Chapter 23
Some archaeological discoveries are heralded with much fanfare; others, for various reasons, are not. Among this latter category must be included the thick and extensive layer of sheet mica found sandwiched between two of the upper levels of the Teotihuacan Pyramid of the Sun when it was being probed for restoration in 1906. The lack of interest which greeted this discovery, and the absence of any follow-up studies to determine its possible function is quite understandable because the mica, which had a considerable commercial value, was removed and sold as soon as it had been excavated. The culprit was apparently Leopoldo Bartres, who had been commissioned to restore the time-worn pyramid by the Mexican government.1
There has also been a much more recent discovery of mica at Teotihuacan (in the ‘Mica Temple’) and this too has passed almost without notice. Here the reason is harder to explain because there has been no looting and the mica remains on site.2
One of a group of buildings, the Mica Temple is situated around a patio about 1000 feet south of the west face of the Pyramid of the Sun. Directly under a floor paved with heavy rock slabs, archaeologists financed by the Viking Foundation excavated two massive sheets of mica which had been carefully and purposively installed at some extremely remote date by a people who must have been skilled in cutting and handling this material. The sheets are ninety feet square and form two layers, one laid directly on top of the other.3
Mica is a not a uniform substance but contains trace elements of different metals depending on the kind of rock formation in which it is found. Typically these metals include potassium and aluminium and also, in varying quantities, ferrous and ferric iron, magnesium, lithium, manganese and titanium. The trace elements in Teotihuacan’s Mica Temple indicate that the underfloor sheets belong to a type which occurs only in Brazil, some 2000 miles away.4 Clearly, therefore, the builders of the Temple must have had a specific need for this particular kind of mica and were prepared to go to considerable lengths to obtain it, otherwise they could have used the locally available variety more cheaply and simply.
Mica does not leap to mind as an obvious general-purpose flooring material. Its use to form layers underneath a floor, and thus completely out of sight, seems especially bizarre when we remember that no other ancient structure in the Americas, or anywhere else in the world, has been found to contain a feature like this.5
It is frustrating that we will never be able to establish the exact position, let alone the purpose, of the large sheet that Bartres excavated and removed from the Pyramid of the Sun in 1906. The two intact layers in the Mica Temple, on the other hand, resting as they do in a place where they had no decorative function, look as though they were designed to do a particular job. Let us note in passing that mica possesses characteristics which suit it especially well for a range of technological applications. In modern industry, it is used in the construction of capacitors and is valued as a thermal and electric insulator. It is also opaque to fast neutrons and can act as a moderator in nuclear reactions.
Erasing messages from the past
Pyramid of the Sun, Teotihuacan
Having climbed more than 200 feet up a series of flights of stone stairs I reached the summit and looked towards the zenith. It was midday 19 May, and the sun was directly overhead, as it would be again on 25 July. On these two dates, and not by accident, the west face of the pyramid was oriented precisely to the position of the setting sun.6
A more curious but equally deliberate effect could be observed on the equinoxes, 20 March and 22 September. Then the passage of the sun’s rays from south to north resulted at noon in the progressive obliteration of a perfectly straight shadow that ran along one of the lower stages of the western façade. The whole process, from complete shadow to complete illumination, took exactly 66.6 seconds. It had done so without fail, year-in year-out, ever since the pyramid had been built and would continue to do so until the giant edifice crumbled into dust.7
What this meant, of course, was that at least one of the many functions of the pyramid had been to serve as a ‘perennial clock’, precisely signalling the equinoxes and thus facilitating calendar corrections as and when necessary for a people apparently obsessed, like the Maya, with the elapse and measuring of time. Another implication was that the master-builders of Teotihuacan must have possessed an enormous body of astronomic and geodetic data and referred to this data to set the Sun Pyramid at the precise orientation necessary to achieve the desired equinoctial effects.
This was planning and architecture of a high order. It had survived the passage of the millennia and it had survived the wholesale remodelling of much of the pyramid’s outer shell conducted in the first decade of the twentieth century by the self-styled restorer, Leopoldo Bartres. In addition to plundering precious evidence that might have helped us towards a better understanding of the purposes for which the enigmatic structure had been built, this repulsive lackey of Mexico’s corrupt dictator Porfirio Diaz had removed the outer layer of stone, mortar and plaster to a depth of more than twenty feet from the entire northern, eastern and southern faces. The result was catastrophic: the underlying adobe surface began to dissolve in heavy rains and to exhibit plastic flow which threatened to destroy the whole edifice. Although the slippage was halted with hasty remedial measures, nothing could change the fact that the Sun Pyramid had been deprived of almost all its original surface features.
