Ancient Egypt's Theory of Everything - Part 2
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The First Old Kingdom Pyramids:
Working with stone became an Egyptian specialty early in the dynastic period. The First Dynasty
Pharaoh Menes is thought to have united upper and lower Egypt about 3100 BC and the capital was
established at Memphis a short distance south of Cairo. A huge stone wall was erected around the
city to protect it from the annual flood and this must have resulted in skills working with stone, using
nothing more sophisticated than copper tools.
The first major pyramid was engineered by Imhotep for the Third Dynasty Pharaoh Djoser. An
extensive underground funerary complex was hewn out of bedrock first and then the pyramid was
erected over it. It is believed to have started as a stone mastaba structure above but was
progressively extended in size and upward in six steps until it became the massive Step Pyramid
reaching a height of 60 meters.
Djoser’s successor Sekhemkhet left an unfinished step pyramid complex nearby. It may be that
six steps were significant because six was regarded as a perfect number. It is both the sum and the
product of its factors. We inherit our measure of circles and the cycles of time from the
Mesopotamian “soss” for 60. Thus we have 60 seconds in a minute, 60 minutes in an hour, 6x60
degrees in a circle and so on. The numbers 6 and 10 were seen as interrelated in Egypt as well as
in Mesopotamia, but it took on a different flavor in Egypt as we shall see.
Another step pyramid at Meidum was covered in a casing to give it a smooth pyramidal shape,
which later fell away. It is usually attributed to Huni, the last king of the Third Dynasty but it may have
belonged to or been completed by Sneferu his son, since there are no identifying inscriptions.
Sneferu built two more pyramids, the Bent Pyramid and the Red Pyramid, the latter achieving a true
pyramid shape. If it was a strictly a funerary objective one wonders why he needed two or perhaps
three pyramids. He was the father of Khufu (Cheops) who built the Great Pyramid.
The Pyramid Complex at Giza and the Great Pyramid:
There are indications that whole pyramid complex at Giza had a prior overall plan to it. An Idea
gained momentum with Sneferu that took three succeeding generations of kings to complete. The
first to be built and the most impressive was the Great Pyramid of Khufu, although the pyramid of his
son Khafra is almost as large. That of Khafra’s son Menkaura, although smaller is also impressive.
There are six so-called Queen’s pyramids that although smaller are still massive, with burial
chambers inside. For example the largest near Menkaura’s pyramid was originally 28.4 meters high,
(93 feet) the other two being somewhat smaller. Three of them are aligned in a row immediately
south of Menkaura’s pyramid, and three are aligned in a row immediately east of Khufu’s Pyramid.
The three beside Khufu’s pyramid are larger. So there are nine pyramids in all. Or should that be ten,
because there is a small single pyramid immediately south of Khafra’s pyramid. Is there some
significance to all this? We will come back to this question later.
Sir Flinders Petrie conducted the first very precise survey of the pyramids between 1880 and
1882. His work is still used as a standard reference. His book “The Pyramids and Temples of
Gizeh” was published in 1883 and can be accessed freely on the net. He also evaluates various
theories that had arisen, discrediting most, confirming others.
Petrie determined that the accuracy of the Great Pyramids workmanship is such that the four
sides have a mean error of only 58 mm in length and 1 minute in angle from a perfect square. The
sides are closely aligned to the four cardinal compass points to within 3 minutes of arc based not on
magnetic north but on true north. Continental drift or the precession of the poles might account for
this small discrepancy. The original design dimensions, as confirmed by Petrie’s survey and all that
followed, were 280 royal cubits in height by 4x440 royal cubits around. (One royal cubit was 0.524
meters.) As these proportions equate to 2xPi to an accuracy of better than 0.05% this was and is
considered to have been the deliberate design proportions. The height of the pyramid was the
radius of a circle whose perimeter was equivalent to the perimeter of the base.
There was an empty sarcophagus found in the king’s chamber.
