The Theosophical Forum – March 1939


Nothing in the history of science is more remarkable than the fundamental influence exerted by the teachings of Pythagoras in mathematics, astronomy and physics. To the great discoveries in those fields, perhaps now may be added a solution of the baffling mystery of electromagnetism.

It has been found that the regularity of planetary intervals which has attracted many astronomers since Kepler's time can be attributed to the action of electromagnetic waves radiated by the sun. This discovery conforms with the original ideas of Johann Kepler, a modern disciple of Pythagoras. Kepler believed the physical basis of his laws was identified with magnetism, which he conceived to be a form of vortical motion.


Through a simple formula it can be shown that planetary distance intervals closely follow a common series of wave frequencies. The numbers derived through the formula are:


The tabulated numbers extended right and left with ratio 3:2 are as planetary mean distances from sun; square roots of the numbers taken in reverse order are as orbital velocities. It will be seen that the serial numbers are paired, i. e., products of pairs are constant: numbers for Mercury and Saturn; Venus and Jupiter; Earth and planetoid; Mars and Vesta. Orbits of Uranus, Neptune and Pluto would pair with possible orbits between Mercury and the Sun.

That corresponding planetary numbers are derived through a formula involving the velocity of light as shown above, leads to the inference that planetary distances and motions are regulated by electromagnetic waves radiated by the sun. This inference is supported by the fact that a related series of numbers shows direct correspondence between the velocity of light and the cube roots of planetary periodic times (in seconds).

P.time numbers 192 256 324 384 486 576 729 972 1380 1728 2048
Planets: Merc. Venus Earth Mars Ves. ptd. Jup. Sat. Uran. Nep. Pluto
Cu. rts. of per time: 197 268 316 390 480 . . . 722 975 1383 1735 2000

The serial numbers are paired, i. e., products of pairs are constant:

Mercury & Saturn; Venus & Jupiter; Earth & planetoid; Mars & Vesta
(192 X 972) (256 X 729) (324 X 576) (384 X 486)

The constant product is 186,624, which when multiplied by appropriate length/time units (1 m.p.s. or 1.6km./s.) equals the velocity of light.

From the foregoing figures the conclusion may be drawn that the frequencies of the solar electromagnetic waves are as the cube roots of the periodic times; these frequencies and the velocity of light determine wave-lengths. (c/t1/3 = λ)

The initial amplitude of the waves would be as the radius of the sun and the electromagnetic intensity (equivalent to gravitational mass) would be as the square of the amplitude.

The space between Mars and Jupiter would correspond to a region of wave interference, directly affecting the orbits of Mercury and Saturn and contributing to orbital ellipticities.

Similar wave elements can be computed for all planet-satellite systems.

The planetary numbers are also related to the characteristic line spectra of all atoms.

The planetary numbers:
     64    96    144    216    324    486
are as the actual vibrational frequencies of:
     C       G       D       A       E       B
on a diatonic scale.

Truly, there is "Music of the Spheres."

The identification of solar system motions with electromagnet-ism is a reminder of the "Central Fire" of Pythagoras.

Solar system bodies often have been compared to giant electromagnets and planetary orbits are comparable to the concentric rings which surround wires carrying electricity familiar to all students of physics.

Thus the sun may be conceived as a great stabilized electromagnetic vortex radiating a continuous succession of spinning ring-waves in which the planets move in obedience to Kepler's laws. The planets would be similar but smaller vortices and the chemical elements would be similar structures on an atomic scale.

Electromagnetism might be defined generally as vortical motion in a Space Plenum. Positive and negative effects would be due to differences in the direction of rotation.

The spiral form and simple numerical relations seem to be characteristic of all natural phenomena from celestial galaxies to atoms. The Pythagorean right-triangle represents the projection of a spiral; Mendeleef's octaves in the chemical table and the helical arrangement of atomic progression shown by de Chancour-tois and Stoney and Mendel's biological laws all illustrate the principle. The progression of genera and species in biology is analagous to the progression of the chemical elements. Leaf formations are universally spiral and the blood stream follows a spiral circuit. And all have a rhythm in harmony with the "Music of the Spheres."

Genung has shown that creative thought follows a spiral law. There are curious traces of this in the history of human beliefs. The vortical nature of electromagnetic motion may be compared to a fiery serpent pursuing its tail. The swastika might be interpreted as a symbol of rotation. Intuitively we perceive the significance of the symbols but a Pythagoras is required to interpret them for us.