By modern archaeological standards this was, of course, an unforgivable act of desecration. Because of it, we will never learn the significance of the many sculptures, inscriptions, reliefs and artefacts that had almost certainly been removed with those twenty feet of the outer shell. Nor was this the only or even the most regrettable consequence of Bartres’s grotesque vandalism. There was startling evidence which suggested that the unknown architects of the Pyramid of the Sun might have intentionally incorporated scientific data into many of the key dimensions of the great structure. This evidence had been gathered and extrapolated from the intact west face (which, not accidentally, was also the face where the intended equinoctial effects could still be seen), but thanks to Bartres, no similar information was likely to be forthcoming from the other three faces because of the arbitrary alterations imposed upon them. Indeed, by drastically distorting the original shape and size of so much of the pyramid, the Mexican ‘restorer’ had possibly deprived posterity of some of the most important lessons Teotihuacan had to teach.
Eternal numbers
The transcendental number known as pi is fundamental to advanced mathematics. With a value slightly in excess of 3.14 it is the ratio of the diameter of a circle to its circumference. In other words if the diameter of a circle is 12 inches, the circumference of that circle will be 12 inches × 3.14 = 37.68 inches. Likewise, since the diameter of a circle is exactly double the radius, we can use pi to calculate the circumference of any circle from its radius. In this case, however, the formula is the length of the radius multiplied by 2pi. As an illustration let us take again a circle of 12 inches diameter. Its radius will be 6 inches and its circumference can be obtained as follows: 6 inches × 2 × 3.14 = 37.68 inches. Similarly a circle with a radius of 10 inches will have a circumference of 67.8 inches (10 inches × 2 × 3.14) and a circle with a radius of 7 inches will have a circumference of 43.96 inches (7 inches × 2 × 3.14).
These formulae using the value of pi for calculating circumference from either diameter or radius apply to all circles, no matter how large or how small, and also, of course, to all spheres and hemispheres. They seem relatively simple – with hindsight. Yet their discovery, which represented a revolutionary breakthrough in mathematics, is thought to have been made late in human history. The orthodox view is that Archimedes in the third century BC was the first man to calculate pi correctly at 3.14.8 Scholars do not accept that any of the mathematicians of the New World ever got anywhere near pi before the arrival of the Europeans in the sixteenth century. It is therefore disorienting to discover that the Great Pyramid at Giza (built more than 2000 years before the birth of Archimedes) and the Pyramid of the Sun at Teotihuacan, which vastly predates the conquest, both incorporate the value of pi. They do so, moreover, in much the same way, and in a manner which leaves no doubt that the ancient builders on both sides of the Atlantic were thoroughly conversant with this transcendental number.
The principal factors involved in the geometry of any pyramid are (1) the height of the summit above the ground, and (2) the perimeter of the monument at ground level. Where the Great Pyramid is concerned, the ratio between the original height (481.3949 feet9) and the perimeter (3023.16 feet10) turns out to be the same as the ratio between the radius and the circumference of a circle, i. e. 2pi.11 Thus, if we take the pyramid’s height and multiply it by 2pi (as we would with a circle’s radius to calculate its circumference) we get an accurate read-out of the monument’s perimeter (481.3949 feet 2 × 3.14 = 3023.16 feet). Alternatively, if we turn the equation around and start with the circumference at ground level, we get an equally accurate read-out of the height of the summit (3023.16 feet divided by 2 divided by 3.14 = 481.3949 feet).
Since it is almost inconceivable that such a precise mathematical correlation could have come about by chance, we are obliged to conclude that the builders of the Great Pyramid were indeed conversant with pi and that they deliberately incorporated its value into the dimensions of their monument.
Now let us consider the Pyramid of the Sun at Teotihuacan. The angle of its sides is 43.5°12 (as opposed to 52° in the case of the Great Pyramid13). The Mexican monument has the gentler slope because the perimeter of its base, at 2932.8 feet,14 is not much smaller than that of its Egyptian counterpart while its summit is considerably lower (approximately 233.5 feet prior to Bartres’s ‘restoration’15).
