MORE PARTS OF THE PATTERN
are Rhythms within Rhythms. The name fractal comes from Bernoit Mandelbrot who discovered fractal geometry. Mandelbrot is a mathematician and IBM researcher who became fascinated with the study of self-repeating patterns. A shape that repeats its pattern is a fractal. With this in mind, Mandelbrot developed a mathematical formula for plotting dots on a plane. It is a simple formula that produces complex and beautiful shapes. What makes it a fractal is that it produces infinite self-similar patterns within patterns. It has been plotted on computers with startling results that are striking to behold. One can zoom in on any part of the pattern with computer magnification to find intricate similarities on different scales. To zoom in far enough anywhere in the pattern is to go through a myriad of patterns that eventually reveals a shape resembling the starting point. This is the Mandelbrot Set.
Mandelbrot created the name "fractal" in 1975 from the Latin adjective fractus, or frangere in verb form, which means to break. Our English words fracture, and fraction are derived from the same root. Fractals are everywhere.(1) Elements of the macrocosm and the microcosm were seen throughout time from ancient mystics, and medieval visionaries, to modern day scientists. Seventeenth century scientist and philosopher Wilhelm Leibniz theorized that the universe is made up of monads that contain miniature universes. Contemporary author Michael Talbot described a "Holographic Universe" in his book by the same name. A hologram proves to be a significant analogy. By shining a light through any piece of a hologram picture, one can reproduce the entire picture from which it came. The light of the spirit shines through all things in creation. It too reveals the Oneness of it all through everything within it.
- The Pattern of Everything Is in Anything.
Manifest nature shows us the pattern. Quartz crystals have molecules joined on six sides each by other molecules, hence, the shape of a crystal is six sided. This is fractal geometry. The stages of growth within the lifetime of a being are similar to the stages of development in its line over millions of years. This is fractal development. Many moons orbit planets like Jupiter and Neptune, which themselves orbit the sun in a process that some astronomers call mini-solar systems within the solar system. This is fractal motion. We live in a universe of self-repeating patterns.
Fractal geometry has shaped us. Fractal branches run throughout our bodies in vascular networks, lymphatic systems and dendritic cell structures of the brain. Each DNA molecule is encoded with the entire makeup of our biology. Any drop of blood can be tested to measure our health. Fractal development is within us. Embryo development in all life forms is similar to the evolutionary changes that have occurred in the life line over eons (embryology). These patterns repeat in the stages of development within in the life span (biogenetic law). When Spengler described the life cycle of civilizations with birth, youth, maturity, senescence and death, he compared them to the life span of a person. Fractal motion is in our Rhythms. We average 18 respirations per minute, or 25,920 times each day. This is exactly equal to the number of years in the precession of the equinoxes. The average heart rate is 72 beats per minute, or 25,920 beats every six hours. Each day we recapitulate the life-death Cycle by waking and sleeping. All is in all.(2)
As there is fractal geometry in the spatial relationship of matter, there is also fractal time.(3) Durations within durations reveal self repeating Rhythms.(4) It is why the Babylonians divided the hour into sixty minutes, then divided the minute into sixty seconds. It is why Chaldeans divided the 25,920 year precession of the equinoxes, or the Great Year, into twelve ages of 2,160 years each, or Great Months, just as we chart the solar year with twelve months. It is why we find harmonics through music. We are in the fractal images of time.
As a Cycle rises and falls in a wavelike motion, short-wave ups and downs form within the larger wave. These are Fractal Rhythms. An upward or downward trend has smaller rises and falls within it. A long wave of economic expansion, for instance, will have micro booms and busts until a Peak. After that, cut backs will outweigh advances until a Trough. To follow economic indicators through these changes is to find that they make upward and downward zigzags on charts. Ascent is like waves in a rising tide, therefore, and descent is like waves on a falling tide. As an old adage reads; three steps forward and two steps back for advance, or, two steps forward and three steps back for retreat. Waves within waves are self repeating patterns on ever larger and smaller scales.
