Reflections on the Harmonic Convergence
As individuals, each of us lives in the world of his or her personal beliefs. Our value hierarchy is determined by our beliefs; we set goals, make choices, and act according to what we believe is real, true, morally right, possible and desirable. We feel more secure when we are with others who share our beliefs and thus validate them. When a personal belief is challenged by a disbeliever, it is normal to respond with anger or fear, especially if we have some doubts about our position. Heresy has historically been met with an attempt to convert the other, with torture and death, or with avoidance and ostracism. Metaphysicians and spiritually enlightened people do not react that way? Try to debunk the Harmonic Convergence and see what kind of response you get.
Is it constructive for people to gather to meditate, pray, and perform rituals for peace and healing for our planet? Emphatically!, at least in my belief system. Do I believe that the Mayas had a metaphysically highly evolved religion, that a grand trine in fire signs is certain to produce important events, that the world will radically change when a theoretical cycle of a Mayan calendar ends (and like all cycles, begins again) or that the last 25 years of one of these Mayan cycles is especially important? No, to all of the above. Should I remain silent about my disbelief lest I offend someone who had a beautiful, mystical experience in the middle of August 1987? Not if silence encourages the belief that mystical experiences require specific astrological configurations, or specific calendar dates, or specific places, or the endorsement of a guru. Belief in the possibility of a mystical, healing experience for oneself and for the planet can encourage the experience, and the belief may be facilitated by supportive beliefs in the power of planets or places, in the wisdom of ancient peoples or of a guru, etc. The power of mass belief can be awesome whether it produces the healing miracles of Lourdes or the lynching of a suspected rapist. The story of the hundredth monkey is as much a fable as the spiritual wisdom of the Mayas, but the power of belief is very real!
My B.A. from the University of Chicago (followed by some years of graduate work there and at the University of Arizona) was in anthropology, especially in its sub-field of archaeology. I continue to follow, to the extent that I have time, the developments in the field. I have not had time to read all of The Mayan Factor by Jose Arguelles, but the chapter that I have plus the quotations from the book and from personal statements by Arguelles which were carried by our newspapers include a mixture of accepted archaeological data, mathematical ignorance, and speculative personal beliefs.
The mathematical errors or misleading statements are the easiest to spot. For example, on page 202, Arguelles emphasizes how distinct the Mayan vigesimal system is from our decimal system because of its numerical progression when you multiply the base number (20) by each successive product of the previous multiplication. For example, 20 times 20 produces 400, times 20 produces 8,000 etc. Arguelles contrasts this with our system, claiming it has a base 1 which only produces 1, no matter how many times you multiply the results by 1. But our system is not a base 1; it is a base 10, and gives the same kind of numerical progression when the base number is multiplied by itself. It is a general mathematical principle that the base number of ANY number system will produce the same type of progression. The smallest number system is the binary with a base 2, where the only digits are 0 or 1. The base number of any system is always one more than the highest named digit in the system. In our system, nine is the highest named digit: there are ten digits including zero. The Mayans did use a 20 base system with 19 named digits plus zero. Though the numerical progression of their base number is a general principle in mathematics and in no way remarkable, the Mayan’s understanding and use of zero is quite remarkable. The concept of zero was presumably independently invented in ancient India and spread to Europe through the Arabs, hence the reason that our numbers are called Arabic numerals. The number system of the ancient Greeks and Romans lacked a zero, leaving them handicapped and incapable of carrying mathematics very far.
Archaeologists are still not certain whether the Mayans themselves developed the concept of zero or whether it came from the Olmecs, a highly mysterious group which preceded the Mayans in southern Mexico. The Olmecs are best known for the huge carved stone heads they left. Their relatively advanced civilization seems to have appeared in the area without visible predecessors. Excavated sites have been dated to 1200 B.C. in contrast to most early Mayan sites which go back to a few hundred years B.C. and Classic Mayan sites which are mostly in the range of 250 to 900 A.D. The September 1987 issue of the National Geographic describes one exception in a very interesting article on El Mirador, a massive ruin about 225 miles north of Guatemala City. Archaeologists have evidence that it was built by pre-Classic Mayas about 1200 B.C. and was abandoned for unknown reasons about 150 A.D. It includes several building complexes with one pyramid and its summit building towering to 18 stories.
