The Inexplicable Precision in the Construction of The Great Pyramid at Giza

The northern face was aligned, almost perfectly, to true north, the eastern face almost perfectly to true east, the southern to true south, and the western face to true west. The average error was only around three minutes of arc (down to less than two minutes on the southern face) – —incredible accuracy for any building in any epoch, and an inexplicable, almost supernatural feat here in Egypt 4500 years ago when the Great Pyramid was supposed to have been built.

An error of three arc minutes represents an infinitesimal deviation from  true of less than 0.015 per cent. In the opinion of structural engineers,  with whom I had discussed the Great Pyramid, the need for such  precision was impossible to understand. From their point of view as  practical builders, the expense, difficulty and time spent achieving it  would not have been justified by the apparent results: even if the base of  the monument had been as much as two or three degrees out of true (an error of say 1 per cent) the difference to the naked eye would still have been too small to be noticeable. On the other hand the difference in the magnitude of the tasks required (to achieve accuracy within three minutes as opposed to three degrees) would have been immense.

Obviously, therefore, the ancient master-builders who had raised the Pyramid at the very dawn of human civilization must have had powerful motives for wanting to get the alignments with the cardinal directions just right. Moreover, since they had achieved their objective with uncanny exactness they must have been highly skilled, knowledgeable and competent people with access to excellent surveying and setting-out equipment. This impression was confirmed by many of the monument’s other characteristics. For example, its sides at the base were all almost exactly the same length, demonstrating a margin of error far smaller than modern architects would be required to achieve today in the construction of, say, an average-size office block. This was no office block, however. It was the Great Pyramid of Egypt, one of the largest structures ever built by man and one of the oldest. Its north side was 755 feet 4.9818 inches in length; its west side was 755 feet 9.1551 inches in length; its east side was 755 feet 10.4937 inches; its south side 756 feet 0.9739 inches. This meant that there was a difference of less than 8 inches between its shortest and longest sides: an error amounting to a tiny fraction of 1 per cent on an average side length of over 9063 inches.

Once again, I knew from an engineering perspective that the bare figures did not do justice to the enormous care and skill required to achieve them. I knew, too, that scholars had not yet come up with a convincing explanation of exactly how the Pyramid builders had adhered consistently to such high standards of precision. What really interested me, however, was the even bigger question-mark over another issue: why had they imposed such exacting standards on themselves?

If they had permitted a margin of error of 1-2 per cent— instead of less than one-tenth of 1 per cent—they could have simplified their tasks with no apparent loss of quality. Why hadn’’t they done so? Why had they insisted on making everything so difficult? Why, in short, in a supposedly ‘primitive’ stone monument built more than 4500 years ago were we seeing this strange, obsessional adherence to machine-age standards of precision?

Very few modern buildings, even the houses we live in, have corners that consist of perfect ninety degree right angles; it is common for them to be a degree or more out of true. It doesn’t make any difference structurally and nobody notices such minute errors. In the case of the Great Pyramid, however, I knew that the ancient master-builders had found a way to narrow the margin of error to almost nothing. Thus, while falling short of the perfect ninety degrees, the south-eastern corner achieved an impressive 89° 56’ 27”. The north-eastern corner measured 90° 3’ 2”; the southwestern 90° 0’ 33”, and the north-western was just two seconds of a degree out of true at 89° 59’ 58”.

This was, of course, extraordinary. And like almost everything else about the Great Pyramid it was also extremely difficult to explain. Such accurate building techniques—as accurate as the best we have today— could have evolved only after thousands of years of development and experimentation. Yet there was no evidence that any process of this kind had ever taken place in Egypt. The Great Pyramid and its neighbours at Giza had emerged out of a black hole in architectural history so deep and so wide that neither its bottom nor its far side had ever been identified.

The 35th course of masonry was a hard one to clamber over, being made  of particularly massive blocks, much larger than any of the others we had  so far encountered (except those at the very base) and estimated to weigh between 10 and 15 tons apiece. This contradicted engineering logic and commonsense, both of which called for a progressive decrease in the size and weight of the blocks that had to be transported to the summit as the pyramid rose ever higher. Courses 1-18, which diminished from a height of about 55.5 inches at ground level to just over 23 inches at course 17, did obey this rule. Then suddenly, at course 19, the block height rose again to almost 36 inches. At the same time the other dimensions of the blocks also increased and their weight grew from the relatively manoeuvrable range of 2-6 tons that was common in the first 18 courses to the more ponderous and cumbersome range of 10-15 tons.

These, therefore, were really big monoliths that had been carved out of solid limestone and raised more than 100 feet into the air before being placed faultlessly in position. To have worked effectively the pyramid builders must have had nerves of steel, the agility of mountain goats, the strength of lions and the confidence of trained steeplejacks. With the cold morning wind whipping around my ears and threatening to launch me into flight, I tried to imagine what it must have been like for them, poised dangerously at this (and much higher) altitudes, lifting, manoeuvring and positioning exactly an endless production line of chunky limestone monoliths—the smallest of which weighed as much as two modern family cars.

