Pythagoras – Mad Shaman or Mathematician?
Christina Sarich, Contributing Writer
“Not only is the Universe stranger than we think, it is stranger than we can think.” -Werner Heisenberg, Across the Frontiers
Buckminster Fuller has described himself as a modern Pythagorean. His geodesic dome has been recreated over 300,000 times according to www.bfi.org. Other visionaries have identified with Pythagoras too, such as Plato, Leonardo Da Vinci, Leary, and a slew of biologists, chemists, musicians, and futurists. While ancient societies used sound to heal, including the Babylonians, Israelites, Hindus, Persians, Egyptians, Sumerians, Chinese Taoists and Aboriginals, just to name a few, Pythagoras, the Grecian mathematician and musician obsessed with the lyre, was curious enough about music to propose an entire cosmology on the repetitive patterns of sound he found one day when walking by a blacksmith’s shop.
Listening to the blacksmith’s iron be forged on the anvil, he noticed that it had a certain musical quality, and upon further inspection, that dependant upon where the anvil hit the iron, there was a consistent note which played as it was made malleable. He later went home and experimented with making the one-string instrument, which became the workshop for his octave discovery and the ensuing cosmology he tried to create from his initial impression at the blacksmith.
“Do you know that our soul is composed of harmony.” Leonardo da Vinci, Notebooks (1451-1519)
“The highest goal of music is to connect one’s soul to their Divine Nature, not entertainment.” Pythagoras (569- 475 BC)
This premise for his entire philosophy and cosmologic portrayal was gleaned not just from the humble observance of a man at work, but also from his study of ancient teachings, which he then recast to Greece, in ‘modern’ terms. He was also the first Westerner to declare that the earth was round instead of flat. Make no mistake, the mathematician was spiritually in-spired. He built an ashram in Kroton, Italy and traveled extensively throughout Asia Minor, Egypt and India. He was inducted into Egyptian mystery schools. He developed a spiritual brotherhood that was vegetarian and devoted to social equality and yogic teachings he learned throughout his travels. He influenced even the likes of Plato with his spiritual take on mathematics and music theory. He was a history-changing figure who defies categorization.
“If you listen to Werner Heisenberg lecturing about Pythagoreanism in his own work on the quantum theory, you will hear him emphasize that the basic building blocks of nature are number and pattern, that the universe is not made out of matter, but music. The historians of science I worked with in the University regarded Pythagoras as a magician, a shamanic madman from the cults of the Near East; yet both Whitehead and Heisenberg regarded him as a genius of highest order who laid the foundation upon which our entire Western civilization is based” – William Irwin Thompson, Darkness and Scattered Light (London: Anchor Press Books, 1978. p. 110.)
Music as a Mathematical Formula
Pythagoras deduced that sound was based on a purely mathematical formula and later insisted that music could heal the non-virtuous thoughts of man, like anger and jealousy. He performed what were called ‘soul-adjustments.’ While many are familiar with the Pythagorean theorems taught in high school math classes, most are never introduced to the visionary’s larger ideas. This Grecian intellectual had more to offer than just equations to memorize for annual exams.
The Pythagorean (or Pythagoras’) Theorem is the statement that the sum of (the areas of) the two small squares equals (the area of) the big one.
In algebraic terms, a² + b² = c² where c is the hypotenuse while a and b are the legs of the triangle.
Pythagoras once told his students that you could soothe many human emotions with ‘musical medicine.’ He would often sit and play the kithara, a stringed instrument akin to a guitar or lyre, singing along with it. It is said that he could soothe both human and beast with his voice and playing. Pythagoras is also credited with discovering the seven modes of music and once dissuaded a drunken man from burning down his unrequited love’s house by urging a flutist playing nearby to change his tune to one of a more slow and even temperament. Aside from the emotional changes that sound can inspire, it seems that Pythagoras also used music to heal physical ailments.
