Maya had preserved most perfectly from the past. With it they inherited
memories of a terrible, earth-destroying flood and an idiosyncratic legacy
of empirical knowledge, knowledge of a high order which they shouldn’t
really have possessed, knowledge that we have only reacquired very
recently ...
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Chapter 21
A Computer for Calculating the End of the World
The Maya knew where their advanced learning originated. It was handed
down to them, they said, from the First Men, the creatures of
Quetzalcoatl, whose names had been Balam-Quitze (Jaguar with the Sweet
Smile), Balam-Acab (Jaguar of the Night), Mahucutah (The Distinguished
Name) and Iqui-Balam (Jaguar of the Moon).1 According to the Popol Vuh,
these forefathers:
were endowed with intelligence; they saw and instantly they could see far; they
succeeded in seeing; they succeeded in knowing all that there is in the world. The
things hidden in the distance they saw without first having to move ... Great was
their wisdom; their sight reached to the forests, the rocks, the lakes, the seas, the
mountains, and the valleys. In truth, they were admirable men ... They were able
to know all, and they examined the four corners, the four points of the arch of the
sky, and the round face of the earth.2
The achievements of this race aroused the envy of several of the most
powerful deities. ‘It is not well that our creatures should know all,’ opined
these gods, ‘Must they perchance be the equals of ourselves, their
Makers, who can see afar, who know all and see all? ... Must they also be
gods?’3
Obviously such a state of affairs could not be allowed to continue. After
some deliberation an order was given and appropriate action taken:
Let their sight reach only to that which is near; let them see only a little of the face
of the earth ... Then the Heart of Heaven blew mist into their eyes which clouded
their sight as when a mirror is breathed upon. Their eyes were covered and they
could only see what was close, only that was clear to them ... In this way the
wisdom and all the knowledge of the First Men were destroyed.4
Anyone familiar with the Old Testament will remember that the reason for
the expulsion of Adam and Eve from the Garden of Eden had to do with
similar divine concerns. After the First Man had eaten of the fruit of the
tree of the knowledge of good and evil,
The Lord God said, ‘Behold, the man has become as one of us, to know good and
evil. Now, lest he put forth his hand and take also of the tree of life and eat and
live for ever, [let us] send him forth from the Garden of Eden ...’5
The Popol Vuh is accepted by scholars as a great reservoir of
1 Popol Vuh, p. 167.
2 Ibid., pp. 168-9.
3 Ibid., p. 169.
4 Ibid.
5 Genesis, 4:22-4
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uncontaminated, pre-Colombian tradition.6 It is therefore puzzling to find
such similarities between these traditions and those recorded in the
Genesis story. Moreover, like so many of the other Old World/New World
links we have identified, the character of the similarities is not suggestive
of any kind of direct influence of one region on the other but of two
different interpretations of the same set of events. Thus, for example:
• The biblical Garden of Eden looks like a metaphor for the state of
blissful, almost ‘godlike’, knowledge that the ‘First Men’ of the Popol
Vuh enjoyed.
• The essence of this knowledge was the ability to ‘see all’ and to ‘know
all’. Was this not precisely the ability Adam and Eve acquired after
eating the forbidden fruit, which grew on the branches of the tree of
the knowledge of good and evil’?
• Finally, just as Adam and Eve were driven out of the Garden, so were
the four First Men of the Popol Vuh deprived of their ability to ‘see far’.
Thereafter ‘their eyes were covered and they could only see what was
close ...’
Both the Popol Vuh and Genesis therefore tell the story of mankind’s fall
from grace. In both cases, this state of grace was closely associated with
knowledge, and the reader is left in no doubt that the knowledge in
question was so remarkable that it conferred godlike powers on those
who possessed it.
The Bible, adopting a dark and muttering tone of voice, calls it ‘the
knowledge of good and evil’ and has nothing further to add. The Popol
Vuh is much more informative. It tells us that the knowledge of the First
Men consisted of the ability to see ‘things hidden in the distance’, that
they were astronomers who ‘examined the four corners, the four points
of the arch of the sky’, and that they were geographers who succeeded in
measuring ‘the round face of the earth’.7
Geography is about maps. In Part I we saw evidence suggesting that the
cartographers of an as yet unidentified civilization might have mapped
the planet with great thoroughness at an early date. Could the Popol Vuh
be transmitting some garbled memory of that same civilization when it
speaks nostalgically of the First Men and of the miraculous geographical
knowledge they possessed?
Geography is about maps, and astronomy is about stars. Very often the
two disciplines go hand in hand because stars are essential for navigation
on long sea-going voyages of discovery (and long sea-going voyages of
discovery are essential for the production of accurate maps).
