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More about the Mayan calendar and the 2012 “End of Time”

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More about the Mayan calendar and the 2012 “End of Time” —a footnote to Astronomical Calendar 2010

Guy Ottewell

The Long Count by which the Maya measured history is justly famous, and I didn’t say enough about it. Being out of touch with popular culture, and behind in reading the magazines, I wasn’t aware of the cosmic fears developing about the year 2012. That I had just traveled in Mayaland and thought of writing about the calendar was a lucky coincidence that should have been crowned with a good laugh at the absurdity of these fears, but I didn’t realize it. Then there was a smaller error to which I have to admit, and which you may well think undermines any authority in what I say about the Maya calendars. I did put two days of thinking-time into understanding the mathematics (at which my brain is neither apt nor trained) but this was early in 2009 and was not quite enough. Fortunately only a few of the figures in two columns of my table of Maya dates for January 2010 have to be changed. The book from which I learned is Calendrical Calculations (Cambridge University Press, 1997) by Nachum Dershowitz and Edward M. Reingold, both of the Department of Computer Science, University of Illinois at Urbana-Champaign. They pointed out that the days of the Haab months were numbered from 0, not 1. Strangely, they had not mentioned that this is true also of the Long Count units. Though there are 20 kin in a winal, each 20th is numbered not 20 but 0; similarly, though there are 18 winal in a tun, each 18th is numbered not 18 but 0. (And likewise for the larger units tun, katun, and baktun.) So here is the table corrected (and improved in a few other ways). The corrections are that our Jan. 6 and 26 are kin 0, not 20; and Jan. 6 to 25 constitute a winal 0, not 18.

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Scaliger (JD) 2455197.5 2455198.5 2455199.5 2455200.5 2455201.5 2455202.5 2455203.5 2455204.5 2455205.5 2455206.5 2455207.5 2455208.5 2455209.5 2455210.5 2455211.5 2455212.5 2455213.5 2455214.5 2455215.5 2455216.5 2455217.5 2455218.5 2455219.5 2455220.5 2455221.5 2455222.5 2455223.5 2455224.5 2455225.5 2455226.5 2455227.5 CE______________________ Maya Long Count________ Maya Haab___ Maya Tzolkin__ Julian_____ Gregorian__ total ba ka tu wi ki month____day num name______ 2009 Dec 19 2010 Jan 1 1870915 12 19 16 17 15 14=Kankin 13 11 15=Men 2009 Dec 20 2010 Jan 2 1870916 12 19 16 17 16 14=Kankin 14 12 16=Kib 2009 Dec 21 2010 Jan 3 1870917 12 19 16 17 17 14=Kankin 15 13 17=Kaban 2009 Dec 22 2010 Jan 4 1870918 12 19 16 17 18 14=Kankin 16 1 18=Etznab 2009 Dec 23 2010 Jan 5 1870919 12 19 16 17 19 14=Kankin 17 2 19=Kauak 2009 Dec 24 2010 Jan 6 1870920 12 19 17 0 0 14=Kankin 18 3 20=Ahau 2009 Dec 25 2010 Jan 7 1870921 12 19 17 0 1 14=Kankin 19 4 1=Imix 2009 Dec 26 2010 Jan 8 1870922 12 19 17 0 2 15=Muwan 0 5 2=Ik 2009 Dec 27 2010 Jan 9 1870923 12 19 17 0 3 15=Muwan 1 6 3=Akbal 2009 Dec 28 2010 Jan 10 1870924 12 19 17 0 4 15=Muwan 2 7 4=Kan 2009 Dec 29 2010 Jan 11 1870925 12 19 17 0 5 15=Muwan 3 8 5=Chikchan 2009 Dec 30 2010 Jan 12 1870926 12 19 17 0 6 15=Muwan 4 9 6=Kimi 2009 Dec 31 2010 Jan 13 1870927 12 19 17 0 7 15=Muwan 5 10 7=Manik 2010 Jan 1 2010 Jan 14 1870928 12 19 17 0 8 15=Muwan 6 11 8=Lamat 2010 Jan 2 2010 Jan 15 1870929 12 19 17 0 9 15=Muwan 7 12 9=Muluk 2010 Jan 3 2010 Jan 16 1870930 12 19 17 0 10 15=Muwan 8 13 10=Ok 2010 Jan 4 2010 Jan 17 1870931 12 19 17 0 11 15=Muwan 9 1 11=Chuwen 2010 Jan 5 2010 Jan 18 1870932 12 19 17 0 12 15=Muwan 10 2 12=Eb 2010 Jan 6 2010 Jan 19 1870933 12 19 17 0 13 15=Muwan 11 3 13=Ben 2010 Jan 7 2010 Jan 20 1870934 12 19 17 0 14 15=Muwan 12 4 14=Ix 2010 Jan 8 2010 Jan 21 1870935 12 19 17 0 15 15=Muwan 13 5 15=Men 2010 Jan 9 2010 Jan 22 1870936 12 19 17 0 16 15=Muwan 14 6 16=Kib 2010 Jan 10 2010 Jan 23 1870937 12 19 17 0 17 15=Muwan 15 7 17=Kaban 2010 Jan 11 2010 Jan 24 1870938 12 19 17 0 18 15=Muwan 16 8 18=Etznab 2010 Jan 12 2010 Jan 25 1870939 12 19 17 0 19 15=Muwan 17 9 19=Kauak 2010 Jan 13 2010 Jan 26 1870940 12 19 17 1 0 15=Muwan 18 10 20=Ahau 2010 Jan 14 2010 Jan 27 1870941 12 19 17 1 1 15=Muwan 19 11 1=Imix 2010 Jan 15 2010 Jan 28 1870942 12 19 17 1 2 16=Pax 0 12 2=Ik 2010 Jan 16 2010 Jan 29 1870943 12 19 17 1 3 16=Pax 1 13 3=Akbal 2010 Jan 17 2010 Jan 30 1870944 12 19 17 1 4 16=Pax 2 1 4=Kan 2010 Jan 18 2010 Jan 31 1870945 12 19 17 1 5 16=Pax 3 2 5=Chikchan

Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun

These must be accurate at least in the sense of coinciding with Dershowitz and Reingold, since I have checked my programming with all 33 of the dates (from 587 BC to 2094 AD) used as samples in the appendix of their book. Here is the beginning of the Long Count, in 3114 BC (written mathematically as —3113):

Scaliger CE______________________ Maya Long Count________ Maya Haab___ Maya Tzolkin__ (JD) Julian_____ Gregorian__ total ba ka tu wi ki month____day num name______ 584282.5 Mon -3113 Sep 6 -3113 Aug 11 0 0 0 0 0 0 18=Kunku 8 4 20=Ahau 584283.5 Tue -3113 Sep 7 -3113 Aug 12 1 0 0 0 0 1 18=Kunku 9 5 1=Imix

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And here is a table for the future month about which there is so much excitement, December 2012:
Scaliger (JD) 2456262.5 2456263.5 2456264.5 2456265.5 2456266.5 2456267.5 2456268.5 2456269.5 2456270.5 2456271.5 2456272.5 2456273.5 2456274.5 2456275.5 2456276.5 2456277.5 2456278.5 2456279.5 2456280.5 2456281.5 2456282.5 2456283.5 2456284.5 2456285.5 2456286.5 2456287.5 2456288.5 2456289.5 2456290.5 2456291.5 2456292.5 CE______________________ Maya Long Count________ Julian_____ Gregorian__ total ba ka tu wi ki 2012 Nov 18 2012 Dec 1 1871980 12 19 19 17 0 2012 Nov 19 2012 Dec 2 1871981 12 19 19 17 1 2012 Nov 20 2012 Dec 3 1871982 12 19 19 17 2 2012 Nov 21 2012 Dec 4 1871983 12 19 19 17 3 2012 Nov 22 2012 Dec 5 1871984 12 19 19 17 4 2012 Nov 23 2012 Dec 6 1871985 12 19 19 17 5 2012 Nov 24 2012 Dec 7 1871986 12 19 19 17 6 2012 Nov 25 2012 Dec 8 1871987 12 19 19 17 7 2012 Nov 26 2012 Dec 9 1871988 12 19 19 17 8 2012 Nov 27 2012 Dec 10 1871989 12 19 19 17 9 2012 Nov 28 2012 Dec 11 1871990 12 19 19 17 10 2012 Nov 29 2012 Dec 12 1871991 12 19 19 17 11 2012 Nov 30 2012 Dec 13 1871992 12 19 19 17 12 2012 Dec 1 2012 Dec 14 1871993 12 19 19 17 13 2012 Dec 2 2012 Dec 15 1871994 12 19 19 17 14 2012 Dec 3 2012 Dec 16 1871995 12 19 19 17 15 2012 Dec 4 2012 Dec 17 1871996 12 19 19 17 16 2012 Dec 5 2012 Dec 18 1871997 12 19 19 17 17 2012 Dec 6 2012 Dec 19 1871998 12 19 19 17 18 2012 Dec 7 2012 Dec 20 1871999 12 19 19 17 19 2012 Dec 8 2012 Dec 21 1872000 13 0 0 0 0 2012 