When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong. – R. Buckminster Fuller
Pythagoras is credited with curing sciatica, but also deformities of the body, citing that, beauty is nothing but a harmonious combination of elements. He believed that by making harmonious sounds, one could heal any disease or deformity. Even as many ‘modern’ societies were using music as a part of their spiritual or religious practices, Pythagoras unequivocally gave music therapy a mathematic and scientific basis upon which to be examined:
The therapeutic music of Pythagoras is described by Iamblichus (ca. 245-330) Preeminent Neoplatonist of his age) thus: “And there are certain melodies devised as remedies against the passions of the soul, and also against despondency and lamentation, which Pythagoras invented as things that afford the greatest assistance in these maladies. And again, he employed other melodies against rage and anger, and against every aberration of the soul. There is also another kind of modulation invented as a remedy against desires.”
It was by dissecting music as a mathematical subtext, that he was able to deduce what ancients knew intuitively, or what was passed down as sacred knowledge in their tribes and villages. The aboriginals, for example, even used the Digeridoo to heal broken bones, and when the sound of this instrument is examined from a theoretical perspective, you can see that it is the same harmonic ratios which Pythagoras demonstrated – one that he tied to all phenomena in nature, including the planets, constellations, and elements of the periodic table – which are responsible for the healing.
It is the energy of the octave, which has gleaned the most attention from every conceivable tradition. The Taoists base the I Ching on the eight trigrams, which compose the 64 hexagrams used to invoke wisdom in its pages. The yogic sage Patanjali is credited for writing the Yoga Sutras, but he gathered most of his material from hundreds of years of oral discourse from varied branches of yogic science and condensed it into the 8-fold path. Buddhists believe in following the middle way, or the Noble 8-fold path. Most mantras are repeated 108 times given the assumption that it takes this number in order to change the vibratory quality of someone’s emotional and spiritual state. Pythagoras likely noticed this number in his travels and observations of musical use in India and Asia in Taoism, Vedanta, Sufism, and Zen.
Furthermore, genetic scientists have studied the conversation between DNA and RNA, and found that is it ‘discussed’ in the language of eights. (Transmission happens in groups of 64 codons, or 8X8) Also, when we are stressed out, we change our bodies on the cellular level. The base letters which form our DNA (ACGT) will actually give a command to the immune system to crash when our stress levels reach toxic levels. This goes for thoughts based in fear and greed as well as physical toxins we take in via our food, air and water. In order to realign the DNA to God-mind we can listen music of 528 hz which supposedly heals DNA.
According to the sound pioneer, Horowitz, human beings are fundamentally “digital, bioholographic, precipitations, crystallizations, miraculous manifestations of Divine frequency vibrations” rendered hydrosonically and metaphysically. Besides all this mind-blowing evidence,Buckminster Fuller deduces that the entire Universe can be deconstructed down to three 8-dominant shapes: the tetrahedron, a 4-sided geometric form, the octet-truss (which has 8 sides), and the coupler (8 facets with 24 phases.) Nikola Tesla’s alternating current generator was supposedly based on the law of Octaves as well.
As Pythagoras suggested, the octave is present even in nature. For example, there are eight families of elements: Alkalis, Alkalines, Borons, Carbons, Nitrogens, Oxygens, Haolgens and Noble Gases. According to Dr. Bach, famous creator of flower essences, certain flowers in nature can resonate with qualities in the human body. Mimulus, for example, helps to develop courage in the human heart chakra. The idea that plants have messages for our bodies and minds is not strange voodoo, but based upon the same resonant frequency science, which Pythagoras first stumbled upon after learning the ancient teachings of the East.
When we resonate with something, after all, that simply means we have connected with something at a deep enough level that we can then hear its message – not unlike the way DNA resonates with the entire human cellular structure via an encoded language. When you then consider the various frequencies like languages with their own idioms and dialects, such as color, light, sound, tone, etc., it is understandable why scientists before and since Pythagoras have had a difficult time understanding the Cosmic Language completely.
