Math

The Meridian Mysteries and the Secret of Time

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The Chaco and Mayan Meridians

In 1990 while studying rock art in the American southwest, James Jacobs noticed that Aztec Ruins and Chaco Culture were on the same meridian or north-south longitude line, and he raised the point with the archaeological community. Then in 1991, he expanded his view to include sites in Mexico, adding Paquimé to the ‘Chaco Meridian’, and he identified a ‘Mayan Meridian’ running through sites in the Yucatán to Tikal in Guatemala. Jacobs believes that this is evidence that ancient Americans practiced geodesy or took accurate measurements of Earth’s size, and he provides analysis of arc distance ratios to support his theory.

In 1999, Stephen Lekson wrote a book called The Chaco Meridian, bringing wider attention to Jacobs’ discovery. But Lekson argues that this is only evidence that the ancient people moved in straight lines north and south. He believes the Ancestral Puebloans used a series of north-south visual bearings to align the sites on the Chaco Meridian, and he points to the great north-south roads of Chaco.

Some critics dismiss both theories and argue that there are so many ancient sites scattered all over North America that any straight line will pass through 3 or more, so any meridian is merely coincidence. So, who’s right? First, the odds that a straight line will run north-south are 1 in 180, so a meridian is not just a random line.

Second, UNESCO recognizes 20 Pre-Columbian settlements as World Heritage Sites in North America, including 1 pre-Mayan, 8 Mayan, 3 Ancestral Puebloan, 5 other contemporaries of the Maya, and 3 post Mayan. All three of the UN-recognized Ancestral Puebloan sites are at 108º longitude: Chaco, Mesa Verde and Paquimé. 6 of the Mayan sites are at 89º longitude: Calakmul, Chichén Itzá, Copan, Quirigua, Tikal and Uxmal. The other 2 Mayan sites are Palenque at 92º and Tak’alik Ab’aj at 91.5º. But Palenque and Tikal are both at 17º latitude. So 100% of the UN-recognized Ancestral Puebloan and Mayan sites are on the same longitude or latitude lines. Statistically, the odds that all 11 independently selected sites share the same three longitudes by accident is 1 in a trillion. Unintentionally, UNESCO confirms both meridians.

The Difficulty of Calculating a Meridian

So, how did the ancient native people build cities on the same latitude and longitude lines before GPS and even before 250 BCE when the Greek Eratosthenes first recorded the idea of plotting longitude and latitude on a grid?

Calculating latitude is easy in the northern hemisphere. Simply measure the angle between the North Star and the horizon. If it’s 90º then you are at the North Pole, and your latitude is 90º. If it’s 0º, then you’re at the equator, latitude 0º.

Calculating longitude accurately is much more difficult, since although the stars stay in place, we orbit the sun every year and rotate every 24 hours. Every 4 minutes, the Earth turns one degree of longitude. So to calculate your longitude, you need to measure a star’s angle on a specific date and time, which requires both a calendar and an accurate measurement of time. For example, we know that the sun is directly overhead at noon, and if we knew which star was directly overhead at midnight on a given date, then we would know our longitude.

There’s a common misperception that calculating longitude requires knowledge of the size of the globe or the location of Greenwich England. While Eratosthenes calculated the Earth’s circumference, longitude measures angle, independently of size, which is why it works the same at every latitude. Greenwich was chosen by committee as our 0º Prime Meridian in 1884 over 100 years after longitude entered common use in navigation with marine clocks. So a useful relative longitude just needs a clock, not membership in any Royal Astronomical Society.

Lekson’s theory of north-south visual bearings might possibly explain the now desert Chaco Meridian sites, but I’ve driven the route which includes some rough elevation changes that would have made it extremely difficult to take accurate bearings over hundreds of miles, even with signal fires. And Lekson’s theory fails completely on the Mayan Meridian, due to the jungle. The hilly Yucatán terrain is covered by fast growing tall trees in a thick jungle that’s difficult to pass. While they built temples that reached above the treetops, that doesn’t explain how they chose the sites in the jungle before building the tall temples. There’s certainly no view of the horizon from the middle of the jungle, even if you clear all the trees for a few miles. So any line of sight explanation is wrong.

