Tao Chapter 6: Is there a rubric that can shed further light on the question of an ideal periodic table?

[Rene]

Is there anyone willing to proof read this chapter from the Tao of the Periodic Table: Western Science, Eastern Mysticism?

The topic is "Is there a rubric that can shed further light on the question of an ideal periodic table?"

Chapter 6 runs to 10,350 words, and has 8 tables.

Proof reading for this purpose encompasses typos, grammatical mistakes, and other writing issues, and forming a view as to whether the chapter is ready for professional editing by the publisher.

The book is aimed at the general reader, and readers interested in science, philosophy, and spirituality.

It's not intended to be an academic tome necessarily steeped in philosophical considerations and profundities, nor primarily a deep dive into the history of the periodic table (Scerri has already addressed the latter). That said, I intend to include some philosophical or historical content, as appropriate.

A glossary of specialized terminology will be included as part of the book, in cases where I haven't provided a definition along the way.

If you're interested please let me know and I’ll provide you with a dropbox link.

René

[Larry T.]

I am not part of this project because of lack of time but I would like to bring to your attention that few years ago I was contacted by a Chinese fellow who was very excited about apparent connection of the periodic table sequences to a Pascal Triangle that actually originate in China and is called Yang Hui's triangle.

Such relationships of The Periodic System to Pascal like numeric structures are described on my web page here.

Larry.

--
You received this message because you are subscribed to the Google Groups "Periodic table mailing list" group.
To unsubscribe from this group and stop receiving emails from it, send an email to PT-L+uns...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/PT-L/D4905ADB-D230-47AA-8642-1B9DFBBAB60E%40webone.com.au.

[Rene]

Thanks Valery. 

I include posts such as this one of yours as contributions to the project.

According to the Wikipedia article on Pascal’s Triangle:

The pattern of numbers that forms Pascal's triangle was known well before Pascal's time. The Persian mathematician Al-Karaji (953–1029) wrote a now-lost book which contained the first formulation of the binomial coefficients and the first description of Pascal's triangle.[5][6][7] It was later repeated by Omar Khayyám (1048–1131), another Persian mathematician; thus the triangle is also referred to as Khayyam's triangle (مثلث خیام) in Iran.[8]

Pascal's triangle was known in China during the early 11th century through the work of the Chinese mathematician Jia Xian (1010–1070). During the 13th century, Yang Hui (1238–1298) defined the triangle, and it is known as Yang Hui's triangle (杨辉三角; 楊輝三角) in China.[9]

In Europe, Pascal's triangle appeared for the first time in the Arithmetic of Jordanus de Nemore (13th century).[10] The binomial coefficients were calculated by Gersonides during the early 14th century, using the multiplicative formula for them.[11] Petrus Apianus (1495–1552) published the full triangle on the frontispiece of his book on business calculations in 1527.[12] Michael Stifel published a portion of the triangle (from the second to the middle column in each row) in 1544, describing it as a table of figurate numbers.[11] In Italy, Pascal's triangle is referred to as Tartaglia's triangle, named for the Italian algebraist Niccolò Fontana Tartaglia (1500–1577), who published six rows of the triangle in 1556.[11] Gerolamo Cardano also published the triangle as well as the additive and multiplicative rules for constructing it in 1570.[11]

Now, Duncan (1996) observed that if the vertical axis of Pascal’s (equilateral) triangle is pushed to the right to achieve the shape of a right-angled triangle (first image attached), and the column at the far right is marked off, then the Madelung Rule sequence corresponds perfectly with the sequence of "triplets" in the right-angle Pascal's triangle. The second attached image shows this correspondence. When I refer to a triplet I mean, to take the example of "8-28-2", the 8 subscript is the row number in the right-angled triangle; the subscript on the right, 2, indicates the position within that row; and the main number (28 in the middle) is the number of ways to choose 2 numbers from 8 numbers, regardless of order.

Starting at the first row of the right-angled Pascal's triangle but omitting the far right column, the sequence of triplets is 1-1-0, 2-1-0, 3-1-0, 2-2-1, 4-1-0, 3-3-1, 5-1-0, 4-4-1, 3-3-2, 6-1-0, 5-5-1, 4-6-2, 7-1-0, 6-6-1, 5-10-2, 4-4-3, 8-1-0, 7-7-1, 6-15-2 and so on. Here, the principal quantum number n is equivalent to the arithmetic n in Pascal's triangle, and s, p, d, and f are equivalent to the m values of n = 0, 1, 2, 3, respectively. These same latter m values are the familiar l values in quantum mechanics.

