The Square of 9 - Nature’s 'Black Box' The Square of 9 - Nature’s Black Box “Extraordinary claims require extraordinary evidence.” Carl Sagan (Astronomer) What secret lies hidden within the Babylonian ziggurats and the pyramids of Egypt? What is the connection between their tiers’ spiralling layout with flooding? And how can a 3000BCE device forecast the ups and downs of today’s financial markets? The answer is: The Square of 9. Centuries of ravaging inundations sent Babylonian astronomers searching for ways to forecast the behaviour of the Tigris and Euphrates Rivers’ annual flood. They referred to the heavens from which in the past they formulated the zodiac, the 365-day calendar and units of time and stumbled upon nature’s ‘Black Box’. Wherein they found a spiral encoded with orderly numbers and the 0.618 and 0.382 proportions of the Golden Mean (Phi). Their remarkable ability to discern order in phenomena, aided by fertile imagination, yielded the zodiac and the spiral - the world’s first two forecasting instruments. The shortcomings of the Tigris and Euphrates rivers in Babylon, and the Nile in Egypt turned the people who settled around them into brilliant problem solvers obsessed with patterns, symmetry and time sequences. The tangible evidence of their discovery lays hidden in the ziggurats and pyramids where the tiers of thousands of gigantic square-spirals, meticulously placed one upon the other, form the blocklayout of an invisible calendar and time-calculator which the builders of antiquity had deliberately obscured from the human eye. The anthropological evidence of this discovery emanates mostly from legends and myths using heroes, gods, metaphors and morals to explain the unexplainable. The absence of archaeological proof makes them a window to an era that would have otherwise remained blank. The first account alluding to a spiral is found in the Old Testament’s legend of Adam and Eve in the Garden of Eden, wherein stood the Tree of Knowledge with a serpent coiling its trunk luring the pair to eat the Tree’s forbidden fruit. As a twofold metaphor, the beast epitomises man’s innate curiosity and the doomed path that led him to discover awareness and knowledge. He became dependant on the land to survive and the heavens for understanding. Man explored and probed the heavenly bodies until he grasped that the Milky Way’s spiral and the 0.618 and 0.382 proportions of Phi hold the universe together and form his earthly and spatial surroundings. From a mathematical view point, the spiral stems from the circular movement of the earth which makes it one of the most important shapes in nature. A physical example of the immense power it contains is the tremendous energy of a whirlwind. The spiral accommodates growth easily and endlessly, changes proportions and direction of growth from outwards to inwards and, at the same time, sweeps a large surface area economically. Wherever in the natural world it crops up, it spins anti clockwise mimicking the shape and direction of the Milky Way and the east to west path of the sun. The right to left spin manifests also in the seed arrangement of sunflowers, pineapples and pinecones, in the cochlear of the human ear and in the pattern of his fingerprints. As the universe’s timetable, the spiral maintains the rhythm of all that ebbs and flows while Phi sets the proportions and boundaries of all that expands and contracts. Together, they form the invisible matrix which preserves order in the universe, supports life, and protects man from ecological and financial catastrophes.
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The square-spiral Dating to the beginning of time, no one knows this square’s original name or whether it ever had one. It constitutes a sequence of orderly numbered blocks spiralling outwards from the number 1 at the centre. A prominent twentieth century American Wall Street trader by the name of William Delbert Gann nicknamed it the ‘Square of 9’ because the first ring of its spiral contains all the numbers from 1- 9 and because the number 1 denotes the sun and the numbers 2 – 9 the planets revolving around it (Figure 3). This square’s most remarkable feature is that when pulled from the number 1, it transforms into a voluminous pyramid. It morphs into an upright vortex whose rings converge each time the pyramid gains a tier. As a miniature replica of the solar system, the square of 9 embraces its geometry and that of millions of like-shaped galaxies populating the universe. It took a great deal of imagination for Babylonian scientists to visualise the Milky Way as a two dimensional plane capable of tracking the heavenly bodies as they circumnavigated the sun. Gann made the pyramidal spiral public, however, in line with his Babylonian and Egyptian forefathers, and with those who subsequently discovered this knowledge, withheld the secret of its core. It took one hundred and fifty more years for the Australian mathematician, physicist and meteorologist, Trevor