Rebuilding the Periodic Debate — Eric Scerri

Rebuilding the Periodic Debate — Eric Scerri

Author: David Bradley

In June 2011, we published a feature entitled Periodic Debate that discussed the ongoing evolution, if not revolution, surrounding the periodic table of the chemical elements. It remains the most popular Research Highlight article on ChemistryViews.org and continues to attract comments on the issues raised. In particular, from those who disagree with the standpoint that there could ever be a definitive two-dimensional table and that it is anything more than a tool or mnemonic to help chemists organize their understanding of the world around us.

I interviewed two of the people driving the debate, Philip Stewart and Eric Scerri. Here, I talk to Eric Scerri about his periodic inspiration.

Chemical Philosopher

After studying chemistry at the universities of London, Cambridge, and Southampton in the UK, Eric Scerri decided to follow his interests in the more conceptual aspects of the subject and did a Ph.D. in History & Philosophy of Science at King’s College, London. He told ChemViews that he was lucky enough to work with Heinz Post, the son of the famous chemist, Fritz Paneth. Post was a highly respected historian and philosopher of science, steeped in scientific details. “This is something that I hope I have emulated in my own work,” Scerri says. In his Ph.D. thesis, he questioned how successful the reduction of chemistry to quantum mechanics has been.

He undertook a postdoc in Karl Popper’s old department at the London School of Economics, UK, and then took up a postdoc at Caltech (Califonia Institute of Technology, USA) where he worked mainly in the history of chemistry. Various brief appointments at a couple of universities in Mid-West USA then led Scerri to settle in Los Angeles as a lecturer in chemistry and history & philosophy of science.

“I have been one of a relatively small group of people trying to put the philosophy of chemistry on the map,” he told us. “One of my own contributions was to start a journal called Foundations of Chemistry which is now in its twelfth year of publication and which I am still editing.” 

Unifying Principle

As his work developed, he began to focus increasingly on the history and philosophy of the periodic table. “The periodic table is the main unifying principle in chemistry,” Scerri says. “It’s comparable to the role played by quantum mechanics and relativity in modern physics and Darwin’s theory in biology.” Scerri’s 2007 book on the subject has, he told us, “opened up many new doors for me, including visiting many countries and being asked to appear, write and consult on radio and TV.” He confesses that, “I enjoy that as much as doing basic research.” A follow-up book, A Very Short Introduction to the Periodic Table will appear in December and he is now working on A Tale of Seven Elements, both to be published by Oxford University Press.

But what underlies Scerri’s fascination with the periodic table? “I’m not quite sure why, but as long as I can remember, I have been enthralled by the idea of a single chart that summarizes, in principle, the whole of chemistry and brings order to the field by providing connections at many different levels.” He points out that the periodic table acts as a bridge between the everyday reactions of the chemical elements and their atomic structure. However, as we discussed in Periodic Debate on ChemViews, despite his thrall, Scerri is not satisfied by the conventional, or medium-long, format of the periodic table. “One of the main problems concerns the placement of certain elements like H, He, La, Ac, Lu and Lr, all of which are debated in the scientific literature,” he says.

Scerri is trying to answer the question of what are the best criteria for the classification of elements into particular groups. In terms of ordering the elements into a simple numerical sequence, the problem was solved about 100 years ago by Van den Broek and Moseley and it is, of course, done through the atomic number of each element. “Classification into groups is not quite so simple,” he asserts, “and it is increasingly appreciated that the use of electronic configurations does not settle the issue in many cases.”

Artificial Versus Optimal

Of increasing interest to Scerri is the notion of an “optimal” periodic table. “This very notion has met with resistance from some philosophers of science who argue that all classifications, even the periodic table, are artificial and therefore do not reflect the way the world actually is.” Scerri is also surprised that a number of chemists also seem to subscribe to the view that there is no such thing as an optimal periodic table because, they claim, it depends on what particular feature about the elements one is trying to represent as to which version will be chosen. “If I am correct, there may be a sense in which we can claim the existence of a best table in terms of the most fundamental criteria instead of in terms of utility,” Scerri adds. As such, although chemists are yet to find this elusive form of the periodic table, Scerri is searching for the new criterion that would provide us with a better classification than we currently have.

“I think that discussions about the foundations of the periodic table will begin to surface more and more and might serve to illuminate the profusion of periodic tables which continue to appear in articles and on websites,” Scerri says. His current favorite is a format that places hydrogen among the halogens and maintains helium in the noble gases, contrary to the much discussed left-step periodic table which places helium at the top of the alkaline earth metals. However, he concedes that he has no hard evidence for this favored version, just some good plausibility arguments. “It would be useful if such questions could become more accessible to experimental verification and if more chemists would take an interest in the philosophical aspects of one of the central pillars of their own discipline.”

In his spare time, Scerri abandons the formal and rigidity of academic work and plays flamenco and blues guitar and a little boogie-woogie piano. Perhaps the optimal periodic table will turn out to be a twelve-bar version …


Eric Scerri, UCLA, USA

Professor Eric Scerri was born in 1953 in Malta. He obtained his bachelors and masters degrees in chemistry from the universities of London, UK, and Southampton, UK, and his Ph.D. in the history and philosophy of science from King’s College, London. He moved to the US for a postdoctoral fellowship at Caltech sixteen years ago and has remained in the US ever since. For 12 years, he has taught chemistry and philosophy of science at the University of California, Los Angeles, USA, and is one of the founders of the field of philosophy of chemistry as well as the founder and editor of the journal Foundations of Chemistry, now in its twelfth year of publication.

Scerri has authored more than 100 journal articles in chemistry, chemical education, and the history and philosophy of science. In recent years, he is turning increasingly towards working in the TV and radio media and to presenting his work to the general public.

Selected Publications

Website


See also:

 

Comments

  1. Jess Tauber

    In my tetrahedral model, which is going to be shown at the upcoming Design Science symposium at RISD (http://expspace.risd.edu/?event=risd-3rd-biennial-design-science-symposium), He is in a straight line relationship with other orbital-ending elements, just as H is with orbital-starting ones, and ml=0 elements are also in-line. BUT, because of various symmetry operations that the system can undergo, one CAN emplace s or p elements in such a way that He still lines up with the nobles, and yet H now lines up with the halogens. Both depictions are equally valid in the tetrahedral model, and neither is mutually exclusive.

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  2. Valery Tsimmerman

    Are all classification systems completely artificial? Is it really true that classification systems used by the scientists have nothing to do with the nature? It is hard to believe that some one would suggest that the current classification of biosphere, for example, does “not reflect the way” the bio-world actually is. The periodic table should classify the atoms based on atomic attributes. Unfortunately, the use of the outdated word “elements” makes it rather confusing, because it makes the argument for the classification based on “properties” rather plausible. The problem is that term “element” is artificial. The elements are not objects, they are simply notions, or ideas, the myths. They are creation of the human mind that we inherited from the period when science did not know much about atomic world. The atoms, on a contrary, are real objects. They do exists! And truly scientific classification should be classifying the atoms, not the elements. Until this proposition is accepted, there will be no clarity with regard to the form of the Periodic System.

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  3. Eric Scerri

    Thanks Valery. I think the argument you are making is an oversimplification. It is not the case that the properties of elements, which is what the periodic table seeks to classify, have been fully reduced to electronic configurations of atoms. If they had we would not have any debates concerning the placement of elements like H, He, La, Ac, Lu and Lr. eric scerri P.S. The next issue of the journal “Education in Chemistry” will feature an article on this question.

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  4. Valery Tsimmerman

    Exactly, Eric. ______The periodic table, as it is currently defined, seeks to classify the properties, that is behavior of “the elements”. This is the root of the problem. ____Mendeleev intuitively was against such approach: “Properties, such as the optical and even the electrical or magnetic ones, cannot serve as basis for the system naturally, since one and the same body, according to the state in which it happens to be at the moment, may show enormous differences in this regard.” However, he had to use whatever knowledge was available to him at that time. So, he used valence among other things to come up with his classification.____ I argue that any properties should be left aside and classification should be based strictly on structural/quantum mechanical attributes of the atoms. _____This is exactly what I did. I completely ignored the properties and tried to build a table using the electronic structure of atoms. What was the result? First, I reinvented Janet’s LSPT and then I cam up with ADOMAH PT. Remarkably, all groups that I came up with coincide with almost all the groups of traditional long form PT, except Helium in my layout is next to Be, not Ne. One element in one out of 32 groups is not a great difference! ____Not at all. So, the electronic structure approach isn’t so bad. The advantage that such approach provides is the agreement with spectroscopic observations, which are completely ignored by the traditional PT and other layouts based on properties. And that is what Mendeleev would have liked: “…every system, however, that is based upon exactly observed numbers is to be preferred, of course, to other systems not based upon numbers because then only little margin is left to arbitrariness..”

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  5. Eric Scerri

    What you have done is reinvented a classification of the gaseous neutral atoms of all the elements. When it comes to chemistry neutral atoms are not all that important. Even though Mendeleev knew nothing of atoms or did not believe in their real existence, his project, and that of most chemists remains the classification of ‘elements’ not their gas phase, neutral atoms. In any case, even if one were devising a periodic table of gaseous neutral atoms alone it is not clear that He would have to be placed among the alkali metals as you favor. eric scerri

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  6. Valery Tsimmerman

    I think that concept of classifying the elements, meaning properties, is flawed. I think that the classification should target the objects, the quantum mechanical systems, in this case the atoms, being in their gas phase, or part of the crystals, or molecules. Just like quarks, which have never been observed completely free floating around in space, are distinguished by their types, colors and spin, atoms should be the subject of a classification. Valery Tsimmerman.

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  7. Philip Stewart

    ‘Helium is an alkali metal’ sounds like nonsense, but if we adopted Janet’s system of naming the groups, the problem disappears: ‘Helium is at the head of the s2 group, and hydrogen at the head of s1 ‘. On this basis there is a problem with elements whose outer electron belongs in the ‘wrong shell’; by that criterion, for example, La and Ac belong in d1, but we should go by their place in the sequence, Ce being in f2 etc. As for what we are classifying, ultimately it is abstract patterns.

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  8. Jess Tauber

    Well, though I do agree about putting elements in the proper places in their rows/blocks re quantum number assignments, that can’t be the only criterion. Still, given that the bulk of the elements do follow this we should give these specifications first priority for DEPICTIVE purposes (and of course go with Janet’s LSPT for ‘best’ 2D depiction in a Cartesian coordinate publishing universe). However we should also remember the effects of relativity and give it second priority. Only after this should come (derived) surface chemical/physical/mathematical behaviors. We need to establish the pecking order here, and people are going to strongly disagree on this.

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  9. Philip Stewart

    It sounds like nonsense to say ‘Helium is an alkali metal’, but if we adopt Janet’s system for labelling the groups, the problem disappears: ‘Helium is at the head of the s2 group, and hydrogen at the head of s1 ‘. On this basis there is a problem with elements whose distinguishing electron belongs in the ‘wrong subshell’; by that criterion, for example, La and Ac belong in d1, but we can base ourselves on the fact that in most cases the nth element in the f-block has n f electrons. What we are building is ultimately a pattern of patterns, not a table of properties. It is not the properties that dictate the pattern, but the patterns explain the properties.

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  10. Philip Stewart

    It sounds like nonsense to say ‘Helium is an alkali metal’, but if we adopt Janet’s system for labelling the groups, the problem disappears: ‘Helium is at the head of the s2 group, and hydrogen at the head of s1 ‘. On this basis there is a problem with elements whose distinguishing electron belongs in the ‘wrong subshell’; by that criterion, for example, La and Ac belong in d1, but we can base ourselves on the fact that in most cases the nth element in the f-block has n f electrons. What we are building is ultimately a pattern of patterns, not a table of properties. It is not the properties that dictate the pattern, but the patterns explain the properties.

