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Spirals appear everywhere in our creation, in seashells, pine cones , animal horns and patterns of plant growth. They also appear in non-living natural objects such as galaxies and in non-living natural processes such as hurricanes or ocean waves.
Virtuous, the Roman architect and author of De Architecture, said, "Nature has designed the human body so that its members are duly proportioned to the frame as a whole." Studies show the proportions of phi (fibonacci) are found in man.
The average height for the navel of a man is .618 of the total body height. The same proportion is found between the bones of the human hand .
The human body, including the head, has a Fibonacci five appendages attached to the torso. The hands and feet each have five fingers or toes. Our senses also number five, sight, smell, taste, touch and hearing.
The Fibonacci sequence has been found in the solar system. Planets with more than one moon have a Fibonacci correlation in the distance from the moons to the planet. A similar Fibonacci relationship holds true for the distance of the planets to the sun.
All souls were created in the beginning and are
spiraling their way back to whence they came.
~ Edgar Cayce ~
All human progress is in a circle;
or, to use a more accurate and beautiful figure,
in an ascending spiral curve.
~ Nathaniel Hawthorne ~
Moral law must be of divine origin,
because, even before the tablets of Moses,
it was already contained in the spiral, genetic code.
~ Salvador Dali ~
We do not go round a circle of existence.
That is an illusion, just as the cycling of
the planets and the stars is an illusion.
We move along a spiral track.
It is not quite the same journey from the
cradle to the grave each time.
Sometimes the differences are small.
Sometimes they are very important.
We set out each time on the same road
but along that road we have a choice of adventures.
~ J. B. Priestley ~ I Have Been Here Before
We have learned much, Siddhartha.
There still remains much to learn.
We are not going in circles, we are going upwards.
The path is spiral: we have already climbed many steps.
~ Hermann Hesse ~ Siddhartha
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All those Philosophers believed more or less in animated
atoms, not in invisible specks of so-called 'brute' matter.
Rotatory motion was generated in their views, by larger
(read, more divine and pure) atoms forcing downwards other atoms,
the lighter ones being thrust simultaneously upward.
The esoteric meaning of this is the ever cyclic curve downward
and upward of differentiated elements through intercyclic phases
of existence, until each reaches again its starting point or birth place.
~ Helena Blavatsky ~ The Secret Doctrine
What is a PHOTON?
I have sought above to convey the message that for the majority of the physics community the photon, which is so much a part of physics, is really an unsolved mystery. It is sending us a coded message in allowing our experiments to measure that number 137.03599 but physicists in general do not know how to decipher that information.
The reason for their ignorance is simply the fact that they are looking into space, where photons abound, but cannot see what is there. They cannot see the aether and so their logic tells them that it does not exist.
They can see the mathematical equations that describe Einstein's Theory and they can see Feynman diagrams by looking at what is written on sheets of paper by those who profess to understand theoretical physics, but yet there is that mystery concerning the photon.
A person willing to come to terms with the reality of the aether can solve the mystery. All that is necessary is to picture the aether as a silent machine with moving parts, a machine that can store energy and return it, a machine that has a simple harmonic style of motion which accepts energy by setting up a reaction in terms of angular momentum, a machine having structure, the geometry of which determines the fine structure constant.
The nearest 'model' of an analogous system in the matter form is that used by physicists to explain the Quantum Hall Effect. It concerns the discovery that electrical resistance is quantized. The model is that of a two-dimensional electron gas controlled by a magnetic field where all the electrons move in harmony.
The Quantum Hall Effect is used to measure h/e2. Combine this with c, the speed of light, and you have that -1 factor.
However, as applied to the aether, this is not just a collection of words. After all, the aether is the seat of the activity determining that fine structure constant on a universal scale. Indeed, what I am describing here in this Physics Lecture is a summary of what can be seen and verified by looking elsewhere in these web pages.
If you think that I am putting my own story concerning the photon in my web pages because I cannot secure publication in a refereed physics periodical, then take note of those four Physics Letters papers which I listed above.
Publication in the orthodox scientific literature is not sufficient, given that the physics community does not want to be led into the sinful ways of believing in the aether, which they see as the realm of the 'devil'. If Einstein is your God then you must keep your faith and remain wandering in the wilderness in fear of falling into a 'Black Hole'.
However, in that context, to me, Aether is God showing us the way to discover the ultimate truth and Einstein is the devil!