Other examples of the magic number eight are in the colors of the seeable rainbow, in the days of the week, in the YinYang symbol (the 6 and 9 blend to make a perfect 8), in George Ivanovich Gurdjieff’s esoteric Christian teachings on the steps from an invertebrate reality to Cosmic Consiousness (also 8 steps), in a twisted zero – a closed spiral which circulates back upon itself, in the important eight meridians in acupuncture which represent the 8 extraordinary vessels. It is even thought that the next dimension we enter into is the eighth, an octave above the one we are experiencing now.
The number eight also stands for infinity, but musically, it is the foundation for multiple harmonics, which may have been the way Pythagoras realized the healing power of music. It was his idea that harmony was, in essence, the distilling of chaos into order, or a lack of discord as conducted through musical patterns.
“For his disciples he arranged and adjusted what were called ‘Preparations’ and ‘Touchings’ which were a mingling certain diatonic, chromatic and enharmonic melodies, through which he easily turned the passions of the soul in a contrary a direction whenever they had been afflicted by sorrow, rage, pity, over-emulation, fear, manifold desires, angers, appetites, pride, collapse or spasms. Each of these were corrected by the rule of virtue, through appropriate melodies, as though some salutary medicine”
In the Pythagorean concept of the music of the spheres, the interval between the earth and the sphere of the fixed stars was considered to be a diapason—a harmonic interval based on specific ratios of sound. For example, when the first and third strings were played on his self-made mono-stringed instrument fashioned with some wood, string and a 12-pound weight, it made a specific sounding chord. It is called the interval of the fifth and the circle of fifths is taught in most European music systems as a basis for understanding key signatures.
The interval between the earth and highest heaven is supposedly a double octave. The sun is considered the lower octave in this harmonic. Pythagoras believed that each planet and heavenly body, in turn had its own musical tone, which was created through aethereal diffusion.
“Having once established music as an exact science, Pythagoras applied his newly found law of harmonic intervals to all the phenomena of Nature, even going so far as to demonstrate the harmonic relationship of the planets, constellations, and elements to each other. A notable example of modern corroboration of ancient philosophical reaching is that of the progression of the elements according to harmonic ratios. While making a list of the elements in the ascending order of their atomic weights, John A. Newlands discovered at every eighth element a distinct repetition of properties. This discovery is known as the law of octaves in modern chemistry.”
The Supreme Wisdom (Prajna) is the Oneness of things; the Supreme Compassion (Karuna) is the Manyness of things (D.T. Suzuki, quoted by F. Franck. 1976. The Book of Angelus Silesius. New York: Vintage Books, p. 49).
The octaves of energy that Pythagoras popularized to western science are the remnants of age-old teachings. Sadly, Pythagoras and his spiritual brotherhood were victims of tyranny and oppression, the misplaced, but often-violent workings of men who wanted to possess his wisdom for profit. Not long after he arrived in Kroton, Italy, he aroused suspicion and Kylon, a wealthy ‘noble’ tried to gain access to Pythagoras’ community and was denied admittance. Kroton responded by murdering many of Pythagoras’ followers and forcing a nearly 100-year old Pythagoras to take asylum in the Temple of Muses were he starved himself to death after deciding not to take food, and to sit in meditation. Hopefully the legacy he leaves us, the incredible dissemination of music as medicine, will not be buried with his memory, even as we learn to understand the music of the Cosmos itself, a word, that Pythagoras coined.
About the Author
Christina Sarich is a musician, yogi, humanitarian and freelance writer who channels many hours of studying Lao Tzu, Paramahansa Yogananda, Rob Brezny, Miles Davis, and Tom Robbins into interesting tidbits to help you Wake up Your Sleepy Little Head, and See the Big Picture. Her blog is Yoga for the New World.
- Horowitz LG. Hydrosonically engineering freedom from infectious diseases. American Academy of Anti-Aging Medicine International Congress. Las Vegas, NV, Dec. 12, 2008. See also: The LOVE CODE Seminar: Musical Healing Celebration, 2008, a DVD production based on the book LOVE The Real da Vinci CODE. Tetrahedron Publishing Group, 2007.)
- Conversations with David Han, Mystic and Engineer
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