Casey, to openly demonstrate that the spiral embedded in the Great Pyramid’s tiers is a replica of the Square of 9 and show how a two-dimensional plane is in fact a time-calculator designed to forecast climatic and, inadvertently, financial events. His 2010 book, The Square Spiral – the Mathematics of Markets, outlines the square’s underlying mathematical structure and explains its qualities as a forecasting tool. The Square of 9 stemmed out from the zodiac which mapped out and partitioned the northern sky into twelve clusters of stars, where each constellation bore the shape of a mythological beast. The Sumerians of 5000BCE used it to track the course of the moon and sun in relation to earth, so that they could tell these planets’ angular position every day of the year. It enabled ship navigation at night, indicated the time of year for sowing, harvesting and when to celebrate these events. They noted that lunar phases and eclipses did not just happen at random, but rather occurred in regular intervals and patterns. Of course, they were unaware that these were caused by the earth blocking the the sun from illuminating the moon, but the predictions they made were accurate. They established that lunar phases governed the moon’s angular position with the sun and earth, dictated the rhythm between tidal swells and retreats, and that the waxing and waning motion of the moon and tides followed strict angular configurations. When the moon was full, it aligned at a 1800 angle with the sun, and when only its first or last quarter was visible, it formed a 900 angle with the earth. As time makes 180 and 3600 alignments identifiable on the Square of 9, it delineates the universe’s grid. Albert Einstein in his 1905 Special Relativity Theory coined it ‘space-time’. Stating that time is the fourth dimension of the universe, he demonstrated that as a mathematical model, space-time combines space and time into a single continuum. For two events separated by a time-like interval, enough time must elapse for there to be a cause-effect relationship between them. That is, in space-time a coordinate grid that spans the 3+1 dimensions locates events rather than just points in space. When time is added as another dimension to the coordinate grid, the coordinates specify where and when events occur. Had Einstein presented this theory to the Babylonians of 3000BCE, they would have told him it was old hat, for they had already established that if a river’s flow spanned 218 days (a duration denoted on the square’s northern cardinal), and the ebb was 96 days long (southern cardinal), then the stages would map onto the square at a 1800 angle in an ‘opposing alignment’ upon its northern and southern cardinals. They had discovered the role of time first. Five thousand years on, Gann discovered that money markets behave likewise. He observed that when two timeframes form a 180 or 3600 angle between them, the market reverses trend. The American S&P500 Index is one of many examples demonstrating this phenomenon at work. It shows how a 3000BCE instrument generated him fifty million dollars at a time when the rest of the world was languishing in the Great Depression.
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The later part of this article contains illustrations based upon authentic Nile records from 622AD to present. They show that when two timeframes meet at an opposing or co-axial alignment on the square, ebb changes into flow and flow into ebb. Time Figure 29 (http://www.safetyinthemarket.com.au/aboutus/default.asp?page=aboutus&aboutus=gann&rcol=ga nn&gann=tele) The number 122 on the square’s north-western diagonal represents 122 days of one inundation season which extended over the first four months of the Egyptian year. It is one of several numerals distributed on the square’s cardinal and diagonal axes denoting important divisions of time. Only two time units, 28 and 139, are cardinal numbers. The first, located on the square’s western cardinal, denotes the length of one lunar month, and the latter, on the square’s southern cardinal, represents 38.2% of days in the solar year. Units, such as 7 days of the week, 31 days of the month, and 13 moons of the lunar year are all diagonal numerals. So too are the respective periods of 226 and 183cd. The first denotes the 61.8% of days in the solar year, as well as Venus’ orbit of the sun, and the second the 50% of days in the solar year (Figure 30). The distinct location of natural time periods on the Square of 9 emphasises its calendric properties. Figure 30 As no historical records of Babylon’s inundations survive, and little remains of Egypt’s, we rely on the uninterrupted Nile data from 622 AD. We know that flooding during the Pharaonic era was extremely regular. The flood began on June 21st of each year and extended over four months until October 21st. Therefore, annual data collections from Nileometer readings entailed 122 annual entries (4 x 30.5 = 122 days). They are the