shells.

Putting this displacing to the right in a left-step or center-step/symmetrical-step (pyramid) is merely shifting geometry and masking/obscuring reality in an artificial form. This is why only a right-step can be correct, and why the displacement of the second set of d-periods to the right by the f-periods shows the only correct orbital filling sequence (yes, with anomalies, but they're called anomalies because of the normal orbital filling sequence) and d- and f-periods orientation (necessarily including the Column of Instability).

Of course, in reality, later orbitals are pushed out away from the nuclei instead of the right or left of the periodic table. This is the concept of the valence orbital/electron/charge density.

The case has been/could be made that secondary or shadow relationships are simply same-numbered lobe/subshell periodicities -- meaning, less than half of 4d- and 5d- elements show common properties (with less than five sets showing two-vertical-element Group trends) simply because elements in same-numbered lobes/subshells often share similar properties (due to the periodic doubling of sequential atomic numbering).

Which would explain why 3d5 Mn, 4d5 Tc, 4f5 Pm, 5f5 Np, and 5g5 125 have the primary relationships and are grouped in the Column of Instability, and why 3d5 and 4d5 and 5d5 and 6d5 have lesser (secondary) relationships. How do we know that 3–6d5 has to be the lesser or secondary? Because sequential atomic numbering and orbital filling shows us that 5d and 6d are displaced by 4f and 5f. 

F-period 57 La comes before d-period 71 Lu no matter how many artificial visual contortions are invented to try and hide/minimize that fact. Claiming La and Ac as d-period elements to try and recuperate artificial forms doesn't change the fact that they are part of the f-periods that come before the 5d- and 6d- periods. There can be no d-block.

Instead, we need to know why this displacing is the case from first principles, as well as why 2–7s1 share trends but not 1s1, 2–7s2 share trends but not 1s2, why 2–7p5 all share trends and 2–7p6 all share trends but not 2–7p1, 2–7p2,  2–7p3, and 2–7p4.

If Chemistry culture finds consensus on Group relationships, then finding the right right-step will be much easier.

As an outsider, I haven't spent decades attached to a form (no intellectual ROI, no cognitive dissonance), only discovering a right-step form four years ago from completely different reasons and then that right-step periodic tables are by far the least represented (and most recent) forms.

[Mario Rodriguez]

I’ve been following this thread and wanted to share a thought.

We shouldn’t conflate chemical reactivity (driven by electron interactions) with nuclear chemistry, governed by nucleons (protons and neutrons).

The conventional periodic table, as well as my periodic spiral (which incidentally aligns well with Laing’s principle of representational economy), describes chemical behaviour based on electronic interactions. This is why we talk about electron orbitals, blocks, valence, electronegativity, and why elements are defined by their number of protons, because this number determines the electron count in a neutral atom.

However, Nuclear chemistry deals with interactions among nucleons. In this context, it makes sense to discuss “columns” or “islands” of stability and instability. For nuclear chemistry, all isotopes must be treated as distinct “elements” in practice, because they differ in nuclear behaviour even though their conventional electron-based chemical properties are the same or very similar. This is why the Segrè chart of nuclides is used: it maps stability and instability across all isotopes, reflecting their different nuclear characteristics.

In nuclear chemistry, even the neutron (or “neutronium”) can be considered an element, since it's a nuclide with a defined nucleon count. But it has no place in the conventional periodic table or spiral, which is rooted in electron-based chemical interactions. A neutron doesn´t have an electron to participate in chemical bonding.

In short, the periodic table or spiral, organized by electron orbitals, is the proper tool for representing chemical reactivity. Nuclear reactivity, governed by nucleons, has to represent all isotopes (and the neutron) as if they were "elements" by themselves. That´s achieved by the Segrè chart or perhaps a new “periodic table of nuclides” or “nuclear periodic table” (where electron orbital blocks doesn´t matter).

Thus, attempting to show nuclear “columns of instability” within the conventional periodic table based on electronic interactions, or trying to depict electron orbitals blocks within a nuclear chart of nuclides, simply doesn’t make sense.

I hope these reflections are helpful.

Mario Rodríguez Peña

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[ERIC SCERRI]

I agree with Mario. 

There is no evidence that nuclear physics influences chemical reactivity. 

The periodic table was retained after the discovery of isotopes specifically by focusing on atomic number and electronic structure. 

See Paneth’s articles on this point and the volume I edited with Elena Ghibaudi, What is a chemical element?  OUP, 2020. https://global.oup.com/academic/product/what-is-a-chemical-element-9780190933784?cc=us&lang=en&

Eric Scerri

On Nov 28, 2025, at 12:31 PM, 'Mario Rodriguez' via Periodic table mailing list <PT...@googlegroups.com> wrote:



To view this discussion visit https://groups.google.com/d/msgid/PT-L/1668714548.3933302.1764361900092%40mail.yahoo.com.