The doctrine of Love which eventually will lead us to a real brotherhood of men, was voiced by great spiritual leaders, including Lao-Tse, Gautama, and Jesus, as well as Pythagoras. Through their beautiful teachings we hope to achieve some day a social state on earth worthy of the sublime harmonies of the Universe now so vaguely apprehended.

Note by C. J. Ryan

Mr. O'Connor's article with its mathematical demonstrations of the orderly relations between the velocity of light (an electro-magnetic phenomenon), the radius of the sun (the distance of the center of the sun from its surface), and the distance of the planets from the center of the solar system, is extremely interesting to students of The Secret Doctrine for many reasons. It is another demonstration that the universe is not a helter-skelter combination of objects thrown together by blind chance, but that there is Mind working in an intelligent way behind the visible manifestations, or, as Sir James Jeans says, the universe is nearer to a great thought than to a great machine.

Mr. O'Connor refers to Pythagoras and his modern disciple, Kepler, with justified admiration; but those great men looked more deeply into the causes of the exquisitely beautiful adjustments of celestial motions than most of our modern physicists. Dr. Max Planck is one of the few who boldly declares the ancient doctrine that consciousness is fundamental, and that matter is derivative from consciousness. Without this vital factor astronomy is a body without a soul.

Kepler, whose three "Laws" of motion have long been accepted as fundamentals, realized that the "harmony of the spheres" was controlled by Cosmic Intelligence in the ether of space, the "Holy Ghost" as he called it. He accepted the ancient belief in an "Angelus Rector," a spiritual conscious entity conducting each planet, and he understood how the Pythagoreans could believe that all the globes disseminated through space were rational Intelligences or Spiritual Powers which may be regarded as Divinities. Even in these prosaic days one leading astronomer has dared to suggest that every star may well be the seat or vehicle of a sublime Being whose conscious life-history transcends our highest conceptions as greatly as his span of years — millions or billions — exceeds that of a human incarnation!

In the 15th century Gilbert of Colchester made his great discoveries in magnetism which must have been known to Kepler, who declared that the sun was a powerful center of magnetism (now scientifically demonstrated). Kepler worked out a curious relationship between the Platonic solids and the orbits of five of the seven "Sacred Planets," naturally omitting the sun and the moon (and of course the outer planets, which were not known in his day).

It is curious that the work of Copernicus and Kepler, which was founded on a mystical basis derived from Plato and Pythagoras and ultimately from Oriental teaching, should have led through Galileo, Newton, and the French Encyclopaedists of the 18th century, and the modern Germans, to a purely mechanistic philosophy of nature and life! Fortunately, Relativity and the new atomic theories bid fair to liberate science from the crude materialism of the 19th century and to open the way to a more spiritual outlook. Speaking of the materialism that was so general at the time she brought Theosophy to the West H. P. Blavatsky says:

It is only with the theories of such men of learning as Kepler, Kant, Oersted and Sir W Herschel, who believed in a Spiritual world, that Occult Cosmogony might treat, and attempt a satisfactory compromise. — The Secret Doctrine I, 589

She shows that Space is a substantial "living entity," the real world, while ours is an "artificial" one. Space is studded with countless phenomenal universes, systems, and mirage-like worlds; a Unity, bottomless at its depths, illusive (maydvi) on its surface. The Ancient Wisdom — Theosophy — has always taught that the real universe is a complex of forces indeed, but not of blind, unintelligent forces. Theosophy is an objective idealism. Students would benefit by a careful perusal of the magnificent philosophic passages in The Secret Doctrine, Vol. I, page 615.

In Mr. O'Connor's presentation we see that a perfectly adjusted rhythm is back of the solar system, a true "harmony of the spheres," corroborating the Pythagorean teaching that a marvelous system of mathematical combinations lies hidden behind the physical appearance. Plato, a Pythagorean, expressed the same idea when he said that God geometrizes. But these mathematical concepts were far from being mechanistic, for it was the gods and their intelligent guidance that were expressed geometrically or numerically in the theogony of the heavenly host.

Pythagoras associated the numerical arrangement of the planets with the harmonic intervals between musical sounds which he is credited with discovering, though "revealing" would probably be a more correct term. Mr. O'Connor carries the analogy into the world of electro-magnetism which perhaps may be called "sound" or vibration on another plane. "Sound," according to the Oriental philosophy, is the great creative power, the Logos, the Word. H. P. Blavatsky devotes many pages to this important topic, and modern science is beginning to study the extraordinary powers of inaudible sounds of high pitch.