Is it accidental that the First Men of the Popol Vuh were remembered
not only for studying ‘the round face of the earth’ but for their
contemplation of ‘the arch of heaven’?8 And is it a coincidence that the
6 Popol Vuh, Introduction, p. 16. See also The Magic and Mysteries of Mexico, p. 250ff.
7 Popol Vuh, pp. 168-9.
8 Ibid.
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outstanding achievement of Mayan society was its observational
astronomy, upon which, through the medium of advanced mathematical
calculations, was based a clever, complex, sophisticated and very
accurate calendar?
Knowledge out of place
In 1954 J. Eric Thompson, a leading authority on the archaeology of
Central America, confessed to a deep sense of puzzlement at a number
of glaring disparities he had identified between the generally
unremarkable achievements of the Mayas, as a whole and the advanced
state of their astro-calendrical knowledge, ‘What mental quirks,’ he
asked, ‘led the Maya intelligentsia to chart the heavens, yet fail to grasp
the principle of the wheel; to visualize eternity, as no other semi-civilized
people has ever done, yet ignore the short step from corbelled to true
arch; to count in millions, yet never to learn to weigh a sack of corn?’9
Perhaps the answer to these questions is much simpler than Thompson
realized. Perhaps the astronomy, the deep understanding of time, and the
long-term mathematical calculations, were not ‘quirks’ at all. Perhaps
/> they were the constituent parts of a coherent but very specific body of
knowledge that the Maya had inherited, more or less intact, from an older
and wiser civilization. Such an inheritance would explain the
contradictions observed by Thompson, and there is no need for any
dispute on the point. We already know that the Maya received their
calendar as a legacy from the Olmecs (a thousand years earlier, the
Olmecs were using exactly the same system). The real question, should
be, where did the Olmecs get it? What kind of level of technological and
scientific development was required for a civilization to devise a calendar
as good as this?
Take the case of the solar year. In modern Western society we still make
use of a solar calendar which was introduced in Europe in 1582 and is
based on the best scientific knowledge then available: the famous
Gregorian calendar. The Julian calendar, which it replaced, computed the
period of the earth’s orbit around the sun at 365.25 days. Pope Gregory
XIII’s reform substituted a finer and more accurate calculation: 365.2425
days. Thanks to scientific advances since 1582 we now know that the
exact length of the solar year is 365.2422 days. The Gregorian calendar
therefore incorporates a very small plus error, just 0.0003 of a day—
pretty impressive accuracy for the sixteenth century.
Strangely enough, though its origins are wrapped in the mists of
antiquity far deeper than the sixteenth century, the Mayan calendar
achieved even greater accuracy. It calculated the solar year at 365.2420
9 J. Eric Thompson, The Rise and Fall of Maya Civilization, Pimlico, London, 1993, p. 13.
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days, a minus error of only 0.0002 of a day.10
Similarly, the Maya knew the time taken by the moon to orbit the earth.
Their estimate of this period was 29.528395 days—extremely close to the
true figure of 29.530588 days computed by the finest modern methods.11
The Mayan priests also had in their possession very accurate tables for
the prediction of solar and lunar eclipses and were aware that these could
occur only within plus or minus eighteen days of the node (when the
moon’s path crosses the apparent path of the sun).12 Finally, the Maya
were remarkably accomplished mathematicians. They possessed an
advanced technique of metrical calculation by means of a chequerboard
device we ourselves have only discovered (or rediscovered?) in the last
century.13 They also understood perfectly and used the abstract concept
of zero14 and were acquainted with place numerations.
These are esoteric fields. As Thompson observed,
The cipher (nought) and place numerations are so much parts of our cultural
heritage and seem such obvious conveniences that it is difficult to comprehend
how their invention could have been long delayed. Yet neither ancient Greece with
its great mathematicians, nor ancient Rome, had any inkling of either nought or
place numeration. To write 1848 in Roman numerals requires eleven letters:
MDCCCXLVIII. Yet the Maya had a system of place-value notation very much like
our own at a time when the Romans were still using their clumsy method.15
Isn’t it a bit odd that this otherwise unremarkable Central American tribe
should, at such an early date, have stumbled upon an innovation which
Otto Neugebauer, the historian of science, has described as ‘one of the
most fertile inventions of humanity’.16
Someone else’s science?
Let us now consider the question of Venus, a planet that was of immense
symbolic importance to all the ancient peoples of Central America, who
identified it strongly with Quetzalcoatl (or Gucumatz or Kukulkan, as the
Plumed Serpent was known in the Maya dialects).17
Unlike the Ancient Greeks, but like the Ancient Egyptians, the Maya
understood that Venus was both ‘the morning star’ and ‘the evening
10 William Gates’s notes (p. 81) to Diego de Landa’s Yucatan before and after the
Conquest.