The Great Pyramid was the world’s tallest building for 4,000 years. It was originally 146.6 meters
or 480.9 feet tall. Each base side was 440x0.524= 230.56 meters or 755.8 feet. There were over
2.4 million stones averaging about two tons. To build it in 20 years meant quarrying, shaping, hauling
and placing a stone every two minutes on average, with great accuracy. The organization required to
accomplish such a feat within Khufu’s lifetime was itself remarkable.
Khafra’s Pyramid:
Khufu’s son, Khafra’s pyramid was also built to very exacting standards. The pyramid has a base
length of 215.25 m (706 ft) and originally rose to a height of 143.5 m (471 ft) The slope of the
pyramid rises at an 53° 10' angle, steeper than its neighbor Khufu’s pyramid which has an angle of
51°50'40". Petrie confirms that this pyramid was built on the plan of a 3, 4, 5 triangle, the only right
angled triangle with all three sides whole numbers. This too has significance which will be pointed
out later.
The SW to NE diagonal axis of Khafra’s pyramid is offset slightly from that of Khufu’s pyramid
although the diagonals and sides remain accurately parallel. This contrasts with the larger offset of
Menkaura’s pyramid which is also rotated slightly in its relative orientation. There is an interesting
theory on this at www.legon.demon.co.uk that relates to the squaring of the circle.
There was a hiatus in building the Giza pyramids. Khufu had several sons and his immediate
successor was his son Djedefre (Radjedef) who for some reason chose to build his pyramid at Abu
Roash north of Giza. There is some speculation among scholars that there was a religious schism
between elder and younger members of Khufu’s successors. In any case Khafra again took up
building at Giza eight years later when he became king after his half brother’s death. There was an
empty sarcophagus found in the main burial chamber hewn into bedrock beneath Khafra’s pyramid.
Menkaura’s Pyramid:
Menkaura’s pyramid was less accurate in its construction, although its original slope was
estimated by Petrie to be 51°20'25", close to that of Khufu’s pyramid at 51°50'40". The bottom
courses were capped with granite which remained rough cut on its outer edges, so that final
surfacing was never completed. The upper courses were capped with limestone and apparently
finished to present a smooth slope.
The main burial chamber was hewn into bedrock beneath the pyramid base. The sarchophagus
was found empty with the lid missing, although pieces of the lid were found. Unlike those of Khufu
and Khafra it was of ornate design, but it was unfortunately lost when the ship carrying it to Britain
sank. Apart from this sarcophagus the Giza pyramids generally lacked any decor or inscriptions of
any kind. This is in sharp contrast to later works and tombs.
The technology certainly existed to attain great accuracy in Menkaura’s smaller pyramid,
suggesting another factor in the overall plan. We will come back to this later.
The Divergence of Later Pyramids:
Pyramid building continued off and on for about 2000 years but later pyramids were smaller and
often shoddily built, lacking the accuracy and significance of the Giza complex. In general tomb
building hewn out of bedrock took precedence over pyramid building and became characterized by
extravagance as at the Valley of the Kings near Luxor. The tombs doubled as a storehouse of
treasures to accompany the pharaoh in the afterlife. Elaborate décor portrayed the pharaohs as
gods, a feature completely absent from the Great Pyramids at Giza.
Whether or not the Giza pyramids were intended as tombs, they certainly have obvious
cosmological significance implicit in the stark simplicity of their geometrical design, lacking in
hieroglyphics or internal décor. Indeed the only likeness of Khufu that has ever turned up is a 3” ivory
carving bearing his cartouche. Petrie found it at the ancient site of Abydos, between Giza and Luxor
(Thebes). Almost nothing is known of Khufu. There is none of the self aggrandizement that
characterized the tombs of later periods.
An Overall Plan Spanning Four Generations:
There must have been some incredible incentive, some driving impulse or insight that instigated
such massive undertakings that strained the whole population of Egypt. The undertaking enlisted the
cooperation and support of the whole populace. The Weighing of the Heart theme is obviously
inconsistent with forced labor on such a scale.
