The message of the Sphinx: a quest for the hidden legacy of mankind (6 page)

The Great Pyramid was originally 481.3949 feet in height (now reduced to just a little over 450 feet) and its four sides each measure some 755 feet in length at the base. The second Pyramid was originally slightly lower—with a designed height of 471 feet—and has sides measuring just under 708 feet in length. The third Pyramid stands some 215 feet tall and has a side length at the base of 356 feet.

When they were built the second Pyramid and the Great Pyramid were both entirely covered in limestone facing blocks, several courses of which still adhere to the upper levels of the former. The Great Pyramid, by contrast, is today almost completely bereft of its casing. We know from historical accounts, however, that it was once clad from bottom to top with smoothly-polished Tura limestone which was shaken loose by a powerful earthquake that devastated the Cairo area in AD 1301. The newly exposed core masonry was then used for some years as a crude local quarry to rebuild the shattered mosques and palaces of Cairo.

All the Arab commentators prior to the fourteenth century tell us that the Great Pyramid’s casing was a marvel of architecture that caused the edifice to glow brilliantly under the Egyptian sun. It consisted of an estimated 22 acres of 8-foot-thick blocks, each weighing in the region of 16 tons, ‘so subtly jointed that one would have said that it was a single slab from top to bottom’.
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A few surviving sections can still be seen today at the base of the monument. When they were studied in 1881 by Sir W. M. Flinders Petrie, he noted with astonishment that ‘the mean thickness of the joints is 0.020 of an inch; and, therefore, the mean variation of the cutting of the stone from a straight line and from a true square is but 0.01 of an inch on a length of 75 inches up the face, an amount of accuracy equal to the most modern opticians’ straight-edges of such a length.’

Another detail that Petrie found very difficult to explain was that the blocks had been carefully and precisely cemented together: ‘To merely place such stones in exact contact at the sides would be careful work, but to do so with cement in the joint seems almost impossible ...’
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Also ‘almost impossible’, since the mathematical value
pi
(3.14) is not supposed to have been calculated by any civilization until the Greeks stumbled upon it in the third century BC,
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is the fact the designed height of the Great Pyramid—481.3949 feet—bears the same relationship to its base perimeter (3023.16 feet) as does the circumference of any circle to its radius. This relationship is 2
pi
(i.e. 481.3949 feet x 2 x 3.14 = 3023.16 feet).

Equally ‘impossible’—at any rate for a people like the ancient Egyptians who are supposed to have known nothing about the true shape and size of our planet—is the relationship, in a scale of 1:43,200, that exists between the dimensions of the Pyramid and the dimensions of the earth. Setting aside for the moment the question of whether we are dealing with coincidence here, it is a simple fact, verifiable on any pocket calculator, that if you take the monument’s original height (481.3949 feet) and multiply it by 43,200 you get a quotient of 3938.685 miles. This is an underestimate by just 11 miles of the true figure for the polar radius of the earth (3949 miles) worked out by the best modern methods. Likewise, if you take the monument’s perimeter at the base (3023.16 feet) and multiply this figure by 43,200 then you get 24,734.94 miles—a result that is within 170 miles of the true equatorial circumference of the earth (24,902 miles). Moreover, although 170 miles sounds quite a lot, it amounts, in relation to the earth’s total circumference, to a minus-error of only three quarters of a single per cent.

High precision

Such fine errors are within the general margins of tolerance found at the Great Pyramid. Indeed, although it has a footprint of over 13 acres, and consists of some six and a half million tons of limestone and granite blocks, the sheer mass and size of this monster of monuments are not its most impressive characteristics. More astounding by far is the incredible high-tech precision that is built into every aspect of its design.

Before going into the details, let us consider the implications of very fine precision in very large monuments.

An analogy with the simple wrist-watch helps. If you are after an accuracy of, say, a few seconds per week, then an ordinary quartz watch costing fifty dollars or less will do the trick. If you want accuracy to within a fraction of a second per year, however, then the quartz watch will no longer serve and you will have to turn to something of the order of an atomic clock.

A similar situation applies in the construction industry. If you are building a brick wall that is to appear straight within plus or minus 1 degree per 100 metres and the whole roughly directed due north, then any good bricklayer should be able to meet your specification. However, if your requirement is for a wall that is straight within 1 arc minute per 100 metres and directed
exactly
due north, then you are going to need a laser theodolite, an ordnance survey map accurate to 10 metres, and a highly qualified team of professionals including an expert setting-out engineer, an astronomer, a surveyor, several master-masons and a week or so to ensure that the precision you are aiming for has in fact been achieved.

Such ‘atomic clock’ precision was achieved by the builders of the Great Pyramid more than 4500 years ago. This is not a matter of historical speculation, or of theory, but of plain, measurable facts.