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  11. Jess Tauber

    Still, by the time you get to 7p and 8s all bets are off, since now spin-orbit coupling is severe enough to trump quantum-level-only placement. I forgot to mention the effects of differential shielding in f,d,p,s in my last post. Any comments?

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  12. Eric Scerri

    This discussion goes to the heart of philosophy of classification. Should one go the reductionist route for more accuracy and thereby risk breaking the connection with the macroscopic objects that one is hoping to classify? Should one give priority to macroscopic properties in difficult cases? Don’t similar issues exist in biological classification? How are creatures like the Red Panda best classified? Is through their DNA or through their morphological features? What is the current status of essentialism among philosophers of science? Certainly the Putnam-Kripke approach to essences is believed to be deeply flawed. Even physicists, surely the arch-reductionsists, are now realizing that the macroscopic level is not to be scoffed at. Much of the interest in quantum decoherence revolves around the fact that in our macroscopic classical word we observe actualities not superpositions of possibilities. This simple fact is given proiority when trying to understand the collapse of the wavefunction. Where does this leave us in the biology of classification? Eric Scerri

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  13. Eric Scerri

    Thanks for your input Philip, I agree with you that calling helium an alkali metal would be a little silly but it’s not what you call it that is the problem. Helium is the least reactive of all the elements and as such surely belongs with the other highly un-reactive elements, namely Ne, Ar, Kr, Xe, Rn. Helium also has a full shell of electrons as do Ne, Ar, Kr, Xe and Rn. Placing He in group 18 does not constitute ignoring it’s atomic structure. eric scerri

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  14. Eric Scerri

    Jess, In spite of relativity’s best efforts there is no element that is out of place in terms of behaving as it should from the classical periodic table. It looked for a while as though elements 104 and 105 were misbehaving due to relativistic effects and that the periodic law was starting to peter out. But when the chemistry of elements 106 and 107 was examined normal chemical behavior was resumed. Hence the title of the article concerning bohrium in Nature which read “Boring Bohrium”, meaning business as usual and no overthrowing of the periodic law by relativistic effects, even though they contribute to the chemical behavior. This is all discussed in my “Very Short Introduction to the Periodic Table”, which will be published by OUP in exactly three weeks. eric

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  15. Jess Tauber

    According to Wikipedia: Element 113 has no isotope stable enough to confirm chemical properties (see http://en.wikipedia.org/wiki/Element_113 ); Extrapolated chemical properties Oxidation states Ununtrium is projected to be the first member of the 7p series of elements and the heaviest member of group 13 (IIIA) in the Periodic Table, below thallium. Each of the members of this group show the group oxidation state of +III. However, thallium has a tendency to form only a stable +I state due to the “inert pair effect”, explained by the relativistic stabilisation of the 7s-orbitals, resulting in a higher ionisation potential and weaker tendency to participate in bonding. Chemistry Ununtrium should portray eka-thallium chemical properties and should therefore form a monoxide, Uut2O, and monohalides, UutF, UutCl, UutBr, and UutI. If the +III state is accessible, it is likely that it is only possible in the oxide, Uut2O3, and fluoride, UutF3. Spin-orbit splitting of the 7p orbitals may stabilize the −1 state as well, as is seen with gold(−1) (aurides). ————————————————————————– Element 114: (see http://en.wikipedia.org/wiki/Element_114 ) Chemical studies performed in 2007 strongly indicate that ununquadium possesses non-eka-lead properties and appears to behave as the first superheavy element that portrays noble-gas-like properties due to relativistic effects. Extrapolated chemical properties Oxidation states Ununquadium is projected to be the second member of the 7p series of chemical elements and the heaviest member of group 14 (IVA) in the Periodic Table, below lead. Each of the members of this group show the group oxidation state of +IV and the latter members have an increasing +II chemistry due to the onset of the inert pair effect. Tin represents the point at which the stability of the +II and +IV states are similar. Lead, the heaviest member, portrays a switch from the +IV state to the +II state. Ununquadium should therefore follow this trend and a possess an oxidising +IV state and a stable +II state. Chemistry Ununquadium should portray eka-lead chemical properties and should therefore form a monoxide, UuqO, and dihalides, UuqF2, UuqCl2, UuqBr2, and UuqI2. If the +IV state is accessible, it is likely that it is only possible in the oxide, UuqO2, and fluoride, UuqF4. It may also show a mixed oxide, Uuq3O4, analogous to Pb3O4. Some studies also suggest that the chemical behaviour of ununquadium might in fact be closer to that of the noble gas radon, than to that of lead.[2] Experimental chemistry Atomic gas phase Two experiments were performed in April–May 2007 in a joint FLNR-PSI collaboration aiming to study the chemistry of copernicium. The first experiment involved the reaction 242Pu(48Ca,3n)287Uuq and the second the reaction 244Pu(48Ca,4n)288Uuq. The adsorption properties of the resultant atoms on a gold surface were compared with those of radon. The first experiment allowed detection of 3 atoms of 283Cn but also seemingly detected 1 atom of 287Uuq. This result was a surprise given the transport time of the product atoms is ~2 s, so ununquadium atoms should decay before adsorption. In the second reaction, 2 atoms of 288Uuq and possibly 1 atom of 289Uuq were detected. Two of the three atoms portrayed adsorption characteristics associated with a volatile, noble-gas-like element, which has been suggested but is not predicted by more recent calculations. These experiments did however provide independent confirmation for the discovery of copernicium, ununquadium, and ununhexium via comparison with published decay data. Further experiments were performed in 2008 to confirm this important result and a single atom of 289Uuq was detected which gave data in agreement with previous data in support of ununquadium having a noble-gas-like interaction with gold.[26] In April 2009, the FLNR-PSI collaboration synthesized a further atom of element 114. ———————————————————————— Element 115: (see http://en.wikipedia.org/wiki/Element_115 ) …a sufficiently stable isotope is not known at this time that would allow chemical experiments to confirm its position. Extrapolated chemical properties Oxidation states Ununpentium is projected to be the third member of the 7p series of chemical elements and the heaviest member of group 15 (VA) in the Periodic Table, below bismuth. In this group, each member is known to portray the group oxidation state of +V but with differing stability. For nitrogen, the +V state is very difficult to achieve due to the lack of low-lying d-orbitals and the inability of the small nitrogen atom to accommodate five ligands. The +V state is well represented for phosphorus, arsenic, and antimony. However, for bismuth it is rare due to the reluctance of the 6s2 electron to participate in bonding. This effect is known as the “inert pair effect” and is commonly linked to relativistic stabilisation of the 6s-orbitals. It is expected that ununpentium will continue this trend and portray only +III and +I oxidation states. Nitrogen(I) and bismuth(I) are known but rare and Uup(I) is likely to show some unique properties [13] because of spin-orbit coupling, Ununquadium may display closed-shell or noble gas-like properties; if this is the case, Uup will likely be monovalent as a result, since the cation Uup+ will have the same electron configuration as Uuq. ————————————————————————– Element 116 (see http://en.wikipedia.org/wiki/Element_116 ) ….a sufficiently stable isotope is not known at this time to allow chemical experiments to confirm its position as the heavier homologue to polonium. Extrapolated chemical properties Oxidation states Ununhexium is projected to be the fourth member of the 7p series of non-metals and the heaviest member of group 16 (VIA) in the Periodic Table, below polonium. The group oxidation state of +VI is known for all the members apart from oxygen which lacks available d-orbitals for expansion and is limited to a maximum +II state, exhibited in the fluoride OF2. The +IV is known for sulfur, selenium, tellurium, and polonium, undergoing a shift in stability from reducing for S(IV) and Se(IV) to oxidizing in Po(IV). Tellurium(IV) is the most stable for this element. This suggests a decreasing stability for the higher oxidation states as the group is descended and ununhexium should portray an oxidizing +IV state and a more stable +II state. The lighter members are also known to form a −II state as oxide, sulfide, selenide, telluride, and polonide. Chemistry The possible chemistry of ununhexium can be extrapolated from that of polonium. It should therefore undergo oxidation to a dioxide, UuhO2, although a trioxide, UuhO3 is plausible, but unlikely. The stability of a +II state should manifest itself in the formation of a simple monoxide, UuhO. Fluorination will likely result in a tetrafluoride, UuhF4 and/or a difluoride, UuhF2. Chlorination and bromination may well stop at the corresponding dihalides, UuhCl2 and UuhBr2. Oxidation by iodine should certainly stop at UuhI2 and may even be inert to this element. ————————————————————————— Element 117: (see http://en.wikipedia.org/wiki/Element_117 ) Although it is currently placed as the heaviest member of the halogen family, there is no experimental evidence that the chemical properties of ununseptium match those of the lighter members like iodine or astatine and theoretical analysis suggests there may be some notable differences. Extrapolated chemical properties Certain chemical properties, such as bond lengths, are predicted to differ from what one would expect based on periodic trends from the lighter halogens (because of relativistic effects[clarification needed]). It may have some metalloid properties, similar to astatine. ————————————————————————— Element 118: (see http://en.wikipedia.org/wiki/Element_118 ) only three atoms (possibly four) of the isotope 294 Uuo have been detected.[9] While this allowed for very little experimental characterization of its properties and possible compounds, theoretical calculations have resulted in many predictions, including some unexpected ones. For example, although ununoctium is a member of Group 18, it may possibly not be a noble gas, unlike all the other Group 18 elements.[1] It was formerly thought to be a gas but is now predicted to be a solid under normal conditions due to relativistic effects. Calculated atomic and physical properties Ununoctium is a member of group 18, the zero-valence elements. The members of this group are usually inert to most common chemical reactions (for example, combustion) because the outer valence shell is completely filled with eight electrons. This produces a stable, minimum energy configuration in which the outer electrons are tightly bound.[43] It is thought that similarly, ununoctium has a closed outer valence shell in which its valence electrons are arranged in a 7s27p6 configuration.[1] Consequently, some expect ununoctium to have similar physical and chemical properties to other members of its group, most closely resembling the noble gas above it in the periodic table, radon.[44] Following the periodic trend, ununoctium would be expected to be slightly more reactive than radon. However, theoretical calculations have shown that it could be quite reactive, so that it can probably not be considered a noble gas.[4] In addition to being far more reactive than radon, ununoctium may be even more reactive than elements ununquadium and copernicium.[1] The reason for the apparent enhancement of the chemical activity of ununoctium relative to radon is an energetic destabilization and a radial expansion of the last occupied 7p subshell.[1][45] More precisely, considerable spin–orbit interactions between the 7p electrons with the inert 7s2 electrons, effectively lead to a second valence shell closing at ununquadium, and a significant decrease in stabilization of the closed shell of element 118.[1] It has also been calculated that ununoctium, unlike other noble gases, binds an electron with release of energy—or in other words, it exhibits positive electron affinity.[46][47][48] Ununoctium is expected to have by far the broadest polarizability of all elements before it in the periodic table, and almost twofold of radon.[1] By extrapolating from the other noble gases, it is expected that ununoctium has a boiling point between 320 and 380 K.[1] This is very different from the previously estimated values of 263 K[5] or 247 K.[49] Even given the large uncertainties of the calculations, it seems highly unlikely that ununoctium would be a gas under standard conditions.[1][50] And as the liquid range of the other gases is very narrow, between 2 and 9 kelvins, this element should be solid at standard conditions. If ununoctium forms a gas under standard conditions nevertheless, it would be one of the densest gaseous substances at standard conditions (even if it is monatomic like the other noble gases). Because of its tremendous polarizability, ununoctium is expected to have an anomalously low ionization energy (similar to that of lead which is 70% of that of radon[51] and significantly smaller than that of ununquadium[52]) and a standard state condensed phase.[1] Predicted compounds Skeletal model of a planar molecule with a central atom symmetrically bonded to four peripheral (fluorine) atoms. XeF4 and RnF4 have a square planar configuration. Skeletal model of a terahedral molecule with a central atom (Uuo) symmetrically bonded to four peripheral (fluorine) atoms. UuoF4 is predicted to have a tetrahedral configuration. No compounds of ununoctium have been synthesized yet, but calculations on theoretical compounds have been performed since 1964.[30] It is expected that if the ionization energy of the element is high enough, it will be difficult to oxidize and therefore, the most common oxidation state will be 0 (as for other noble gases).[53] Calculations on the dimeric molecule Uuo2 showed a bonding interaction roughly equivalent to that calculated for Hg2, and a dissociation energy of 6 kJ/mol, roughly 4 times of that of Rn2.[1] But most strikingly, it was calculated to have a bond length shorter than in Rn2 by 0.16 Å, which would be indicative of a significant bonding interaction.[1] On the other hand, the compound UuoH+ exhibits a dissociation energy (in other words proton affinity of Uuo) that is smaller than that of RnH+.[1] The bonding between ununoctium and hydrogen in UuoH is very limp and can be regarded as a pure van der Waals interaction rather than a true chemical bond.[51] On the other hand, with highly electronegative elements, ununoctium seems to form more stable compounds than for example copernicium or ununquadium.[51] The stable oxidation states +2 and +4 have been predicted to exist in the fluorinated compounds UuoF2 and UuoF4.[54] This is a result of the same spin-orbit interactions that make ununoctium unusually reactive. For example, it was shown that the reaction of Uuo with F2 to form the compound UuoF2, would release an energy of 106 kcal/mol of which about 46 kcal/mol come from these interactions.[51] For comparison, the spin-orbit interaction for the similar molecule RnF2 is about 10 kcal/mol out of a formation energy of 49 kcal/mol.[51] The same interaction stabilizes the tetrahedral Td configuration for UuoF4, as distinct from the square planar D4h one of XeF4 and RnF4.[54] The Uuo–F bond will most probably be ionic rather than covalent, rendering the UuoFn compounds non-volatile.[4][55] Unlike the other noble gases, ununoctium was predicted to be sufficiently electropositive to form a Uuo–Cl bond with chlorine.[4] ————————————————————————— Element 119: (see http://en.wikipedia.org/wiki/Element_119 ) attempted syntheses of this element have been unsuccessful. Since it is below the alkali metals it might have properties similar to those of francium or caesium. Like other alkali metals, it should be extremely reactive with water and air. A predicted oxidation state is 1. Ununennium would be the first element in the eighth period of the periodic table and possibly the seventh alkali metal, though relativistic effects might make it less reactive than francium and caesium. ————————————————————————— Element 120: (see http://en.wikipedia.org/wiki/Element_120 ) Since unbinilium is placed below the alkaline earth metals it possibly has properties similar to those of radium or barium. Extrapolated reactivity Unbinilium should be highly reactive, according to periodic trends, as this element is a member of alkaline earth metals. It would be much more reactive than any other lighter elements of this group. If group reactivity is followed, this element would react violently in air to form an oxide (UbnO) and in water to form the hydroxide, which would be a strong base and highly explosive in terms of flammability. It is also possible that, due to relativistic effects, the element has noble gas character, which may be also the case for ununquadium. A predicted oxidation state is II.