To summarize my case, I regard the photon as a 3x3x3 cubic lattice array of 27 aether charges in a state of spin.
This is all described in the PHYSICS section of my web pages in the TUTORIAL section, see particularly Tutorial No. 8. Keep in mind that all that physics textbooks can tell you about the photon amounts to little more than saying that it is an energy quantum having virtually no mass but travelling at the speed of light, even though it has angular momentum (spin 1) of h/2 and even though experimental evidence concerned with quantum theory seems now to indicate a superluminal speed of communication between photons emitted together but going in opposite directions.
My photon theory is based on the hypothesis that a photon is not something that moves from A to B, but it is something that can be at A in a state of spin. By virtue of its cubic structure, as a transiently independent unit within the enveloping cubic structure of aether comprising those aether charges, its state of spin nudges surrounding aether four times per revolution and propagates waves which travel at the speed of light.
Those waves are intercepted by encounter with matter, typically an electron, at B and this sets up a separate photon spin at B. The spin at B adapts so as to absorb the wave arriving from B and so there is communication at the speed of light between A and B.
For a photon emission from A setting up a wave which spreads in opposite directions, this means that absorption at C could be affected by what happens at B and vice versa, A being intermediate B and C. Without the aether serving the role of keeping the energy and momentum books in balance one cannot then have a co-ordinated absorption/non-absorption event as between C and B seemingly implying superluminal co-ordination between C and B.
Now, the key step in developing a photon theory is that of explaining how the frequency is determined in linear proportion to the energy quantum involved in the two transactions between matter and aether at A and B. The constant of proportionality is Planck's constant h, and you cannot have a photon theory worth the mention if you cannot deduce the value of h from first principles.
That means analysis of that cubic structured aether model to determine the dimensionless constant involved. One cannot assume that the Creator of the Universe opted to use the c.g.s. (cm-gm-s) system of units by fixing a definite value of h those units. So the task is one of deriving by pure theory the value of h in terms of the electric charge of each of those aether particles and the speed of light, both being aether properties.
I make the assumption that the electric charge is of the same in magnitude as the electron charge, which so far as we know is really universal and really fundamental.
It is all described in those Tutorial Notes, where I show you how to calculate hc/2e2 to part per million precision that is fully in accord with the measured value.
The photon is produced at A when energy shed by matter drops into the energy sink of the aether. The aether keeps track of the event in two ways. It sets up waves which propagate signals into surrounding space. The message broadcast says to matter elsewhere: "Here is your chance to tap energy from the aether!"
It also imparts linear momentum to the cubic structure of that enveloping aether, the amount of such momentum being E/c, where E is the photon energy quantum and c is the speed of light. The two phenomena work together. The momentum determines direction and the aether keeps track of photon energy that has been pooled with its own reserve of energy. It seeks to preserve its equilibrium and is active in shedding energy as necessary, whether by creating electrons and protons and their antiparticles or in exciting the spin state of photons.
The frequency of those waves signals the permissible amount of energy that a photon spin induced by encounter with matter at some point B can take from the aether in absorbing that same momentum quantum and attenuating the waves that are propagating with that frequency.
What this amounts to is an activity governed by probability, but the energy books are kept in balance by a natural equilibrium plus that momentum. I have not brought into this argument that angular momentum of the spin unit or the specific energy of spin.
The reason is that my theory told me that a photon having spin-1 angular momentum has a spin energy equal to the rest-mass energy of the electron.
I saw this as meaning that two photon spins at a source position A could be developed by an event involving the demise of an electron-positron pair, a quantum electrodynamic phenomenon occurring in the vacuum as such, but really an aether phenomenon.
What this meant was that we should look to the photon mechanism as involving creation and interplay between two compliant photons, with the electromagnetic wave generation not being at the very high Compton electron frequency, the jitter frequency of the aether, but being at the difference frequency as between the nudging frequency of one such photon unit and that Compton electron frequency.
This allows a compatible spin state to develop as between the two photons, one spinning at a slightly faster speed and the other spinning at a slightly lower speed than the spin rate of the zero-energy photon. Here I use 'zero' to signify a photon combination producing zero frequency waves.
Now this may all sound very complicated but this picture of the photon situation occurred to me some 30 years ago when I was challenged by someone high in the physics Establishment to show that my aether theory could explain the Schroedinger equation as used in wave mechanics.