Short-wave Fractalrhythms happen twelve times within each revolution of the host cycle. Twelve Fractalrhythms within the 28-year Physical Cycle last for 28 months or 2.33 years each. Fractalrhythms of the 36-year Emotional Cycle last 36 months or 3 years each. The 44-year Intellectual Cycle has Fractalrhythms lasting 44 months or 3.67 years each. Each Fractalrhythm may be complete with its own Highs and Lows, Quarters of development, and Crossovers. They are microcosms of the whole.
Rhythms are in living systems great and small.(5) The same Rhythms found in a person can be found in a nation. They occur in nations over longer periods of time because larger institutions are slower to change. They occur again in slower moving global eras of world change over even longer periods of time. These global changes affect all the nations within the world, and all the people within them. Physical, Emotional and Intellectual Cycles are found again and again. As we move forward in time, the ride is full of Cycles within Cycles. Is it any wonder that Blake spoke of seeing the entire universe in a single grain of sand?(6)
- Fractalrhythms Reveal the Trans-dimensional Recurrence of Time.
develop between pauses that step across revolutions of the Cycle. This contrasts with the Continuous Progression that normally moves in the Cycle. The following is a comparison to the norm.
Continuous Progression comes without interruption. Something new may be Founded in the First Quarter of a Cycle, Improved in the following Second Quarter, Reviewed in the Third Quarter, then abandoned for Alternatives in the Fourth Quarter. This will happen within a single revolution of Cycle.
Note: for purposes of demonstration, examples from the Geo-Rhythms of the United States were used below.
The principle outlined here applies to the Geo-Rhythms of any nation and to the Mega-Rhythms of the World.
First, the following exmaple offers a look at Continuous Progression so that it may be compared with Step Progression. Since both the Emotional and Intellectual Cycles have often been in the same Quarters at the same time since the 1950s, they are used to show two examples of Continuous Progression.
Rock and Roll emerged in the 1950s, (Dbl. 1st Qtr. Foundation), then branched off into various forms of "Rock" in the 1960s, (Dbl. 2nd Qtr. Variation), and became heavily reviewed as "Golden Oldies" in the 1970s & 1980s, (Dbl. 3rd Qtr. Review), then faded out as "Alternative" music made the charts in the 1980s and 1990s (Dbl. 4th Qtr. Alternatives).
The Space Program launched the first American satellite into space in 1958, (Dbl. 1st Qtr. Foundation), put a man on the moon in 1969, (Dbl. 2nd Qtr. Variation), but limited space missions to Earth's orbit after 1973, (Dbl. 3rd Qtr. Regression), then abandoned construction on any more Space Shuttles in 1991, (4th Qtr. Alternatives). Now, in our new 1st Qtr., we made the first landing on Mars in 1997.
Step Progression may move across revolutions of a Cycle with pauses between stages of development. A precedent established in the 1st Qtr. of Foundation might remain unchanged throughout the following 2nd Qtr. of Improvement and Variation. Many revolutions of the Cycle could go by while the precedent remains unchanged. At a later time, the precedent may then spin off into variations. That will happen during a 2nd Qtr. of Improvement and Variation in the Cycle at that time. Any 2nd Qtr. can pick up precedents founded long ago to bring them to fruition.
After changes have come, 3rd Qtr. Review will follow. A step through time could happen here also. Improvements from
preceding 2nd Qtrs. might receive lttle review and be forgotten for a while. Revolutions later in the Cycle, however, events may be picked up from long ago. They may become nostalgic, deemed of historic importance, and remembered. That will still happen during a 3rd Qtr. Review. Successive stages of progression may step through revolutions of a Cycle, but still follow the respective sequence of Quarters. This type of continual progress is Step Progression.
The following examples offer a look at examples of Step Progression. The first examples shows Step Progression in the Physical Cycle. The next example shows Step Progression in an industry affected by all three Cycles.
Step Progression can be found in rocket development. Robert H. Goddard first test his
liquid-fueled rocket in 1915, (1st Qtr. Foundation). Advancement of Goddard's rocket came not in the following 2nd Qtr. of Variation of the Cycle (1922 – 1929), but in a later 2nd Qtr. that came with the next revolution of the Cycle. The Atomic Powered Rocket appeared in 1956, (2nd Qtr. Improvement and Variation 1950 – 1969)). Then many Missiles were destroyed after the US negotiated the Intermediate Nuclear Forces (INF) with Soviet leader Mikail Gorbachev in 1987, (3rd Qtr. Regression and Reform 1985 – 1992). This Progression through Quarters of development spanned across revolutions of the Cycle.