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  16. Jess Tauber

    Descending order this time. Element 112 (see http://en.wikipedia.org/wiki/Element_112 ) In the periodic table of the elements, it is a d-block element, which belongs to transactinide elements. During reactions with gold, it is shown[2] to be a volatile metal and a group 12 element. Copernicium is calculated to have several properties that differ between it and its lighter homologues, zinc, cadmium and mercury; the most notable of them is withdrawing two 6d-electrons before 7s ones due to relativistic effects, which confirm copernicium as an undisputed transition metal. Copernicium is also calculated to show predominance of oxidation state +4, while mercury shows it in only one compound at extreme conditions and zinc and cadmium do not show it at all. Difficulty of oxidation of copernicium from its neutral state compared to group 12 elements has also been predicted. Extrapolated oxidation states Copernicium is the last member of the 6d series of transition metals and the heaviest group 12 element in the periodic table, below zinc, cadmium and mercury. It is predicted to differ significantly from lighter group 12 elements. Due to stabilization of 7s electronic orbitals and destabilization of 6d ones caused by relativistic effects, Cn2+ is likely to have [Rn]5f146d87s2 electronic configuration, breaking 6d orbitals before 7s one, unlike its homologues. In water solutions, copernicium is likely to form +2 and +4 oxidation states, with the latter one being more stable.[42] Among lighter group 12 members, for which the +2 oxidation state is the most common, only mercury can show +4 oxidation state, but it is highly uncommon, existing at only one compound (mercury(IV) fluoride, HgF4) at extreme conditions.[43] The analogous compound for copernicium, CnF4, is predicted to be more stable. The diatomic ion Hg2+ 2, featuring mercury in +1 oxidation state is well-known, but the Cn2+ 2 ion is predicted to be unstable or even non-existent. Oxidation of copernicium from its neutral state is also likely to be harder than those of previous group 12 members.[42] Experimental atomic gas phase chemistry Copernicium has the ground state electron configuration [Rn]5f146d107s2 and thus should belong to group 12 of the periodic table, according to Aufbau principle. As such, it should behave as the heavier homologue of mercury and form strong binary compounds with noble metals like gold. Experiments probing the reactivity of copernicium have focused on the adsorption of atoms of element 112 onto a gold surface held at varying temperatures, in order to calculate an adsorption enthalpy. Due to relativistic stabilization of the 7s electrons, copernicium shows radon-like properties. Experiments were performed with the simultaneous formation of mercury and radon radioisotopes, allowing a comparison of adsorption characteristics.[44] The first experiments were conducted using the 238U(48Ca,3n)283Cn reaction. Detection was by spontaneous fission of the claimed parent isotope with half-life of 5 minutes. Analysis of the data indicated that copernicium was more volatile than mercury and had noble gas properties. However, the confusion regarding the synthesis of copernicium-283 has cast some doubt on these experimental results. Given this uncertainty, between April–May 2006 at the JINR, a FLNR-PSI team conducted experiments probing the synthesis of this isotope as a daughter in the nuclear reaction 242Pu(48Ca,3n)287Uuq. In this experiment, two atoms of copernicium-283 were unambiguously identified and the adsorption properties indicated that copernicium is a more volatile homologue of mercury, due to formation of a weak metal-metal bond with gold, placing it firmly in group 12.[44] In April 2007, this experiment was repeated and a further three atoms of copernicium-283 were positively identified. The adsorption property was confirmed and indicated that copernicium has adsorption properties completely in agreement with being the heaviest member of group 12. —————————————————————————————————————————————————————— Element 111 (see http://en.wikipedia.org/wiki/Element_111 ) a sufficiently stable isotope has not yet been produced in a sufficient amount that would confirm this position as a heavier homologue of gold. Extrapolated chemical properties Oxidation states Roentgenium is projected to be the ninth member of the 6d series of transition metals and the heaviest member of group 11 (IB) in the Periodic Table, below copper, silver, and gold. Each of the members of this group show different stable states. Copper forms a stable +2 state, while silver is predominantly found as silver(I) and gold as gold(III). Copper(I) and silver(II) are also relatively well-known. Roentgenium is therefore expected to predominantly form a stable +3 state. Gold also forms a somewhat stable -1 state due to relativistic effects, and roentgenium may do so as well. [edit] Chemistry The heavier members of this group are well known for their lack of reactivity or noble character. Silver and gold are both inert to oxygen, but are attacked by the halogens. In addition, silver is attacked by sulfur and hydrogen sulfide, highlighting its higher reactivity compared to gold. Roentgenium is expected to be even more noble than gold and can be expected to be inert to oxygen and halogens. The most-likely reaction is with fluorine to form a trifluoride, RgF3. ————————————————————————————————————————————————————————- Element 110 (see http://en.wikipedia.org/wiki/Element_110 ) a sufficiently stable isotope is not known which would allow chemical experiments to confirm its place. Extrapolated chemical properties Oxidation states Darmstadtium is projected to be the eighth member of the 6d series of transition metals and the heaviest member of group 10 in the Periodic Table, below nickel, palladium and platinum. The highest confirmed oxidation state of +6 is shown by platinum whilst the +4 state is stable for both elements. Both elements also possess a stable +2 state. Darmstadtium is therefore predicted to show oxidation states +6, +4, and +2. Chemistry High oxidation states are expected to become more stable as the group is descended, so darmstadtium is expected to form a stable hexafluoride, DsF6, in addition to DsF5 and DsF4. Halogenation should result in the formation of the tetrahalides, DsCl4, DsBr4, and DsI4. Like other Group 10 elements, darmstadtium can be expected to have notable hardness and catalytic properties. ———————————————————————————————————————————————————————————- Element 109 (see http://en.wikipedia.org/wiki/Element_109 ) a sufficiently stable isotope is not known at this time which would allow chemical experiments to confirm its position, unlike its lighter neighbours. Extrapolated chemical properties Physical properties Mt should be a very heavy metal with a density around 30 g/cm3 (Co: 8.9, Rh: 12.5, Ir: 22.5) and a high melting point around 2600–2900°C (Co: 1480, Rh: 1966, Ir: 2454). It should be very corrosion-resistant; even more so than Ir which is currently the most corrosion-resistant metal known. Oxidation states Meitnerium is projected to be the sixth member of the 6d series of transition metals and the heaviest member of group 9 in the Periodic Table, below cobalt, rhodium and iridium. This group of transition metals is the first to show lower oxidation states and the +9 state is not known. The latter two members of the group show a maximum oxidation state of +6, whilst the most stable states are +4 and +3 for iridium and +3 for rhodium. Meitnerium is therefore expected to form a stable +3 state but may also portray stable +4 and +6 states. Chemistry The +VI state in group 9 is known only for the fluorides which are formed by direct reaction. Therefore, meitnerium should form a hexafluoride, MtF6. This fluoride is expected to be more stable than iridium(VI) fluoride, as the +6 state becomes more stable as the group is descended. In combination with oxygen, rhodium forms Rh2O3 whilst iridium is oxidised to the +4 state in IrO2. Meitnerium may therefore show a dioxide, MtO2, if eka-iridium reactivity is shown. The +3 state in group 9 is common in the trihalides (except fluorides) formed by direct reaction with halogens. Meitnerium should therefore form MtCl3, MtBr3 and MtI3 in an analogous manner to iridium. ————————————————————————————————————————————————————————- Element 108 (see http://en.wikipedia.org/wiki/Element_108 ) Experiments have confirmed that hassium is a typical member of group 8 showing a stable +8 oxidation state, analogous to osmium. Extrapolated chemical properties Oxidation states Hassium is projected to be the fifth member of the 6d series of transition metals and the heaviest member of group VIII in the Periodic Table, below iron, ruthenium and osmium. The latter two members of the group readily portray their group oxidation state of +8 and this state becomes more stable as the group is descended. Thus hassium is expected to form a stable +8 state. Osmium also shows stable +5, +4 and +3 states with the +4 state the most stable. For ruthenium, the +6, +5 and +3 states are stable with the +3 state being the most stable. Hassium is therefore expected to also show other stable lower oxidation states. Chemistry The group VIII elements show a very distinctive oxide chemistry which allows facile extrapolations to be made for hassium. All the lighter members have known or hypothetical tetroxides, MO4. The oxidising power decreases as one descends the group such that FeO4[33] is not known due to an extraordinary electron affinity which results in the formation of the well-known oxo-ion ferrate(VI), FeO42−. Ruthenium tetroxide, RuO4, formed by oxidation of ruthenium(VI) in acid, readily undergoes reduction to ruthenate(VI), RuO42−. Oxidation of ruthenium metal in air forms the dioxide, RuO2. In contrast, osmium burns to form the stable tetroxide, OsO4, which complexes with hydroxide ion to form an osmium(VIII) -ate complex, [OsO4(OH)2]2−. Therefore, eka-osmium properties for hassium should be demonstrated by the formation of a volatile tetroxide HsO4, which undergoes complexation with hydroxide to form a hassate(VIII), [HsO4(OH)2]2−. Experimental chemistry Gas phase chemistry Hassium is expected to have the electron configuration [Rn]5f14 6d6 7s2 and thus behave as the heavier homolog of osmium (Os). As such, it should form a volatile tetroxide, HsO4, due to the tetrahedral shape of the molecule. The first chemistry experiments were performed using gas thermochromatography in 2001, using 172Os as a reference. During the experiment, 5 hassium atoms were detected using the reaction 248Cm(26Mg,5n)269Hs. The resulting atoms were thermalized and oxidized in a He/O2 mixture to form the oxide. 269 108Hs + 2 O2 → 269 108HsO4 The measured deposition temperature indicated that hassium(VIII) oxide is less volatile than osmium tetroxide, OsO4, and places hassium firmly in group 8.[34][35] In order to further probe the chemistry of hassium, scientists decided to assess the reaction between hassium tetroxide and sodium hydroxide to form sodium hassate(VIII), a reaction well-known with osmium. In 2004, scientists announced that they had succeeded in carrying out the first acid-base reaction with a hassium compound:[36] HsO4 + 2 NaOH → Na2[HsO4(OH)2]