It may or may not have begun with Imhotep, the builder of Djoser’s Step Pyramid, which seems to
have been an ad hoc affair that evolved during construction. It nevertheless could be indicative of
insights that came as a staged development. Djoser’s successor Sekhemkhet left an unfinished
step pyramid complex nearby. There were no inscriptions apart from his name inscribed on the
stoppers of clay jars found in the pyramid. When his still sealed sarcophagus was opened in the mid
20th century, it was found empty.
Sneferu (2613 to 2589 BC), the first king of the Fourth Dynasty, was certainly possessed of a
compulsion to build pyramids, probably three in all. He passed his compulsion on to his son Khufu,
who reached extraordinary heights. Then another two generations followed at Giza in what has the
earmarks of an overall plan spanning four generations. There are specific relationships between the
pyramids, their geometry, and their history, to clearly suggest this.
The circle suggests a time-like dynamic principle whereas a straight line of fixed length suggests
a static extension in space. Hence the tools of the sacred geometry were the ruler and compass.
And one way to reconcile the two is to draw the square whose perimeter is the same as the
perimeter of a circle. It is called squaring the circle.
There was an interesting book published by John Michell, City of Revelation, 1972. In it he
explores many correspondences between esoteric subjects, from St. John’s revelation of the New
Jerusalem, to the ground plan of Glastonbury Abbey, to Stonehenge, to the Great Pyramid, to
gematria, to ancient systems of measure, and so on. Without going into the sense or reliability of all
of them, a few salient features stand out as undeniable, and that deserve review.
A central theme of Michell’s book is that there was a sacred geometry that was passed down
through works in stone as a secret tradition of masonry. It may be connected to the establishment of
the Masonic Lodge but the connection is lost in the mists of history somewhere in the Middle Ages
along with the sacred geometry associated with it. Nevertheless the emblem of the Masonic Lodge
is the ruler and compass.
There is a common feature of the creative process that does not make rational sense. If we
draw a circle on a piece of paper the diameter of the circle can not be measured completely
accurately in the same units used to measure the circumference, and vice versa, and yet the circle is
clearly there on the page. For this reason the ratio between diameter and circumference, known as
Pi, is called an irrational number. It has no completely discrete value. It goes on for ever and ever
with no discernable pattern to the endless sequence of numbers. The diameter and circumference
are said to be incommensurable. It is like the indeterminacy principle of quantum mechanics where
the static position and dynamic momentum of a moving particle can never be known accurately
together.
The Great Pyramid is thus a monumental example of squaring the circle, since its height is
related to the perimeter of its base by the ratio 2 Pi. In this sense it is a monument that reconciles
subjective spiritual dynamics to objective spatial regularities.
Squaring the circle is often dismissed by academics as simply impossible since Pi is an
irrational number, but they miss the point. The point is that the linear regularities of space are
reconciled with the cyclic dynamics of the heavens through living processes. And the heavens are
dominated by circular motions. The universe is a throbbing living reality. That was the theme of the
sacred geometry.
The Relationship of the Earth and Moon to the Khufu and Khafra Pyramids:
As Michell points out, if we draw a scale diagram of the earth and moon so that they are
touching, and enclose each in a square, a surprising relationship becomes obvious. It is illustrated in
the diagram (borrowed from my book Fisherman’s Guide.)
The triangle with apex at the center of the moon and base across the diameter of the earth has
the same proportions as the Great Pyramid of Khufu. The circle scribed through the center of the
moon concentric with the earth has a circumference equal to the square that contains the earth to an
accuracy of 0.0588%. The earth radius of 6,378 km and moon radius of 1,738 km are taken from
standard reference tables. They could be out by that much given the irregularities of the earth and
moon surfaces. So the dimensions of Earth and Moon themselves represent squaring the circle.