Another obvious Arguelles error on page 203 is the statement that 72 equals 1/2 of a sine wave. A sine wave is 360 degrees, so 72 degrees is 1/5 of it. The source of the other numbers which Arguelles claims are harmonics of earth, of its poles, time, space, etc. is not given in the material that I have, nor is the definition of how Arguelles is using the word “harmonic.” John Nelson used the term to refer to what astrologers call “aspects,” angular distances between the planets based on divisions of a circle by whole numbers. John Addey started his harmonic studies by analyzing groups of charts, plotting on a graph the distribution of all of their Moons, etc., and noting where they peaked. Three peaks (increased numbers of Moons, for example) at approximately equal intervals around the circle would produce a third harmonic (an astrological trine). Addey then shifted to a consideration of individual charts, exploring the Hindu concept of “Harmonic charts” which are produced by multiplying the natal chart by the chosen “harmonic number” and then subtracting as many full circles (360) as needed to bring the planet positions back into a 360 degree range. In Hindu astrology, the Navamsa or ninth harmonic chart is considered as important as the natal chart.
In early music, scales were produced through fractional ratios which are similar to aspects. Pythagoras used a kind of one-string violin called a monochord, and demonstrated these fractional ratios. A true octave is a two to one ratio such as half the length of a string. Plucking the string in the middle produces an oscillating sine wave as the string vibrates back and forth (up and down). If the string is held in the middle and one side is plucked, the resulting tone will be an octave of the original tone. The word “octave” comes from the modern scale which was set in its current form of eight notes in relatively recent years as mass production developed and we moved from the clavichord (which was re-tuned for each piece of music and could produce a variety of scales) to the piano which is maintained to produce the single modern western scale. The notes of this modern scale are a series of compromises rather than the traditional true ratios (2/1, 3/2, 5/4, etc.) of the ancient world. A tone is a physical vibration of so many cycles per second. A note is a symbol “in the region of” a tone. The modern piano (and flute etc.) are digital instruments, with set intervals between their notes. The violin (and most ancient instruments, including the human voice) are analog instruments capable of producing tones which can slide and vary depending on their context.
Compared to our single, compromise western scale, India has at least 200 scales. Ancient Greece had about 20 different scales. By the middle ages, the Church was down to 12 scales. It is fascinating to hear music played in the different scales. Most scales have 5, 6, or 7 tones per octave, though occasionally there is one with 8 or 9. Out of an infinite number of possible tones, each culture picks one or more sets, always with ratios which come out even. The music that I have heard played with oriental scales (Chinese and Korean) sounded distinctly oriental. One of the ancient Greek scales used the Fibonacci number series which has been found widely present in the plant world. The scale used by Pythagoras is fairly close to our modern western scale, but the one from ancient Sumeria (3,000 B.C.) is also surprisingly similar. You can clearly hear the roots that have come down to us. In the 12th century, the Arabs were using a scale with ratios that were precise to 6 figures! By the 14th century, they had simplified the ratios to figures like 32/27, and the tones sound muddy in comparison to the earlier precision. Of course, when true ratios are used, there are varying intervals between the tones so some of these scales sound very strange to ears accustomed only to our compromise system with its similar intervals between tones.
The preceding material about early musical scales comes from Steve Nachmanovitch, a violinist and computer expert in the Los Angeles area. I heard him lecture last April, and was fascinated by the parallels he pointed out between music, mathematics, and mysticism. He described some of the ideas of Robert Fludd, a Renaissance writer who suggested that the planet locations around the sun corresponded to the Pythagorean scale and provided a template (grid) for all vibratory phenomena. I generally use the word “model” for what Steve called a template or grid. Fludd tried to superimpose everything on the basic grid, including traditional astrology’s picture of the zodiacal signs superimposed on the form of a human from Aries on the head to Pisces on the feet. Steve suggested that some of the data is distorted to make it fit, to produce unity. The ancient myth of the Procrustean bed describes the process in a rather gruesome form. It seems to be a basic human need to have order and symmetry to gain a sense of understanding and control of the cosmos.
As Steve defines them, the even (whole number) divisions of a string are called “harmonics”, and the resulting tones are heard as harmonic tones. So we are right where we started with Nelson’s use of the word “harmonic” to refer to divisions of the circle (equivalent to a string on a musical instrument). Traditional astrology divided the circle by 2, 3, 4, and 6 to produce the Ptolemaic aspects (along with the conjunction which might be thought of as a division of the circle by 1). Later astrologers began dividing the circle by 8 and 12. Still later, some astrologers added quintiles (division by 5), deciles (division by 10) etc. Nelson divided the circle by 48, 32, and 20 to get aspects of 7 1/2, 11 1/4, and 18, used every multiple of these resultant aspects (e.g. 7 1/2, 15, 22 1/2 etc.) and called these extra aspects harmonics. Addey suggested dividing the circle by every number up to 180. The latter would give an aspect of 2 degrees. As described above, different cultures have selected a variety of divisors out of the infinite number which are possible, in order to create hundreds of different musical scales. Astrology is still exploring the potential of some of the “new” aspects. Midpoints are a variation of the same principles.