I say 'challenged', but it is more appropriate to say 'dismissed on the basis that there was no way in which my aether theory for the photon could possibly lead to that Schroedinger Equation'.
In the event, I found that I was faced with a fairly straight-forward task given that quantum-electrodynamic activity, meaning photon creation and electron-positron pair creation and annihilation are ongoing in an atom, even one that is excited into a radiating condition.
I included the full analysis of this at pages 63-74 of my 1969 book Physics without Einstein (now out-of-print). I had recourse later to bring some aspects of this effort into play in explaining the rather curious properties of single particle wave diffraction, one of the mystery phenomena of quantum theory.
See that paper I have already mentioned above 'A Causal Theory for Neutron Diffraction', Physics Letters, v. 119A, pp. 105-108 (1986).
You see, the task of explaining the photon is not just concerned with the wave frequency as related to the energy quantum involved. It concerns also the action where there are no waves propagating into remote space from the photon system but yet there is evidence of wave properties as exhibited by diffraction properties.
It is as if a photon system can exist by exchanging energy within its own system and not letting any escape, so that if that whole system is involved in an encounter with matter it surprises us by somehow exposing its internal wave activity.
Ignorance or Swindle as Factors in Physical Theory
As will be appreciated I am in this Physics Lecture seeking to bring some balance into the way in which some aspects of theoretical physics are presented to us in our physics education.
We are usually told about the mainstream opinion on a certain subject without being given a background survey of alternative possibilities.
Yet the mainstream seems so often to flow out into an open sea of turmoil without taking you to the promised land, meaning the solutions to those great mysteries we well know await solution.
A theory unifying gravitation and electromagnetism, a theory for proton creation, a theory allowing you to calculate the value of the fine structure constant are primary amongst those mysteries. My task has been to reveal to you the aether pathway which takes you to those solutions.
You must, however, be on the look out for errors whether errors by chance or attributable to ignorance and even the well-intentioned expressions of hope in developing a theory which we have seen Professor Belinfante refer to as 'swindles'.
Suppose I say that physics offers you two quite separate ways in which to relate a physical quantity A to a physical quantity B, both being pure numbers in that they are dimensionless physical constants. Discovering such relationships is what 'unification' is all about, but what if you are confronted with two different formulae linking A and B?
Both A and B can be measured to very high precision and, within the prevailing limits of experimental error in measurement, they give equally valid results. Here the task you face, as I see it, is first of all to check every step of the derivation of each of those formulae, looking for error or 'swindle', the latter meaning a 'tentative and perhaps unwarranted assumption that helps to bring the result into agreement'.
It seems quite illogical for both formulae to be based on sound physical principles. One method must be wrong. However, with the formulae relating the electron g-factor and the fine structure constant in mind, firstly the one quoted by the equation already presented, and secondly the rival equation I derived in that Physics Letters, v. 119A, pp. 109-111 (1986) paper, how can you decide which uses the correct method? That latter equation is:
g/2 = 1 + /[2(1+31/2/N) - ]
where N is the nearest prime number to 3/2.
Since -1 is approximately 137, N is 647 and the two equations can be combined to give:
-1 = 137.3599
g/2 = 1.0011596522
and these happen to be precisely equal to the value of these constants as measured.
I submit then that you can only decide which theory is correct by looking at the merits and methods of the two theories involved. You could, as is implied by the combination of the equations, suppose that both theories are valid in a physical sense, but if you do that you are saying that those two constants are both determined by these formulae.
However, in that case you encounter the same problem again when you find that one or other of the theories, QED or the aether method, can explain without the help of the other theory. My aether theory began by telling me how to derive in such an independent way, the free space value being found to be 137.0359148.
That same theory also gave the result that the proton-electron mass ratio is slightly larger than 1836.152, as can be seen from the paper 'Theoretical Evaluation of the Fine Structure Constant', Physics Letters, v. 110A, pp. 113-115 (1985).
In these circumstances how do you think theoretical physics should be advanced? Should physicists hold faith with quantum electrodynamics (QED) with its renormalization problems, or should they embrace my aether theory and its onward introduction to the solution of the unification of gravitation and electromagnetism, with G itself yielding to a pure theoretical evaluation.
All I can say is that if theory A is your brainchild as a physicist then so far as I can see from the exercise of human nature you will try to suppress interest in theory B, which is my brainchild.