Alien Technology or Magic?!?

But the experts say that neither the Ancestral Puebloans nor the Mayans kept time accurately. So, the lack of a satisfactory explanation for how ancient people could apparently calculate longitude has caused a few people to speculate wildly. They imagine that the Knights Templar visited the Mayans while searching for New Atlantis, that maybe aliens gave technology to the Mayans, or that some other magic knowledge of invisible Earth energy—ley lines—is the explanation. No.

Cultural Clues to Calculations

While his original book was criticized for a few errors, Lekson is correct that there is a cultural connection between the ancient sites that made the meridians important to the people who built temples there. The sites share some historic overlapping, they were on established trade routes, and there are some basic architectural similarities, such as buildings oriented north-south. Agricultural societies are acutely aware of seasons, and each season has a different view of the stars at night as the earth orbits the sun. There are observatories at many sites, including at Chichén Itzá below, at Palenque and Xochicalo—with view holes in the observatory roof similar to a planetarium—, so there’s lots of evidence that accurate angles could be calculated on specific days and even at specific times of night. So Lekson’s basic theory, that there was an educated priestly elite with detailed knowledge of astronomy that likely traveled between sites, fits the known facts well.

Importantly, the three main sites on the Chaco Meridian all have advanced irrigation systems. The Greeks used water flowing through fixed diameter holes to measure time, like an hourglass measures time with the flow of sand. Surely, some Ancestral Puebloans tried to measure accurately how long their water supply would last. Yet for some reason, the idea that the ancient North American natives could calculate time is dismissed.

The Mayans were obsessed with the passage of time. The Mayan calendar has 365 days, uses a base 20 number system, and describes cycles of both 52 years and 5,125 years. You may have heard that the Mayans predicted the end of the world on December 21st, 2012. What they actually said was that their long count would reset on that day to begin a new five millennia era. Counting the days and monitoring the sun were central to their daily lives. The pyramid at Chichén Itzá has 365 steps, and the shadow of a serpent appears to climb them on the solstices. They believed the Sun God brought order to the day and transformed into a jaguar to pass through the perilous night.

And similar beliefs were common across pre-Columbian civilizations. From the Caves of Mitla & Yagul to El Tajin’s 365 daily shadowed alcoves, the ancients contemplated the underworld and the sun’s ordered journey across the sky. The tallest temple in Mexico is the Temple of the Sun at Teotihuacán, where a ‘town crier’ would beat his drum to signify important events. And yet some experts today would stand at the feet of the pyramids, perfectly aligned with the sun at noon, while shadows cast points across the plazas and claim that not one of the ancient people knew the time of day.

I do not understand how anyone can argue that the Mayans recorded their dynasties for centuries without having any interest or ideas on how one might calculate shorter time periods. These ancient agricultural societies had tens of thousands laboring in the fields, military groups coordinating jungle raids, traders delivering on precise daily schedules over hundreds of miles—in Tenochtitlan Montezuma ate fresh fish carried by relay runners from the Pacific—, and had thousands of laborers building precise pyramids, and yet some otherwise smart folks maintain the absurd position that none of the natives had any idea how long a day was nor could anyone organize anything that today requires a clock.

The simplest and only remaining logical explanation of the meridians is that some elite of both the Ancestral Puebloans and Mayans had a rudimentary way to calculate time accurately, most likely some type of shadow tracking and water flow systems, as they used both. They may have guarded that secret and kept it from the masses, but someone must have figured out how to tell time or there would be no meridian mysteries. Once we recognize that ancient American astronomers had the ability to measure time accurately, then we know that they could measure the angle of the a star on a particular day and time and calculate their relative longitude at different places. The time would only need to be accurate to within a few minutes at each location in order to mark a new temple within a degree of any known meridian, even in the jungle without a view of the horizon.

But Why Did They Build on Meridians?