Step Progression, with breaks, is found in photography and cinema. The Thomas Edison laboratory produced the first motion picture camera, the Kinetograph, which used George Eastman's celluloid roll film in 1888. It was patented in 1891 along with the Kinetoscope, a motion picture viewing machine. This was during a 1st Qtr of Foundation in the Physical Cycle. A major improvement came to the Kinetoscope, not in the following 2nd Qtr of Improvement in the 1890s, but one revolution later in the Second Quarter, in 1922, when the first film with sound was demonstrated in a comedy with Chic Sale. "Talkies" had come to movies. Silent film was later revived by famed film-maker Mel Brooks with the first silent motion picture made in years, "Silent Movie" in 1976, during a 3rd Qtr. Review in both the Emotional and Intellectual Cycles. Whether with Continuous Progression or Step Progression, stages of change will follow the procession of Quarters.
The ancients knew the Cycles of time, Kala. Even before Vedic scripture, the Kalanemi was the "Rim of the Wheel of Time," a great star-wheel at the rim of the universe, sometimes pictured as the World Serpent that encircles the earth with its tail in its mouth. The study of lunar kalends, noted the change of seasons, holy days and festivals. This is the origin of our word, calendar. Kalends were also the new moon sabbaths of ancient Latinium. Priests of the Moon-goddess in Sinai were kalu. Prietesses of the moon-goddess, "the Goddess Kele," in prehistoric Ireland were kelles, from whom we get the name Kelly. The Saxon Kale used the lunar calendar with kalends and marked Spring with the month of SproutKale.
Our solar calendar now begins the year on January 1, an arbitrary date. In previous solar calendars, January 1 fell on the first day of Spring, the vernal equinox. The word "January" comes from "Janurarius" which is Latin for festival. A festival was held each year on January 1 to celebrate the first day of Spring. The true length of the solar year was not known, at that time, however. It was once thought to be 360 days. The calendar was later revised to 365 days, then 365.25 days, then to our current measure of 365.2422 days (with leap years and leap centuries). Meanwhile, January 1 has phase shifted out of place until it now falls in winter, shortly after the winter solstice. A correction has never been made.
A more natural way to measure Kalarhythms is with recourse to nature's measurable Rhythms of seasonal cycles, solstices and equinoxes, as the calendar was designed to do. A Kalarhythm year will begin on the first day of Spring. If, for instance, the 28-year Physical Cycle begins a new revolution in 1999, it will begin on March 21, 1999. The 28-year revolution of the Physical Cycle will complete on until March 21, 2027, and a new revolution of the Cycle will begin. Any particular year within the Cycle begins in Spring, and lasts until the following Spring. To refer to a Kalarhythm year of 2000, for instance, is to refer to March 21, 2000, to March 21, 2001.
The United States began with the Revolutionary War. The war began in 1775 when a new set of Rhythms emerged and a new nation was born. That year began with Spring, March 21, 1775. Just weeks after new Cycles emerged, fighting broke out between American founders and the British army. That was the beginning. We drafted the Declaration of Independence the following year to document our self realization. While we celebrate the signing of the Declaration of Independence on July 4, 1776, as our nation's birthday, the nation had to already exist before it could declare its own existence. Our nation was born on March 21, 1775, (see Chapter VIII: A Walk Through the 18th Century under 1775/76: The Birth of a Nation for supportive argument).
Market analysis helps confirm the beginning date of American Cycles. The stock market follows change on a daily basis (during business days), and records are plentiful. A composite of Kalarhythms was compiled to combine sine waves of the three Cycles into a single moving line, or Cycle Composite, (see Chapter XI: Kalarhythms & the Market). This allows the many market indicators to be compared to the overall energy of Cycles with a common frame of reference. To attempt a beginning date for Kalarhythms at July 4, 1776, is to make a composite graph that is consistently out of step with market trends by 16 months. Even comparing a line from this starting date to macro-economic indicators like the Dow-Jones Industrial Average – de-trended data, or the Kondratieff Wave, the Cycle Composite will be out of phase. To move the Cycle Composite of Kalarhythms until ups and downs coincide with market indicators, however, the beginning date for the Kalarhythms of the United States must be moved back to March 21, 1775, just before the outbreak of the Revolutionary War. A composite chart and market data will then be in synchronization with notable similarities. After more than two centuries of change, the Cycle Composite remains in phase with market data today.