When neither theory is of your own creation then, so far as I can judge from experience, you opt to support the theory that your teachers have introduced as part of your physics education, this being the mainstream theory A.
If, however, you have read this far in browsing through these web pages on PHYSICS and the TUTORIALS, then I hope you will at least be responsive to the alternative prospect of what theory B has to offer and help me to divert the channel of mainstream opinion.
Mathematics is the language of the Universe.
All things resonate to certain geometric frequencies - sometimes referred to as the Sacred Geometry.
The doctrine of Kabbalah existed at the core of both the Hebrew and the old Arabic religions. It was a traditional (oral) method of handing down moral and occult truths. It was/is a metaphysical system that defines and illustrates the nexus between God and Man by means of symbolism and the alphabetical/numerical system known as Gematria.
Within this ancient and complex system was an understanding of the levels of 'existence' or rather of spiritual forms and forces, of Intelligences that ascended from the microcosmic world of man through a hierarchy of angels and archangels and principalities, of powers, virtues and dominations, of thrones and cherubim and seraphim to God, the omnipotent life force. Within this system was also accounted a Qlipoth of demonic intelligences.
Kabbalism contains an 'experience' of many lifetimes of study and meditation and spiritual development that is still pursued today both within the Jewish faith and in the Western Mystical Tradition of Qabalah. The disciplines of astrology and the Tarot are closely tied to this tradition.
Within this great system of study works the Gematria that links the lineage of number to the letters of the written alphabet(s) and to the language itself. Likewise, each Arabic letter has a numerical value and each number has significance. The names of and words for all things contain numeralogical meaning , and thence comes a magical linking between all things acrosstime and space.
Groups of letters had significance and were used in amuletic inscriptions. As they also had numeralogical significance the concept of Magical Squares came about. When and where the signs of the entities or the spirits of the planets and the invention of magical squares came about is not known, but it is probable that they are of Sumerian or Indian origin.
Great significance was attributed to the observed planets moving around us and significant names were given to the planets connecting them with entities and metals and qualities, founding both the science of astronomy and the discipline of astrology. The knowledge of arithmetic required by those who constructed magic squares was considerable and it seems to have formed the foundation of the Arab science of mathematics.
The Kabbalists called the magical squares "Kamea", which translates as "Amulet". They were worn as pendants and the word "Cameo" derives from it.
CYCLES, NUMBERS AND UNIVERSAL CODING
The role of number in formulating the language of the Universe was perhaps most eloquently described by the Greek mathematician, Pythagoras, and his followers. It was he who tied together the fundamental concepts of ratios, geometries and harmonics. If the concepts of ratios, geometries and harmonics strike one as a little too abstract, they may be substituted with the more familiar terms of number, form and vibration.
Ratios simply describe the relationship between two or more numbers, such as the familiar 2:1 ratio that we associate with the octave in music. In fact, any single number may be represented by a ratio.
Even the so-called irrational numbers like p and Ö 2 that are, by definition, infinite may be approximated by a ratio between two whole numbers. Our Universe is described by ratios that are incorporated into the forms (geometries) and vibrations (harmonics), comprising everything that we see, feel and hear. In essence, geometries and harmonics are simply expressions or symbols of number. So monumental was this Pythagorean understanding that it serves as the basis for everything from music theory to subatomic physics.
Whether symbols are spoken in the form of words (vibrations) or written in the form of characters (geometries), they are indeed based on number (ratios). It was the belief of the ancient Greeks, as well as a myriad of other ancient cultures, that number represents the sacred language of God or Spirit or the Creator.
Ancient and modern philosophers have repeatedly raised the question of whether "God is number." Ratios between two or more lengths, areas, volumes, angles, spirals or tones were considered to represent a numeric code by which creation is manifested from the infinite unmanifested potential of the Universe that I will refer to as the Absolute.
The well-known Greek concept of logos, which is often used to denote the manifesting potential of the Creator, is actually rooted in the word meaning "proportion."
Proportion refers to the relationship among two or more ratios.
For instance, 1:2:3:6 or one is to two as three is to six indicates that the same proportion underlies both ratios. One could think of the relationship among numbers, ratios and proportions as being analogous to the relationship among letters, words and language.
Vibration
In many ancient traditions, numbers were considered divine in their roles as changeless principles underlying a world of matter that was constantly changing.