world’s longest collection of records of any kind. The effort that has gone into collecting this data highlights the importance of the Nile region to ancient and modern civilisations alike. The Nile data available today comes in adjusted and raw forms. The series differ from one another by 8.15 metres throughout: the adjusted form is based on the floor level of Cairo’s Rhoda Island Nileometer positioned at 8.15 metres above sea level. It became operational in 622 AD, the very year during which data collection for the Nile resumed. The raw data series use the sea level as benchmark for denoting the river’s level above or below it. The graphs and sketches included herein are based upon the adjusted data series. A climatic cycle unfolds in a six-stage pattern which clearly distinguishes between growth and decay phases (Figure 32). As water levels vary from day to day, week to week and season to season, the pattern repeats on all scales, irrespective whether the time period involved is minute, intermediate, or large. The pattern enabled speedy interpretation of graphically presented records and forecasts of near, short, and long-term river behaviour. The growth phase of this cycle, which comprises two main upward swings separated by a short decay stage, can be established from visual study of the model. This explains why ancient civilisations so diligently collected and maintained historical flood records. They relied upon patterns which helped them establish that the cycle’s decay phase forms two long decay stages separated by a short growth stage, while growth has two long phases and a short decay period between them (Figures 31 & 32). Figure 31
Figure 32
Cycles 1 and 2 The opening graph shows the first sixty-one records of the Nile beginning at the low in 626 AD and ending 57 years later, at the third major low of 683. Cycles 1 and 2, both of which appear complete are indicated by the dotted lines on the graph. The upper and lower oscillations denote the highest Page 3
and lowest points the river had reached throughout the given period. The six- wave structure of cycle 2 is less evident than that of cycle 1; its three-stage growth phase ended in 660 AD, and the decay that followed in 683. The duration of the final growth stage (654- 660) was one year longer than the preceding decay (649-654), while the 649 and 660 AD peaks show similar water levels. The three-stage decay phase of the cycle ended in 683 AD making its final stage (668- 683) five years long. It was two years longer than the preceding growth that dominated the cycle from 665 to 668 AD. At the end of this cycle water levels fell to 1.21 meters above the sea level, slightly below the lows of stage 1 (660 – 665 AD) which recorded 1.4 meters in height. Cycles 1 and 2 offer essential clues to the river’s immediate and distant future; for example, the first growth stage of both cycles appears distinctively longer than the last indicating that the first growth stage of each cycle, in order to build momentum, absorbed the bulk of the expansion. Geometrical symmetry between the first and second stages of cycle 1 (626 to 630 and 630 to 632) is another prominent feature visible on the graph. The 4 and 2-year durations manifested a 2:1 relationship, while the overall life spans of cycles 1 and 2, which extended over 19 and 38 years (626 to 645 and 645 to 683), make cycle 2 twice the length of 1. Thus in addition to the six-stage pattern formed by each of the cycles, the ratio of 1:2 between them confirms their completion and the beginning of a new phase. The upper and lower oscillators on the graph depict the river’s amplitudes from 622 to 683. Cycles 1 and 2 capture the water rise from an average low of 0.96m in 626 to the highest level of 10.3 meters in 633. The graph shows that throughout the 57-year period of the two cycles the Nile neither exceeded the 626 low, nor did it surpass the 633 peak. The overall analysis of the stages shows that the years 626, 645, and 683 experienced major episodes of low water discharge, the year 626 in particular. Moreover, had the 626 AD bottom been expressed in raw data values, it would have shown an alarming depth of 7.19 meters below the sea level (0.96 – 8.15 = -7.19m). Based on this information it is possible to deduce that the river’s AD 626 bottom marked the end of the previous decay cycle - an era for which no records are available. The year 626 AD was possibly the pivot during which a new growth phase emerged. A further examination of the graph shows that river fluctuations do not happen at random, but rather in accordance with the proportions of the golden mean. The phenomenon is evident from the advance/decline stages of cycles 1 and 2 of which the ebb and flow indicate the presence of these divine proportions. The first upsurge of cycle 1 (626 – 633 AD) for example measured 751cm (847cm – 96cm), and that of the second (632 –633 AD) was 291cm. A division of the second range by the first (291: 751) produces 387 - a value