[René]

Hi Scott

Thanks for your comments regarding representational economy and the various "step-based" periodic table formats. A few thoughts follow, point by point.

Representational economy. I agree with you; the capstone step-pyramid is less than economical. It has no vertical columns for Groups and must instead use sloping lines to show primary relationships. It also shows secondary relationships via dashed sloping lines.

The right-step variation you mentioned likewise suffers from a lack of economy. As well, its left side includes vertical sequences such as N-P-V-Nb-Ta-Pr-Pa, spanning p-, d-, and f-elements; these are not primary relationships, which again necessitates sloping lines to indicate the actual primary ones. In that sense the layout prioritises a stylised s-p-d-f block sequence over a straightforward depiction of chemical relationships.

Group labels. Yes, the capstone pyramid uses extra rows of Group labels. That said, this doesn't invalidate symmetries that the design does exhibit—for example, metals and nonmetals on each side, and four block types in each half. But using sloping lines for both primary and secondary relationships inevitably makes those relationships less obvious. Disagreements about H, He, and the composition of Group 3 etc., are separate issues and don't affect the intrinsic merits or drawbacks of using sloping lines.

OTOH, the various forms of right step table have no Group numbers—surely a missing hallmark of periodicity?

Symmetry. Jensen referred to the overall aesthetic appeal of the step-pyramid table resulting from its symmetric shape, noting that this is not a universal cultural preference. Still, symmetrical representations can facilitate learning since fewer observations are required to describe the applicable system i.e. concepts that possess symmetry can be more easily grasped than those that do not.

Curiously, the asymmetric 18-column conventional periodic table has metals and nonmetals, and four block types, on either side of the Axis of Instability. Perhaps this explains why H is in group 1 and He is in group 18 :)

Vertical groups. Regarding your other right-step forms: none of those show all 18 conventional Groups as vertical columns. For that reason I suggest the right-step form cannot be said to be “correct” in any absolute sense.

Of course, the conventional periodic table shows the 18 conventional Groups using vertical columns. The secondary relationships can be discerned via Group (n) and Group (n+10) relationships, for Groups 2-8 and 12-18.

Axis (or Column) of Instability. This can already be discerned quite well in a conventional 18-column table, when Ce-Th are aligned under Group 4. The set Mn-Tc-Pm-Np, which you refer to, doesn't represent a primary chemical relationship. The primary sequence is Mn-Tc-Re-Bh. One may argue for the instability axis running down Group 7 and through Pm-Np, but this is a pattern of anomalies and radioactivity, not chemical similarity.

No d-block? Your statement “there can be no d-block” is unfounded. There certainly can be a d-block, at least in a taxonomical sense, just as there is an f-block.

First principles? Since the periodic table is a classification, not a physical theory, it cannot be derived from first principles.

Need for right-step tables? Chemistry has more or less reached broad consensus on Group relationships; there is no intrinsic need for a right-step arrangement within this context. Variants of right-step tables have existed since at least 1928. Their relatively limited modern representation is likely because they are generally not seen as offering sufficient advantages to displace the established forms.

I hope this clarifies my perspective.

René

[johnmarks9]

On your eight pertinent thoughts:

1. Agreed.

2. Agreed.

3. Chemically, H shouldn´t be grouped with the alkali metals.

4. Agreed.

5. "The set Mn-Tc-Pm-Np, which you refer to, doesn't represent a primary chemical relationship." 

Strange. La has valency 3, Ce 4, Pr 5. You would expect Nd 6 and Pm 7 to be found on a chemical basis.

6. So bizarre it must be a typo. Why on earth can there not be a d-block?

7. Succinct.

8. Agreed.

What would be your analogous thoughts on this PT:

It´s in the Leach database as PT1279.

John

[Mark Leach]

Hi All,

3. Chemically, H shouldn´t be grouped with the alkali metals

Why not? At high pressure hydrogen almost certainly forms a metallic phase. ChatGPT says:

In summary: there is strong experimental hint that hydrogen can exhibit metallic behavior under ultra-high pressure. But fully convincing, conclusive proof — especially of the classic “atomic metallic hydrogen” phase predicted by early theorists — remains elusive. The science community treats the question as open.

Mark Leach

meta-synthesis

On 30 Nov 2025, at 16:54, johnmarks9 <johnm...@hotmail.com> wrote:

On your eight pertinent thoughts:

1. Agreed.

2. Agreed.

3. Chemically, H shouldn´t be grouped with the alkali metals.

4. Agreed.

5. "The set Mn-Tc-Pm-Np, which you refer to, doesn't represent a primary chemical relationship." 