The 2pi formula that worked at the Great Pyramid does not work with these measurements. A 4pi formula does. Thus if we take the height of the Pyramid of the Sun (233.5 feet) and multiply it by 4pi we once again obtain a very accurate read-out of the perimeter: 233.5 feet × 4 × 3.14 = 2932.76 feet (a discrepancy of less than half an inch from the true figure of 2932.8 feet).
This, surely, can no more be a coincidence than the pi relationship extrapolated from the dimensions of the Egyptian monument. Moreover, the very fact that both structures incorporate pi relationships (when none of the other pyramids on either side of the Atlantic does) strongly suggests not only the existence of advanced mathematical knowledge in antiquity but some sort of underlying common purpose.
The height of the Pyramid of the Sun × 4pi = the perimeter of its base. The height of the Great Pyramid at Giza × 2pi = the perimeter of its base.
As we have seen the desired height/perimeter ratio of the Great Pyramid (2pi) called for the specification of a tricky and idiosyncratic angle of slope for its sides: 52°. Likewise, the desired height/perimeter ratio of the Pyramid of the Sun (4pi) called for the specification of an equally eccentric angle of slope: 43.5°. If there had been no ulterior motive, it would surely have been simpler for the Ancient Egyptian and Mexican architects to have opted for 45° (which they could easily have obtained and checked by bisecting a right angle).
What could have been the common purpose that led the pyramid builders on both sides of the Atlantic to such lengths to structure the value of pi so precisely into these two remarkable monuments? Since there seems to have been no direct contact between the civilizations of Mexico and Egypt in the periods when the pyramids were built, is it not reasonable to deduce that both, at some remote date, inherited certain ideas from a common source?
Is it possible that the shared idea expressed in the Great Pyramid and the Pyramid of the Sun could have to do with spheres, since these, like the pyramids, are three-dimensional objects (while circles, for example, have only two dimensions)? The desire to symbolize spheres in three-dimensional monuments with flat surfaces would explain why so much trouble was taken to ensure that both incorporated unmistakable pi relationships. Furthermore it seems likely that the intention of the builders of both of these monuments was not to symbolize spheres in general but to focus attention on one sphere in particular: the planet earth.
It will be a long while before orthodox archaeologists are prepared to accept that some peoples of the ancient world were advanced enough in science to have possessed good information about the shape and size of the earth. However, according to the calculations of Livio Catullo Stecchini, an American professor of the History of Science and an acknowledged expert on ancient measurement, the evidence for the existence of such anomalous knowledge in antiquity is irrefutable.16 Stecchini’s conclusions, which relate mainly to Egypt, are particularly impressive because they are drawn from mathematical and astronomical data which, by common consent, are beyond serious dispute.17 A fuller examination of these conclusions, and of the nature of the data on which they rest, is presented in Part VII. At this point, however, a few words from Stecchini may shed further light on the mystery that confronts us:
The basic idea of the Great Pyramid was that it should be a representation of the northern hemisphere of the earth, a hemisphere projected on flat-surfaces as is done in map-making … The Great Pyramid was a projection on four triangular surfaces. The apex represented the pole and the perimeter represented the equator. This is the reason why the perimeter is in relation 2pi to the height. The Great Pyramid represents the northern hemisphere in a scale of 1:43,200.18
In Part VII we shall see why this scale was chosen.
Mathematical city
Rising up ahead of me as I walked towards the northern end of the Street of the Dead, the Pyramid of the Moon, mercifully undamaged by restorers, had kept its original form as a four-stage ziggurat. The Pyramid of the Sun, too, had consisted of four stages but Bartres had whimsically sculpted in a fifth stage between the original third and fourth levels.
There was, however, one original feature of the Pyramid of the Sun that Bartres had been unable to despoil: a subterranean passageway leading from a natural cave under the west face. After its accidental discovery in 1971 this passageway was thoroughly explored. Seven feet high, it was found to run eastwards for more than 300 feet until it reached a point close to the pyramid’s geometrical centre.19 Here it debouched into a second cave, of spacious dimensions, which had been artificially enlarged into a shape very similar to that of a four-leaf clover. The ‘leaves’ were chambers, each about sixty feet in circumference, containing a variety of artefacts such as beautifully engraved slate discs and highly polished mirrors. There was also a complex drainage system of interlocking segments of carved rock pipes.20
This last feature was particularly puzzling because there was no known source of water within the pyramid.21 The sluices, however, left little doubt that water must have been present in antiquity, most probably in large quantities. This brought to mind the evidence for water having once run in the Street of the Dead, the sluices and partition walls I had seen earlier to the north of the Citadel, and Schlemmer’s theory of reflecting pools and seismic forecasting.