closely approximating the lesser golden mean proportion of 38.2, one which confirms termination of the two stages. Likewise, the water amplitude of cycle 1’s second stage (630 - 632) measured 108cm (8.47 – 7.39), while the range of the final stage (632 - 633) was 291cm (10.3cm – 8.34cm). The division of 108: 291 results in 371. A similar behaviour emerges from correlating the first and second stages of cycle 2. The river’s amplitude was 835cm (970cm – 135cm), while the ensuing decay measured 138cm (970cm – 832cm). The division of the first range by the second (835: 138) produces 605; it emulates the greater golden mean proportion of 61.8. Figure 33 Schematic 35 features cycle 1’s six-wave pattern from 626 to 645. The model delineates the river’s growth and decay phases and shows that the cycle extended over nineteen years (626 – 645) ending on the eastern cardinal. The seven-year growth phase generated an upward zigzag pattern made up of two lengthy upsurges and a short retreat between them. Also a zigzag, the phase of decay was twelve years long; it is a retrograde depiction of the growth phase. The illustration shows that the cycle’s first growth stage from 626 to 630 absorbed the bulk of the overall thrust. While the expanding stages of the river extended over seven seasons (north-eastern diagonal) in all, the sketch also points out that the final upsurge (632 – 633 AD) was only one year long. In fact the message it delivered was that the final growth stage failed sooner than would be expected. And while the cycle unfolded in accordance with the six-wave pattern, it broke the rule in that the final stage was one season shorter than the preceding counter stage. Given that acute changes in the river’s behaviour have the potential to spell catastrophe upon the land and people, the most crucial task was to detect these unexpected departures from the sixstage cyclic pattern. The Nile data indicates that indeed deviations from the pattern took place and the river’s discharge often required careful monitoring, sometimes for decades. This happened in Page 4
633 AD when the final growth stage of the cycle failed and folded only one season after setting in. The period from 632 – 633, which denotes the final upsurge of cycle 1, was expected to endure for at least three years, failed. The growth, shorter by one year than the preceding 630 – 632 retreat, posed a disturbing irregularity; one which warranted a close observation of the water output the following season. In fact, the monitoring of the river extended for 13 years. In 635 AD, as the Nile flagged again, the waters neither matched nor exceeded the highs of 633. The end of that season would have triggered fears that the good inundation years were over for a long time. Indeed, a graphic display of the ensuing Nile records shows that Egypt endured a lengthy aridity phase. As the Nile began to decay, the final of the down stages, from 635 to 645 AD, took ten years to complete. Since the overall decay phase was twelve years long, it significantly exceeded the stages of growth (626 – 633), therefore regardless of the high water yields the bottom seen in AD 626 could not have been the absolute trough of the cycle. Technically, it was still in a decaying mode. Since records for the beginning of cycle 1 were unavailable, surveyors lacked the means by which to forecast the river’s immediate trend. Nevertheless, it is likely that the cycle’s growth phase extended over many years in addition to the seven known. The pattern thus had to be monitored until longer growth than decay stages became apparent. Yet, in spite of the missing records to 622 AD, a turnaround in the river output for the year 646 AD could be projected using the Square of 9. The alignment of 7 and 13 years shows that the two periods form a 1800 opposition on the south-western and north-eastern diagonals. Since the cycle also manifested a six-wave pattern, it indicated an intermediate end to the decay. From a short-term analysis, it is possible to deduce that the Nile would reverse trend during the next inundation season. If, indeed, the year 645 AD marked the cycle’s trough, than the growth phase of the ensuing cycle, in order to confirm the turnaround, would need to be longer than 12 years. Yet it failed. Figure 34 As water amplitudes at the low and high ends of cycles 1 and 2 manifested similar levels, which indicates several healthy inundation seasons, their total life spans were 19 and 38 years. The growth phase of cycle 2 expanded over 15 years and decayed over 23 ending in 683 AD at an 1800 upon the northern and southern cardinals (Figure 35).
Figure 35 Given that the downstages of both cycles were longer than the phases of growth, the 683 trough marked the low of a larger cycle, one that spanned over 57 years (626 to 683). Cycles 1 and 2 can therefore be seen as the first and second stages of a higher scale-order cycle which took 50 years to phase out, and of which the duration growth phase is unknown.