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  17. Jess Tauber

    Obviously we are lacking data on a good number of late 6d, 7p and 8s elements to really say which way the wind blows with regard to severity of relativistic effects. However, from the Wiki sources it seems that where we do have such data, a significant fraction of the elements do exhibit somewhat anomalous behaviors. Element 108 is typical of later members in its group- I’ll have to remember that it is supposed to have a +8 oxidation state, since that might link it numerologically with ruthenium, osmium, and xenon. For ex. 108+76=184, the nuclear magic number. And so on. Element 112 seems to have anomalous electronic behavior. Element 114 may have noble character. Element 118 NOT noble Elements with unknown chemical behavior are 109, 110, 111, 113, 115, 116, 117 (but experiments under way), 119, 120.

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  18. Valery Tsimmerman

    Jess, First, despite all those alleged relativistic effects that your refer to, n+l rule holds, meaning that all element in 8th period of Janet’s LSPT have same n+l=8. Second, most of that stuff is theoretical and is not confirmed by spectroscopic data.______ The construction convention for the PT should be following:_ 1) line up all the elements in accordance with the values of Atomic Number to get Mendeleev’s line;_2) find maximum n+l value for each element;_3) chop up Mendeleev’s line in places where maximum value of n+l changes to get periods;_4) stack up the periods so they are lined up on the right side (corresponding to “n max.” and “l min.”). _____Four easy steps and all the groups of the traditional PT are recreated (except He is next to Be, not next to Ne).____ This took almost 150 years of painstakingly studying and arguing about properties of “the elements”! Isn’t it the time to stop the arguments?

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  19. Eric Scerri

    Dear Valery, Sometimes arguments are required. You are taking up the reductionist argument and appear to claim reductionism as your own while chemists flounder around helplessly for 150 years. However, you do not speak for reductionism in general since you have a very specific take on the periodic table. It is just as reductionist to point to the full shell structure of the atom of helium and thus keep He in group 18. I suggest that you try to separate arguing in terms of atomic properties and neglecting macroscopic properties (a form of reductionism) from your specific brand of reductionism which places spectroscopy of neural gas phase atoms above everything else. As you know in some of my articles I have claimed that we can use atomic number triads to settle the question of where to place helium, an approach that you reject as I recall. This is an even bigger dose of reductionism since it concerns the structure of the nucleus. It is not enough to just wave the banner of reductionism. One needs to stipulate precisely why an approach should be adopted within an overall reductionist approach.

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  20. Jess Tauber

    As I’ve written before on other discussions, in the tetrahedral mapping n+l and n-l give symmetrically distributed sets. I thought it might be interesting to combine these and tried out sq(n)-sq(l). The resulting set has a bunch of interesting properties. Curiously, the only places where the numbers match are 4s and 5f, with sum 16. What other functions might have things to tell us about the way quantum numbers work together?

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  21. Valery Tsimmerman

    Eric, Many consider the Periodic Table as settled science. Couple of posts back I illustrated how one can arrive at almost the same Periodic Table following simple 4-step procedure that completely disregards the properties of “the elements”. There are only couple of small differences: 1)Helium is next to Beryllium, and 2) Blocks are arranged in f,d,p,s order (corresponding to l=3,2,1,0) instead of s,f,d,p order (corresponding to l=0,3,2,1).______ You may argue that I am engaging in some type of unacceptable brand of reductionism, but result speaks for itself: this procedure works and is extremely accurate with regard to the groups of the elements. ____On the contrary, history shows that one can not build the periodic table based on the triads.

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  22. Jess Tauber

    Yet some triads are extremely useful in pointing out some of the ‘nontraditional’ relationships, since certain combinations cause these to be between, and not within, blocks. One would need to define different types of triadic relationships, as they tend to go with different structural features (for ex. nearest neighbor triads help define Mendeleev’s Line). The question then arises as to how much of the periodic table can be built on these. I wonder whether this issue has been painstakingly examined in any kind of comprehensive, and mathematically plausible, manner.

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  23. Jess Tauber

    Question for the experts here. At what point in the PT does this happen where we can say it is less than more likely that 2 s electrons can participate in bonding easily with p,d,f? Given the ‘knight’s move’ relation, it has to be after 3d, but where? What Z? What I’m after here is some sort of ‘balance point’ dividing the PT into two parts. If it isn’t at one element a range will do. Thanks.

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  24. Eric Scerri

    We seem to be talking past each other so let me try something new if I may. For sometime now I have been thinking about the relationship between an 8 column short form table (as many of the early tables were) and the current medium long form 18 column table. Although I have argued for one optimal table when it comes to placement of elements I also hold the view that in many ways the 8 column table is ‘just as good as’ an 18 column table. After all one can still achieve the same placement of H, He, La, Ac, Lu and Lr in a short form table as far as grouping is concerned. For example, what the 8 column table emphasizes and embodies is the simple rule of 8 which is also the basis of the Lewis octet rule and a good first approximation to explaining chemical bonding. Although the medium-long form is more accurate in separating out the transition metals into their own groups it is somewhat paradoxical in moving away from the rule of 8. There is also a nagging fact that I keep thinking about. Of the 6 noble gases (He, Ne, Ar, Kr, Xe, Rn), only the first three have genuinely full shells and yet the rule of 8 still holds in that all these atoms, except He, strive for an ns2, np6 configuration, regardless of whether the shell is really full or not. This fact suggests that the short form table if fundamentally correct. I realize that I am groping around a little here but I would be interested in any comments on these thoughts.

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  25. Philip Stewart

    Neon is the only element to have a full shell of 8 electrons; argon lacks the 3d subshell. Helium is peculiar because the K shell is full with only 2 electrons. The d block can only be squeezed into an 8-group table by Mendeleev’s expedient of putting three groups into group VIII, and the f block has to be foot-noted. My own way of including the f block in the main sequence without using too wide or tall an outline is to portray the system as an elliptical spiral, which can be fitted on to a standard nx1,414n page.

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  26. Valery Tsimmerman

    Lewis was trying to come up with his version of atomic structure based on cubes. Octet rule is a rule of thumb for atom bonding that is mostly useful for the first 20 elements. It has exceptions even among the light elements: helium is one, boron is the other (BF3).____I think going back to Mendeleev’s 8-period table is a move in the wrong direction. What is next, going back to Newland’s law of octaves?____ We know now what the atomic structure is. And it is not cubical. Jess, I and others have noticed tetrahedral character of the Periodic System that has nothing to do with bonding, but has everything to do with the interplay of the quantum numbers. Because of that we were accused in Platonism. Cube is also platonic structure. Does it make Lewis a Platonist too?

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  27. Jess Tauber

    Hmmm- we have cubes for early elements, square pyramids (which are sort of half-octahedra, and there are PT models which seem to be full octahedra). Could there also possibly be dodecahedral and icosahedral relationships here? In other words, does the PT use all possible configurational motivations? I’ve speculated that some of the mappings on my T3 appear to correspond to ‘shadows’ from other parts of a larger compound of five (or ten) tetrahedra, inscribed within a dodecahedron, and within this figure one also has intersections of the five tetrahedra giving the vertices of an icosahedron. Within the dodecahedron one may also inscribe cubes and other figures. Interestingly the outer dodecahedron establishes, quite directly through trigonometry, the Golden Ratio as part of the system.

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  28. Jess Tauber

    Now looking into whether the metal means are related to the Rydberg formula. This would be striking if it holds. More numerology, hurrah!

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  29. Valery Tsimmerman

    Eric is right. We are talking past each other. I think that I understand what we are looking for.______142 years ago Dmitri Mendeleev thought that he discovered one of the fundamental laws of nature, he called it the Periodic Law. Soon it had become clear that it is not fundamental at all. There is something more fundamental behind the apparent periodicity of the properties of atoms.____ Many attempts were made to find the reason for the periodicity. Some tried to explain it on a basis of the atomic structure/ Quantum mechanics. But that had only limited success. Strange relationships, such as n+l rule were discovered, but they only partially accurate. ____ The question is what causes periodicity? Eric has couple of interesting ideas: 1) The elements are defined only by the atomic numbers; 2) the atomic numbers are subject to interesting mathematical relationships, the atomic number triads._____ Triads hint to some numerical pattern, but one can not recreate the periodic table based on triads. What is behind the triads? What is behind n+l rule? What is behind atomic structure? What is behind Shroedinger equation? There is something at the basis of all of the above.____The Shroedinger equation uses peculiar numbers that are the means of quantization of energy and orbital momentum. Those numbers are not unrelated. They indeed are subject to the interesting relationship. Jess claims that he noticed that Periodic table has tetrahedral character in 1979. Later, in 2007, I have established that tetrahedral relationship between the quantum numbers is responsible for that tetrahedral character. ____ Now we are getting more fundamental. We are on a level of mathematics. Again, Jess has noticed that every other alkaline earth atomic number corresponds to the tetrahedral number that can be found in forth diagonal of the pascal triangle. I have established that it is not quite Pascal triangle, but modified Pascal triangle where in the second diagonal every even number is suppressed to make it 1,0,3,0,5,0,7….., instead of 1,2,3,4,5,6,7…. _ The periodicity of the elements is the direct result of the interplay of the quantum numbers. The quantum numbers are not arbitrary. There is a some sort of code that ties them together and that code is the foundation for the quantum mechanics and for, that matter, of everything else.____Despite lack of time, I participate in such discussions as this one only because I hope to alert the scientific community to these very important numerical patterns. ______Best regards, Valery Tsimmerman

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  30. Philip Stewart

    0, 1, 2, 3, 4, 5, point, line, triangle, square, pentagon… The simplest arithmetic and geometric relations seems to underlie the material world. No wonder Plato thought mathematics ruled the Universe, which is all right if you just want to meditate. But what is passionately interesting is the complex forms that are built on these simple bases. I think it is rather fruitless to argue endlessly about the precise representation of the Periodic System. Janet’s was very good and Valery’s is even better, and I think mine is quite pretty, so lets just accept one of them and get on with the chemistry! For a start, I still want to know why s and p or s and d electrons can behave like a single set.

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  31. Eric Scerri

    Philip, thanks for correcting me on Ar. Of course you are correct. This actually strengthens my point since now we can say that the majority of the noble gases lack a full outer-shell. Thanks also to Valery and Jess for stimulating comments. Incidentally, I am not recommending going back to a short form table. I am just suggesting that thinking about the relationship between the short and medium-long forms could be productive. The fact that Lewis based his rule of 8 on the 8 corners of a cube is neither here nor there. The fact remains that the acquiring of a full ns2 np6 configuration is a good guide to bond formation in many, many compounds. Not just the first 20 elements incidentally Valery. Consider iodine for example. In forming compounds such as NaI or KI it is accepting an electron to produce not a properly full outer shell but a full ns2 np6 configuration in its outer shell. The rule of 8 persists throughout the periodic table, irrespective of the value of Z and irrespective of whether electrons lie on the corners of cubes or not.