I believe I'm impressed. I’ll have to think about where and how to mention this in the book.

BTW, Duncan’s article (attached) was neither well written nor well presented.

René

Duncan RL 1996, Electronic configuration pattern found in Pascal’s Triangle, Journal of Chemical Education, vol. 73, no. 8, pp. 742–743 

On 10 May 2024, at 02:05, Larry T. <ora...@gmail.com> wrote:

I am not part of this project because of lack of time but I would like to bring to your attention that few years ago I was contacted by a Chinese fellow who was very excited about apparent connection of the periodic table sequences to a Pascal Triangle that actually originate in China and is called Yang Hui's triangle.

[Larry T.]

This is what impresses me the most in the whole story of periodicity.

VT

[Julio gutierrez samanez]

Dear René:

 I am not in this project either, perhaps because I am ignorant of much of the philosophy of the Tao, I came somewhat closer to it during my stays in Japan (1993) and China (2023), where I observed, - despite my Western rationalist training - the profound mysticism oriental that made me reflect on indigenous Andean American mysticism. That predisposition to understand the world as something dual, in which the "unity" is not "one" but "two" or the "pair", something that comes from the art of flat weave, since there the unit is formed by two warp threads: one "up" and the other "down" thread, alternately, to make a figure with the "weft" thread. This is clearly seen. especially when both threads are of different colors.

 The indigenous American peoples, in many things, distinguish what is "female" from what is "male", like yin and yang, oriental, but with the difference that they are not perfect symmetrical like "male, male" or "female." , female", but the complementary pair - "female and male".  They distinguish this in plants, animals and in society, because there the "citizen" is the one who has a "partner", the single man or woman are still considered dependent on their parents.

 In the periodic table I found something similar, the even periods are actually units of the same number of elements, but at a different level or in another spiral, on a different plane of development: "female and male".  And that, when completed in number, give rise to the birth of another pair or binode, because a new "daughter" entity is "bred" between them, which did not exist before, and which makes the difference.  Therefore, new periods grow in number and develop in a complementary way on different planes or levels.

 While in the Tao things and phenomena seem to me to be pendulous, (repetition, without growth).

 In Native American thought, things develop, grow, and become harmoniously complicated, both complementary, like "woman and man": a weak entity and a strong one that give rise to a new offspring.

 This "game" or behavior is what I show in my graphics, already well known to you.  Both in the Binodic Step form (function 4n^2) and in its development (function (4(Sum n^2). And in a table that I called "Genome of Matter" that Mark Leach published, and also in my video " Spiral of chemical elements".

 Perhaps you, friend René, can consider something of these that you find necessary, for that "ideal periodic table" to have something from all the cultures of this world.

 Julio

 Forgive my Google translation

Estimado René:

Tampoco estoy yo en este proyecto quizá porque ignoro mucho de la filosofía del Tao, algo me acerqué a ella en mis estadías en Japón  (1993} y China (2023), donde observé, - pese a mi formación racionalista occidental-, el profundo misticismo oriental que me hizo reflexionar acerca de misticismo indígena andino americano. Esa predisposición a comprender el mundo como algo dual, en el que la "unidad" no es "uno" sino "dos" o el "par", cosa  que viene del arte del tejido plano, pues allí la unidad está formada por dos hilos de la urdimbre: uno "arriba" y el otro hilo "abajo", alternativamente, para hacer una figura con el hilo de la "trama",. Eso se vé con nitidez, sobre todo, cuando ambos hilos son de distinto color. 

Los pueblos americanos indígena, en muchas cosa distinguen lo que es "hembra" de lo que es "macho", como el yin y yang, oriental, pero con la diferencia de que no son simétricos perfectos como "varón, varón" o "hembra, hembra", sino el par complementario - "hembra y  macho". Eso distinguen en las plantas, animales y en la sociedad, pues allí el "ciudadano" es el que tiene "pareja", el soltero o la soltera son considerados aún dependientes de sus padres. 

En la tabla periódica encontré algo parecido, los períodos pares son en realidad unidades del mismo número de elementos, pero en diferente nivel o en otra espiral, en diferente plano de desarrollo: "hembra y macho" . Y que, al completarse en número, dan lugar al nacimiento de otro par o bínodo, porque se "cría" entre ellos una nueva entidad "hija", que no había antes, y que hace la diferencia. Por lo tanto, los nuevos periodos crecen en número y se desarrollan de modo complementario en planos o niveles distintos. 

Mientras en el Tao las cosas y fenómenos me parece que son pendulares, (repetición, sin crecimiento).

