Moseley and Pythagoras: On Number and Causality

Aricle by Philip Brown published in EdgeScience Issue 52

The English physicist Henry (Harry) Gwyn Jeffreys Moseley is renowned for his research on the X-ray emissions of atoms and the organization of the elements of the Periodic Table. He died in action on August 10, 1915, in the First World War, after a sniper’s bullet passed through his head.

It is not possible for me here to give a full account of how I became interested in the life and accomplishments of Henry Moseley, but it did have something to do with him having the same birthdate as me (November 23), and a coincidence relating to the number 137, which will be explained below. My academic background is mostly in pure mathematics (complex analysis). In 2016 somebody challenged me to write something interesting about the number π, so I wrote an article about the expression of π in different number bases, which was published in a mathematics education journal (Brown, 2017). This research led to another article about mysticism and numerology connected with the fine structure constant and the number 137 (Brown, 2020).

As I delved deeper into Henry’s life, I stumbled across more coincidences relating to dates and numbers, which led me to suspect that there exists a mysterious causality connecting numbers and events in the world. My suspicions were bolstered when I discovered, as will be summarized in this essay, that mystics and philosophers through the ages, beginning with Pythagoras in the West, have expounded on causality and the deeper meaning of number.

On August 10, 2017,  the 102^nd anniversary of Henry Moseley’s death, astronomers at NASA’s Chandra X-ray Observatory released an image of the IC 10 starburst galaxy, a small galaxy about 2.2 million light years from Earth that had been discovered by the American astronomer Lewis Swift, in 1887. The image shows about 110 X-ray sources, which includes about ten double star systems, known as “X-ray binaries” (Laycock, 2017). 1887 is also the year that Henry was born. There is something surprising about the number 102 in connection with him that will be explained in the next paragraph.

Henry Moseley was nominated for the Nobel prizes in Physics and Chemistry in 1915 by the Swedish scientist Svante Arrhenius. It has been speculated that he, instead of Charles Barkla, would have been awarded the 1917 Nobel Prize for physics had he not died in the war; or, if he had lived, he may have gone onto other major achievements and a Nobel prize (Trimble & Mainz, 2017). For this reason, there is something whimsical about the fact that 102 is the atomic number of the transuranic element Nobelium, named in honor of Alfred Nobel, who bequeathed his fortune to establish the Nobel prize.

Henry Moseley was nominated for the Nobel prizes in Physics and Chemistry in 1915 by the Swedish scientist Svante Arrhenius. It has been speculated that he, instead of Charles Barkla, would have been awarded the 1917 Nobel Prize for physics had he not died in the war; or, if he had lived, he may have gone onto other major achievements and a Nobel prize (Trimble & Mainz, 2017). For this reason, there is something whimsical about the fact that 102 is the atomic number of the transuranic element Nobelium, named in honor of Alfred Nobel, who bequeathed his fortune to establish the Nobel prize.

Another coincidence of dates relates to August 29. When the First World War broke out in the summer of 1914, Henry was on his way to Australia to attend a meeting of the British Association for the Advancement of Science. Before the close of the conference in August, 1914, he had decided to offer his services as a foot soldier to his government. Thus his scientific career ended when he departed by ship from Australia on August 29, 1914, to return to England and begin his enlistment (Jaffe, 1972, p. 115). Henry’s mentor and supervisor at the university of Manchester had been Sir Ernest Rutherford. In a short review of Henry’s research on X-ray spectra that was published by Rutherford in Nature magazine, on August 29, 1925, he confirmed the discovery of three of the four elements (technetium, hafnium and rhenium) whose existence had been predicted by Henry (Rutherford, 1925).

