Rediscovering Duality
07/01/07 10:50
In this ancient worldview, Nature was commonly described using the principles of music harmony that integrated the Arts and Sciences into a unified system of meaningful study. Passed down from Egyptian, Babylonian and Indian Brachmane mystery schools to the Greeks, the study of astronomy, geometry and harmonic proportions formed an educational system of natural philosophy. Some of mankind’s greatest discoveries were inspired by this system, including arithmetic, algebra, geometry and trigonometry, astronomy, calendar making, and music itself. In Western Europe, this pedagogy evolved into the Roman school and later Catholic quadrivium system during the Middle Ages.
As Christianity replaced pantheism, the harmonic duality system was replaced with a belief in an intrinsic error of Nature, clearly separated from the concept of a perfect God. Discovery of this error, often attributed to Greek philosopher Pythagoras, originated from the musical discovery that a single tone produces harmonics that align perfectly in octaves while a stack of equal tones (e.g., perfect 5ths) never aligns with a higher octave to the bass. This small misalignment in music harmony, called a comma, is attributable to the logarithmic spiral of pitch frequency. Theosophically, it was considered proof positive of an irreconcilable error, an embarrassment really, built into Nature. Inherited from Greek mythologies of Persiphone, with her apple of knowledge in the Underworld, and goddess Harmonia’s deadly necklace, this error in Nature became known simply as “original sin”.
In Western civilization, the idea of “original sin” had the effect of splitting the ancient duality of God in Nature into two independent singularities - God in Heaven and Man in Nature. From this, the central project of Western religion became the missionary work of God in Heaven, enforcing the non-deification of Nature and routing out anyone who still believed in the old harmonic duality. With the idea of symmetrical balance gone, Nature became an asymmetrical study of “the limited” entirely detached from the infinite. To mend this schism between God and Nature an Intermediary was added, creating what became known as a “holy trinity”.
By the 17th century, the study of Nature was difficult at best, proceeding under threat of imprisonment, torture and death at the hand of the Inquisition. In Italy, this threat was surely felt most by astronomer Galileo Galilei. In an attempt to minimize conflict and eliminate religious interpretation of his work, Galileo recommended the separation of natural philosophy from natural science. He argued science should simply observe, prove and report on Nature’s mechanics in the hope that objective truth might speak for itself without threat to the regime in power. Galileo nonetheless suffered ridicule, discredit and imprisonment for his support of the Copernican heliocentric theory of the solar system. But his idea of a science devoid of meaning took root.
From this point on, science chose to limit itself to an asymmetric model of Man in Nature, defining everything in terms of mechanical interactions. The old harmonic worldview was gone, replaced by the independent projects of God in Heaven by Western religion and Man in Nature by natural science. Dropping from the middle of these two modern pillars of thought like an unwanted child was the harmonic science of music. Landing in the nostalgic study of history and accepted conventions, music joined the “humanities” of fine art, language and grammar, literature, dialectic (logic), rhetoric and other such liberal and philosophical arts. Science, once a direct threat to the Church, had reformed itself into an ally of Western religion.
By the 20th century, the idea that music harmony could inform scientific endeavor had become as laughable as any suggestion to the Greeks that music did not describe Nature. Yet as the industrial revolution gained a full head of steam, the comfortable mechanistic methods of science started to unravel. It began with Einstein’s General Theory of Relativity followed by the discovery that light itself exhibited a dual nature as both a wave and a particle. This led to the Heisenberg Uncertainty Principle and discovery of “spooky” action at a distance, otherwise known as entanglement. Together, these revelations demonstrated that the study of Nature could not be entirely objective nor described in full by mechanical interactions. The human observer had become a participant in the equation, mysteriously affecting the results of experiments at the lowest levels of energy and matter.
Georges Lemaitre, a Catholic priest who developed the Big Bang theory in 1927, dealt yet another blow to mechanistic science. By reversing the expanding nebulae backward in time to the precise moment the Universe began, he concluded that everything must have fit into an infinite point of space comprising an infinite amount of energy. Ironically, he called this primordial moment The Singularity. We might expect from these discoveries that science had at last found its way back home to natural philosophy, ending happily ever after in a marriage of spirituality and science. But strangely nothing happened.