In the Pythagorean tradition, numbers were based on harmonic motion (e.g., swinging of a pendulum or vibration of a string) and an entire cosmology was built on the laws of sound or tonal frequencies inherent in vibrating strings.
1 Just in case one were to consider the Pythagorean ideas to be out of touch with modern science, the latest theory that physics has put forth to explain the nature of both matter and spacetime is known as superstring.
Superstring theory supposes that particles are represented by vibrating strings that are about 1020 (100 billion billion) times smaller than a proton; such that each subatomic particle is represented by a single string vibrating at a distinct frequency.
2 In this theory, particles of the Universe are not fundamental, but are simply the harmonies created by an almost infinite number of these tiny vibrating strings. Astrophysicists have furthered this notion by postulating the existence of cosmic strings to account for the observed pattern of galaxies. So whether we are talking about quarks or quasars, it all seems to come down to vibration.
Vibration exits as waves that are present in a vacuum (e.g., outer space) as well as in a medium such as air and water. What we refer to as sound or tone is just waves traveling through a medium such as air or water, permitting the vibration to be detected by our senses of hearing and touch.
Science tells us that visible light and audible sound are just two examples of a much wider electromagnetic spectrum (including microwaves, X-rays, radio, etc.) that may be distinguished by their unique vibration or wavelength. For the purposes of this discussion, vibration and waves are interchangeable inasmuch as they create and are created by each other.
While air and water are ubiquitous media through which waves travel on Earth, this is not the case for most of the Universe. One might inquire as to the medium through which waves travel in the vacuum or void of "outer space." The ancient Greeks would have answered this question by saying that waves travel through the mysterious substance known as aether (i.e., akasha in the Hindu tradition).
This aether has been redefined by modern physics as higher dimensions of space that are hidden within the world we observe with our five senses.
Vibration may be defined simply as an oscillation about a reference position (e.g., a pendulum or a pinwheel). Each oscillation is considered a cycle or a change from one state to the opposite state and then back through a common reference point.
The number of times that a system moves through this oscillatory cycle per unit time is referred to as its frequency. We commonly use the time unit of one second to quantify frequencies, which are expressed as the familiar "cycles per second" or hertz.
In this manner, we have a common reference period for comparing one or more vibrations.
For instance, the tone associated with middle A on the piano has a frequency of about 440 hertz, while red light has a frequency of about 1014 hertz and the rotation of the Milky Way Galaxy has a frequency of about 10-14 hertz. As such, the time required to complete one cycle ranges from less than a trillionth of a second for visible light to millions of years for a galaxy.
Understand that there is nothing magical about the units of cycles per second (hertz) and that we could just as easily define our unit of measure as cycles per year or cycles per millennium or cycles per revolution of the planet Jupiter --- the choice is arbitrary.
Any vibration in the Universe may be described by its characteristic frequency or by its wavelength and energy. Therefore, vibration and waves and energy are simply different descriptions of the same thing.
That "thing" is what comprises our world and, for the sake of consistency, I will refer to it by vibrational frequency rather than by wavelength or energy. However, keep in mind that vibrations, waves and energy are interchangeable.
Every unique expression of that "thing" has a distinctive vibration known as its natural frequency. All natural frequencies include a unique fundamental vibration, as well as a set of harmonics or overtone vibrations.
While it is beyond the scope of this article to explain how the harmonics are generated, it is enough to understand that there are no pure tones (i.e., those without harmonics) in nature.
Pythagoras was the first to explain why two or more vibrations or tones, referring to frequencies within the audible range, may result in a sound that is either consonant (i.e., harmonious or pleasing to the ear) or dissonant (i.e., disharmonious or disagreeable to the ear).
In essence, the degree of consonance or dissonance is a function of whole number ratios.
If whole numbers in the ratio are small, such as 1:1 (unison), 1:2 (octave), 2:3 (fifth) or 3:4 (fourth), then the resulting musical sound is consonant.
If the whole numbers in the ratio are relatively large, such as 8:15 (major seventh) or 15:16 (minor second), then the resulting musical sound is dissonant.
This rule holds whether we are talking about two different fundamental tones or a fundamental tone and one or more of its overtones (i.e., harmonics).
The common thread is number, which underlies all natural frequencies and the countless harmonics that are inherent in them.