The physicist Wolfgang Pauli was obsessed with the number 137 because 1/137 is the approximate value of the fine structure constant (a fundamental constant in physics). The room number of the hospital in Zürich where he died was 137 (Miller, 2010, p. 269). Pauli had been a patient of the famous psycho-analyst Carl Jung and many of his dreams that Jung analyzed involved numbers, including 137. There is also a connection between 137 and the death of Henry Moseley. In the biography by Bernard Jaffe, his death is announced in the third paragraph on page 137. ‘From one of Moseley’s fellow officers there came suddenly the dreadful news: “Let it suffice to say,” it read in part, “that your son died the death of a hero, sticking to his post to the last. He was shot through the head, and death must have been instantaneous” (Jaffe, 1972).

The physicist Wolfgang Pauli was obsessed with the number 137 because 1/137 is the approximate value of the fine structure constant (a fundamental constant in physics). The room number of the hospital in Zürich where he died was 137.

We turn now to Pythagoras. It is largely due to two of his followers, Philolaus and Archytas of Tarentum, who left written records and communicated with other philosophers, notably Plato, that we know anything about Pythagoras at all. Philosophers and biographers, including members of the Athenian Academy, from the 5^th to 3^rd century BC., the Neopythagoreans from the 1^st century BC. to the 2^nd century AD. (in Rome and Alexandria) and the Neoplatonists from the 3^rd to 5^th century AD. (in Alexandria and Athens), commented on, embellished, or added to the legend of Pythagoras.

According to the theosophist and Freemason, William Wynn Westcott, the followers of Pythagoras (Pythagoreans) believed that all things, including persons and ideas, are related to numbers in an essential way and are, therefore, subject to the relations governing those numbers (Westcott, 1890, p. 9). An important illustration that number is fundamental to everything is in the correspondence of the basic intervals of music, the octave, fifth and fourth to the numerical ratios 2:1, 3:2 and 4:3, respectively. This is explained by the fact that if a string of length 12 units is stopped at 6, 8 and 9 units, the notes produced by plucking the shortened string produce notes an octave, fifth and fourth above the note of the full string, respectively.

The Canadian mystic, Manley P. Hall, states the following about Pythagorean mathematics:

Concerning the secret significance of numbers there has been much speculation. Though many interesting discoveries have been made, it may safely be said that with the death of Pythagoras the great key to the science was lost. For nearly 2500 years, philosophers of all nations have attempted to unravel the Pythagorean skein, but apparently none has been successful. (Hall, 1973)

Whether or not Pythagoras did indeed introduce a great science of numbers, we may dispute Hall’s statement that there has been no successful attempt at discovering the deeper meaning of Pythagorean number theory. For example, we will mention below the spiritual revelations of Emanuel Swedenborg, the Calculus Universalis of Gottfried Leibniz, the numerical cosmology of René A. Schwaller de Lubicz, the universal numbers of John Michell, and Carl Jung’s idea of the Unus Mundus.

The 18^th century Swedish polymath, Emanuel Swedenborg, had a spiritual awakening in his mid-fifties. He was also a mathematician, and he believed that the deeper meaning and symbolism of numbers were the basis of an angelic language that was known to ancient people. With numbers it is possible to communicate complex ideas and concepts that cannot be expressed in words. Every idea has its own number.

It has often been shown me that the spiritual things of heaven, such as those which the angels think and speak, also fall into numbers. When they were discoursing, their discourse fell into pure numbers, and these were seen upon paper; they afterwards said that it was their discourse which had fallen into numbers, and that those numbers in a series contained everything they uttered. (Swedenborg 1960 p. 429)

This notion of a “cosmic mathematics” is also resonant with Gottfried Leibniz’s dream of developing a “calculus universalis”, which he described in a letter to Nicolas Redmond in 1714 as:

 …. a kind of general algebra in which all truths of reason would be reduced to a kind of calculus. At the same time, this would be a kind of universal language or writing, though infinitely different from all such languages which have thus far been proposed; for the characters and the words themselves would direct the mind, and the errors – excepting those of fact – would be calculation mistakes. It would be very difficult to form or invent this language of characteristic, but very easy to learn it without any dictionaries. (Loemker, 1969).