Lacking a grand theory of everything, science continued its mechanical drill down in search of truth at the bottom. As paradox after paradox piled up, only a few scientists had the courage to question the conventional scientific model. British physicist David Bohm was the first to declare that Nature was no machine and there was certainly no bottom to be found. He pointed out that the mechanistic approach considers only foreground structure while ignoring the role of an infinite background from which structure emerges. It is this infinite and irrational background that Bohm said proved the Universe was not a giant machine after all, but in fact something closer to a holonomic-vibratory projection of energy.
To understand this post-Newtonian vision of reality, a basic understanding of holography is helpful. Laser holography, discovered accidentally by Dennis Gabor in 1947 while working on the electron microscope, depends on the intersection and interference pattern of two beams of coherent light energy. These two beams must be frequency-locked and perfectly in-phase, so are usually produced from a single beam split in half with a mirror. Both beams are then in the form of two synchronous standing waves of light, never changing phase or frequency. As one such beam bounces off an object (the “object beam”) and intersects with the other (the “reference beam”), the resulting interference is exposed onto film, creating odd swirling patterns. When a laser or pinpoint of light is then projected through the hologram, it aligns with the reference beam fringes to project a 3-dimensional image from the 2-dimensional surface. David Bohm proposed that the same thing happens with energy in the Universe.
In Bohmian physics, a new duality is proposed for Nature called the implicate and the explicate. The explicate is what we normally experience, a 3-D holographic materialization of crystallized energy in space-time. The implicate is then like the 2-D film, an interference pattern without any energy projected through it. The implicate is a sort of template - Nature’s “holy ghost” if you will - for what might become, unseen with our physical senses yet still very much a part of our reality. And just as a small piece of a hologram displays a fuzzy version of the entire scene, an atom represents a fuzzy version of the whole Universe. In this model, it’s easy to see how everything must be entangled and affect everything else, no matter how small or far away. Of course, this includes thoughts and dreams as well.
We can find in this neo-duality the same harmonic worldview of the ancients. The standing wave of a musical tone really is the same as a standing wave of laser light. A musical tone resonates sympathetically at higher frequencies to produce harmonics or overtones, as does laser light when injected with extra energy. The harmonics of a musical tone form at whole number multiples (2X, 3X, 4X, etc.) of the bottom frequency, as does laser light harmonics. Music harmony even creates an interference pattern on the surface of our eardrums to form auditory geometries in our brain just like those of a visual object in a hologram or a material object in Bohmian space. In each case, there is a fundamental duality existing between the harmonic foreground structure and infinite background. Given that the foreground is composed of energy and matter (i.e., condensed energy), what shall we say is the composition of the infinite background?
Counter to what we have been taught, the ancients knew something modern science is only now rediscovering. They understood the infinite background to be the fractional space between whole number harmonic proportions as they intersect and interfere with one another. They knew this background space was as important as the foreground structure itself. They knew it was, in fact, related to the golden ratio.
The golden ratio, represented by the Greek letter Phi, is approximately equal to 1.61803. Like Pi, it is an irrational and infinite number - however, Phi actually plays a very special role within a standing wave of energy. Around Phi spirals a special set of proportions called the Fibonacci series. These proportions are produced by adding preceding pairs of numbers, such as {1, 1, 2, 3, 5, 8, 13, 21, etc.}, then taking the ratio between adjacent pairs, {1:1, 2:1, 3:2, 5:3, 8:5, 13:8, 21:13, etc.}. The more this sequence is extended, the closer it gets to the value of Phi, though never reaching it. Known by the Indian Brachmanes in 450 BC as Maatraameru, the Fibonacci series was believed to be a way to reach for God without actually looking him in the face. They found these proportions everywhere in Nature - wherever coherent periodic activity emerged - in the growth patterns of plants and animals, mineral structures and the orbital patterns of planets.