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  32. Jess Tauber

    I keep thinking of Costner’s ‘Postman’ movie…danged Holnists…. Anyway, isn’t the limit of total bonds (when coordination compounds are also considered) limited to 16 by steric considerations? And 16 is twice 8. Starting to look like another Pascal Triangle relationship? The sums of horizontal rows through that figure keep doubling. Re Valery’s modified Pascal- any way to get this by interacting the classical Pascal Triangle with the 2,1 sister? Both are involved in the PT. Parallel to the 2’s side, the analogue to the natural number diagonal has only odd numbers; the triangular numbers are replaced by square numbers, and the tetrahedral numbers by the square pyramidal numbers. We can make 3D PT models either tetrahedral or pyramidal. Squares are as important as triangular numbers in the PT (but different functions). Odd numbers mark less stable isotopes, as well as half-orbital lengths. Some time ago, on other discussions, we went into interactions between numbers from different Pascal diagonals. Could these be motivated by mathematical interactions between different Pascal sisters?

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  33. Jess Tauber

    Forgot to reiterate that the Classical (1,1) Pascal also generates the Fibonacci numbers, all of which (up to 89) are leftmost in orbital half rows in the PT (first singlet (for odd Fib) or first doublet (for even Fib). Note that in the Fib sequence itself we find repeated odd,odd,even triplets (Valery wants a code, a beginning here?). The (2,1) Pascal sister generates the Lucas numbers, which map positionally (up to 18) to rightmost positions in orbital half rows (last singlet, last doublet, with the same odd/even split). With 29 and 47 (copper, silver in the same group) though they are positionally offset the anomalous electronic configurations actually fit the Lucas trend to half- or completely full orbitals. 76, osmium, can behave like xenon, with a full orbital.

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  34. Jess Tauber

    Forgot to reiterate that the Classical (1,1) Pascal also generates the Fibonacci numbers, all of which (up to 89) are leftmost in orbital half rows in the PT (first singlet (for odd Fib) or first doublet (for even Fib). Note that in the Fib sequence itself we find repeated odd,odd,even triplets (Valery wants a code, a beginning here?). The (2,1) Pascal sister generates the Lucas numbers, which map positionally (up to 18) to rightmost positions in orbital half rows (last singlet, last doublet, with the same odd/even split). With 29 and 47 (copper, silver in the same group) though they are positionally offset the anomalous electronic configurations actually fit the Lucas trend to half- or completely full orbitals. 76, osmium, with 6 d electrons, can behave like xenon, with a full orbital.

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  35. Eric Scerri

    A few days ago Valery wrote,_____________________________________The periodic table, as it is currently defined, seeks to classify the properties, that is behavior of “the elements”. This is the root of the problem. ____Mendeleev intuitively was against such approach: “Properties, such as the optical and even the electrical or magnetic ones, cannot serve as basis for the system naturally, since one and the same body, according to the state in which it happens to be at the moment, may show enormous differences in this regard.” However, he had to use whatever knowledge was available to him at that time. So, he used valence among other things to come up with his classification.____ I argue that any properties should be left aside and classification should be based strictly on structural/quantum mechanical attributes of the atoms. _____This is exactly what I did. I completely ignored the properties and tried to build a table using the electronic structure of atoms. What was the result? First, I reinvented Janet’s LSPT and then I cam up with ADOMAH PT. Remarkably, all groups that I came up with coincide with almost all the groups of traditional long form PT, except Helium in my layout is next to Be, not Ne. One element in one out of 32 groups is not a great difference! ____Not at all. So, the electronic structure approach isn’t so bad. The advantage that such approach provides is the agreement with spectroscopic observations, which are completely ignored by the traditional PT and other layouts based on properties. And that is what Mendeleev would have liked: “…every system, however, that is based upon exactly observed numbers is to be preferred, of course, to other systems not based upon numbers because then only little margin is left to arbitrariness..”___________________________________________ ____________I would like to respond to this again to argue that we cannot merely concentrate on the properties of atoms and forget all about chemical properties. Consider the periodic law, as stating something like; the properties of the elements recur approximately after certain regular intervals. If that is the case then it is perfectly OK to seek a reductionist explanation in terms of atomic structure and this is what is done as a matter of course in modern chemistry and physics. However we cannot lose sight of the fact that the periodic law is about macroscopic chemical and physical properties showing recurrences. We cannot jettison macroscopic properties altogether as Valery seems to want to. Otherwise we would be left with something like the properties of atoms such as electronic configurations recur after certain intervals and these recurrences can be explained by appeal to the same configurations. In other words we would have a circular and therefore empty explanation. In order to have a reduction we need to keep the two different levels in mind and make a connection between macroscopic properties and the putative properties that do the reducing at the microscopic level. Reduction involves a relationship between two levels, not the denial of the level that we are seeking to explain. Eric Scerri

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  36. Jess Tauber

    For me the PT seems to have many of the features one sees in complex hierarchical systems, including human languages. The levels are not merely built one atop the other- higher tiers also appear to feed back in some respects to affect the lower ones. One sees this also in the genetic code and its interactions hierarchically. Even so, if one is lucky there are certain primitives and rules that shine through the mishmash. The quantum system is one such, and we also have to include differential screening and relativistic effects. This certainly isn’t ALL that is going on, but is still a good deal of it. What is fascinating, for me, is that we know that complex dynamic hierarchical system rework themselves over time, adapting to new conditions, sometimes cyclically. I don’t know what this portends for the PT, since our own local neck of the universal woods doesn’t give us enough sense of the variability that may be out there in the larger cosmos, whether within our light cone or not. Expecting simple one-size-fits-all answers diminishes the probable grandeur of the actual situation, and we’ll need more than just a few wise blind men feeling around the elephant.

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  37. Jess Tauber

    While reading (yet again…) about current attempts to produce tabletop nuclear combination reactions (call it what you will) I ran across the following Wiki article on Nickel-62: http://en.wikipedia.org/wiki/Nickel-62 Interestingly, this is the most stable nuclide of all- NOT Iron-56. AND as I’ve pointed out many times, 62 is the rounded off valued of 100x the smaller value of the Golden Ratio, where we have 1/2(sqrt5-1). Of course this is just another valueless mathematical coincidence. It is also coincidental that with 28 protons, there must be 34 neutrons, the latter being a Fibonacci number. Hmmm, while I’m at it, there is also the useless fact that 28=4×7, both of which are Lucas numbers.

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  38. Valery Tsimmerman

    Eric,_ In your previous email your wrote: “…. we would be left with something like the properties of atoms such as electronic configurations recur after certain intervals and these recurrences can be explained by appeal to the same configurations”. Sorry for not expressing myself clearly. In My previous posts I was talking about two levels. I pointed to the great similarity of results that were obtained by two approaches: one being content of PT groups using traditional approach based on the properties of the elements and the other being content of the groups that was derived based on operating with the quantum numbers using tetrahedral sphere packing and Pascal triangle. So, there were two levels that I referred to.____ I consider electron configurations to be the attributes of the atoms, not the properties. When I refer to the properties, I mean physical and chemical properties, such as boiling and melting points, bonding, volatility, valence…___ What I was trying to say is that I was able to pinpoint a method of derivation of the groups by operating strictly with numbers, that is atomic numbers and quantum numbers n, l and ml. As well as, application of Pascal triangle method, for derivation of complete group of Alkaline earth elements!____ This is what I find amazing: there is a strictly mathematical method of derivation of the groups of the elements in periodic table. And according to some accounts, Mendeleev believed that there would be a mathematical explanation of his Periodic Law ___Frankly, I did consider such atomic attributes as electron configurations in order to arrive at ADOMAH PT, but that was only an intermediate step. I hope that this makes it clear. __Valery.

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  39. Philip Stewart

    Mendeleev most certainly did want a mathematical derivation for his “law”, so that it would be like Newton’s Laws. Failing to find it he lost interest in his table after 1871, coming out of chemical “retirement” from time to time to comment on discovery of a predicted element or to receive a prize. If he could have lived into his eighties, he would have acclaimed Bohr’s quantum-based version. Indeed he might have redrawn his table much sooner than that if he had taken the lanthanides seriously. After all Janet, born only 15 years after Mendeleev, saw the way to regularize the table at the age of 78, before he heard of Bohr’s work. I think we should represent the periodic system in its most fundamental form; the rest is commentary. Looked at from the top that is reduction, but viewed from the base it is elaboration.

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  40. Jess Tauber

    Half the alkaline earth atomic numbers are represented in the classical Pascal Triangle: 4, 20, 56, (120), in the tetrahedral diagonal. As has been discussed ad nauseum, the intermediate alkaline earth numbers differ from the equivalent intermediate tetrahedral numbers by monotonically increasing amounts: 2-1=1; 12-10=2; 38-35=3; 88-84=4…. Valery found a way to generate ALL the alkaline earth atomic numbers in a Pascal Triangle analogue where one suppresses the even numbers in the natural number line on one side of the triangle. Doubling the results the triangular number diagonal then gives squares, and the tetrahedral diagonal gives all the alkaline earth atomic numbers. What is still mysterious is how to derive the suppression in a motivated way. I’ve been exploring combinations of different triangles, but it may be simpler than this- the triangle might fold back on itself. Or triangles might combine out-of-plane. If so could there be some larger figure involved, such as an icosahedron or dodecahedron? In such cases the part of the triangle used would be bounded- and we only have evidence of part of the triangle used to motivate mathematical aspects of the PT.

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  41. Eric Scerri

    That’s an interesting story you tell on behalf of Mendeleev but I dont believe there is any evidence for any of your claims. Can you cite any textual evidence whatsoever for the notion that Mendeleev “lost interest…” or that he might have acclaimed Bohr’s account of the periodic table? As to the rare earths I believe that only 3 or 4 were known in Mendeleev’s time so what is the relevance of this? On the other hand there is much textual evidence which points to Mendeleev’s not believing that atoms existed literally, for an overall anti-reductionist stance given that he did not approve of Prout’s hypothesis. He also did not buy into the discovery of the electron or radioactivity. Mendeleev repeatedly stressed the individuality of the elements rather than seeing them as all made of the same ‘stuff’. I cannot therefore see why you or anyone else would portray Mendeleev as being in favor of reductionism. all the best, eric scerri

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  42. Philip Stewart

    “A law always expresses a relationship between variables” – Mendy 1899, but the only variable he could point to was Z. His last major paper on his PT was 1871. He followed the chemical literature until 1875 (discovery of Ga), but he had to be told about Sc and Ge. The table in the 1906 edition of his textbook differs from that in the first in only one significant way: he had added group zero the noble gases (and six places between H and He!). By then all the lanthanides were known except Lu and Pm, but the only ones he showed were La, Ce and Yb. Meanwhile look at his careers: searching for the ether 1871-81, Russian science policy and economics 1880s, work on smokeless gunpowder 1890-94, Director of the Bureau of Weights and Measures during his last years. He was quite right to do all this; it can’t be good for a man to spend too much of his life thinking about the Periodic System.