A cornerstone of Leibniz’s project was an arithmetization of Aristotelian logic that he proposed in nine manuscripts in 1679. Mathematician, Klaus Glashoff, explains that in the sophisticated third model that Leibniz proposed the numbers pairs (or characteristic numbers denoting concepts) that he introduced can be interpreted as rational numbers (i.e., ordinary fractions). In this model the relation of divisibility of numbers mirrors the relation between genus and species; the “higher” concept belongs to the smaller number which divides the larger number corresponding to the “lower” concept (Glashoff, 2002).

In the cosmology of R. A. Schwaller de Lubicz, an Egyptologist of the nineteenth century, numbers have both a qualitative and quantitative function. They are the ideal and the concrete relationship in the universe. Consequently, they have an immanent abstract life and a manifested life. As the first cause of the creative idea, they constitute the principle of life and the vital impulse of the cosmos (Schwaller de Lubicz, 1986, p. 30). The first Unity, or abstract One, can only exist as the perfect stabilization of two essentially contrary natures. The is the reason for the disengagement of multiplicity from Unity.

Schwaller de Lubicz talks about an occult science of numbers, which is the science of the basic laws of the universe. Numbers are the purest expression of the truth because they determine the exact relation between cause and effect. In addition to the physical cause of all things, there is an “occult cause” that can only be known by an initiate who has succeeded in merging with space. Furthermore, he makes the following enigmatic and profound statement:

By numbers one can specify the dates (duration, in relation to unity: day, year, lunar month, etc.) of cosmic genesis, both macroscopic and microcosmic. Thus, the initiate will know all the essential conditions necessary for the development (birth, life, and death) of all things, not only the stars, minerals, plants, animals, and man, but also their “hierarchy”, that is to say, their evolutionary arrangement into races and sub-races. In this does the marvelous power of numbers consist; this is its “utilitarian” goal. (Schwaller de Lubicz, 1986, p. 35)

The British researcher and author, John F. C. Michell, describes, in several books, an ancient cosmic code of number and geometry, with many names: the perennial philosophy, cosmic canon, divine law, heavenly city, garden of paradise, philosopher’s stone and the holy grail (Michell & Brown, 2009, p. 6). The basis of this universal scheme is a “numerical pantheon” including certain multiples of 72 and powers of 12, in which every deity has its place according to its characteristic number (Michell, 1988, p. 56). In ancient times, temples or architectural sites were constructed to attract the gods or forces to which they were dedicated. The basic principle by which this was achieved was “sympathetic resonance” or “like attracts like”, by orienting a temple to the season or astronomical body associated with the deity and expressing the characteristic numbers of the deity in the dimensions of the structure (Michell & Michell, 1983, p. 124).

The philosopher Carl Jung believed that the connection between events may in certain circumstances be other than directly causal, and therefore required another explanation. As a psychoanalyst, he was particularly interested in the meaningful coincidence of psychic states (of the observer) and physical (external) events in the world. If the coinciding event occurred in the observer’s field of awareness, he called it synchronous. If the event was separated in space and time, but afterward verifiable, he called it synchronistic. He chose the term synchronicity to designate a hypothetical factor equal in rank to causality (in space and time) as a principle of explanation.

Jung believed in the existence of a collective unconscious, or psychoid realm, that was made up of archetypes, i.e. latent possibilities or patterns, that crystalized in the conscious mind as images or symbols, under certain conditions. Furthermore, phenomena of simultaneity or synchronicity were bound up with the archetypes. With regards to number, Jung believed that both numbers and archetypes possess numinosity and mystery as their common characteristics. “Hence it is not such an audacious conclusion after all if we define number psychologically as an archetype of order which has become conscious” (Jung & Hull, 1972, p. 40). He referred to the “dwelling place” of the archetypes as the Unus Mundus (Unitary World), corresponding to Plato’s Realm of Forms. The natural numbers as archetypes are its primary constituents.

Jung believed that both numbers and archetypes possess numinosity and mystery as their common characteristics. “Hence it is not such an audacious conclusion after all if we define number psychologically as an archetype of order which has become conscious.”