Figure 36 The next schematic depicts the higher order cycle constituting a six-stage pattern; it shows the first stage of decay noticeably longer than the final growth stage. This becomes clear from examining the 645 -660 stage; it was seven years shorter than the 660 - 683 stage of decay. This scenario repeats in the cycle’s two final stages, the growth period from 665 to 671 AD was six years shorter than the decay from 671 to 683, which was twelve years long. Figure 37 But the decay in the Nile output continued. A graph depicting an even larger cycle, one that extended over 162 years (northern cardinal) from 626 to 784 AD, confirms it indeed. The records show that for 158 years from the 626 AD low, and 151 years from the 633 peak, the Nile had declined. It finally reached the unprecedented depth of 0.62 meters above the sea level, which if expressed in raw data terms, would show that it sank to -7.54 meters below the sea level. The Page 5
period from 622 - 784 AD therefore denotes an even greater cycle, which unfolded according to the wave pattern too. Figure 38 Figure 39 The final graph in this article shows that for at least one hundred and fifty more years the Nile did not recede to the 784AD lows. In fact, the illustration points out that at the top of the range, water level remained stable, while the subsequent troughs gradually manifested higher troughs, a sign pointing the river’s slow but sure recovery. Figure 40 Time, as a distance-measuring tool, remained largely forgotten until Albert Einstein introduced the theory of special relativity in 1905 arguing that time is the fundamental unit for measuring distances in the universe. He declared time the fourth dimension of the universe stating that space (length, width, height) and time constitute different dimensions of the same solar system. It was during that time that Gann emerged on Wall Street and demonstrated that the “law of vibration” governed also the money markets. “Had this law been not existent neither the radio nor the telephone nor the telegraph would work. Because ebbs and flows form harmonious repetitive patterns and advance and decline stages in nature correspond to strict time frames and proportions, their direction and duration are predictable.” The early 1900s also witnessed the discovery of the Minoan civilization on Crete, Machu Picchu in the Peruvian Andes, and Flinders Petrie’s excavation of the Pyramid of Senurset in Egypt. Countless articles, books and films, each attempting to unravel the secret the pyramids hold, how they were built and for what purpose, appeared during that time. Ancient calendars, time forecasting methods, collection of the Nile’s records and the geometry of the pyramidal tier were of particular interest to Gann who from the age of thirteen found it inconceivable that the future was unpredictable. He studied the 1650BCE Rhind Mathematical Papyrus - the only surviving document which outlines the geometry of a truncated pyramid, demonstrating the then high level of Egypt’s mathematical capability. Put together by a scribe named Ahmes, the document includes several formulae for computing pyramidal volume and a comment by Ahmes saying it contains “The correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets.” One thousand years later, Pythagoras declared the Great Pyramid “the secret to the universe”, while not long thereafter, Aristotle proposed that the route along which time progresses is circular. The 2000BCE Mayans and 1400 AD Aztecs in the western hemisphere, as well as the Chinese in the Far East, also discovered that the solar system comprises a spiral and replicated it in pyramids of their own. The Aztecs’ Great Pyramid in Mexico’s Cholula boasts a volume of 4.45 million cubic metres which makes it one third larger than Egypt’s Great Pyramid. The one in Mexico’s Chichen Itza, erected by the Mayans around 1050, is monument to a no less accurate calendar than the Square of 9, which in many ways it resembles. However, unlike the Square of 9 whose secret existence has never been publicised, the Mayan calendar speaks of a sudden apocalyptic end to the world in December 2012.
Figure 41 – Mayan calendar Scientific American Space March 16, 2012
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China’s ancient city of Xi’an boasts one hundred pyramids of which the Great White Pyramid, spotted as late as 1947 by a TWA pilot, Colonel Maurice Sheahan, also dwarfs those of Egypt. Sheahan estimated that the structure is at least 1,000 feet high and 1,500 feet wide, whereas before erosion took toll on Egypt’s Great Pyramid, it measured 480.6 feet in height and 755.9 in Page 6
width. It appears that each of these manmade mountains was designed to embody cosmic knowledge built according to geometrical proportions that would last for all time. Equally intriguing is the fact that a number of eastern and western civilisations, unlikely to have had contact with each other, built massive structures so remarkably similar, all of which replicate the Square of 9.
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The truth is that time actually has a true or real value of space that is the angle of space within a 360⁰ degrees Circle (Arc Angle). The geometric wisdom is to cause the CIRCLE, SQUARE, and TRIANGLE to interact to each other. Some call it “CIRCLE SQUARED “or enclosing a SQUARE within a CIRCLE or a CIRCLE within a SQUARE. The only way it’s possible to use a CIRCLE, SQUARE, or TRIANGLE as geometric applications is to apply it to time and space. It needs to be known at a specific time and angle of space to be considering a true geometric point.
How it works is two Octave Points on the Matrix Grid produces a Square and Triangle. Counting from anywhere on the matrix a third Octave Point in duration to the Squares and Triangles forms the tops and bottoms in the market. At least one of these geometrical points will be the factor in tops or bottoms. This is the Hidden Order to where energy points may be damping (Lost Motion), or if the resonant pump (Vibration Oscillations) is intact (Tops/Bottoms). In physics this effect in nature is call the Law of Resonance. Remember all members of the forum that I do not use price as space movements. In fact when I say space I am saying that every point of time has a real space value. In physics time and space exist at the same point, and its easy to know time but what is its space value. That is why I said space has its own true angle of space (Arc Angle within 360 degrees).
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