But why bother? This is another problem with Lekson’s theory. Even if you accept that ancient people were very attuned to direction and solstices, such annual calendaring doesn’t require longitude at all, while latitude is only incidentally useful. So what’s the practical benefit of building two buildings on the same meridian? For that matter, why bother calculating the size of the earth, if Jacobs is correct about ancient American geodesy? Who cares that the arc distance between two distant buildings is 1% of the circumference of the globe, especially if your number system isn’t even based on 10 or 100?

To understand why, consider your last visit to a planetarium show. They likely showed which constellations appeared in the skies on that date and showed how the stars moved over time. If an ancient priest knew in advance which stars would rise into the sky at what time, then they could plan to tell a story about the stars that fit each day of the year. We know from many sites that the ancient Americans had a deep belief system involving day and night, believing that the labor of those on earth and the struggles of those in the underworld were connected to the rise of the sun each day. The stories of the stars may have revolved around heroes or rulers who had passed on to the afterlife, like the Greek myths that appear in the constellations.

If you had two temples on the same meridian, you could tell the exact same story on the same day beginning at the same time, and the sky would follow your words precisely. Even in daylight, using the same measuring sticks, the shadows would appear exactly at the moment you predict. This, perhaps, was the purpose of building your most important temples on the same meridian: to demonstrate the power of math and knowledge before the ignorant masses.

Although much of the history, language and culture of the ancient Americans was lost, the Yucatán pyramids and great kivas of the southwest have survived, demonstrating that there were at least a few ancient people who maintained the same astrological, calendaric, cartographic, chronologic, geometric, mathematical and navigational knowledge across generations and across cultural boundaries. They intentionally convinced others to build multiple cities on the same meridians to keep their predictions and myth-making consistent for at least a thousand years. The alignment of North American Native American World Heritage Sites proves this indisputably, without a plausible, logical alternative explanation. And if we refuse to recognize their accomplishments that still stand today, then we are the ignorant and irrational ones.

Rational Thinking

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Most humans live in their instinctual feelings: love, guilt, hate, fear, pride, anger, happiness, awe…. Unless something reverberates in our beating heart, the idea doesn’t feel real to us. Logic can seem as alien as Spock. We cocoon in the comfort of our instincts, and our modern technology entertains us with exciting fantasies about alien technology manipulating our brains. Ironically, our cable TV hearth targets our instinctual responses, in order to keep our attention on imaginary loves and fears for profits. Instinctual thinking limits us to recognizing our confusion, delusions, and fear. But then what?

No. If we’re going to solve our trouble with thinking, we need to overcome the limits of our instinctual thinking, ask honest questions, organize how we think, be methodical and logical. We need a far more advanced way of thinking: rational thinking. How do we go about that? Fortunately, rational thinkers keep records.

Socrates began the western history of rational thought by asking questions methodically, and his Socratic method is still employed at advanced universities. His student Plato believed that knowledge acquired through reason is more ideal than what our senses and experiences teach us. And Plato’s student Aristotle tempered that view to organize all thought rationally, whether the ideas came from observation or logic, inventing the scientific method and categorizing knowledge into physics, biology and politics. Aristotle’s logic helped him determine that the Earth was a sphere and that rain resulted from evaporation, around 350 BCE. In China around the same time, Confucius, Mencius & Xunzi similarly codified more rational ways of thinking. Math was already long known to the Egyptians and was advanced by later Greeks like Euclid and Archimedes.

But, most humans still being primarily instinctual thinkers, the ancient rationalism was almost lost after the Visigoths, Vandals and other barbarians sacked Rome, and in the Dark Ages of Europe, when only one story was read, the world turned flat and stupid again. Math continued to advance in the Muslim world, where the Indian decimal system was combined with Greek math and ancient Babylonian formulae. Around 825, the Persian Muhammad ibn Musa Al-Khwarizmi used the Indian concept of zero to balance equations, inventing Algebra. Some 375 years later, an Italian named Fibonacci brought this math to Europe.