The author Arthur I. Miller, in his discourse on the long relationship of Carl Jung with Wolfgang Pauli, comments as follows on Jung’s thoughts on causality:

In the Western World, we usually assume that events develop sequentially, one after the other, by a process of cause and effect. But Jung was convinced that as well as a vertical connection, events also might have a horizontal connection – that all the events occurring all over the world at any one moment were linked in a kind of grand network. (Miller, 2010, p. 188)

The Swedish author, Mats Winther, mentions that Jung was familiar with the works of Emanuel Swedenborg, and argues that Swedenborg should be regarded as Jung’s true spiritual father. Furthermore, both Swedenborg and Jung should be viewed in the context of the Neoplatonic tradition of late antiquity, and the philosophy of Proclus, in particular. In Proclus’ thinking, numbers are “projections” by the soul of innate intelligible principles, and both the soul and the world are governed by the divine aspects of number (Winther, 2013). Referring to the work of Professor Dominic J. O’Meara (O’meara, 1989, p. 156 – 206), Winther adds that, to Proclus, number also has a non-mathematical sense:

He denotes their properties as “the paternal” [monad], “the generative” [dyad], “the perfective” [triad], “the protective” [tetrad], etc. Mathematical terms must be understood in a higher sense. Proclus bestows on number qualitative aspects and world creating properties as building stones of both psyche and the world. (Winther, 2013)

Thus, we find in the Pythagorean tradition, through Plato and Neoplatonism, Swedenborg, and modern philosophers represented by Jung, that numbers are not merely quantitative symbols. They are projections from a “higher plane”, in which they have a meaning and independent reality. Their existence is immanent in the cosmology recounted by Schwaller de Lubicz. In addition, there is the possibility of “celestial communication” by means of a language of number, as suggested by Leibniz, and purportedly experienced by Swedenborg.

We may ponder whether the “coincidences” mentioned at the beginning have something to do with Jungian synchronicity. At the very least, they were the inspiration for this essay.

In the year 1911, when Henry Moseley began his short career in experimental physics, physicists in Europe had begun to probe the structure of the atom. The electron was discovered by J. J. Thompson in 1897. Ernest Rutherford announced his discovery of the atomic nucleus in 1911 and proposed the planetary model of the atom of electrons orbiting the nucleus. Consequently, members of Rutherford’s research group, and others, had conjectured that there was an ordinal number, called the atomic number, that could be associated with an atom of any element that was not just an ordering number of the periodic table, but a number that corresponded to a physical property of the atom (Jaffe, 1972, ch. 7). A hypothesis of this type had been made a century before by the English chemist William Prout, who suggested that every element was a grouping of hydrogen atoms. The American philosopher and chemist, Eric Scerri, describes Prout’s motivation as “the seductive lure of the Pythagorean tradition for seeking simple ratios” (Scerri, 2020, p. 39). It was Moseley’s novel experiments and diligent work that allowed him to discover a formula, now known as Moseley’s Law, which determines that the spectral frequencies of X-rays emitted by excited atoms are proportional to the square of an ordinal number. He expressed the importance of his discovery as follows:

We have here the proof that there is in the atom a fundamental quantity, which increases by regular steps as we pass from one element to the next. This quantity can only be the charge of the central positive nucleus, of the existence of which we already have proof. (Moseley, 1913, p. 1031).

Thus, Harry Mosely gave new meaning to the Pythagorean credo “all is number”.

Author’s Bio

Philip R. Brown, Ph.D. is associate professor and assistant division head in the Department of Foundational Sciences at Texas A&M University at Galveston. His area is mathematics, with a specialty in complex analysis. He has authored twelve publications in peer-reviewed, international journals, and has received funding from the Mexican government as a participant in two National Council of Science and Technology research grants. He has also done research on certain fundamental constants, including Pi and the fine structure constant. Prof. Brown teaches undergraduate courses in calculus and differential equations from freshman to senior level. He has published a college textbook titled Foundations of Mathematics and is also the co-author of a geometry problem-solving manual for high school students.

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