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  43. Eric Scerri

    Thanks Philip, All that you say is correct, and fully described in Michael Gordin’s book but does not necessarily amount to losing interest in the periodic table. Nor have you provided any evidence for his being a reductionist. One detail I never knew was that “he had to be told about Sc and Ge”. Can you tell me of your source of information on this? As to the rare earths, yes many more were known towards the end of Mendeleev’s life but as you know he handed the problem to Brauner to deal with. And what a problem which could not be reasonably solved at the time. Pieter Thyssen in Leuven and book review editor for Foundations has become the expert on this aspect. I’ll see what he says. all the best, eric

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  44. Valery Tsimmerman

    Eric,__ There is plenty of evidence that Mendeleev was looking for mathematical underpinnings of the Periodic System. See Shchukarev, S.A. Zhurnal Obshchei Kimii, Vo. 47, No.2, Feb, 1977pp246-259: “Mendeleev expected that the secret of the Periodic law would probably be discovered through the theory of numbers”. _____I would like to refer you also to J.W. van Spronsen’s ” The periodic System of Chemical Elements” published in 1969 by Elsevier Publishing. He writes on pages 136 and 187 that Mendeleev felt strongly that the system had to be three-dimensional, namely cubical. ___________________________________Regarding the Jess comment on modified Pascal triangle and what it really means I would like to respond that suppression of the even numbers and alkaline earth’s atomic numbers can be generated by the tetrahedral packing of spheres of two colors, as presented on my web site http://www.PerfectPeriodicTable.com/Novelty. ___If you use spheres of the same color, you will come up with the result that can be found in regular Pascal Triangle, namely the tetrahedral numbers, but if you use two colors, you will come up with Alkaline earth’s atomic numbers.__ Best, Valery

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  45. Philip Stewart

    Mendy wanted to reduce the Periodic Law to a mathematical formula. He couldn’t do it. He gave up. As regards Sc, Cleeve wrote to him: “I have the honour to inform you that eka-B has been isolated”. And it was Richter, not Mendy, who informed Winkler that Ge was eka-Si (Gordin pp 40-42). And you now admit that Mendy had given up on the lanthanides. As I said he made no substantial changes to his textbook’s table between 1871 and 1906, apart from adding group zero. He also added those hypothetical elements between H and He, and he wrote that fatuous article about the ether and coronium. I call that renunciation of serious thought. Never mind! He was thinking about the Russian economy, the Czarist State, weights and measures, ballooning and art criticism. A big man!

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  46. Eric Scerri

    OK so I need to be a little more careful in the presence of such experts as yourselves, such big men! As I argued in my book (p.119-121), which incidentally Van Spronsen had good things to say about on the back cover of the first printing, there are some senses in which Mendeleev was a reductionist and some senses in which he was not. One other sense which neither of you has brought up yet was the notion that the elements were ordered strictly according to atomic weight and that there were no exceptions to this. Of course you are correct to point out that he sought a mathematical law. He also regarded himself as the Newton of chemistry and believed that ‘weight’ was somehow fundamental. All this is true. But when philosophers of science speak of reductionism they usually mean reduction to physical theory not mathematics. They also mean reduction to some physical ontology or physical components such as atoms, or later electrons. In this sense Mendeleev was definitely not a reductionist. Philip I am not sure why you introduced the notion that Mendeleev “lost interest” in the periodic table. Does this have a bearing on the question of reductionism? All the best, eric

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  47. Valery Tsimmerman

    Eric, ____ you are right that classical view of reductionism from the chemist perspective is reduction to physics. My, perhaps unorthodox view of reduction is following process: Biology > Chemistry > Physics > Math. So, Mendeleev skipped one step, namely physics.

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  48. Jess Tauber

    One can construct Valery’s triangle by starting with 2 on one side all the way down, while on the other side we have 2, -2, 6, -6, 10, -10, 14, -14, 18, -14…i.e. the block lengths of the PT in both + and -. I’ve now worked out the Fibonacci- analogue on the 2’s side of this modified triangle. If one takes the differences between every other number in this series, and then the differences between these, they come out as twice the Lucas numbers. Thus the relation to the Golden Ratio is indirect, buried inside the sequence at a deeper level. But it is there. Next comes the sequence on the other side. This might be interesting too.

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  49. Eric Scerri

    Thanks Valery, I am glad you are taking the time and trouble to clarify your earlier statements. However the main point I was responding to was your claim that chemistry is reducible entirely to atomic physics and that in order to reach the best periodic table we need only to consult the properties of atoms such as in your own preferred periodic table. In making this claim you are NOT skipping the reduction to physics step but in fact affirming it, sometimes in the name of Mendeleev. But now you concede that Mendeleev himself did not argue for reduction of the periodic table to physics. _____________Perhaps you could take a little more time to explain where you stand, without appealing to Mendeleev for support. Do you still believe that it it is reasonable to discuss chemical periodicity and the periodic table just in terms of the quantum numbers, the relationships between them and electronic configurations and to abandon all talk of macroscopic ‘properties’ ? eric scerri

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  50. Philip Stewart

    Eric: I don’t know about Valery, but I certainly don’t pretend that it would be possible to derive chemistry from physics. But chemical behaviour can be best explained by reference to the physics of atoms and their combinations. Even the noble-gas behaviour of helium is explained by the fact that the K shell is full with only two electrons. That of neon depends on the peculiar fact that the s and p subshells can behave as one. I’d like to know why argon et al., with incomplete outer shells, behave like noble gases, or why elements in the d block can have highest oxidation states that go up to viii; but I’m sure the explanation comes from physics. As for why Mendy stopped trying to improve his table, it is surely clear that he could not achieve a mathematical formulation without knowing about atomic number and quantum theory. He was a big man in admitting his impotence and getting on with other things.

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  51. Valery Tsimmerman

    Eric,__ I do not believe that it is possible at this point of time to achieve complete reduction of chemistry to the quantum mechanics, simply because we do not have complete understanding of the quantum world. In the beginning of 19th century de Laplase argued that the universe is completely deterministic. In the beginning of 20th century scientists could not explain orbit of Mercury on a basis of Newton’s theory of gravitation, which stated that objects attracted each other with a force that depended on distance between them. Einstein could not agree with that because that would mean that if one body is moved the force on the other one would change instantaneously, thus sending a signal that would travel with infinite velocity. This led him to his famous General Theory of relativity that treats gravity as a product of space-time curvature which, in turn, helped him to explain the orbit of Mercury in its entirety.____ Similarly, at this point of time chemistry can not be reduced to physics, meaning quantum mechanics, in its entirety because our understanding of QM is not yet complete. Working on periodic table I have noticed strange tetrahedral relationship between the quantum numbers n, l, ml and ms. New theory is needed in order to explain this, and perhaps other things. Without such theory complete reduction of chemistry to the quantum mechanics is not possible. Although our knowledge of physics is mature enough to explain such things as deviation of Mercury’s orbit, as well as many other things, it has yet to reach the level of maturity that is necessary to explain all intricacies of the Periodic System. Valery Tsimmerman.

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  52. Eric Scerri

    Thanks Valery, Yes of course reduction is never complete. That’s a given. To get back to the periodic table, can you and Jess perhaps say more about the tetrahedral relationships that you have both noticed. Please resist the temptation to say it all at one and concentrate on the simplest and most central ideas first. I frequently get lost in your and Jess’s postings when you launch into further aspects and types of numbers and all that. Please keep it simple for now.

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  53. Jess Tauber

    Ok, imagine a young college chemistry major musing about the periodic table inside the cover of one of his books when it suddenly hits him that if the depiction were snipped apart the bits and pieces could be reassembled in 3D but not randomly. He make a paper copy and does this. The results aren’t perfect- He finds that he has to place H together with He, re-sort some of the f and d, and extend the table to 120 to make the model work. He shows his chemistry professors, who invite him to present it informally at the local upcoming ACS meeting, where it draws yawns at best. Later he notices that there is a relation between the lengths and widths of the blocks, making him realize that the relationship really is tetrahedral. All this took place in 1979.

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  54. Jess Tauber

    Like Valery I saw that to make the model into a perfect tetrahedron the re-structured blocks had to have individual element-cell widths halved, and the blocks themselves had to be specially interspaced. At this time I wasn’t aware of the other relationships, and discontinued active work on this, though I did present my original findings in various venues, either in person or on-line, for many years after. Occasionally I searched the WWW for any new references to a tetrahedral mapping to the PT, but only found my own.

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  55. Valery Tsimmerman

    I am okay with looking at macroscopic properties of the elements but I do not think that adequate resolution of such questions as absolutely correct positions of La, Ac, Lu and Lr, as well as H and He in the periodic table can be found by continuously observing and arguing about them. At some point one has to look deeper in order to find the resolution. Just as orbit of Mercury could not be adequately explained by continuing observations, speculations and discussions, history indicates that adequate position of the elements in the table can not be established strictly on a basis of observation of their macroscopic properties. The fact that QM, in its present form, can not explain periodicity in its entirety does not mean that we should stop our attempts to look there and beyond for answers. Mendeleev felt intuitively that organizing elements in the periodic table on a basis of properties can not serve as adequate explanation of the system itself. Therefore, he was looking to math and 3D geometry for answers, since he had no idea about QM at that time. Just as Lewis, Bohr, Janet and many others did. I, with Jess’ help, happened to stumble on some mathematical methods that can generate same sequences of the elements that were derived on a basis of the macroscopic properties. Those mathematical methods allow construction of the system of numbers that coincides to a great degree with the system of atomic numbers of the elements as depicted in the periodic table without any reference to the macroscopic properties of the atoms. I and others find it fascinating.___ I will be glad to expand on the tetrahedral theory at later time .___ Valery.

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  56. Jess Tauber

    Then just a few years ago after reading about another synthesized element I searched again on a whim, and ran across some of Valery’s postings on others’ blogs- this eventually led to a web address for his own site, http://www.perfectperiodictable.com. I read through the pages on the site, contacted him, and the rest, as they say, is history. Unlike Valery, I’d never realized that one could use close packed spheres in the model. This was an eye-opener, and led to a renewed effort on my own part. He also linked the tetrahedral model to the quantum numbers, which I’d never done.

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  57. Jess Tauber

    Before coming together both of us had discovered what he calls the ‘perimeter rule’- that in a PT tetrahedron of 120 elements the sum of block heights plus half-widths is always 9. This leads to the doubling up of element representations in square cells when not using spheres, and two elements per sphere when utilizing them in close-packed configuration. After we started interacting I came to the conclusion that this was a defect in the model I couldn’t continue to live with, and began playing with other ways to distribute elements. Well it turns out that in the close-packed sphere model there are as many spheres with two elements as there are without any- all you have to do is send the extras back home to the empty spheres. But how?

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  58. Jess Tauber

    Before coming to this conclusion Valery and I had toyed with the notion that the empty spheres in his model might represent antimatter elements, but these would be doubled up just as the normal ones would be. It’s always fascinating to follow the sudden ‘aha’ moments when your thinking expands beyond the box. No antimatter- just divide up the elements you already have and stick the spares into the empty spheres. In the 120-sphere tetrahedron the layers of spheres with doubled s-block elements start with the 1×8=8 spheres on one edge, then next come 2×7=14 empty spheres, followed by 3×6=18 doubled p-block elements, after which there is a layer of 4×5=20 empty spheres, now 5×4=20 double-d-block element spheres, next 6×3=18 empty spheres, afterwards 7×2 doubled f-block element spheres, and finally 8×1=8 empty spheres. You may no doubt notice that not only are there an equal number of empty to double-filled spheres, they have the SAME block structure, but with a reversed order of occurrence (and in the actual model at right angles to the filled set). Thus the simplest way to redistribute the doubled elements is just to throw them in the same way into this second set of layers in mirror-image fashion.

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  59. Jess Tauber

    I still have the notes where I was trying out variations of the tetrahedral theme. I gave up the idea of keeping the linear order of the principle quantum number on the edges, and began trying out orders from the center outward, from the vertices inward, and so on. Looking at one such drawing some kind of mental image inversion took place, and I quickly jotted down a sketch of the result. It looked good, but flat depictions aren’t the best proofs. I dragged out my own built physical model of Valery’s 3D Adomah, and started counting. A ring of four of the six edges of the 120-sphere model contained 28 spheres, fitting the requirements of the f-block. Then one move inwards there were two smaller angled rings of 20 spheres, for 40, the required number for the d-block. Within these were three still smaller angled rings of 12 spheres, equal to 36, for the p-block, and finally, there was a central axis of four angled rings of 4 spheres, for 16 elements in the s-block. It all fit. Even so, at this time I still rationalized the system as angled rings, and only later saw that you could split the system into angled nested rhombi containing dual periods.