Amazingly, it is little known today that the central function of the golden ratio and Fibonacci series in Nature is to suppress destructive resonance and provide order. For instance, the near-Phi (and inverse) dimensions of 1.62 X 1 X 0.62 are used in rectangular speaker enclosures and music halls to cancel, or damp, unwanted sound wave reflection. In fact, any fractional sound frequency inside the Fibonacci “vortex of silence” converging to Phi will be damped, which is why a near value like 1.62 does the job. We find Phi’s “perfect damping” central to Hermetic wisdom and its “sacred geometry” dating back to the Egyptians. This is nowhere more evident than in the Great Pyramid whose dimensions are based on Phi-damping proportions sqrt(Phi) X 1 X Phi, otherwise known as the Egyptian triangle. The Egyptians were well aware that the infinite background underlying harmonic structure was the golden ratio and so used Phi as a launch pad for King Khufu’s after life.
Inside all standing waves, whether in sound, light, electromagnetic energy or matter, there are always two such Phi-damping frequency locations per wave cycle. Around these locations a little space is carved out by Fibonacci ratios, canceling all fractional vibrations and providing the needed space for whole number harmonics to oscillate without collision. A standing wave will simply cease to exist without this policing action.
In this way, Fibonacci damping is really an anti-harmonic force between harmonic structures. It is the reason electrons orbit their nucleus in whole number proportions. It is the reason that spacing of planets in our solar system conforms to a mean proportion of Phi. It is the reason a musical octave divides best into 12 steps and why we are able to anticipate the directional energy flow in music harmony. But most importantly, it is the reason the carbon-12 atom, as the most stable element and standard measure of atomic weight, is found abundantly in all life.
At the bottom of everything, inside the vacuum of space itself, we find an infinite and all-pervasive background field. Since atoms spontaneously organize as harmonic structures inside this field, we can only conclude that it is really a tightly packed matrix of tiny swirling Fibonacci vortices – pairs of infinitesimal black holes circling Phi – perforating everything in support of standing wave structure. Whether we call this a Quantum Chromodynamic Lattice (“Lattice QCD”), a holonomic universe, a crystalline space lattice or the “divine matrix,” this is where the “resonance of an all-pervasive energy field” produces the Casimir Effect and free Zero-Point Energy. And it is through this background field where we might connect with whatever we like to think of as God.
While mainstream science is only beginning to acknowledge the idea of the discrete lattice structure of space and the idea of harmonic resonance and damping in the vacuum, it must sooner or later come to terms with this grand scientific musical reality. When it does, it will bring about the dramatic reform of science and religion, returning us to Nature as a unified harmonic duality passed down by ancient civilizations.
As Christianity replaced pantheism, the harmonic duality system was replaced with a belief in an intrinsic error of Nature, clearly separated from the concept of a perfect God. Discovery of this error, often attributed to Greek philosopher Pythagoras, originated from the musical discovery that a single tone produces harmonics that align perfectly in octaves while a stack of equal tones (e.g., perfect 5ths) never aligns with a higher octave to the bass. This small misalignment in music harmony, called a comma, is attributable to the logarithmic spiral of pitch frequency. Theosophically, it was considered proof positive of an irreconcilable error, an embarrassment really, built into Nature. Inherited from Greek mythologies of Persiphone, with her apple of knowledge in the Underworld, and goddess Harmonia’s deadly necklace, this error in Nature became known simply as “original sin”.
In Western civilization, the idea of “original sin” had the effect of splitting the ancient duality of God in Nature into two independent singularities - God in Heaven and Man in Nature. From this, the central project of Western religion became the missionary work of God in Heaven, enforcing the non-deification of Nature and routing out anyone who still believed in the old harmonic duality. With the idea of symmetrical balance gone, Nature became an asymmetrical study of “the limited” entirely detached from the infinite. To mend this schism between God and Nature an Intermediary was added, creating what became known as a “holy trinity”.
By the 17th century, the study of Nature was difficult at best, proceeding under threat of imprisonment, torture and death at the hand of the Inquisition. In Italy, this threat was surely felt most by astronomer Galileo Galilei. In an attempt to minimize conflict and eliminate religious interpretation of his work, Galileo recommended the separation of natural philosophy from natural science. He argued science should simply observe, prove and report on Nature’s mechanics in the hope that objective truth might speak for itself without threat to the regime in power. Galileo nonetheless suffered ridicule, discredit and imprisonment for his support of the Copernican heliocentric theory of the solar system. But his idea of a science devoid of meaning took root.