How much of this “model making” is arbitrary? How can anyone talk about “the” harmonic of light, or space, or time, or the earth or its poles if a simple string can produce an infinite number of number ratios? As mentioned already, pianos (and modern computers) are digital instruments with notes which are either on or off and which have nothing in between the set notes. A voice (and a violin) can slide up or down so the range is infinitely divisible. Steve has written a computer program which works on an IBM or clone and a Yamaha synthesizer with an interface to produce all of the known musical scales in a more precise way than any traditional instrument of wood, string, etc. I asked him if he had a Mayan scale, but he doesn’t. He promised to add it to his program if I could find a record of the mathematical ratios which they used. Of course, if the Hindus have 200 scales, the Mayans may have had more than one, but I have not yet pursued the matter.
I did skim through several of my archaeological reference books while checking some of Arguelles’ statements. The most interesting book was a recent purchase which was stacked with dozens of others waiting for more reading time. It is called The Mystery of the Mayan Hieroglyphs by Richard Luxton with Pablo Balam. Richard, the writer, spent months with Pedro, a Mayan descended from an ancient lineage, exploring the current Mayan culture and looking for clues to interpret the ancient writing, much of which is still undeciphered. Richard felt that he was guided to an understanding of a few of the 20 day names in the Mayan calendar which had 18 “months” of 20 days each. To produce a year closer to the actual earth’s orbit of the sun, the Mayas added 5 days to the end of the 360 day year. Those final five days were considered unlucky.
Richard suggests that the 20 days of the Mayan month were a description of a shamanic dream walk to the spirit world. Ahau, the day that ends each month, pictures a face with a rounded mouth which symbolizes the power of breath and speech. Ahau is the spokesman who explains all the rest. Next to the masculine Ahau is Imix, feminine and representing a grain of maize, the sacred food of many native American Indians. Imix is the seed which marks the beginning of life and each new month. Ahau (lips and breath) and Imix (breasts and seed) are in the west of the circle, at the gate of the Realm of Shadows. The fifth sign, Chicchian, is the serpent, the seer in the depths of the underworld, and opposite it is Men (the 15th sign), which represents an eagle as seer of the heart of the sky. Richard notes that at an early Olmec site, La Venta, which is dated to 500 B.C., there are jaguars carved with serpents’ tongues and feathers for eyebrows. He theorizes that the 20 day signs symbolize a shaman’s paranormal dream walk through the realm of shadows and the heart of the sky in order to gain wisdom. The feathered serpent (Quetzalcoatl to the Aztecs; Kulkulkan to the Mayas) is described in the Mayan book, the Popol Vuh, as a spirit lord who became a serpent and then an eagle. The 11th day sign, Oc, stands for foot(print) in Mayan, from the verb “to enter.” In the circle, it is in the east where light enters as the shaman moves from the underworld toward the sky. The next sign, Chuen, is “artisan” in Mayan, joining the action of hand and foot.
Richard Luxton credits the Mayan with paranormal (shamanic) psychic ability, but he does not make the unprovable claim that the Mayans (or at least their leaders) came from outer space and returned there. Some of the most recent archaeological conclusions about the Mayas are even less flattering, suggesting that they practiced human sacrifice and even tortured some of the victims whereas the Aztecs killed far more individuals but usually did it quickly. Archaeologists who commented on Arguelles’ theories denied that his 26 year period (1987 to 2012) came from the Mayas. Arguelles states that August 16, 1987 is nine 52-year cycles from the date that Cortez landed in Mexico though my Britannica says he landed in February 1519. The actual conquest of the Aztecs was not complete until August 23, 1521. Luxton confirms the Nahua (Aztec-Toltec) origin of the 52 year cycles and indicates that they were mainly found in the Yucatan area which used a “short count” calendar in contrast to the Classic Mayan “long count.” The incommensurability of the two forms of measurement can be seen if we add 52 years to 1987 to complete another cycle, we are well past the “long count” date given as 2011 or 2012. Barbara Hand Clow in an article in the Libra 1987 issue of Mark Lerner’s journal, Welcome to Planet Earth, exemplifies the incompatibility of the two systems. She writes that August 17, 1987 was the beginning of the last Katun in the (long count) cycle to end in 2012. But a Katun (which is 20 Tuns of 360 days each) is 19 years and 73 days. Adding that to August 17, 1987 would get us to the fall of 2006, not to 2012.