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  60. Jess Tauber

    At this point I’d discovered what I called the T3 model (after the last names of Valery and myself, and the Tetrahedron). I hadn’t really thought about the mathematics behind the scenes. So I started looking for some answers- checking out Wiki and other sources. Their article on the tetrahedron pointed to many other links, including the Pascal Triangle. That page of course showed the diagonals, and how they motivate filling of larger structures out of close-packed spheres. Seemed promising enough. But my model didn’t use triangular layers stacked one atop the other. Even so, I suddenly noticed that in the tetrahedral diagonal every other tetrahedral number was identical to every other alkaline earth atomic number. THAT was quite a surprise, but then I didn’t yet understand how this was connected to squares, and the Janet Left-Step PT.

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  61. Jess Tauber

    After getting involved in all this I started the Yahoo discussion list on alternative periodic tables ( tech.groups.yahoo.com/group/tetrahedronT3 ). I had hoped to get much more discussion of other tables than just tetrahedral ones, but I suppose there weren’t enough discussants defending their own. Even so there was plenty of give and take. This was the venue where it was first announced that every other tetrahedral number in the Pascal Triangle’s tetrahedral diagonal was identical to every other alkaline earth atomic number: 4, 20, 56, 120. The intermediate alkaline earth atomic numbers are the means of the flanking tetrahedral ones added to the earlier ones (or subtracted from the later ones). The matching tetrahedral numbers differ from these by amounts increasing by increments of one. So… (4-0)/2=2; 0+2=2 (He); (20-4)/2=8; 4+8=12 (Mg) and so on. Then subtracting by tetrahedral numbers: 2-1=1; 12-10=2; 38-35=3; 88-84=4 etc. so we have increasing differences 1,2,3,4… It was Valery who saw that this related directly to the famous triads which were so important in the early work on the PT.

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  62. Jess Tauber

    The other day I noted that Nickel-62 was the most stable isotope, relating to the Golden Ratio, and also to its possession of 34 neutrons (Fibonacci). Today I was again looking through that font of received wisdom, Wikipedia, this time at the page on the PT, and was interested to note that 94 elements were found naturally (3 incidentally, 91 otherwise). 94 is twice 47, the Lucas number.

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  63. Jess Tauber

    Oh, lest I forget, some of us believe that 120 may be the last element. If so, then there are 26 elements remaining. This is twice 13, the Fibonacci number. Weird stuff.

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  64. Jess Tauber

    Atomic numbers 43, and 61. Both are five positions into their respective blocks (d, f). Both highly unstable relative to other below lead. 61-43=18, Lucas number. 61+43=104=8×13, both Fibonacci numbers.

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  65. Jess Tauber

    The other ‘incidentally occurring’ element, Np, element 93, is right below Pm, also in the 5th position in the f block. 93 is 3×31, just as 62 is 2×31. Element 62, Sm is right above Pu, 94 (again 2×47 Lucas). Also in the sixth positions here are 26, Fe;, 44, Ru; and 76, Os. The latter are capable of attaining the maximum 8+ oxidation state along with Xe, 54. And curiously, 54 is half 108, the atomic number of Hs (also able to take +8?) below Os. There is a kind of hidden grand pattern here.

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  66. Philip Stewart

    One of the aims of my Chemical Galaxy was to remind people that matter exists in all sorts of places where it behaves very differently from on earth, for example in neutron stars like the fictional Dragon’s Egg. To anyone who thinks He is best described as a ‘noble gas’, I offer this suggestion of something very different: http://arxiv.org/abs/1111.1343 My posting on emergent properties seems to have got lost in the system. It was to say that chemistry will never be derived from physics because as you go from simpler to more complex systems, unforeseen properties emerge. This strange form of helium is an example of behaviour that no physicist had anticipated,

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  67. Valery Tsimmerman

    Thanks, Philip. It is interesting that Helium can form crystals within the white dwarfs. Not quite like other noble gases.

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  68. Valery Tsimmerman

    Eric,__ As promised, I would like to explain you briefly the idea behind the statement that I made earlier: “Sequences of the atomic numbers of the elements in the periodic table can be derived mathematically without any regard to the properties of the elements.”___I would like to start with Pascal Triangle that was known to ancients. First, write down the row of 1’s like this: 1,1,1,1,1,1,1,1,…This represents zero dimensional space mathematically. Then start the second row with 1 also. To get the second member of second row, add number above it (that is 1) to the first member of the second row (also 1). You will get 2. Repeat this to find the third member: add 1 that is above to the 2 that is on the left and you will get 3. Repeat this procedure to get 4,5,6. So the second row will be natural number sequence: 1,2,3,4,5,6,7….. Mathematically this represents single dimension. ___Start third row with 1. The second number of the third row will be derived by adding number above to the number on the left: 2+1=3. The third number of the third row will be: 3+1=4 and so on. The third row is the sequence of so-called triangular numbers: 1,3,6,10,15,21,28,36. Mathematically they represent two- dimensional space.___ The reason why they are called triangular is because if you try to form triangles using coins, for example, you will get 1 coin for the basic triangle, 3 coins per triangle, 6 coins per triangle, 10 coins, 15, 21……____ Now, start forth row of the numbers with 1. To get the second member of the forth row add number from the third row above to the number on the left: 3+1=4. To get the third member of the forth row again add number above to the number on the left: 6+4=10. By doing that you will generate sequence of so-called Tetrahedral Numbers: 1,4,10,20,35,56,84,120. This sequence mathematically represents 3D space. You can come up with such sequence if you build tetrahedrons using marbles for example. One marble represents basic tetrahedron, then you can build another tetrahedron with 3 marbles in base layer and one marble on top, then you can add three marbles to the base layer, two marbles to the second layer and one marble on top. You will get the tetrahedron with 10 marbles. And so on to get the tetrahedrons with 20,35,56,84,120 marbles.__ (to be continued)

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  69. Valery Tsimmerman

    Couple of years ago Jess noticed similarity between the tetrahedral numbers 1,4,10,20,35,56,84,120…and alkaline earth atomic numbers: Z=4,12,20,38,56,88,120.____ Few years before that, in 2007, I published on internet my ADOMAH Periodic Table. That web site also includes page on tetrahedral character of the periodic table and the system of the quantum numbers n, l, ml and ms that shows my tetrahedral constructions using spheres of two colors: red and green. I built my tetrahedron alternating red and green spheres so that red spheres comprise always odd rows and green comprise even rows.____I came up with three dimensional Aufbau diagram that shows not only n and l, but also ml. Later I noticed that such two-colored tetrahedron can be represented by suppressing even numbers in the second sequence of the Pascal, that is instead natural numbers 1,2,3,4,5,6,7… I would write down 1,0,3,0,5,0,7,0,…. in the second sequence. Then using same Pascal procedure as described above I got 1,1,4,4,9,9,16,16…, instead of triangular numbers. Those numbers represent number of red spheres in triangular layers of the tetrahedron, if multiplied by 2 they also represent lengths of periods in Janet’s LSPT: 2,2,8,8,18,18,32,32.____ Next row, corresponding to the tetrahedral numbers would be 1,2,6,10,19,28,44,60 – number of red only spheres in the tetrahedrons. If multiplied by two they will give you alkaline earth atomic numbers (including He): 2,4,12,20,38,56,88,120.___ The question is why to multiply by two? Because each element is represented by an electron-proton pair and electrons, as all particles of matter, have spin s=1/2, us was confirmed by Paul Dirac in 1928. Therefore, each red sphere in my tetrahedrons represents a pair of elements, not one element. This is where I and Jess disagree. Jess decided that it does not look right and started to search for another system where each sphere would represent one element and there would be no green, as he calls them, “empty” spheres. I argue that my tetrahedral system represents nature more accurately by pairing the elements to account for 1/2 spin. The green spheres in my system represent atoms of antimatter that could exist, but are not with us because of apparent CPT symmetry violation.____ I hope this will give you good head start and you would go to http://www.PerfectPeriodicTable.com/novelty for more information. Best Regards, Valery Tsimmerman.

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  70. Jess Tauber

    Some time back I announced on the Yahoo tetrahedronT3 group that I had found a way to fold up an unbroken sequence of elements into a tetrahedron of close-packed spheres, as a variation of the skew-rhombi theme of the T3 model. That version was a bit off-kilter in terms of placement of elements within the figure, but on the positive side used an entirely consistent procedure, resulting in the distribution of the s-block element around the tetrahedral ‘equator’. I’ve now found another way to fold the line, with a procedure that uses mirror image folding. This new model first completes a 20-sphere tetrahedron and then starts a new jacket of 100 around that completing a 120-sphere tetrahedron.

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  71. Valery Tsimmerman

    So, to make it even more simple and to avoid references to the Pascal triangle, following procedure can be used: In order to build geometric representation of atomic sequences in the periodic system, buy bunch of red and green marbles. Take one red marble, write H and He on it and put it on top of table, then take two green spheres and put them next to the red to form a triangle. Take another red sphere and write Li and Be and put it on top of the triangle. Take three more red spheres and put them on the table next to two green. Write B, C and N on them, then write O an the marble marked with B, F on the marble marked with C and Ne on the marble marked with N (this is to account for Hunds rule). Take two green spheres and place them next to red sphere in second row. Then, take one one red sphere, put it on top to complete the tetrahedron. Mark it with Na and Mg____ Start new layer by putting 4 green spheres on top of the table next to three red spheres. Put three red spheres on top of green in the second layer and write Al, Si, P and then write S next to Al, Cl next to Si and Ar next to P. Place two green spheres in the third layer on top of three red and then put one green sphere on top of third layer to complete the tetrahedron. Mark last red sphere with K and Ca. Continue this procedure for the rest of the elements of the periodic system. I am sure you will enjoy it.__ Best, Valery.

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  72. Jess Tauber

    It is another property of tetrahedra of close packed spheres that once you establish a core of 20 in a tetrahedral arrangement (20 being a tetrahedral number) every surrounding ‘jacket’ uses the same formula for count, being the sum of two contiguous squares of even integers. That is, 20 is 4+16, and the next jacket of 100 has 36+64. This relates directly to tetrahedral diagonal numbers, but doesn’t stacked triangular layers.

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  73. Jess Tauber

    I left off my story of the development of the Pascal math so that Valery could chime in with the explanation he came up with for element triads after the discovery of the tetrahedral number explanation- why only HALF possible triads actually work within-group in the PT. How about it??

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  74. Philip Stewart

    Jess’s comment about nickel 62, the most stable of all nuclei, suggests the way to the ‘island of stability’. Ni 56 has a half life of 6 days, but in the explosion of a supernova it can reach Ni 62 by neutron capture. To get enough neutrons on to the heaviest nuclei we need to create them in a neutron flux like that of a supernova. Remember the neutron bomb?! Dangerous, but perhaps do-able.

