Uxmal, Yucatan On a stormy afternoon, kilometers north of Palenque, I began to climb the steps of yet another pyramid. It was a steep building, oval rather than square in plan, feet long at the base and feet wide. It was, moreover, very high, rising feet above the surrounding plain. These names were derived from a Maya legend which asserted that a dwarf with supernatural powers had raised the entire building in just one night.

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Uxmal, Yucatan On a stormy afternoon, kilometers north of Palenque, I began to climb the steps of yet another pyramid. It was a steep building, oval rather than square in plan, feet long at the base and feet wide. It was, moreover, very high, rising feet above the surrounding plain. These names were derived from a Maya legend which asserted that a dwarf with supernatural powers had raised the entire building in just one night.

My instinct was to lean forward, flatten myself against the side of the pyramid, and cling on for dear life. Instead I looked up at the angry, overcast sky above me. Flocks of birds circled, screeching wildly as though seeking refuge from some impending disaster, and the thick mass of low-lying cloud that had blotted out the sun a few hours earlier was now so agitated by high winds that it seemed to boil.

The Pyramid of the Magician was by no means unique in being associated with the supernatural powers of dwarves, whose architectural and masonry skills were widely renowned in Central America. What was I to make of this? Could it be relevant that memories of almost identical miracles were preserved in Ancient Egypt?

Maya History and Religion, p. It consisted of a single corbel-vaulted chamber from the ceiling of which large numbers of bats hung suspended. Like the birds and the clouds, they were visibly distressed by the sense of a huge storm brewing. In a furry mass they shuffled restlessly upside down, folding and unfolding their small leathery wings. I took a rest on the high platform that surrounded the chamber.

From here, looking down, I could see many more crosses. They were everywhere, literally all over this bizarre and ancient structure. I remembered the Andean city of Tiahuanaco and the crosses that had been carved there, in distant pre-Colombian times, on some of the great blocks of stone lying scattered around the building known as Puma Punku.

II, p. And now, here at the Pyramid of the Magician in the Mayan site of Uxmal, I was confronted by crosses yet again. Bearded men How likely was it to be an accident that symbols as distinctive as these should repeat themselves in widely separated cultures and at different periods of history? Why were they so often built into the fabric of sophisticated works of art and architecture? A science of prophecy Not for the first time I suspected that I might be looking at signs and icons left behind by some cult or secret society which had sought to keep the light of civilization burning in Central America and perhaps elsewhere through long ages of darkness.

I thought it notable that the motifs of the bearded man, the Plumed Serpent, and the cross all tended to crop up whenever and wherever there were hints that a technologically advanced and as yet unidentified civilization might once have been in contact with the native cultures. And there was a sense of great age about this contact, as though it took place at such an early date that it had been almost forgotten.

I thought again about the sudden way the Olmecs had emerged, around the middle of the second millennium BC, out of the swirling mists of opaque prehistory. All the archaeological evidence indicated that from the beginning they had venerated huge stone heads and stele showing bearded men. I found myself increasingly drawn to the possibility that some of those remarkable pieces of sculpture could have been part of a vast inheritance of civilization handed down to the peoples of Central America many thousands of years before the second millennium BC, and thereafter entrusted to the safekeeping of a secret wisdom cult, perhaps the cult of Quetzalcoatl.

Much had been lost. Nevertheless the tribes of this region—in particular the Maya, the builders of Palenque and Uxmal—had preserved something even more mysterious and wonderful than the enigmatic monoliths, something which declared itself even more persistently to be the legacy of an older and a higher civilization. We see in the next chapter that it was the mystical science of an ancient star-gazing folk, a science of time and measurement and prediction—a science of prophecy even—that the Maya had preserved most perfectly from the past.

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. Must they also be gods? 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. 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 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 Popol Vuh is much more informative. 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. See also The Magic and Mysteries of Mexico, p. Knowledge out of place In J. Perhaps the answer to these questions is much simpler than Thompson realized.

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 and is based on the best scientific knowledge then available: the famous Gregorian calendar. Thanks to scientific advances since we now know that the exact length of the solar year is The Gregorian calendar therefore incorporates a very small plus error, just 0.

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 Their estimate of this period was They possessed an advanced technique of metrical calculation by means of a chequerboard device we ourselves have only discovered or rediscovered? 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. 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. 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.

Venus revolves around the sun every 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 days was only an approximation and that the movements of Venus are by no means regular.

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 years.

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. Or did they inherit, in good working order, a calendar engineered to fit the needs of a much earlier and far more advanced civilization? 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. As we have seen, it was also believed that the cycle will come to an end, amid global destruction, on 4 Ahau 3 Kankin: 23 December AD 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 years allotted to our present creation. Every last penny of that debt is going to be called in when the figure on the meter reads 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 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. There were also tun periods pictun and ,tun periods calabtun to mop up even larger calculations. 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 undauntedly retrod that road seeking its starting point. A fresh view, leading further backward, unfolded at every stage; the mellowed centuries blended into millennia, and they into tens of thousands of years, as those tireless inquirers explored deeper and still deeper into the eternity of the past.

On a stela at Quiriga in Guatemala a date over 90 million years ago is computed; on another a date over million years before that is given. These are actual computations, stating correctly day and month positions, and are comparable to calculations in our calendar giving the month positions on which Easter would have fallen at equivalent distances in the past.

The brain reels at such astronomical figures But there was precious little else that these jungle-dwelling Indians did which suggested they might have had the capacity or the need to conceive of really long periods of time. So how come the Maya got handy with big periods like hundreds of millions of years? Was it a freak of cultural development?

Or did they inherit the calendrical and mathematical tools which facilitated, and enabled them to develop, this sophisticated understanding? What had they designed it for? We have seen that the obsessive concern of Mayan society, and indeed of all the ancient cultures of Central America, was with calculating—and if possible postponing—the end of the world. Could this be the purpose the mysterious calendar was designed to fulfill? Could it have been a mechanism for predicting some terrible cosmic or geological catastrophe?


Egyptian Estimates of the Size and Shape of the Earth

Good values were obtained by employing round figures expressed in atur. This was important because the surface and the volume of the earth, being huge quantities, were calculated in square and cubic atur, starting from the length of the average radius. Geodesic Surveys. Since the shape of the earth is irregular, today we try to express its dimensions by constructing an ellipsoid, called ellipsoid of reference, which fits as closely as possible the actual contour of the earth, called the geoid in scientific language.


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