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1.3 “Long Learning” ­ Building Cultural Knowledge

The Example of the Mesoamerican Calendar

Human beings settled in the Americas about 20,000 years ago, after traveling from Asia across a northern “land bridge” that connected to what is now Alaska. There is evidence of agricultural settlements in Mesoamerica since about 1500 BCE. Many different cultures and civilizations arose in the region, but the Mayans in particular stand out for their written language and advanced form of calendar.

The Mayan calendar is unique in its complexity and sophistication. It is actually a combination of two types of calendars, each of which is its own system of interlocking cycles. The calendar round provides a way to ​ ​ specify unique dates over a 52 year period. This is useful for chronicling and describing events on the scale of a human life. The long count is a calendar with a much longer time scale; it was created to be able to ​ ​ reference dates at any point in a great age, a period of over 5000 years. The Mayans saw time as cyclical, and ​ ​ that at the close of one great age, the world would be destroyed and re-created, and the calendar would reset and begin again.

The calendar round is built from three different cycles. The Mayan number system is a base-20 system, ​ ​ meaning that there are 20 different digits. It is no surprise, then, that the first cycle is 20 days long, with a particular glyph (a character in the Mayan written language) associated with each day (see Table 1.1 below). There is also a second cycle of 13 days, and each day is assigned a number in sequence. This means that each day the calendar date advances by one glyph of the 20 day cycle and one number of the 13 day cycle; a date is specified using both the glyph and the number. This pair of interlocked cycles will produce 260 unique dates before it starts to repeat itself. This 260-day cycle is known as the tzolkin, and it was in widespread use ​ ​ throughout Mesoamerica starting around 500 BCE. It is interesting that doesn’t appear to be tied to the seasons, or any astronomical cycle.

Table 1.1 The 20 day cycle of the tzolkin. Two forms of each glyph are shown, one for inscriptions (left) and one for written text ​ ​ (right)20

1. 6. 11. 16. Imix Cimi Chuen Cib

2. 7. 12. 17. Ik Manik Eb Caban

3. 8. 13. 18. Akbal Lamat Ben Etznab

4. 9. 14. 19. Kan Muluc Ix Cauac

5. 10. 15. 20. Chicchan Oc Men Ahau

20 https://en.wikipedia.org/wiki/Tzolk%27in ​

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Figure 1.21 Mayan numerals. The numbers 1 through 13 were used to count the days of the 13-day cycle of the Tzolkin21

The Mayans combined the tzolkin with another cycle, the haab, which is similar to the ancient Egyptian year ​ ​ of 365 days. The haab consisted of 18 uinals of 20 days apiece, totalling 360 days, plus 5 extra days that ​ ​ weren’t part of an uinal. When the haab is combined with the tzolkin, it takes three pieces of information to specify the date: the haab date and the 20-day glyph and 13-day number of the tzolkin date. This results in 18,980 unique combinations, which takes about 52 tropical years to complete. See Figure 1.22 below for a mechanical representation of this combination of cycles.

Figure 1.22 Diagram of the interlocking cycles of the Mayan calendar round. The innermost gear is the 13-day cycle. That ring ​ and the 20-day ring that encompasses it make up the tzolkin, which takes 260 days to run through all combinations of day names. The tzolkin is also connected to the haab, only a portion of which is shown, which has 365 days in its cycle. Each of the three gears advances one day at a time, resulting in a 18,980 unique combinations of day names to form the date in the red box. It takes about 52 years for this cycle to repeat.22

21 https://commons.wikimedia.org/wiki/File:Maya.png 22 Adapted from ​ http://www.doaks.org/library-archives/library/library-exhibitions/the-ancient-future-mesoamerican-and-andean-timekeeping/ maya

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The long count date is structured in a way that might seem more familiar to us, as it is conceptually similar to ​ ​ our modern Gregorian calendar but with more layers of units. Just as we combine days into months and months into years, the long count combines units of time into units of longer time spans. In the long count, 20 days form a uinal, 18 uinal form a tun, 20 tun form a katun, and 20 katun form a baktun.

Table 1.2 Units of Time ​ Gregorian Calendar Units Mayan Long Count Units

1 month = 28-31 days 1 uinal = 20 days

1 year = 12 months ⋍ 365 days 1 tun = 18 uinal = 360 days

1 century = 100 years ⋍ 36,500 days 1 katun = 20 tun = 7200 days

1 millenium = 10 centuries ⋍ 365,000 days 1 baktun = 20 katun = 144,000 days

1 great age = 13 baktun = 1,872,000 days

There are several things that make the Mayan calendar remarkable. One is that it is based on cycles that have no connection to the tropical year, lunar phases, or even the motions of the planets. The cycle lengths of 13, 18, and 20 seem to be numerically significance, as they show up in a variety of places, but we don’t know what they relate to in Mayan culture. This very elaborate and complex calendar was not an attempt to predict seasonal changes or celestial phenomena, as the Egyptian and Mesopotamian calendars were. It is also very interesting that while the calendar round seemed designed to measure time on a human scale, the long count was designed to measure time on a truly cosmic scale. What was the worldview that made it important to measure such vast expanses of time?