En el pensamiento indígena Americano, las cosas se desarrollan, crecen, se complican de modo armónico de par en par, ambos complementarios, como "mujer y varón": una entidad débil y otra fuerte que dan una cría nueva. 

Este "juego" o comportamiento, es el que muestro en mis gráficos ya muy conocidos por ustedes. Tanto en la forma Escalonada binódica (función 4n^2) como en su desarrollo (función (4(Sum n^2). Y en una tabla que llamé "Genoma de la Materia" que publicó Mark Leach, y también en mi vídeo "Espiral de los elementos químicos".

Quizá usted, amigo René, pueda considerar algo de estas que le oarezca necesarias, para esa "Tabla periódica ideal" que tener algo de todas las culturas de este mundo. 

--
You received this message because you are subscribed to the Google Groups "Periodic table mailing list" group.
To unsubscribe from this group and stop receiving emails from it, send an email to PT-L+uns...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/PT-L/CAM1noHV3cUJ%2BycQWL3HARw31zN12nq1u0ovrEx0Pm%2Bsg8U4s9w%40mail.gmail.com.

[Rene]

Thanks Julio

Knowing about Eastern mysticism is a nice-to-have rather than a need-to-have. Chapter 1 of Tao, which I wrote some time ago, provides an historical overview of Western science and Eastern mysticism. Capra’s Tao of Physics (1975) is another good entry point. I have a 17,000 word compilation of the topic sentences from the paragraphs in his book, and they provide a good summary.

Incidentally, according to the Oxford English Dictionary, the word "binode" appears in the English language from 1869. It means, "A point on a surface at which there are two tangent planes."

*     *     *

The idea of paired periods has a long history, preceding Janet, and Baca Mendoza. It seems to have originated with Werner in 1905. According to Jensen:

The temptation to read more into the shape of the table than is really there is almost overwhelming. Even someone as great as Werner was tempted (1905). Having postulated a missing element between H and He, he decided to perfect the symmetry of his table by guaranteeing that rows of differing length always occurred in pairs. Consequently, he further postulated a row of three missing elements lying above the H-X-He row.

Jensen WB 1986, Classification, symmetry and the periodic table, Computers & Mathematics with Applications, vol. 12B, no. 12, pp. 487–510 (508)

Wemer A 1905, Beitrag zum Aufbau des periodischen Systems. Ber. Deut. Chem. Ges. vol. 38, pp. 914–921, 2022–2027.

As you know, the idea of paired periods (i.e. 2, 2, 8, 8, 18, 18 etc) was referred to by Rydberg (1913, pp. 12–13). He postulated the existence of two elements, ‘coronium’ and ‘nebulium’ (for which spectral lines were thought to exist), having positions between hydrogen and helium. He used a formula 4n^2 for the number of elements in the periods.

Rydberg JR 1913, Untersuchungen über das system der grundstoffe, Lunds Univ. Ärsskrift, vol. 9, no. 18. In French: 1914, Recherches sur le système des éléments, Journal de Chimie Physique, vol. 12, p. 585

Of course, Janet’s left-step table (1928) had paired periods, at the expense of He over Be, and scrambling the left to right trend in metallic to nonmetallic character. Among other problems, these two go a long way to explaining the unpopularity of this form.

In 1931, Saz suggested that the first four elements of the first period were electron, proton, H and He. In order to maintain the mathematical relationship idealized in Rydberg's studies, he included two new entities (E and Pn) in his periodic table, lighter than hydrogen (image attached). He divided the elements into four periods. Thus period 1 has 4 elements; period 2 has 16 elements; period 3 has 32 elements, and the fourth period has 64 elements, although he does not appreciate that there is an An series to complement the Ln series.

Saz E 1931, Iberica, vol. 35, p. 186. The image is from: Puig I 1935, Elementos de Química, 4a série, Livraria do Globo, Porto Alegre; see https://rsdjournal.org/index.php/rsd/article/view/25824/22612, p. 7

Achimov (1946) depicted a table with doubled periods referred to as “diads”. He achieved this by adding a period zero, with the electron and neutron in it, above H and He.

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=776

In the periodic table of Baca Mendoza (1953. p. 35) the paired periods have lengths of 8, 8, 18, 18, 32, 32, 50, 50 etc,

Baca Mendoza O 1953, Leyes Genéticas de los elementos Químicos, Nuevo Sistema Periódico, National University of Cusco, https://www.meta-synthesis.com/webbook/35_pt/Mendoza_PT.pdf, accessed May 12, 2024

Aside from Janet, neither Werner, Rydberg, Saz, Achimov nor Mendoza showed He over Be. 