It is exceedingly difficult to explain to those who have been trained in the mechanistic schools of the West what is meant by intelligent, creative forces as understood by Oriental philosophers. The subject is so important that H. P. Blavatsky and the Masters of Wisdom devoted many pages of The Secret Doctrine to its elucidation. A few modern scientist-philosophers, such as Dr. Gustaf Stromberg of Mount Wilson Observatory in his The Soul of the Universe, etc., and perhaps Sir Oliver Lodge, have approached very nearly to the Oriental position. Dr. Stromberg's hypothesis of an "immaterial" fine-structure in space through which the Cosmic Consciousness can express itself intelligently in atomic, electronic, or perhaps still finer forms of matter is a close approach to H. P. Blavatsky's "real world," the substantial (not material) "living entity, Space." For the benefit of those readers who have no copy of The Secret Doctrine at hand we will quote a comprehensive passage from Vol. I, page 493:

The Occultist sees in the manifestation of every force in Nature, the action of the quality, or the special characteristic of its noumenon; which noumenon is a distinct and intelligent Individuality on the other side of the manifested mechanical Universe. Now the Occultist does not deny — on the contrary he will support the claim — that light, heat, electricity and so on are affections (not properties or qualities) of matter. To put it more clearly: matter is the condition — the necessary basis or vehicle, a sine qua non — for the manifestation of these forces, or agents, on this plane.

In regard to Mr. O'Connor's demonstration of the electro-magnetic vortex theory of the solar system, the following quotation from Scientists are Human by David Lindsay Watson, just published by Watts and Co., London, will interest our readers as illustrating the trend toward entirely new views in regard to the forces of nature, which is exactly what H. P. Blavatsky said would occur before the 20th century was very old. Mr. Watson seems to agree with the principle advanced by Mr. O'Connor:

The orthodox gravitational theory of the sun, the mathematics of which is impeccable, will probably go into the discard for this reason. . . [the lack of sufficient imagination being used by scientists in not giving due consideration to all sides of a problem before starting to work it out] . . . The recent theory of Ross Gunn, on the contrary, suggests that the stability of the sun and the configuration of the solar system can be adequately explained only if previously-ignored electro-magnetical forces are taken into account — not gravitational forces alone. The accepted theories have hypnotised the scientific world by the elegance of their mathematics, and this elegance has retarded the realization that electro-magnetic forces are crucial to the problem. — page 99

Dr. Ross Gunn is a member of the Naval Research Laboratory at Washington. In 1933 he criticized the estimates of the solar temperature in view of his observations of the magnetic conditions of the sun's atmosphere and the corona. He claimed that electro-magnetism and suchlike forces have a major part to play in solar phenomena. Since then moving pictures of the solar prominences have revealed phenomena, hitherto unseen, which are said strongly to suggest the activity of electro-magnetic forces.

Mr. O'Connor's reference to vortical and spiral motions in Cosmic and atomic phenomena is particularly interesting in view of the importance attached to them in the Esoteric Philosophy. While the vortical movement is one of the oldest conceptions of Greek philosophy it is really an echo of the far older archaic wisdom, wherein it is found in the Tibetan teaching about "Fohat," the dynamic energy of Cosmic Ideation. H. P. Blavatsky defines Fohat as the intelligent guiding power in all manifestation, the "Thought Divine" transmitted and manifested through the "Dhyan Chohans," the Architects of the visible world, the mysterious link between Mind and Matter, the animating principle electrifying, as it were, every atom into life. Christian theology called such Intelligences Archangels, Seraphs, and the like. She says Fohat is the key to Occultism and that it unriddles many mysteries of the Egyptian, Chaldaean and Indian religious philosophies. Quoting from the archaic Stanzas of Dzyan, on which The Secret Doctrine is based, she writes in regard to the "circular and spiral" action of Fohat:

Fohat traces spiral lines to unite the six to the seventh [the inner to the outer]. . . .

How does Fohat build them? [the worlds]. . . He makes balls of fire, runs through them and round them, infusing life thereinto; then sets them into motion, some one, some the other way. They are cold — he makes them hot. They are dry — he makes them moist.

They shine — he fans and cools them.

Thus acts Fohat from one Twilight to the other during Seven Eternities. — The Secret Doctrine, I, 118, 144

The cycles of evolution, of involution, of reincarnation and other forms of reimbodiment, are also connected with the activity of Fohat in "running circular errands," a quaint though expressive archaic expression of the Stanzas of Dzyan.

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