Both are needed to fully understand the method. Finally, we propose some exercises and suggest how to use the material in the classroom. Classical Maya civilization was highly advanced and developed many areas of science. Perhaps the most significant one was astronomy, which was important for agriculture. Based on astronomical observations, the Maya invented an elaborate system of calendars.
In this article we discuss some relationships between the calendars from the mathematical standpoint. We illustrate our discussion with actual examples of dates found on a stela in Coba and on the Leyden Plaque, in which we show how to convert from Long Count dates into Tzolkin and Haab dates. The Tzolkin Calendar, also called the Tonalamatl or Sacred Calendar, uses 20 names of gods with 13 days attached. As a result dates are formed, which constitute 1 Tzolkin year.
The year begins with 1 Imix and ends with 13 Ahau.
To each god the numbers 0, …, 19 are attached as in our Gregorian calendar. The least common multiple of and is 18, The Round Calendar date gives us the exact day within one cycle of 18, days, but we cannot locate the date in time as the Round Calendar cycles are not numbered like our years, e.
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To locate dates over long periods of time, the Maya used Long Count dates. For example, the Long Count date 9. We are now living in the fourth creation. The previous creations have ended at the conclusion of the 13 th baktun, or in Long Count dates, the day after The date December 21, , has received much media attention in recent months and years. The popular disaster movie, , released toward the end of , depicted cataclysmic events occurring on this day.
While it is true that December 21, marks the end of a grand cycle in the Long Count calendar, none of the thousands of Maya hieroglyphic texts says a word about disasters, new ages of enlightenment, or the end of time. But that is not to say that the present world age will also last 13 Baktuns. One thing is certain: the Maya regarded the turn of katuns and baktuns as times of renewal and transformation. If the ancient Maya could witness the current crop of doomsayers wringing their hands over the arrival of the 13th Baktun, they would probably be dismayed.
Inevitably, changes were to be ushered in through dedicated action, sacrifice, and joyful celebration. In this section we will present a method of converting a Long Count date to the corresponding Round Calendar date. This means, given a Long Count date, we will locate it in the Round Calendar 18,day cycle by identifying the corresponding Tzolkin and Haab dates. The Long Count date 9. This means that 69 Round Calendar cycles elapsed and the date we seek is the 11, rd kin or day from the starting date of 4 Ahau 8 Cumku in the Round Calendar cycle.
To do this, we divide R by 13 days and by 20 gods :. Since the Tzolkin date for the beginning of the Maya world was 4 Ahau, we add 9 days to 4 days and 3 gods to Ahau, obtaining the Tzolkin date 13 Akbal. Since the Haab date for the beginning of the Maya world was 8 Cumku, we add 3 days to 8 days, obtaining the Haab Calendar date 11 Cumku.
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Example 2 will illustrate this last case. The Convergence article " Maya Cycles of Time ," by Sandra Monteferrante , provides an excellent graphic of the Calendar Round with an iteractive calendar, which we have reproduced in Figure 4. Figure 4: Interactive Calendar Round. Millersville University students in Math regularly use this Java Applet to check the accuracy of the calendar conversions they have done by hand. The Long Count date 8. This plaque, a jade pendant, has the shape of a miniature stela with a human figure in the front and a long count date in the back.
It is possible that the plaque is originally from Tikal. This means that 66 Round Calendar cycles elapsed and the date we seek is the 1, nd kin or day from the starting date of 4 Ahau 8 Cumku in the Round Calendar cycle. To do this we divide R by 13 and by Since the Tzolkin date for the beginning of the Maya world was 4 Ahau, we add 10 days to 4 days, which gives But there are only 13 day numbers in the Tzolkin calendar, so our Tzolkin number is 1.
To see this, we imagine the numbers 1 through 13 on a circle like the numbers 1 through 12 on a clock face. If we begin at 4 and move 10 days forward, we will end at 1. Another way to say this is to say that 14 modulo 13 is 1.