This will always be a point of contention with the binodic table: it relies on He over Be.

As well, and as noted previously, mathematlcal regularity already exists in the standard periodic table:

• the number of subshells in each double period is given by 2n+1 = 3, 5, 7, 9;
• period lengths are given by 2 x⎣(n+2)/2⎦^2; and
• the size of any double period is given by 4x^2 + 4x + 2 where x is equal to⎡n/2⎤and n is the principal quantum number of the first element of either row (second image attached).

René

On 11 May 2024, at 01:34, Julio gutierrez samanez <kut...@gmail.com> wrote:

Dear René:

 I am not in this project either, perhaps because I am ignorant of much of the philosophy of the Tao, I came somewhat closer to it during my stays in Japan (1993) and China (2023), where I observed, - despite my Western rationalist training - the profound mysticism oriental that made me reflect on indigenous Andean American mysticism. That predisposition to understand the world as something dual, in which the "unity" is not "one" but "two" or the "pair", something that comes from the art of flat weave, since there the unit is formed by two warp threads: one "up" and the other "down" thread, alternately, to make a figure with the "weft" thread. This is clearly seen. especially when both threads are of different colors.

 The indigenous American peoples, in many things, distinguish what is "female" from what is "male", like yin and yang, oriental, but with the difference that they are not perfect symmetrical like "male, male" or "female." , female", but the complementary pair - "female and male".  They distinguish this in plants, animals and in society, because there the "citizen" is the one who has a "partner", the single man or woman are still considered dependent on their parents.

 In the periodic table I found something similar, the even periods are actually units of the same number of elements, but at a different level or in another spiral, on a different plane of development: "female and male".  And that, when completed in number, give rise to the birth of another pair or binode, because a new "daughter" entity is "bred" between them, which did not exist before, and which makes the difference.  Therefore, new periods grow in number and develop in a complementary way on different planes or levels.

 While in the Tao things and phenomena seem to me to be pendulous, (repetition, without growth).

 In Native American thought, things develop, grow, and become harmoniously complicated, both complementary, like "woman and man": a weak entity and a strong one that give rise to a new offspring.

 This "game" or behavior is what I show in my graphics, already well known to you.  Both in the Binodic Step form (function 4n^2) and in its development (function (4(Sum n^2). And in a table that I called "Genome of Matter" that Mark Leach published, and also in my video " Spiral of chemical elements".

 Perhaps you, friend René, can consider something of these that you find necessary, for that "ideal periodic table" to have something from all the cultures of this world.

 Julio

[Rene]

Is there anyone willing to proof read either or both of these chapters from the Tao of the Periodic Table: Western Science, Eastern Mysticism?

The topic is "Can symmetry provide an answer on the question of an ideal periodic table?"

Chapter 7A (representing the "no" case) is 8,885 words; 7B (the well, "yes, maybe" case) has 8,960.

Proof reading for this purpose encompasses typos, grammatical mistakes, and other writing issues, and forming a view as to whether the chapter is ready for professional editing by the publisher.

The book is aimed at the general reader, and readers interested in science, philosophy, and spirituality.

It's not intended to be an academic tome necessarily steeped in philosophical considerations and profundities, nor primarily a deep dive into the history of the periodic table (Scerri has already addressed the latter). That said, I intend to include some philosophical or historical content, as appropriate.

A glossary of specialized terminology will be included as part of the book, in cases where I haven't provided a definition along the way.

If you're interested please let me know and I’ll provide you with a dropbox link or two.

René

[Rene]

Dear Julio

Please find attached an updated version of a binodic table that does not rely on He over Be.

e = electron; n = neutron

René

[Rene]

Is there anyone willing to proof this chapter from the Tao of the Periodic Table: Western Science, Eastern Mysticism?

You do not need a background in Eastern mysticism.

Chapter 8 runs to 8,100 words.

Proof reading for this purpose encompasses typos, grammatical mistakes, and other writing issues, and forming a view as to whether the chapter is ready for professional editing by the publisher.

The book is aimed at the general reader, and readers interested in science, philosophy, and spirituality.

It's not intended to be an academic tome necessarily steeped in philosophical considerations and profundities, nor primarily a deep dive into the history of the periodic table (Scerri has already addressed the latter). That said, I intend to include some philosophical or historical content, as appropriate.

A glossary of specialized terminology will be included as part of the book, in cases where I haven't provided a definition along the way.

If you're interested please let me know and I’ll provide you with a dropbox link.

René