FORM
Ancient philosophers considered that the orderly principles or Laws of Nature giving rise to the physical world were not only knowable, but describable using numbers.
Born from the aether or akasha, the four Elements (i.e., fire, air, water and earth) were considered to be vibratory in nature and represented by number in the form of frequencies or tonal ratios. These same ratios were used to describe the relationship among angles, which give rise to the characteristics (e.g., vertices, faces, edges) of a very special class of 3-dimensional (3-D) geometries known as the Platonic solids.
The Platonic solids were believed to make symbolically visible the orderly movement from the Absolute to the endless array of interconnected forms that we know as matter or the manifested world. According to Robert Lawlor, 1 "the Platonic solids serve as essential forms and numbers that interface between the higher and lower realms and that possess, through their analogues with the Elements, the power to shape the material world."
In other words, matter is created through the number or ratios contained within these Platonic solids.
The five Platonic solids were considered essential because they are the only volumes which have all interior angles equal and because their rotation or spin generates a sphere.
Sacred geometry associates the sphere with the unmanifest and, as such, the Platonic solids are the only angular 3-D geometries that form a perfect interface with the Absolute. All other volumes or 3-D geometries in the Universe are created from these five, which include the tetrahedron (fire), octahedron (air), cube (earth), icosahedron (water) and the dodecahedron (aether).
Because they symbolize the creation of matter itself, the Platonic solids are the likely precursors of many familiar written symbols or glyphs.
For example, each Platonic solid is composed of faces representing the triangle, square and pentagon, which constitute the template for many glyphs. Similarly, a 2-D representation of the star tetrahedron yields the six-pointed Star of David and symbolizes the yin-yang.
It is through these spinning or rotating Platonic solids that our material world is connected to the Absolute and that time is intrinsically linked with movement in space. Not surprisingly, the same ratios that describe consonant tones in music can be derived from the ratios of angles, faces, edges, vertices and other parameters describing the Platonic solids.
For instance, just the ratio of vertices to faces yield the unison (1:1 in the tetrahedron), the fourth (3:4 in the octahedron) and the major sixth (3:5 in the icosahedron). Similarly, the ratio of vertices to edges yield the octave (1:2 in the octahedron) and the fifth (2:3 in the tetrahedron, cube and dodecahedron). Physics has shown us that matter is created, not from fundamental particles, but from waves or energy or vibrations that are brought to focus at a point in spacetime.
As such, matter is simply a special manifestation of energy and the two may be converted according to Albert Einsteinıs famous equation, E=mc2.
Form is no different than vibration, and both are underlain by a sacred code that we refer to as number. The famous British scientist and inventor, Buckminster Fuller, considered there to be only two possible covariables in the design of the Universe.
3 The first of these is frequency (for modulating waves or vibrations or energy) and the second is angle (for modulating forms or geometries or matter). But angle and frequency are just different expressions for the same variable --- number. Herein lies the root of the ageless question asking whether God is number. Is God (a.k.a. Creator, Absolute, Spirit, Source) actually number or does number represent a more fundamental expression of nature?
CYCLES
To answer the question of whether number represents something more fundamental, we need to return to our discussion of vibration.
Cycles are fundamental to the Universe inasmuch as everything is a vibration. Recall that vibrations are defined as cycles per unit time, but time itself represents just another cycle or portion of a cycle. In essence, the only way in which we are able to describe or quantify a vibration is in terms of a ratio of cycles; otherwise, the concept of a cycleıs "duration" is utterly meaningless. Letıs examine why this is true. If we use the familiar units of hertz, then all cycles are referenced to the time increment of one second.
But what is a second?
A second is simply a cycle described by one 86,400th of the Earthıs rotation on its axis. Our most accurate measure of a second is the periodic ejection of a particle from the nucleus of a cesium atom.
In both cases, a second is nothing more than a cycle or a portion thereof.
Cycles repeat infinitely and are independent of the relative measure we use to quantify them. Whatever we select as our reference cycle will simply change the ratio and thus alter the numeric value of frequency; however, the cycles themselves are obviously unchanged. Hence, ratios are necessary to describe all vibrations because one cycle can only be described in relation to another. Stated most simply, vibrations express the ratio of one cycle to another.
While this notion may seem odd to us, many ancient cultures were well aware that all phenomena are cyclic and that cycles are the basis of spirals, vortices and a myriad of other natural forms.