INTERNAL ABERRATIONS originate from within the nation. A few of our economic downturns came while no Crossover or significant Low was in the Cycles, (i.e., 1837, 1893). A few economic booms came while no significant High was in the Cycles (i.e., the California gold rush in 1849). These events were counter-Cyclic. The aberrations passed. The Cycles remained.
EXTERNAL ABERRATIONS originate from outside the nation. We faced a World War in 1914 that began with other nations. We faced another World War in the 1940s. The nations where the wars began have their own Cycles and international relations. We jumped into action with a psycho-social hypothalamus in response to a threat. Natural catastrophes have also been a cause. A drought in the 1930s wiped out crops in the Southwest and turned it into a dust bowl. Social and economic causes were going on as well but some of the causes came from outside our auric field.
The world of physical causality sometimes produces autonomous aberrations from Rhythmic change. This is Disynchronicity. Aberrations render only temporal effects against tides of Rhythmic change, for we soon go back to where our Cyclic course would have us be. On October 19, 1987, the worst stock crash in the history of the New York Stock Exchange
occurred. The Dow-Jones Industrial Average fell 508 points and lost 22.6% of the market, almost twice the decline of the crash in 1929. More than 604 million shares changed hands, almost twice the previous record volume. Despite the crash, the market quickly bounced back to close up 2.26% for the year. Unlike 1929, no great depression was ushered in. Unlike 1929, no Crossovers were in place at the time. Aberrations do not change the river's course, they create ripples within it. The river continues. That is important to remember. Set your sights on the river's course, not on an aberration. Cycles will tell the difference.
To act in harmony with one's environment is to move with Rhythm.(8)To sail between distant shores, for instance, one would navigate the trade winds and ocean currents. Thus as we navigate history, we must steer with both the currents of change and the tides of time in mind because of the Cycles of change.
- The Mathematics of Cycles is a Map of Time.
1. Vivasara Tantrain: What is here is elsewhere.
2. The Flower Garden Sutra of Buddhism, also the Avatmasaka Sutra in Sanskrit, and the Chinese Hua Yen Sutra: In the heaven of Indra there is said to be a network of pearls, so arranged that if you look at one you see all the others reflected in it. In the same way each object in the world is not merely itself but involves every other object and in fact is everything else.
3. From the poet Wu-Men of 13th century China: One instant is eternity, eternity is the now. When you see through this one instant, you see through the one who sees.
4. Hsi T'u: All movements of the world are constantly subject to one and the same rule.
5. Hippolytus, Refutation, Bk. 7, Chapt. 1: The primal Being is symbolized as the seed of the Fig-tree, the mathematical point which is everywhere, smaller than small, greater than great, containing in itself infinite potentialities…the manner of the infinite generation of things is also figured by the fig-tree, for from the seed comes the stem, then branches, then leaves, and then fruit, the fruit in its turn containing seeds, and thence other stems, and so on in infinite manner; so all things come forth.
6. Lao Tzu: Man follows the ways of Earth, Earth follows the ways of Heaven, Heaven follows the ways of Tao, Tao follows the way of Nature.
7. Black Elk, Oglala Sioux holy man (1863 – 1950): You have noticed that everything an Indian does is in a circle, and that is because the Power of the World always works in circles, and everything tries to be round… Even the seasons form a great circle in their changing, and always come back again to where they were. The life of a man is a circle from childhood to childhood, and so it is in everything where power moves.
8. Wen Yen's remarks on the Ch'ien hexagram of the I Ching: The Great Man, in his attributes, is in harmony with Heaven and Earth; in his brightness, with the sun and the moon; in his orderly procedure, with the four seasons; and in his relation to the good and bad issues, in harmony with the names of the spirits.