It is important to note that although the calendar system had no apparent relationship to astronomical phenomena, the Mayans were clearly sophisticated and accomplished astronomers. The peak of Mayan civilization occurred around 800 CE, and built into the impressive cities of that time are careful alignments of buildings with celestial directions. There are many examples of temples with architectural features aligned with the rising and setting points of the Sun at important moments of the year, including the famous El Castillo pyramid at Chichen Itza, in the Yucatan. At sunrise on the day of the vernal and autumnal equinoxes, the edge of the pyramid casts a serpent-like shadow on the side of its staircase, seemingly connected to the large snake head at the base of the pyramid. As the Sun rises, the shadow wriggles down the length of the staircase, evoking an animated image of the feathered serpent god, Kukulkan. ​ ​

Figure 1.23 The “El Castillo” pyramid at ​ Chichen Itza, as seen at sunrise on the day of the vernal equinox. The edge of the pyramid casts an undulating shadow that looks like the body of the feathered serpent god whose head is at the bottom of the staircase.23

23 https://upload.wikimedia.org/wikipedia/commons/9/98/ChichenItzaEquinox.jpg

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Also at Chichen Itza is a building named “El Caracol” (the snail) because of the peculiar round shape of its upper structure. Built into the round structure are a series of windows that provide sight-lines to the horizon that align with important rising and setting points of the Sun. There are also windows that are aligned with the rising and setting points of the planet Venus, a planet whose motions were studied and catalogued carefully in the few surviving Mayan texts..

Figure 1.24 a “El Caracol”at Chichen Itza. The upper structure of the building is round, which is unusual in Mayan ​ architecture, and appears to be designed as a sort of observatory.24

Figure 1.24b The lower part of the round structure was Figure 1.24c The smaller, top part of the round structure ​ ​ built with important solar alignments. 25 has sighting windows aligned with the extreme rising and ​ setting points of the planet Venus. 26 ​

24 https://upload.wikimedia.org/wikipedia/commons/5/58/Chichen_Itza_4.jpg 25 http://www.exploratorium.edu/ancientobs/chichen/HTML/caracol.html ​ 26 ibid

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We can deduce a great deal from the architectural alignments still discernable in the ruins of the great Mayan cities, but the Mayans also had a sophisticated written language which they used for inscriptions on buildings and for extensive records in the form of books. The most complete surviving Mayan book is known as the Dresden Codex, so named because it is part of the collection of a museum in Dresden, Germany. It consists of ​ 40 pages made from the flattened bark of a fig tree and assembled edge to edge, accordion style. Only about seventy percent of the text has been successfully translated so far, but what can be read is a set of highly accurate astronomical tables, almanacs, and instructions for important rituals. One page of it is reproduced in Figure 1.25 (on the following page); it is a list of the dates of solar eclipses and a description of the omens associated with them. The Mayans kept extensive records of the lunar and solar positions, and could predict eclipses with great accuracy. Another prominent part of the Dresden Codex is the Venus Table, which records ​ ​ the apparent motions of the planet Venus.

The Dresden Codex is one of only three surviving Mayan books, and although it was damaged during the World ​ ​ War II bombings of Dresden, it is the most complete of the three. It has been an important key to decoding Mayan writing, Mayan mathematics, and the Mayan calendar. The other resource that has played an important role in understanding pre-Columbian Mayan civilization is the writing of Diego de Landa Calderon, a bishop of the Roman Catholic Archdiocese of Yucatan. Landa arrived in the Yucatan in 1541 during the Spanish Conquest, and was one of the first Franciscans charged with bringing the Catholic faith to the Mayan people. His book Relacion de las cosas de Yucatan outlined the Mayan religion, language, and culture, but there is irony in ​ ​ the fact that it has helped modern scholars reconstruct the past. Concerned about the continued idol worship of the converted Mayan population, Landa ordered an inquisition and set out to systematically destroy the indigenous culture and its historical legacy. He implemented widespread torture, and at the conclusion of the process in 1562, he burned what he thought was the entire library of Mayan books. To him, the books represented proof of anti-Christian beliefs and practices. He wrote about the event as follows:

“We found a large number of books in these characters and, as they contained nothing in which were ​ not to be seen as superstition and lies of the devil, we burned them all, which they (the Maya) regretted to an amazing degree, and which caused them much affliction.” 27 ​

27 Clendinnen, Inga. Ambivalent Conquests: Maya and Spaniard in Yucatan, 1517-1570, 2nd. ed. Cambridge: University Press, 1987. ​ ​ ​ p70

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Figure 1.25 A single page from the Dresden Codex. This page is an astronomical “warning table” identifying the dates of solar eclipses. The area labeled A is the Mayan sign for a solar eclipse, ​ ​ showing the Sun suspended from the sky band, within a half-light and half-dark field. The box labeled B is a single date in the tzolkin ​ ​ calendar, consisting of a number and a glyph (this example: 2 - Ahau). That section of the page lists the dates of 12 different solar eclipses. The portion of the page marked C ​ details the omens associated with this type of event.28

28 Adapted from Walker, C. ed. “Astronomy Before the Telescope”. St. Martin’s Press, NY. 1996. p.277

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Physics as a Project of Human Civilization It is tragic that the 2000-year legacy of Mayan scholarship and learning was almost destroyed in a single, intentional act. As we will see in upcoming chapters, European science had much to learn from other cultures at the time of the Spanish conquest of Mesoamerica. From our modern perspective the destruction of the Mayan record was an unthinkably ethnocentric act, and it seems strange that none of the scientific knowledge developed in the Americas was allowed to have any influence on the burgeoning science of the European renaissance. The roots of our modern scientific ideas come instead from many other ancient civilizations, such as Mesopotamia and Egypt.