The Church was unable to stop the Black Death, and the survivors started to rethink everything. Muslim scholars arrived in Spain and Italy to share their knowledge, and Renaissance scholars dusted off the Ancient Greek tomes and hit the books. The Medici, a merchant family in Florence, funded some of the most important scientists of the Renaissance: Brunelleschi, Da Vinci and Galileo. After exploring Roman ruins, Brunelleschi designed a huge, unsupported dome for the Florence Cathedral, proving that math still works even after being forgotten for centuries. Da Vinci studied human anatomy by dissecting cadavers, describing the nerves that connect our senses directly to our brains.

Then, Copernicus explained that the Earth revolved around the sun—as proposed by Aristarchus 1800 years earlier—, publishing both his observations and the math behind them. The Scientific Revolution had begun. Despite the Church’s opposition—including burning Giordano Bruno, who theorized that distant stars were like our sun with planets of their own, at the stake in Rome—Galileo made more detailed observations, expanding Physics and Astronomy, describing the moons of Jupiter, Saturn’s rings and the Milky Way, before being imprisoned for the remainder of his life. Francis Bacon described the scientific method (2,000 years after Aristotle). Newton reduced Physics to simple formulae, requiring neither God nor magic to employ.

René Descartes wrote cogito, ergo sum, ‘I think, therefore I am’, and, much as Plato before him, Descartes decided to believe only in what was supported by reason. The Age of Enlightenment began. Now, not just the infallibility of Church dogma, but the Divine Right of Kings was threatened. The ancient Greek ideal of Democracy returned. Revolutions followed. Americans who believe that our founders were guided by Christian faith have history exactly backwards. America was founded by rational thinkers, like Franklin, Jefferson and Madison, whose philosophy was explained by their compatriot founding father, Thomas Paine, in his book, The Age of Reason.

Rational thinking survived the collapse of civilizations, barbarian invasions, centuries of religious inculcation, enforced ignorance, public executions, tyranny, torture and wars. In the modern era, irrational fears and fact-free conformity still vie with what Judge Learned Hand called “the eventual supremacy of reason”. Rational thinking has proven itself to be both correct and valuable. Rational thinking is how we solve problems using facts, logic and math.  Rational thinking is what we learn in school and what we use in many professions, such as ecology, economics and engineering.  Boring, repetitive, linear, slow, and pain-staking though it may be, Edison consistently applied rational thinking to develop marketable light bulbs, transmitters, recording devices, movie cameras, batteries, coffee percolators and more in his lab and study below.

The general objective of rational thinking is to get the right answer.  The specific problem and methods vary, but we do not think rationally in order to get the wrong answer.  That would be stupid.  Rational thinking is smart.  The origin of your rational thinking is especially important.  If your thinking begins with a neutral observation, a plain fact, without embellishment, without judgement and without any bias of personal feelings, then you may begin thinking clearly in a rational way.  We gather information, make sure the facts and data are accurate, we use reliable methods, and we check our work.  The reason we went to school, studied, did our homework and passed tests, is so that when we need to solve a problem, we have the skills to think rationally to solve it.  

While others may wallow in their instinctual thinking, many of us primarily think rationally.  Fighting is counter-productive.  People should be more logical.  Facts matter, which is why we keep track of them in history books and databases.  If you want to know which player is better, look at their statistics.  Get the information you need, be organized and think it through step by step.  

This is how to succeed at work and in life.  Status matters less than income, and income matters less than savings.  You decide what you eat by cost, time to prepare, variety, nutrition and sufficient calories.   When you attend social events, you seek out those who are informative, especially in a way that might profit or benefit you.  Marriage is desirable for many reasons: two can live as cheaply as one, two heads are better than one, you can share life’s burdens and each of your strengths will compensate for the other’s weaknesses.  You want your children to be well-educated and financially successful.  You are planning for your retirement and even your death. 

Rational thinkers view their way as correct and believe that the world would be better off if more people thought rationally. Yes. Rational thinking may not feel real to instinctual thinkers, but air travel is a reality. And to rational thinkers, physics is what makes the world go round.