Strange. La has valency 3, Ce 4, Pr 5. You would expect Nd 6 and Pm 7 to be found on a chemical basis.

6. So bizarre it must be a typo. Why on earth can there not be a d-block?

7. Succinct.

8. Agreed.

What would be your analogous thoughts on this PT:

<M-RS6.png>

It´s in the Leach database as PT1279.

John

On Sunday, November 30, 2025 at 12:17:51 PM UTC+1 René wrote:

Hi Scott

Thanks for your comments regarding representational economy and the various "step-based" periodic table formats. A few thoughts follow, point by point.

Representational economy. I agree with you; the capstone step-pyramid is less than economical. It has no vertical columns for Groups and must instead use sloping lines to show primary relationships. It also shows secondary relationships via dashed sloping lines.

The right-step variation you mentioned likewise suffers from a lack of economy. As well, its left side includes vertical sequences such as N-P-V-Nb-Ta-Pr-Pa, spanning p-, d-, and f-elements; these are not primary relationships, which again necessitates sloping lines to indicate the actual primary ones. In that sense the layout prioritises a stylised s-p-d-f block sequence over a straightforward depiction of chemical relationships.

Group labels. Yes, the capstone pyramid uses extra rows of Group labels. That said, this doesn't invalidate symmetries that the design does exhibit—for example, metals and nonmetals on each side, and four block types in each half. But using sloping lines for both primary and secondary relationships inevitably makes those relationships less obvious. Disagreements about H, He, and the composition of Group 3 etc., are separate issues and don't affect the intrinsic merits or drawbacks of using sloping lines.

OTOH, the various forms of right step table have no Group numbers—surely a missing hallmark of periodicity?

Symmetry. Jensen referred to the overall aesthetic appeal of the step-pyramid table resulting from its symmetric shape, noting that this is not a universal cultural preference. Still, symmetrical representations can facilitate learning since fewer observations are required to describe the applicable system i.e. concepts that possess symmetry can be more easily grasped than those that do not.

Curiously, the asymmetric 18-column conventional periodic table has metals and nonmetals, and four block types, on either side of the Axis of Instability. Perhaps this explains why H is in group 1 and He is in group 18 :)

Vertical groups. Regarding your other right-step forms: none of those show all 18 conventional Groups as vertical columns. For that reason I suggest the right-step form cannot be said to be “correct” in any absolute sense.

Of course, the conventional periodic table shows the 18 conventional Groups using vertical columns. The secondary relationships can be discerned via Group (n) and Group (n+10) relationships, for Groups 2-8 and 12-18.

Axis (or Column) of Instability. This can already be discerned quite well in a conventional 18-column table, when Ce-Th are aligned under Group 4. The set Mn-Tc-Pm-Np, which you refer to, doesn't represent a primary chemical relationship. The primary sequence is Mn-Tc-Re-Bh. One may argue for the instability axis running down Group 7 and through Pm-Np, but this is a pattern of anomalies and radioactivity, not chemical similarity.

No d-block? Your statement “there can be no d-block” is unfounded. There certainly can be a d-block, at least in a taxonomical sense, just as there is an f-block.

First principles? Since the periodic table is a classification, not a physical theory, it cannot be derived from first principles.

Need for right-step tables? Chemistry has more or less reached broad consensus on Group relationships; there is no intrinsic need for a right-step arrangement within this context. Variants of right-step tables have existed since at least 1928. Their relatively limited modern representation is likely because they are generally not seen as offering sufficient advantages to displace the established forms.

I hope this clarifies my perspective.

René

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<M-RS6.png>

[johnmarks9]

Dear Mark,

Is hydrogen more like sodium or chlorine? is an endless debate but what do you think of this argument:

"Consider sodium chloride, a white, crystalline salt, and substitute each atom in turn with H, what happens?

Replacing sodium gives you HCl, an acrid diatomic gas like inter-halogen compounds.

Replacing chlorine gives you NaH, a white crystalline solid.

∴ Hydrogen is more like chlorine."

QED.

[René]

On 1 Dec 2025, at 04:41, Mark Leach <ma...@meta-synthesis.com> wrote:

Hi All,

3. Chemically, H shouldn´t be grouped with the alkali metals

Why not? At high pressure hydrogen almost certainly forms a metallic phase…

Well, as I understand it, since all non-metallic elements are expected to metallise at sufficiently high pressures, the fact that H does (or will) likewise has no bearing on its placement—or non-placement—among the alkali metals.

René