11 This is evident from the Dresden Codex. See, for example, An Introduction to the
Study of Maya Hieroglyphs, p. 32.
12 The Maya, p. 176; Mysteries of the Mexican Pyramids, p. 291; The Rise and Fall of
Maya Civilization, p. 173.
13 Mysteries of the Mexican Pyramids, p. 287.
14 The Maya, p. 173.
15 The Rise and Fall of Maya Civilization, pp. 178-9.
16 Cited in The Maya, p. 173.
17 World Mythology, p. 241.
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star’.18 They understood other things about it as well. The ‘synodical
revolution’ of a planet is the period of time it takes to return to any given
point in the sky—as viewed from earth. Venus revolves around the sun
every 224.7 days, while the earth follows its own slightly wider orbit. The
composite result of these two motions is that Venus rises in exactly the
same place in the earth’s sky approximately every 584 days.
Whoever invented the sophisticated calendrical system inherited by the
Maya had been aware of this and had found ingenious ways to integrate it
with other interlocking cycles. Moreover, it is clear from the mathematics
which brought these cycles together that the ancient calendar masters
had understood that 584 days was only an approximation and that the
movements of Venus are by no means regular. They had therefore
worked out the exact figure established by today’s science for the
average synodical revolution of Venus over very long periods of time.19
That figure is 583.92 days and it was knitted into the fabric of the Mayan
calendar in numerous intricate and complex ways.20 For example, to
reconcile it with the so-called ‘sacred year’ (the tzolkin of 260 days, which
was divided into 13 months of 20 days each) the calendar called for a
correction of four days to be made every 61 Venus years. In addition,
during every fifth cycle, a correction of eight days was made at the end of
the 57th revolution. Once these steps were taken, the tzolkin and the
synodical revolution of Venus were intermeshed so tightly that the degree
of error to which the equation was subject was staggeringly small—one
day in 6000 years.21 And what made this all the more remarkable was that
a further series of precisely calculated adjustments kept the Venus cycle
and the tzolkin not only in harmony with each other but in exact
relationship with the solar year. Again this was achieved in a manner
which ensured that the calendar was capable of doing its job, virtually
error-free, over vast expanses of time.22
Why did the ‘semi-civilized’ Maya need this kind of high-tech precision?
Or did they inherit, in good working order, a calendar engineered to fit
the needs of a much earlier and far more advanced civilization?
Consider the crowning jewel of Maya calendrics, the so-called ‘Long
Count’. This system of calculating dates also expressed beliefs about the
past—notably, the widely held belief that time operated in Great Cycles
which witnessed recurrent creations and destructions of the world.
According to the Maya, the current Great Cycle began in darkness on 4
Ahau 8 Cumku, a date corresponding to 13 August 3114 BC in our own
calendar.23 As we have seen, it was also believed that the cycle will come
18 The Maya, p. 176.
19 The Rise and Fall of Maya Civilization, p. 170; Mysteries of the Mexican Pyramids, p.
290.
20 The Rise and Fall of Maya Civilization, p. 170.
21 Ibid., 170-1.
22 Ibid., 169.
23 Breaking The Maya Code, p. 275.
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to an end, amid global destruction, on 4 Ahau 3 Kankin: 23 December AD
2012 in our calendar. The function of the Long Count was to record the
elapse of time since the beginning of the current Great Cycle, literally to
count off, one by one, the 5125 years allotted to our present creation.24
The Long Count is perhaps best envisaged as a sort of celestial adding
machine, constantly calculating and recalculating the scale of our
growing debt to the universe. Every last penny of that debt is going to be
called in when the figure on the meter reads 5125.
So, at any rate, thought the Maya.
Calculations on the Long Count computer were not, of course, done in
our numbers. The Maya used their own notation, which they had derived
from the Olmecs, who had derived it from ... nobody knows. This
notation was a combination of dots (signifying ones or units or multiples
of twenty), bars (signifying fives or multiples of five times twenty), and a
shell glyph signifying zero. Spans of time were counted by days ( kin),
periods of twenty days ( uinat), ‘computing years’ of 360 days ( tun),
periods of 20 tuns (known as katun), and periods of 20 katuns (known as
bactun). There were also 8000- tun periods ( pictun) and 160,000- tun
periods ( calabtun) to mop up even larger calculations.25
All this should make clear that although the Maya believed themselves
to be living in one Great Cycle that would surely come to a violent end
they also knew that time was infinite and that it proceeded with its
mysterious revolutions regardless of individual lives or civilizations. As
Thompson summed up in his great study on the subject:
In the Maya scheme the road over which time had marched stretched into a past
so distant that the mind of man cannot comprehend its remoteness. Yet the Maya