For example the earth’s equatorial circumference of 24,902 miles works out at around 132 million feet, with the result that a degree of latitude at the equator is equivalent to approximately 366,600 feet (i.e. 132 million feet divided by 360 degrees). Each degree is divided into 60 arc minutes, which means that 1 arc minute represents just over 6100 feet on the earth’s surface, and each arc minute is then further subdivided into 60 arc seconds—with the result that 1 arc second is equivalent to a distance of about 101 feet. This system of measuring by degrees is not a modern convention but rather an
inheritance
of scientific thinking, connected to ‘base 60’ mathematics, that dates back to the remotest antiquity.
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Nobody knows where, or when, it originated.
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It seems, however, to have been employed in the geodetic and astronomical calculations that were used to locate the Great Pyramid—for the monument is positioned barely a mile to the south of latitude 30, i.e. almost exactly one third of the way between the equator and the north pole.
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5. Geodetic location of the Great Pyramid of Giza on latitude 30 degrees north (one third of the way between the equator and the north pole) and at the centre of the world’s habitable landmasses.

It is unlikely that this choice of location could have come about by chance. Moreover, because no suitable site for such a massive structure exists a mile or so to the north, it would be inadvisable to assume that the fractional offset from the thirtieth parallel could have been caused by a surveying error on the part of the Pyramid builders.

This offset amounts to 1 arc minute and 9 arc seconds—since the Pyramid’s true latitude is 29 degrees 58’ 51”. Interestingly, however, as a former Astronomer Royal of Scotland has observed:

‘If the original designer had wished that men should see with their bodily, rather than their mental eyes, the pole of the sky from the foot of the Great Pyramid, at an altitude before them of 30 degrees, he would have had to take account of the refraction of the atmosphere; and that would have necessitated the building standing not at latitude 30 degrees, but at latitude 29 degrees 58’ 22”.’
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In other words the monument turns out to be situated less than half an arc minute to the north of
astronomical
latitude 30 degrees, uncorrected for atmospheric refraction. Any ‘error’ involved is thus reduced to less than half of one-sixtieth of one degree—a hair’s breadth in terms of the earth’s circumference as a whole.

The same obsessive concern with accuracy is found in the orderly evenness of the Pyramid’s base:
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The variation between the longest and shortest sides is therefore less than 8 inches—about one tenth of 1 per cent—quite an amazing feat when we consider that we are measuring a distance of over 9000 inches carpeted with thousands of huge limestone blocks weighing several tons each.

There is no sign that the ancient Pyramid builders were in any way daunted by the task of maintaining such fastidious standards of symmetry on such a grand scale. On the contrary, as though willingly seeking out additional technical challenges, they went on to equip the monument with corners set at almost perfect right-angles. The variation from 90 degrees is just 0 degrees 00’ 02” at the north-west corner, 0 degrees 03’ 02” at the north-east corner, 0 degrees 03’ 33” at the south-east corner, and 0 degrees 00’ 33” at the south-west corner.
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This, it must be conceded, is not just ‘atomic clock’ accuracy but the Rolex, BMW, Mercedes Benz, Rolls-Royce and IBM of building engineering all rolled into one.

And there is more.

It is fairly well known that the Pyramid was aligned by its architects to the cardinal points (with its north face directed north, its east face directed east, etc., etc.). Less well known is just how eerily exact is the
precision
of these alignments—with the average deviation from true being only a little over 3 arc minutes (i.e. about 5 per cent of a single degree).
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Why such meticulousness?

Why such rigour?

Why should even the most megalomaniacal of Pharaohs have cared whether his massive ‘tomb’ was aligned within 3 arc minutes of true north—or indeed within a whole degree of true north? To the naked-eye observer it is virtually impossible to determine such a deviation. Indeed most of us could not spot a misalignment within 3 whole degrees (180 arc minutes), let alone within 3 arc minutes (and some people have trouble telling the general direction of north at all). So the question has to be asked: what was all this incredible precision for? Why did the builders burden themselves with so much extra work and difficulty when the effects of their additional labours would not be visible to the naked eye anyway?

They must, one assumes, have had a powerful motive to create what is truly a miracle of the surveyor’s art.

And what makes this miracle all the more remarkable is the fact that it was not performed on a perfectly flat area of ground, as one might expect, but with a massive natural mound, or hill, left exactly in the middle of the site on which the Great Pyramid was being erected. Estimated to be almost 30 feet high—as tall as a two-storey house—and positioned dead centre over the base area (of which it occupies approximately 70 per cent), this primeval mound was skilfully incorporated into the lower courses of the growing edifice. No doubt its presence has contributed down the epochs to the structure’s legendary stability. It is extremely difficult, however, to understand how the ancient surveyors were able to square the base of the Pyramid in its early and most important stages with the mound so solidly in the way (squaring the base normally involves taking repeated diagonal measurements across the corners).
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All that we can say for sure is that the base
is
square and that the monument
is
locked into the cardinal axes of our planet with great care and precision.

6. Cross-section of the Great Pyramid of Egypt showing the natural mound of bedrock that is known to be built into its lower courses.