From this point on, science chose to limit itself to an asymmetric model of Man in Nature, defining everything in terms of mechanical interactions. The old harmonic worldview was gone, replaced by the independent projects of God in Heaven by Western religion and Man in Nature by natural science. Dropping from the middle of these two modern pillars of thought like an unwanted child was the harmonic science of music. Landing in the nostalgic study of history and accepted conventions, music joined the “humanities” of fine art, language and grammar, literature, dialectic (logic), rhetoric and other such liberal and philosophical arts. Science, once a direct threat to the Church, had reformed itself into an ally of Western religion.
By the 20th century, the idea that music harmony could inform scientific endeavor had become as laughable as any suggestion to the Greeks that music did not describe Nature. Yet as the industrial revolution gained a full head of steam, the comfortable mechanistic methods of science started to unravel. It began with Einstein’s General Theory of Relativity followed by the discovery that light itself exhibited a dual nature as both a wave and a particle. This led to the Heisenberg Uncertainty Principle and discovery of “spooky” action at a distance, otherwise known as entanglement. Together, these revelations demonstrated that the study of Nature could not be entirely objective nor described in full by mechanical interactions. The human observer had become a participant in the equation, mysteriously affecting the results of experiments at the lowest levels of energy and matter.
Georges Lemaitre, a Catholic priest who developed the Big Bang theory in 1927, dealt yet another blow to mechanistic science. By reversing the expanding nebulae backward in time to the precise moment the Universe began, he concluded that everything must have fit into an infinite point of space comprising an infinite amount of energy. Ironically, he called this primordial moment The Singularity. We might expect from these discoveries that science had at last found its way back home to natural philosophy, ending happily ever after in a marriage of spirituality and science. But strangely nothing happened.
Lacking a grand theory of everything, science continued its mechanical drill down in search of truth at the bottom. As paradox after paradox piled up, only a few scientists had the courage to question the conventional scientific model. British physicist David Bohm was the first to declare that Nature was no machine and there was certainly no bottom to be found. He pointed out that the mechanistic approach considers only foreground structure while ignoring the role of an infinite background from which structure emerges. It is this infinite and irrational background that Bohm said proved the Universe was not a giant machine after all, but in fact something closer to a holonomic-vibratory projection of energy.
To understand this post-Newtonian vision of reality, a basic understanding of holography is helpful. Laser holography, discovered accidentally by Dennis Gabor in 1947 while working on the electron microscope, depends on the intersection and interference pattern of two beams of coherent light energy. These two beams must be frequency-locked and perfectly in-phase, so are usually produced from a single beam split in half with a mirror. Both beams are then in the form of two synchronous standing waves of light, never changing phase or frequency. As one such beam bounces off an object (the “object beam”) and intersects with the other (the “reference beam”), the resulting interference is exposed onto film, creating odd swirling patterns. When a laser or pinpoint of light is then projected through the hologram, it aligns with the reference beam fringes to project a 3-dimensional image from the 2-dimensional surface. David Bohm proposed that the same thing happens with energy in the Universe.
In Bohmian physics, a new duality is proposed for Nature called the implicate and the explicate. The explicate is what we normally experience, a 3-D holographic materialization of crystallized energy in space-time. The implicate is then like the 2-D film, an interference pattern without any energy projected through it. The implicate is a sort of template - Nature’s “holy ghost” if you will - for what might become, unseen with our physical senses yet still very much a part of our reality. And just as a small piece of a hologram displays a fuzzy version of the entire scene, an atom represents a fuzzy version of the whole Universe. In this model, it’s easy to see how everything must be entangled and affect everything else, no matter how small or far away. Of course, this includes thoughts and dreams as well.
We can find in this neo-duality the same harmonic worldview of the ancients. The standing wave of a musical tone really is the same as a standing wave of laser light. A musical tone resonates sympathetically at higher frequencies to produce harmonics or overtones, as does laser light when injected with extra energy. The harmonics of a musical tone form at whole number multiples (2X, 3X, 4X, etc.) of the bottom frequency, as does laser light harmonics. Music harmony even creates an interference pattern on the surface of our eardrums to form auditory geometries in our brain just like those of a visual object in a hologram or a material object in Bohmian space. In each case, there is a fundamental duality existing between the harmonic foreground structure and infinite background. Given that the foreground is composed of energy and matter (i.e., condensed energy), what shall we say is the composition of the infinite background?