If the four Elements, which were believed to be the basis of music, are represented as a repeating cycle of four ascending musical notes, an expanding spiral is created.
4 The proportion of each Element used to create matter is described by tonal ratios or musical chords, thus illustrating that it is the ratio of cycles which are coded by the numbers describing vibration and matter.
One of the ancient cultures that left behind the most detailed description of cycles (e.g., seasonal, lunar, solar and galactic) was the ancient Maya of Central America.
Their calendrics and understandings of how seemingly unrelated cycles were synchronized to one another is so precise that only now are we able to recognize their significance.
The Mayan calendar is derived from a more fundamental 260-unit radial matrix known as the Tzolkin, which codes cycles as number (e.g., ratios, harmonics, geometries) and accurately describes things as diverse as planetary orbits and the sequencing of DNA. These descriptions are facilitated by calculating the relationship among cycles that otherwise appear to be independent.
For example, the Mayan system tracks the waxing and waning of sunspots on the surface of Sun such that shorter cycles (tens of years) are nested within longer cycles (hundreds of years) that are nested within even longer cycles (thousands of years). These shorter cycles accurately predict the solar activity that routinely disrupts Earthıs upper atmosphere, affecting telecommunication systems and satellite orbits. The longer periods predict changes in tropical ocean temperatures, global climate trends and human behavior patterns.
The so-called Great Cycle of the Maya is 5,125 years in length. The current Great Cycle is believed to have begun in 3113 bc and will end in 2012 ad, at which time we will enter yet another Great Cycle --- thatıs the thing about cycles! Interestingly, archeological and geological records dating back to the beginning of this Great Cycle (~3000 bc) suggest a dramatic cultural shift that occurred simultaneously all over the world.
5 Furthermore, it appears that the modern version of the El Nino phenomenon began about the same time, as perhaps did the movement of our Solar System into an interstellar cloud or bubble. It is fascinating to note that science is discovering actual links between these cultural, climatic, solar and galactic events --- all of which are cyclic.
The tabulation of cycles as rhythms gives rise to our perception of time and space. In other words, counting cycles gives rise to 3-D space and linear time and thus relates number (quantity) to vibration and form (qualities).
Since both vibration and form are cycles, number is simply a coding of cycles. The idea that our perception of "reality" is based on counting cycles is one that is supported by more than the ancient Greeks and Maya. Recent neurological research has indicated that the common rhythmic pulsing of synchronized nerve cells throughout the body generate the brain wave states (e.g., alpha, theta, delta) that have been recognized and quantified for many years.
6 The rhythmic electric output of synchronized neurons throughout the body give rise to our visual perception and to brain functions such as memory and attention.
According to the Mayan understanding of a Universe as cycles within cycles, it is ridiculous to separate time from space when, in fact, both are cyclic. The illusion of our senses tells us that space, as a rather arbitrary 3-D cross section of spacetime, is simply pushed along the axis of linear time.
There are those who believe that recent popular interest in the Mayan calendar signals a change in the collective perception of time as cyclic, rather than linear. This may actually permit us to experience a 4-D world rather than a temporally constrained 3-D one.
This is not to say that time is exclusively the fourth dimension because we could have four or more dimensions of space (n) folded upon each other, always leaving time as the n+1 dimension. Astrophysicists postulate that, immediately following the Big Bang, ours was a 10-D Universe (9 space + 1 time).
The energy of this new Universe was so intense that this arrangement could not be sustained and, through the breaking of symmetry, quickly split into our familiar 4-D (3 space + 1 time) Universe.
The remaining 6 dimensions of space were folded or rolled-up into our 4-D reality, where they may comprise what the mystics referred to as aether.
The mathematics of superstrings suggest that unification of physical forces occurs in both 10 and 26 dimensions, the latter of which may characterize other Universes
Perhaps the most poignant of ancient texts regarding the importance of cycles is the so-called
Emerald Tablets, which are believed to have been left behind by the great master of ancient Egyptian writing known as Thoth. In his translation of the tenth Emerald Tablet, Doreal writes,
"Chanted they the songs of the cycles, the words that open the path to beyond. Aye, I saw the great path opened and looked for an instant into the beyond. Saw I the movements of the cycles, vast as the thought of the Source could convey."
If the nature of the Absolute is indeed cycles, then number appears to be the sacred code.
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