Modern western culture places a high value on individualism. We tend to want to identify and celebrate heros and ascribe to them the credit for advancing our scientific understanding. There have certainly been important figures who have introduced a new perspective and transformed a field of study. But when we focus too much on a single character, we lose sight of the rich context of knowledge that they worked and thought in, and the many other contributors, contemporary and in the past, who helped shape their thinking. The development of physics has been a collective human endeavor that has continued since the dawn of civilization, and remains an evolving story that many cultures have, and many more cultures will, contribute to.

Bernard of Chartres was 12th century French philosopher whose work was focused on the writings of Plato. None of his original writings remain, but we know of his ideas from John of Salisbury’s 1159 CE review of contemporary scholarship, the Metalogicon. In Book 3, John wrote: ​ ​

“Bernard of Chartres used to compare us to [puny] dwarfs perched on the shoulders of giants. He pointed out that we see more and farther than our predecessors, not because we have keener vision or greater height, but because we are lifted up and borne aloft on their greater stature.”29

This image was more famously communicated by Sir Isaac Newton, one of the most celebrated figures in the history of physics, 500 years later. In a letter he wrote in 1671 CE to Robert Hooke, a collaborator and sometimes rival, he remarked “If I have seen farther, it is by standing on ye shoulders of giants.” ​

Figure 1.26 Excerpt from a letter written by Sir Isaac Newton to Robert Hooke in 1671, in the middle of which appears his ​ famous quote about “standing on the shoulders of giants.” 30

29 John of Salisbury. McGarry, D. tr. The Metalogicon. Paul Dry Books, Philadelphia, PA. 2009. p.167 30 http://digitallibrary.hsp.org/index.php/Detail/Object/Show/object_id/9285 ​

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The idea that science and philosophy are slowly developed by the contributions of generation after generation of thinkers seems to have been deeply ingrained in the mindset of the European renaissance. In fact, building successful scientific theories is not unlike what it took to build a cathedral in the middle ages; it might take hundreds of years for the project to be completed, generations of builders and sculptors dedicating themselves to a task much larger in scale than their own lifetime.

This perspective seems foreign to us today, as we are caught up in a day-to-day world of rapid change and quick progress. Brian Eno, a contemporary musician and philosopher, wrote an essay entitled The Big Here ​ and the Long Now to challenge that way of thinking. He asks us to recognize that our actions today are part ​ of the larger fabric of human endeavor, deeply rooted in the past, and with profound consequences for the future. Here is an excerpt from that essay:

"Now" is never just a moment. The Long Now is the recognition that the precise moment you're in grows out of the past and is a seed for the future. The longer your sense of Now, the more past and future it includes. It's ironic that, at a time when humankind is at a peak of its technical powers, able to create huge global changes that will echo down the centuries, most of our social systems seem geared to increasingly short nows. Huge industries feel pressure to plan for the bottom line and the next shareholders meeting. Politicians feel forced to perform for the next election or opinion poll. The media attract bigger audiences by spurring instant and heated reactions to human interest stories while overlooking longer-term issues - the real human interest.31

Stewart Brand, the president of the Long Now Foundation, has introduced a framework for thinking about the ways that civilization changes on different levels, which he calls the pace layers of change. In ​ ​ his model, things like fashion and commerce change quickly, perpetually introducing new ideas and innovations. These outer, fast moving payers pull the deeper layers, along, but the deepest layers are hard to move, and provide necessary stability and continuity. This, then, is a model for what a civilization that is capable of learning looks like.

Figure 1.27 Stewart Brand’s framework for “the pace layers of change.”. The upper layers change most quickly, and are the ​ source of innovation and new ideas. The lower layers change more slowly, providing stability.32

31 http://longnow.org/essays/big-here-long-now/ ​ 32 Brand, S. The Clock of the Long Now: Time and Responsibility. Basic Books, NY. 2008, p.37

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This picture of “long learning”is a great model for the evolution of science. Science in general, and Physics in particular, is a story that we tell about the world. That story has been crafted and recrafted by every human culture that has ever existed. We see evidence, from the earliest remnants of civilizations on every continent, that people have always tried to find order and meaning in the events that surround them. Every generation further develops the story that they inherited, and our most modern ideas in physics are built on a legacy of thousands of years of thought and observation. As we will see throughout this book, the richest periods of scientific advancement occurred when different cultures came into close contact with one another, either through trade or the expansion of empires, and were eager to learn. Seen this way, Physics is a perpetual project of the whole of human civilization.