Dec 9 2012 Dec 22 1872001 13 0 0 0 1 2012 Dec 10 2012 Dec 23 1872002 13 0 0 0 2 2012 Dec 11 2012 Dec 24 1872003 13 0 0 0 3 2012 Dec 12 2012 Dec 25 1872004 13 0 0 0 4 2012 Dec 13 2012 Dec 26 1872005 13 0 0 0 5 2012 Dec 14 2012 Dec 27 1872006 13 0 0 0 6 2012 Dec 15 2012 Dec 28 1872007 13 0 0 0 7 2012 Dec 16 2012 Dec 29 1872008 13 0 0 0 8 2012 Dec 17 2012 Dec 30 1872009 13 0 0 0 9 2012 Dec 18 2012 Dec 31 1872010 13 0 0 0 10 Maya Haab___ Maya Tzolkin__ month____day num name______ 13=Mac 3 10 20=Ahau 13=Mac 4 11 1=Imix 13=Mac 5 12 2=Ik 13=Mac 6 13 3=Akbal 13=Mac 7 1 4=Kan 13=Mac 8 2 5=Chikchan 13=Mac 9 3 6=Kimi 13=Mac 10 4 7=Manik 13=Mac 11 5 8=Lamat 13=Mac 12 6 9=Muluk 13=Mac 13 7 10=Ok 13=Mac 14 8 11=Chuwen 13=Mac 15 9 12=Eb 13=Mac 16 10 13=Ben 13=Mac 17 11 14=Ix 13=Mac 18 12 15=Men 13=Mac 19 13 16=Kib 14=Kankin 0 1 17=Kaban 14=Kankin 1 2 18=Etznab 14=Kankin 2 3 19=Kauak 14=Kankin 3 4 20=Ahau 14=Kankin 4 5 1=Imix 14=Kankin 5 6 2=Ik 14=Kankin 6 7 3=Akbal 14=Kankin 7 8 4=Kan 14=Kankin 8 9 5=Chikchan 14=Kankin 9 10 6=Kimi 14=Kankin 10 11 7=Manik 14=Kankin 11 12 8=Lamat 14=Kankin 12 13 9=Muluk 14=Kankin 13 1 10=Ok

Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon

Between Dec. 20 and 21 of our calendar, the Long Count rolls into “a string of zeros, like the odometer turning over on your car,” as E.C. Krupp puts it in his amusing article about “The Great 2012 Scare,” for the November 2009 issue of Sky & Telescope. This is the end of one baktun and the beginning of another; so its component katuns, tuns, winals and kins all start again at 0. According to Dershowitz and Reingold, who number the first baktun as 0, the baktun now ending is 12; according to others it is 13. Either way, it is the 13th since the start-date of the Long Count. What the 2012 Scaremongers are claiming is: —The end of this 13th 144,000-day baktun is the end of the Mayan calendar, or of a huge cycle in it. — “Thirteen was a sacred number for the Maya.” —Also on 2012 Dec. 21 the sun comes to its winter solstice point; and, in 2012, that point will be “aligned with,” indeed will “eclipse,” the center of our Milky Way galaxy. —And, for good measure, the planets will on that date be “lined up.”