Indeed, the more I thought about it the more it seemed that water had been the dominant motif at Teotihuacan. Though I had hardly registered it that morning, the Temple of Quetzalcoatl had been decorated not only with effigies of the Plumed Serpent but with unmistakable aquatic symbolism, notably an undulating design suggestive of waves and large numbers of beautiful carvings of seashells. With these images in my mind, I reached the wide plaza at the base of the Pyramid of the Moon and imagined it filled with water, as it might have been, to a depth of about ten feet. It would have looked magnificent: majestic, powerful and serene.
The Akapana Pyramid in far-off Tiahuanaco had also been surrounded by water, which had been the dominant motif there – just as I now found it to be at Teotihuacan.
I began to climb the Pyramid of the Moon. It was smaller than the Pyramid of the Sun, indeed less than half the size, and was estimated to be made up of about one million tons of stone and earth, as against two and a half million tons in the case of the Pyramid of the Sun. The two monuments, in other words, had a combined weight of three and a half million tons. It was thought unlikely that this quantity of material could have been manipulated by fewer than 15,000 men and it was calculated that such a workforce would have taken at least thirty years to complete such an enormous task.22
Sufficient labourers would certainly have been available in the vicinity: the Teotihuacan Mapping Project had demonstrated that the population of the city in its heyday could have been as large as 200,000, making it a bigger metropolis than Imperial Rome of the Caesars. The Project had also established that the main monuments visible today covered just a small part of the overall area of ancient Teotihuacan. At its peak the city had extended across more than twelve square miles and had incorporated some 50,000 individual dwellings in 2000 apartment compounds, 600 subsidiary pyramids and temples, and 500 ‘factory’ areas specializing in ceramic, figurine, lapidary, shell, basalt, slate and ground-stone work.23
At the top level of the Pyramid of the Moon I paused and turned slowly around. Across the valley floor, which sloped gently downhill to the south, the whole of Teotihuacan now stretched before me – a geometrical city, designed and built by unknown architects in the time before history began. In the east, overlooking the arrow-straight Street of the Dead, loomed the Pyramid of the Sun, eternally ‘printing out’ the mathematical message it had been programmed with long ages ago, a message which seemed to direct our attention to the shape of the earth. It almost looked as though the civilization that had built Teotihuacan had made a deliberate choice to encode complex information in enduring monuments and to do it using a mathematical language.
Why a mathematical language?
Perhaps because, no matter what extreme changes and transformations human civilization might go through, the radius of a circle multiplied by 2pi (or half the radius multiplied by 4pi) would always give the correct figure for that circle’s circumference. In other words, a mathematical language could have been chosen for practical reasons: unlike any verbal tongue, such a code could always be deciphered, even by people from unrelated cultures living thousands of years in the future.
Not for the first time I felt myself confronted by the dizzying possibility that an entire episode in the story of mankind might have been forgotten. Indeed it seemed to me then, as I overlooked the mathematical city of the gods from the summit of the Pyramid of the Moon, that our species could have been afflicted with some terrible amnesia and that the dark period so blithely and dismissively referred to as ‘prehistory’ might turn out to conceal unimagined truths about our own past.
What is prehistory, after all, if not a time forgotten – a time for which we have no records? What is prehistory if not an epoch of impenetrable obscurity through which our ancestors passed but about which we have no conscious remembrance? It was out of this epoch of obscurity, configured in mathematical code along astronomical and geodetic lines, that Teotihuacan with all its riddles was sent down to us. And out of that same epoch came the great Olmec sculptures, the inexplicably precise and accurate calendar the Mayans inherited from their predecessors, the inscrutable geoglyphs of Nazca, the mysterious Andean city of Tiahuanaco … and so many other marvels of which we do not know the provenance.
It is almost as though we have awakened into the daylight of history from a long and troubled sleep, and yet continue to be disturbed by the faint but haunting echoes of our dreams …