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To find the appropriate god, we advance 12 steps clockwise mod 20 from Ahau around the Tzolkin cycle to the god Eb. Therefore the Tzolkin date is 1 Eb. The day we seek is the th day from the starting date of 8 Cumku in the Haab Calendar cycle. This means exactly 6 day months have passed since 0 Pop.
If we count 6 gods forward from Pop, we find the god Yaxkin. Therefore, the Haab Calendar date is 0 Yaxkin. More sophisticated mathematics students could approach these examples using more formal modular arithmetic notation. They would consider the dates in both the Tzolkin and the Haab calendars as ordered pairs Number, God. December 6, at pm. This article addresses two important points: 1 more extreme and frequent weather events are happening now and will continuing happening until 2 changes we make now begin taking affect in the future. Natural disasters like Hurricane Sandy as Kerri mentioned are happening in faster succession to one another and are causing increasing amounts of damage.
Yet, skeptics continue to deny that our climate is changing. Capturing what makes people alter their behavior without an immediate reward or punishment will be key in getting people to reduce their contribution to global warming and to live a more sustainable lifestyle in the present.
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December 7, at am. This was timely considering Hurricane Sandy just barreled through the east coast. Natural disasters are definitely one issue that we as Americans at least do not devote enough attention—and frankly respect—to. I think that there is a false notion that humans have the ability to engineer our way out of any and every problem. This kind of thinking is not without cause. Look at prosthetics, reconstructive surgery, drought-resistant plants, nutrient-enriched produce, and earthquake-resilient buildings just to name a few. Despite all of our fancy toys, earthquakes still manage to tear down buildings, wildfires run rampant in California, and hurricanes dance through our rendering us powerless.
I know for a fact that right now someone somewhere is considering a way to stop a hurricane by producing a counter acting force to reduce the wind speeds or dry out a hurricane. There is nothing that we can do to stop natural disasters. Of our choices, prevention is definitely the best route. The problem, as you pointed out, is that the necessity of changing our behavior is not obvious until after natural disasters strike. By that time and energy is focused on reconstruction and prevention is left to the wayside.
As a native Floridian I have noticed that it seems like hurricanes are acting with more irregularity and occurring with greater frequency. The cost of preparing for natural disasters and recovery could be a significant burden on future generations that could experience natural weather disasters as a result of climate change. As an individual it may seem daunting to convince a world that seems bent on continuing with business as usual. However, as many students of the environment may know, the one of the best things an individual can do to decrease their energy and carbon footprint is to eat less pork, and gets even better if meat consumption is reduced even further.
Kerri posted a related article on vegetarianism and sustainability in the latest blog update. One day, hopefully, history will view sustainability life choices like these as prudent and vital for the continuation of any business at all in a habitable world. And as an aside, the Mayan Long Count calendar does end on December 21st, but then another begins. The idea of the end of the world at the end of the calendar was not prophesized by the Mayan priests; rather it is a misinterpretation of the end of a cycle by those unfamiliar with Mayan culture, particularly the poetry of dualities revered by their religion.
Mignolo at Duke. December 9, at pm. Our response to global climate change is undoubtedly the issue that will define our generation. If we fail to rise to the challenge, the Mayan prediction of the impending end of the world may indeed come to fruition. The central challenge of confronting global climate change is implicated in its very name; climate change, and its negative effects, is a global issue.
The unilateral actions of any single nation will not significantly nor satisfactorily mitigate sea level rise, temperature changes or any of the other effects that Caroline mentioned. To save the planet, everyone on the planet needs to get on board.
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International negotiations and climate conventions have thus far proven to be very ineffectual. It seems to me that the lack of recognition of climate change as a problem is a serious contributing factor to this impotence. As terrible as natural disaster are, maybe more Mayan level disasters will be the impetus for substantive action on an international level. You must be logged in to post a comment. Lori Bennear Research Group. Search for:. Mayan Apocalypse? Next post Have a Beer, Support Sustainability. Kerri Devine December 6, at am.
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