Luxton writes specifically that the Toltecs and later the Aztecs were infiltrating the Mayan area for centuries, and obscuring the specifically Mayan system. According to don Miguel, a Mayan shaman who talked to Luxton in Merida before he met Pedro Balam, the end of the Mayan building of massive stone pyramids and temples around 900 A.D. was due to the instructions of their shaman-priests. “Their gods told them to do that, to hide what they knew and to disappear. The gods distanced themselves at that time so the lords had to go in search of them” according to don Miguel. (p. 43) We are left to wonder whether the Mayas were hiding their knowledge from the infiltrating Nahuas from central Mexico, or from the psychically anticipated arrival of the Spanish which did not occur until several hundred years later though Luxton does say that the Nahuas were associated with the 9 Lords of Hell. Archaeologists agree that the 8th century was the end of Classic Maya culture but they are unsure of the cause, speculating about soil exhaustion, overpopulation, and political upheaval such as the farmer-laborers rebelling against the ruling priests and kings. At least one sizable area is known to have been abandoned after a major volcanic eruption which covered hundreds of square miles with a heavy layer of ashes and lava, but that did not explain the relatively sudden end of major stone building and calendar carving by many geographically separate groups of Mayas.
Luxton’s description of the 52 year cycle as Nahuan rather than Mayan is supported by a newspaper interview with Dr. Harrison, an adjunct associate professor of anthropology at the University of New Mexico. Harrison confirmed that the Mayan calendar ended in 2012, and he suggested that Arguelles was mixing the Aztec 52 year cycle with the Mayan calendar. Further confusion appears when we read in Luxton that Richard Montejo first came to the Yucatan area in 1527 and stayed six months. In 1539, one Katun after the arrival of Cortez in Mexico, Montejo’s son returned to the Yucatan with an army to make a permanent settlement. Luxton writes that the founding of Merida was actually accomplished in 1541, in the first year of a new 256 year cycle of 13 Katuns, and even in the first month (Pop) of the new cycle. He describes how the coming of the new people and the end of the Mayan customs at this time was predicted long before the coming of the Spanish.
Since the Mayan source of this prediction was written years after the coming of the Spanish, it may have been hindsight rather than foresight. And since Montejo senior stayed in the Yucatan long enough to learn something of the Mayan calendar and beliefs, he may have instructed his son to come when the Mayas expected the invasion and would not resist it, believing it to be inevitable. But if the settlement of Yucatan is the important one to the Mayas, it would seem that we should date from that rather than from the arrival of Cortez as Arguelles does, using an Aztec count and the attack on the Aztecs and trying to connect that to the end of the Mayan “Long Count.” Richard Luxton confirms the Mayas knowledge of the approaching end of their long cycle. He says that today they speak of the end of this present world around the year 2,000 A.D. “The few years’ margin is referred to humorously in Mayan as the ‘beak of time.’“ p. 201 This statement seems to support the idea that Arguelles’ 26 year period is his own creation whether it was an effort to make the different systems fit or his own personal revelation which he later tried to justify with some elaborate number games that didn’t quite mesh. In one reported interview with Arguelles, (Los Angeles Times, August 12, 1987) he is quoted as having a vision in 1983 while driving down Wilshire Boulevard in Los Angeles to return a rented car. His vision was that at sunrise on August 16, 1987, people around the world would participate in “ritualistic surrender” to the Earth.
Luxton admits that we do not know why the Mayas selected the date they did for the beginning of their long cycle. Nor do we know the reason for their calendars. There are no obvious astronomical correlates to either their 20 day “month” or to their 260 day ritual calendar. They do seem to have been devoted to the numbers 20 and 13, and may have created their elaborate system of uinals, tuns, katuns, baktuns, pictuns, calabtuns, kinchiltuns, and alautuns from that commitment and then tried to make the “real world” fit their system as, for example, adding 5 days to the tun to get a 365 period that was closer to the earth’s trip around the sun. They may be one of our best examples of how humans create their own mental world and live in it, including the Mayan self-fulfilling prophecy of being enslaved by the Spanish which Luxton says led them to give in, and the Aztec expectation of the return of Quetzalcoatl which certainly helped Cortez to conquer the Aztecs.