How long had the pyramid taken to complete? How many men had worked on it? The consensus among Egyptologists was two decades and 100,000 men. It was also generally agreed that the construction project had not been a year-round affair but had been confined (through labour force availability) to the annual three-month agricultural lay-off season imposed by the flooding of the Nile.

It wasn’’t just the tens of thousands of blocks weighing 15 tons or more that the builders would have had to worry about. Year in, year out, the real crises would have been caused by the millions of ‘average-sized’ blocks, weighing say 2.5 tons, that also had to be brought to the working plane. The Pyramid has been reliably estimated to consist of a total of 2.3 million blocks. Assuming that the masons worked ten hours a day, 365 days a year, the mathematics indicate that they would have needed to place 31 blocks in position every hour (about one block every two minutes) to complete the Pyramid in twenty years. Assuming that construction work had been confined to the annual three-month lay-off, the problems multiplied: four blocks a minute would have had to be delivered, about 240 every hour.

Such scenarios are, of course, the stuff construction managers’ nightmares are made of. Imagine, for example, the daunting degree of coordination that must have been maintained between the masons and the quarries to ensure the requisite rate of block flow across the production site. Imagine also the havoc if even a single 2.5 ton block had been dropped from, say, the 175th course.

The physical and managerial obstacles seemed staggering on their own, but beyond these was the geometrical challenge represented by the pyramid itself, which had to end up with its apex positioned exactly over the centre of its base. Even the minutest error in the angle of incline of any one of the sides at the base would have led to a substantial misalignment of the edges at the apex. Incredible accuracy, therefore, had to be maintained throughout, at every course, hundreds of feet above the ground, with great stone blocks of killing weight.

Rampant stupidity

How had the job been done?

At the last count there were more than thirty competing and conflicting theories attempting to answer that question. The majority of academic Egyptologists have argued that ramps of one kind or another must have been used. This was the opinion, for example, of Professor I.E.S Edwards, a former keeper of Egyptian Antiquities at the British Museum who asserted categorically: ‘Only one method of lifting heavy weights was open to the ancient Egyptians, namely by means of ramps composed of brick and earth which sloped upwards from the level of the ground to whatever height was desired.’

John Baines, professor of Egyptology at Oxford University, agreed with Edwards’s analysis and took it further: ‘As the pyramid grew in height, the length of the ramp and the width of its base were increased in order to maintain a constant gradient (about 1 in 10) and to prevent the ramp from collapsing. Several ramps approaching the pyramid from different sides were probably used.’

To carry an inclined plane to the top of the Great Pyramid at a gradient of 1:10 would have required a ramp 4800 feet long and more than three times as massive as the Great Pyramid itself (with an estimated volume of 8 million cubic metres as against the Pyramid’s 2.6 million cubic metres). Heavy weights could not have been dragged up any gradient steeper than this by any normal means.

If a lesser gradient had been chosen, the ramp would have had to be even more absurdly and disproportionately massive. The problem was that mile-long ramps reaching a height of 480 feet could not have been made out of ‘bricks and earth’ as Edwards and other Egyptologists supposed. On the contrary, modern builders and architects had proved that such ramps would have caved in under their own weight if they had consisted of any material less costly and less stable than the limestone ashlars of the Pyramid itself.

Since this obviously made no sense (besides, where had the 8 million cubic metres of surplus blocks been taken after completion of the work?), other Egyptologists had proposed the use of spiral ramps made of mud brick and attached to the sides of the Pyramid. These would certainly have required less material to build, but they would also have failed to
reach the top. They would have presented deadly and perhaps insurmountable problems to the teams of men attempting to drag the big blocks of stone around their hairpin corners. And they would have crumbled under constant use.

Most problematic of all, such ramps would have cloaked the whole pyramid, thus making it impossible for the architects to check the accuracy of the setting-out during building.

But the pyramid builders had checked the accuracy of the setting out, and they had got it right, because the apex of the pyramid was poised exactly over the centre of the base, its angles and its corners were true, each block was in the correct place, and each course had been laid down level—in near-perfect symmetry and with near-perfect alignment to the cardinal points. Then, as though to demonstrate that such tours-de-force of technique were mere trifles, the ancient master-builders had gone on to play some clever mathematical games with the monument’s dimensions.

For some reason, too, it had taken their fancy to place the Great Pyramid almost exactly on the 30th parallel at latitude 29° 58’ 51”. This, as a former astronomer royal of Scotland once observed, was ‘a sensible defalcation from 30°’, but not necessarily in error:

For if the original designer had wished that men should see with their body, rather than their mental eyes, the pole of the sky from the foot of the Great Pyramid, at an altitude before them of 30°, he would have had to take account of the refraction of the atmosphere; and that would have necessitated the building standing not at 30° but at 29° 58’ 22”.

Compared to the true position of 29° 58’ 51”, this was an error of less than half an arc minute, suggesting once again that the surveying and geodetic skills brought to bear here must have been of the highest order.

Excerpts taken from the book “Fingerprints of the Gods” by Graham Hancock