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—All this will cause our planet to be devastated, or possibly renewed. (By any or all of many imaginable drastic mechanisms: f lood, earthquake, cosmic impact, nuclear war, electromagnetic fields, spiritual energy?) —The Maya foresaw this, and that’s why, inventing their calendar sometime after 200 AD, they set the starting-date for their Long Count where they did in 3114 BC. Apparently they knew that time would reach an “end” exactly 1,872,000 days after that date. —And, to quote one of the commentators: “ . . . humanity is creating its own ecological disasters and desperately needs ancient indigenous wisdom.” Well . . . The most obvious f law is that the end of the 13th baktun is no more significant than the end of the 12th (on 1618 Sep. 17) or the 14th. The next larger cycle, called a piktun, is composed not of 13 but of 20 baktun. The Maya did apparently believe that the world is destroyed and remade at the turn of each piktun. (Our present world, then, would date from 3114 BC.) But there will be 7 more baktun—7 times 144,000 days, or about 2,760 years—till the end of the current piktun. There may be a more plausible scare in our year 4772:
Scaliger (JD) 3464281.5 Thu 3464282.5 Fri 3464283.5 Sat CE______________________ Maya Long Count________ Maya Haab___ Maya Tzolkin__ Julian_____ Gregorian__ total ba ka tu wi ki month____day num name______ 4772 Sep 8 4772 Oct 12 2879999 19 19 19 17 19 7=Yaxkin 12 9 19=Kauak 4772 Sep 9 4772 Oct 13 2880000 0 0 0 0 0 7=Yaxkin 13 10 20=Ahau 4772 Sep 10 4772 Oct 14 2880001 0 0 0 0 1 7=Yaxkin 14 11 1=Imix

As to whether the number 13 was “sacred”: in Maya arithmetic and certainly in the calendar systems the dominant number is 20. In the Long Count all the factors are 20 or 18; in the Haab calendar, also 20 and 18; in the Tzolkin, 20 and 13. What about the December solstice? It is the moment when the earth’s north pole is tilted most away from the sun (giving midwinter for our northern hemisphere, midsummer for the southern). The sun appears to travel along the ecliptic, a great circle that has to cross every other great circle at two points, and one of these great circles is the galactic equator, or midline of the Milky Way. In 2012 the instant of the solstice is Dec. 21 11h11m Universal Time. The solstice point, like all points on the ecliptic, moves slowly westward (rightward), by about 1/72 of a degree per year, because of precession. The claim is that in 2012 it will have arrived at the exact point where the ecliptic crosses the galactic equator. This will last have happened 25,800 years ago (the length of the precessional cycle). This might be true (more probably not: I figure the solstice point actually passed across the galactic equator in 1998). But it would be true in the same sense as being in the precise center of a river, or of a hank of cotton wool. The galactic equator is the midline of the Milky Way as seen from earth. The Milky Way’s edges fade outward like those of a cloud of steam, a very irregular one. (The midline is partly traced, also very irregularly, by dark dust-clouds.) The galactic equator is defined by conM
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vention, and has been defined in at least two ways (the “old” or “Ohlson” and the “new” or “IAU”). It is not entirely arbitrary, because the position of the radio source at the galaxy’s center is known. The equator represents roughly the “plane” of the galaxy as we look out through its vast disk of stars. But the sun is thought to lie now about 26 light years north of the physical midplane; so it is a plane in which we do not ourselves lie. And the point where the ecliptic crosses the galactic equator is not the same as “the center of the galaxy.” That is about 6.6° southwest along the galactic equator. So the half-degree-wide sun is never in the same direction as—can never “eclipse”—that center. (It is a degree or so nearer a couple of days earlier.) And what possible effect could there be on a planet at that moment just because its north pole is tipped in a certain direction away from its star? The center of the galaxy is about 28,000 light years away—nearly 2 million times as far from us as the sun. Imagine two specks of soil in your yard, an inch apart, going into special convulsions because of the inf luence of a stone 28 miles away, when there are billions of other bits of soil in between. And will the planets be “aligned” in December 2012? No, they will be scattered in pretty random directions.

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Solar-system diagram like those in the Astronomical Calendar. Lines point to the positions of the outer planets, which are at far greater distances.

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As for “ancient indigenous wisdom”: it appears that the Maya of more than a thousand years ago were remarkably clever but not outstandingly wise. Maya civilization collapsed from about 900 AD onward because of ecological foolishness, war, and a luxurious and cruel ruling elite. If they didn’t see that coming, they are unlikely to have made reliable predictions about the world of centuries later.

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