Counter to what we have been taught, the ancients knew something modern science is only now rediscovering. They understood the infinite background to be the fractional space between whole number harmonic proportions as they intersect and interfere with one another. They knew this background space was as important as the foreground structure itself. They knew it was, in fact, related to the golden ratio.
The golden ratio, represented by the Greek letter Phi, is approximately equal to 1.61803. Like Pi, it is an irrational and infinite number - however, Phi actually plays a very special role within a standing wave of energy. Around Phi spirals a special set of proportions called the Fibonacci series. These proportions are produced by adding preceding pairs of numbers, such as {1, 1, 2, 3, 5, 8, 13, 21, etc.}, then taking the ratio between adjacent pairs, {1:1, 2:1, 3:2, 5:3, 8:5, 13:8, 21:13, etc.}. The more this sequence is extended, the closer it gets to the value of Phi, though never reaching it. Known by the Indian Brachmanes in 450 BC as Maatraameru, the Fibonacci series was believed to be a way to reach for God without actually looking him in the face. They found these proportions everywhere in Nature - wherever coherent periodic activity emerged - in the growth patterns of plants and animals, mineral structures and the orbital patterns of planets.
Amazingly, it is little known today that the central function of the golden ratio and Fibonacci series in Nature is to suppress destructive resonance and provide order. For instance, the near-Phi (and inverse) dimensions of 1.62 X 1 X 0.62 are used in rectangular speaker enclosures and music halls to cancel, or damp, unwanted sound wave reflection. In fact, any fractional sound frequency inside the Fibonacci “vortex of silence” converging to Phi will be damped, which is why a near value like 1.62 does the job. We find Phi’s “perfect damping” central to Hermetic wisdom and its “sacred geometry” dating back to the Egyptians. This is nowhere more evident than in the Great Pyramid whose dimensions are based on Phi-damping proportions sqrt(Phi) X 1 X Phi, otherwise known as the Egyptian triangle. The Egyptians were well aware that the infinite background underlying harmonic structure was the golden ratio and so used Phi as a launch pad for King Khufu’s after life.
Inside all standing waves, whether in sound, light, electromagnetic energy or matter, there are always two such Phi-damping frequency locations per wave cycle. Around these locations a little space is carved out by Fibonacci ratios, canceling all fractional vibrations and providing the needed space for whole number harmonics to oscillate without collision. A standing wave will simply cease to exist without this policing action.
In this way, Fibonacci damping is really an anti-harmonic force between harmonic structures. It is the reason electrons orbit their nucleus in whole number proportions. It is the reason that spacing of planets in our solar system conforms to a mean proportion of Phi. It is the reason a musical octave divides best into 12 steps and why we are able to anticipate the directional energy flow in music harmony. But most importantly, it is the reason the carbon-12 atom, as the most stable element and standard measure of atomic weight, is found abundantly in all life.
At the bottom of everything, inside the vacuum of space itself, we find an infinite and all-pervasive background field. Since atoms spontaneously organize as harmonic structures inside this field, we can only conclude that it is really a tightly packed matrix of tiny swirling Fibonacci vortices – pairs of infinitesimal black holes circling Phi – perforating everything in support of standing wave structure. Whether we call this a Quantum Chromodynamic Lattice (“Lattice QCD”), a holonomic universe, a crystalline space lattice or the “divine matrix,” this is where the “resonance of an all-pervasive energy field” produces the Casimir Effect and free Zero-Point Energy. And it is through this background field where we might connect with whatever we like to think of as God.
While mainstream science is only beginning to acknowledge the idea of the discrete lattice structure of space and the idea of harmonic resonance and damping in the vacuum, it must sooner or later come to terms with this grand scientific musical reality. When it does, it will bring about the dramatic reform of science and religion, returning us to Nature as a unified harmonic duality passed down by ancient civilizations.