As far as archaeology has taken us, I do not know of any precise events associated with the beginning of the Mayan cycle on August 12, 3113 B.C. The union of Upper and Lower Egypt to form the First Dynasty occurred around 3100 B.C. The great Minoan civilization on Crete dates its beginning to around 3000 B.C. Sumer in Mesopotamia, supposedly the original source of writing, was at its height about the same time. The great cities in the Indus valley were developing then or soon afterwards. I even looked at the dates when the tropical zero Aries reached the various stars of the constellation of Taurus to see if there was a correspondence, but our Aries point reached Alpha about 3222 B.C. and did not get to the next star, Tau, until 3047 B.C. The total interval during which zero Aries was moving in front of the constellation lasted from 4143 B.C. to 1689 B.C., about 2454 years. Virgo and Pisces are even longer. The Gemini 1984 Mutable Dilemma has an article giving the dates of all the astrological ages based on the precession of the equinoxes as zero Aries (the intersection of the ecliptic and the equator) makes a circle in front of the backdrop of the groups of stars that we call constellations.
So what can we conclude about the great fire trines which coincided with a major plane crash in Detroit and which were followed by major forest fires in many western states? Such incidents are common with an excess of fire which tends to encourage excesses of all kinds. The “true believers” will be unaware of the nonsense in Arguelles’ book and will prefer his theories to the denials of scientists. After all, what can science offer us to compare with Arguelles’ statements that after 144,000 people have participated in the August rituals, the extraterrestrials will decide that we earthlings finally have trust and can be trusted, and they will come help us. The Los Angeles Times quotes Arguelles as saying: “This is a trigger event. We have a five-year clean-up ahead of us. In nitty-gritty terms, we are talking about dismantling governments, the military, polluting industries...” “And by 2012 ... the earth will have been cleansed and purified; humans will have rediscovered their original state of trust, of innocence. And we’ll take our rightful place in the galactic community.” (Los Angeles Times, August 12, 1987)
But even if this particular vision is a fantasy, has good come out of the rituals, the gathering of the believers to share their love and reinforce their faith in the ultimate triumph of good? The possible breakthrough of the Arias plan in Central America began in early August and there is still hope that Nicaragua can move toward more democracy and that the destruction of the Contras can stop, though the statements by the Reagan officials are not encouraging. As this is written in mid-September, a first step by the U.S.A. and Russia toward nuclear disarmament has been announced in Washington, DC. Some experts think that Iran may be sufficiently war-weary to consider ending the bitter war with Iraq, but the capture of an Iranian mine-laying ship has heated up the Gulf confrontation. An agreement has been reached by the major countries of the earth to slow down the production of chlorofluorocarbons which may be destroying the ozone layer that protects us against harmful ultraviolet light. I don’t expect a Golden Age until we have Golden People, but maybe we can continue to take some small steps in that direction.
I hope eventually to get the full birth data for Jose Arguelles. At present, I have only a date of birth and his current residence; January 24, 1939, now living in Boulder, CO. Naturally, I expected a strong Neptune in the chart and was not surprised to find natal Moon in Pisces and quite possibly in orb of an opposition to Neptune (depending on birth time) along with progressed Sun currently in Pisces and opposite Neptune. Natal Pallas is also in Pisces, closely opposite Neptune, while Jupiter is in early Pisces. If he was born in the neighborhood of 4 to 8 A.M., he could have progressed Jupiter on natal Moon and progressed Moon sextile natal Jupiter in the summer of 1987. An afternoon birth could put progressed Neptune opposite natal Moon for much of his life. Of course the Neptune prominence fits both his career in art history and his galactic vision.
As a postscript to this article, in the midst of the August excitement, I had a phone call from a man in one of the Carolinas. He urged me to notify people that the most important time might be on the evening of August 17 rather than the dawn of August 16. He had discovered that a grand quintile would exist at that time if one put zero Aries on the Ascendant. I ran the chart for zero Aries rising for Tokyo, Moscow, London, Washington, and Los Angeles, and he was right. The 5th and 25th harmonics were very strong in all the charts, though less so in Tokyo. Washington and Los Angeles were especially emphatic, with the Moon within a one degree opposition to Saturn. The local times when zero Aries rose ranged from just before 8 P.M. in Tokyo to just after 8:47 P.M. in Moscow, but I failed to note anything remarkable in the world around that time. Maybe one of our readers was paying more attention. (I alternate between reading three daily newspapers and not reading any when I get behind on activities like getting The Mutable Dilemma written.) I know the tragic plane crash in Detroit was a day earlier, on the evening of August 16 just before 8:45 P.M. EDT. Saturn was exactly on the MC and Mars close to an opposition to the Ascendant from the 6th house. At sunrise on the 16th, we were hosting a Tibetan lama, head of the Zog Chen teaching, and he led a chanting service in our chapel, but his chart and more on his teaching will have to wait for the next issue of The Mutable Dilemma. In the meantime, we can keep on praying and working for peace even if we remain skeptical about the spiritual wisdom of the ancient Mayas and the likelihood of joining a galactic federation in the near future.