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  75. Valery Tsimmerman

    Jess,__ thanks for giving me opportunity to comment on triads, unless you are setting me up for the conflict with Eric (just kidding). I agree with Eric that triads played important role in the past to alert early chemists about relationships between the elements. I think that in our tetrahedral theory triads also play important role as a confirmation of its validity.___As Eric wrote in his famous book, triads are products of doubling the periods. For example, in traditional periodic table, triad Ar-Kr-Xe exists because 4th and 5th periods have same lengths 18 elements each. In other words, triads exist because, starting with second period, lengths of periods recur: 8,8,18,18,32,32. The problem of the traditional periodic table is its inconsistency in regard to the length of its 1st period: 2,8,8,18,18,32,32, as well as placement of He. In traditional periodic table He and Be are members of triads (He-Ne-Ar, Be-Mg-Ca) and Hydrogen, as well as all other group first elements are not members of triads! Something is terribly wrong with this picture. It shows that in traditional PT He and Be are the exclusions. But this happens only because of period length rule violation. If lengths of the periods were made consistent 2,2,8,8,18,18,32,32, He and Be would not be members of the triads therefore they would cease to be exclusions from the general rule.____ Some time ago Jess has noticed that atomic numbers of Be, Ca, Ba and Ubn match every other tetrahedral number and atomic numbers of the rest of the alkaline earths are exact arithmetic means of the atomic numbers of their neighbors in the group. Guess what? I was able to match all the atomic numbers of the alkaline earths exactly by stacking spheres of two colors or by modifying pascal triangle by suppressing every even number in the sequence of natural numbers and multiplying the forth sequence by factor of two to account for S=1/2 spin._____ Therefore, Eric, I argue that instead of trying to increase number of triads, we should optimize number of triads by re-arranging the Periodic Table to have period lengths 2,2,8,8,18,18,32,32…___Valery Tsimmerman

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  76. Jess Tauber

    Note also that although traditionally the Pascal Triangle’s outer numbers are generally set at 1, others start with an ever further outer layer of 0. This DOES work (as Fibonacci series shows). And if you DO start with 0, then the tetrahedral number diagonal also starts with 0. This means that as part of the ‘every other tetrahedral number’ sequence, 0 is available to start a triad. Thus 1/2(4+0)=2, placing He squarely (or half squarely, pun intended) between 0 and 4 (Be).

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  77. Jess Tauber

    If we have a 0 position, then the one before it would be -1. For He, then, the triad it belonged to would be set by 1/2(3+(-1)), or 1. The math works.

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  78. Valery Tsimmerman

    Oops too._____ I just realized that I made a mistake in my post on Triads this morning. Here is the correction: ….If lengths of the periods were made consistent 2,2,8,8,18,18,32,32, He would not be a member of the triad and Be would not be the first member of the group, therefore they would cease to be exclusions from the general rule…..

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  79. Jess Tauber

    ‘Intermediate’ triads from the alkaline earth group: If we start with He, then 1/2(12+2)=7, at a half-filled p block position. 1/2(38+12)=25, at a half-filled d block position. 1/2(88+38)=63, at a half-filled f-block position. This trend works forever (for ideal quantum positioning in blocks). But what it really does is establish where He really goes.

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  80. Jess Tauber

    It is absolutely true that the triad 1/2(18+2)=10 works, AND that He behaves like the noble gases Ne and Ar. BUT we can extend this triadic trend: Ne and Ar are p-block right members. Ok, if we start with Mg, watch this- 1/2(48+12)=30, where 30 and 48 are contiguous d-block right members. Now start with Sr- 1/2(102+38)=70, where 70 and 102 are contiguous f-block right members. In other words, this kind of triadic relation takes every other intermediate alkaline earth group member as lower triad bound, and then chooses the first two rightmost members of successive blocks as the other two. I guess the question to ask is whether there is any sense in which the s-block members of these intermediate triads do in fact act like the p-,d- and f-block elements they team up with. We know that this is true for He. What about Mg? Sr?

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  81. Jess Tauber

    1/2(120+56)=88. A normal alkaline earth triad. But 1/2(188+88)=138, where 138 and 188 are rightmost positions in the new g block. Its curious how we see familiar numbers plus 100. So, 20, 120; 38, 138; 88, 188. For 12 we have 112, which is a d block rightmost member- another triad relation? 2,102, f block rightmost. 120, 220, s block rightmost. 56 and 156 don’t work, nor does 4, 104.

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  82. Jess Tauber

    Extending the trend rightward for He-noble triadic relation, consider: 1/2(2+(-2))=0. This still works. AND it is like both trends. It is an in-group triad (if you position this above 0, 2_), but also the lowest bound is in alkaline earth position, and the next two are rightmost members of the s-block. Its a nexus for both periodic types.

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  83. Jess Tauber

    Plutonium, most unusual metal (according to the chapter in the last post), among other landmark properties. 94 protons, which is twice 47. And the important isotope 239 has 145 neutrons. That’s 5x 29. Kaboom!!!

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  84. Jess Tauber

    Element 170 is the end of the next period after 120, by standard block structure extrapolation. That’s 5x 34 (Fib)

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  85. Jess Tauber

    A friend who just defended his doctoral thesis in Linguistics at UArizona investigated for his topic Golden Ratio biases in language structure. What he is finding is that syntactic movement, where pieces of clause and phrase structure shift positions in hierarchical fashion, appears to prefer re-positionings that simplify the overall structure on the one hand, but preserve Fibonacci and Lucas node counts within the moved pieces. Now modern linguistics tends to utilize branching nodal representations to display syntactic structures, but back in the day boxes within boxes were the norm (I remember them from grade school English). What is interesting here is that the filling of later electronic (and earlier nuclear) structures appears to operate along the same principles. I’ve written ad nauseum how electronic counts are based on the Pascal Triangle, with structural layouts motivated by a) the natural numbers (Mendeleev’s Line), b) triangular number differences leftwards from the alkaline earths to block’s half-row midpoints (which Valery thankfully equated with ml=0; my mental filters wouldn’t have caught that), c) tetrahedral numbers for every other alkaline earth atomic number. Don’t know if later Pascal diagonals really map well to the PT, but there IS a kind of repeated herringbone motif in the LSPT based on counts of five, and the pentatope diagonal does display a bias towards multiples of five (note that the Golden Ration is based on the square root of five, certain combinations of Fib/Lucas give multiples of five and so on). The Pascal Triangle also maps Fibonacci numbers as sums of numbers sampled from every other diagonal (odd or even dimensions), and the Fib numbers map to leftmost positions in the PT half-rows. Lucas numbers map less well to rightmost positions in half-rows within blocks, and Lucas numbers come out of Pascal math too. Now the idealized splits within the nucleon counts of growing nuclei pattern to DOUBLE natural, triangular, and tetrahedral numbers, though spin-orbit energy differences mix the levels early on. What I would like to know is whether this mixing (part of a larger pattern that also includes distortions from sphericality that create new ‘magic’ numbers, such as 162 neutrons in Hassium (there’s that 100x Phi again…) is associated with the kind of phenomenon that my linguist friend has found in syntactic structure. Though many seem to now discount him, Linus Pauling proposed, in his ‘Spheron’ theory, that this kind of thing indeed does go on. He was right on the cusp of noticing the double tetrahedral relationship but apparently never made the mental leap. In this theory the internal structure of the nucleus starts to count over again after already establishing earlier counts. There is also the possibility that DNA structure responds to re-ordering constraints of this sort. We know now that the global genome nucleotide counts stay within bounds that are defined by Golden Ratio mixtures (Fib and Luc). There is also now evidence from brain studies that brainwave frequencies are similarly managed, evidently to optimize the system that has a tension between optimal informativity, and optimal transmission/processing.

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  86. Jess Tauber

    3-Phi (or 2-phi, takes your pick), or 1.381966011…. is an important number in Nature. You can generate approximations by dividing any Lucas number by the next lower Fibonacci number, such as 199/144. Anyway, half the fraction is one of the bounds marking the variation in DNA content of the four nucleotides. Well I’m finding it seems to be involved in atomic numerology as well. If you take the nuclear magic number and divide it by this half number, 184/.691, you get 266…, just shy of 267, which is 3×89, the Fibonacci number. Another nuclear magic number: 114/.691=164.98, essentially 165 which is 3×55, Fib. And the weak magic number 70/.691=101…, just shy of 102, which is 3×34, Fib. Might be a coincidence, and then maybe not. I’m still working out the other numerical relations. Will report back later.

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  87. Jess Tauber

    Been going over again Linus Pauling’s Spheron model (see http://osulibrary.orst.edu/specialcollections/rnb/26/26-012-large.html , etc.). A curious coincidence followed (even I have to admit this is coincidental…): he describes the ‘helion’ (alpha particle) as having a packing volume of 24f (femtometers?) with a radius of 1.62f. The latter number of course is the rounded Golden Ratio. And 24 keeps showing up in the math I’ve been doing. That these numbers match actual measurements is quite amusing. What are the odds of THAT? (Spock, any help here?).

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  88. Jess Tauber

    Further reading and experimenting with numbers from Pauling’s papers on sphereons reveals other hidden patterns which he either never noticed or kept to himself. One of the shell-filling count sequences is 1, 12, 32, 72, where wh are talking about spherons. That is, 1 spheron core, surrounded by a 12 spheron jacket, surrounded again by a 32 spheron jacket, and a further 72 spherons surrounding this. The sums are then 1, 13, 45, 117, each sum representing a larger approximation of a sphere through the buildup of polyhedra. Well, here is where things start to get weird. Again with the 100x numbers related to the Golden Ratio. First, 117. I had seen this just days ago, while playing with Phi, before looking at the Pauling papers. If you divide 199 by 144 (any larger Lucas over smaller Fib) you approximate 1.38…, or 2-phi, 3-Phi etc. But flipping the numerator/denominator values of Luc and Fib you get 1.17. It turns out that 1.17 is the cube root of the Golden Ratio 1.618…. It also turns out that 117/45= 2.6, approximating the square of Phi (and 45/117=0.38.., or 1.38-1). 117/13= exactly 9. I don’t know how many other shell-filling sequences posited by Pauling fit similar patterning but this is really something.

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  89. Jess Tauber

    I meant to include that when flipping the numerator/denominator relation between Lucas and Fibonacci numbers you had to keep the larger, smaller aspect the same, so we’re NOT talking about reciprocals. Thus 199/144= 1.38…, and 233(Fib)/199(Luc)=1.17, NOT 144/199.

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  90. Jess Tauber

    Yikes, how ’80’s. One of the things Mendeleev had wanted was to derive a geometrical structure for the PT, correct? Preferably cubic? Well, I was thinking again today about the symmetries of a tetrahedron. You get obvious tetrahedral symmetry using just the four faces or four vertices, but then there are the edge centers, which I use in my T3 model. An axis going right through the tet center from the centers of two edges at right angles provides the main motivation for T3, with dual periods forming angled rings about this axis. But there are still two others available, and I’ve never really explored how they might interact with the first. Interestingly, when you fit the tet into a cube, these three axes are orthogonal to each other, and correspond to the three axes of the cube!

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  91. Jess Tauber

    WIth Herman Cain out, Mitt Romney stagnating and the others falling by the wayside, looks like I’m headed to be the Republican Presidential candidate after all. Wait, that’s Newt, not me. TIme for those meds… But I do seem to be the only one here at the moment. Been thinking about correspondences between the Pascal-based mathematical motivations on the one hand, and how they map to actual spatiotemporal distribution of particles in atoms, on the other. Clearly there is a bias towards sphericality, if one remembers that the Janet quantum periods end with the alkaline earths. As each period fills we have lower and lower l numbers, and so simpler additions. This is despite the MATH pointing to tetrahedral counts of electrons! The sphere and its N-dimensional kin are what you get when you multiply polytope edges/faces/volumes infinitely. Yet the triangle, tetrahedron, etc. have the LOWEST numbers of edges/faces etc. So there is some sort of inversion quality/quantity-wise here. In the nucleus we know of course that the magic numbers tend to be positioned where the nuclei are spherical, or nearly, and yet again we are faced with double tetrahedral and triangular number totals, increements and so on (quadruple if both P and N considered in an idealized nucleus up to Ca, but still related when N and P differ but are still both magic). Why would Nature be set up this way? Is is some sort of mirror principle, which might interact with both holographic and fractal mappings? What happens in between the magic numbers? All sorts of energy level inversions- we know this. But what does this mean spatiotemporally, for nucleons? Do the intermediate patterns deviate from sphericality? Yes, often. Is it mathematically motivated as well- that is, we see the tetrahedral system at certain points, but do the intermediate ones use other polyhedra??? And if the tetrahedron maps to a sphere when inverted, do these other polyhedra map to distortions FROM a sphere? A very interesting puzzle. But go back to what you were doing. Will just have to work this myself…(ho-hum…).

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