Also the triangle that joins the square of the moon to the square of the earth has sides in the ratio of
3, 4, and 5. This same ratio corresponds to the slope of Khafra’s pyramid as confirmed by Petrie
according to his meticulous survey. Michell also points out that the two concentric circles are in the
same proportion as the bluestone and sarsen circles of Stonehenge.
It is a remarkable coincidence that the actual dimensions of Earth and Moon correspond to
squaring the circle. There are other remarkable coincidences that will be explored later.
The Nine Giza Pyramids and Fractals of Unity:
Try a little test. Sketch four separate circles on a piece of paper. Now try and draw all of the ways
that four circles can be arranged with respect to their inside and outside. For example one can be
drawn inside one of the others but separate from the remaining two. Or the remaining two can also
be drawn one inside the other but separate from the other two. Or the circles can be drawn as four
concentric circles. And so on. How many ways are there? You will find that there are only nine
possible ways to do it.
These nine ways that derive from four circles correspond to the nine Terms of System 4 at www.
cosmic-mindreach.com. The circles represent active interfaces. They share a common active center
inside and a common passive periphery outside. Because they share a common active center we
can call them centers. How they relate to one another in each Term and between Terms outlines the
basis of meaning. This System is introduced on the website. We will come back to this later.
All nine ways relate to the same four circles that are employed to explore a unifying principle of
subjective to objective relationships. This is analogous to squaring the circle, since the circle
represents the subjective animating principle inside living creatures as they relate to the linear
regularities of objective experience outside. This self-similar analogy is apparent in the way the
whole of experience is integrated. It is representative of the cosmic order.
Number systems thus also exhibit self-similar analogous patterns that are hierarchically
subsumed. This means that arithmetic and mathematics in general derive from the way the cosmic
order works, not vice versa.
The Egyptians assigned no symbol for zero although their number system was designed on the
base ten. They had separate symbols for 1, 10, 100, 1,000, 10,000 100,000, and 1,000,000 and so
they generally had no need for a symbol for zero. Their number system was based on progressive
whole number powers of ten. In other words it was logarithmic to the base ten but only in terms of the
whole number digits from 1 to 9. There are only nine repeated ones between 1 and 10. There are
only nine repeated tens between 10 and 100. There are only nine repeated 100’s between 100 and
1,000 and so on. The subsumed repetition of nine holistic elements of counting is essentially a
fractal representation of Unity.
Egyptian Fractions as Fractals related to the Giza Pyramids:
The fractal representation of unity extends to fractions. Egyptians allowed only unit fractions. They
saw fractions as reciprocals of whole numbers. Their understanding of numbers, mathematics and
measurements was implicitly holistic in nature and related to the cosmic order.
This brings us to another peculiarity of the numbers from 1 to 9. The reciprocals of the numbers
3, 6 and 9 repeat themselves to infinity. They yield the infinite numbers 0.3333etc., 0.16666etc., and
0.11111etc. The reciprocal of the number 7 is also an infinite number but it is the repeating
sequence of the remaining six numbers, namely 0.142857142857142857etc.
The numbers from 1 to 9, apart from 7, when each divided by 7 also result in the same repeating
six digit sequence but it starts at different places in the sequence. The number 7 divided by itself is
Unity of course, so there is something about the reciprocal of 7 that regenerates the other numbers
endlessly as they relate to unity. Numbers as fractals of unity proliferate as reciprocals of themselves
and the number 7 represents the memory of the computational proliferation. In fact any number
divided by 7 has decimal positions that endlessly repeat the same six digit sequence, unless the
number is an exact multiple of 7. The Egyptians had a system of division that worked in such a way
that they must have known this. They must also have known about irrational numbers that are
incommensurable.
This is a further indication that the Giza pyramids represent the comic order in their stark
geometry and in the overall plan. The obvious fact that there are three large pyramids and six small
ones suggests a direct correspondence without getting into a lot of spurious speculation. The
reciprocals of 3, 6 and 9 relate to the three large pyramids. The repeating six member sequence of
7 relates to the six small pyramids. The tiny tenth pyramid indicates the decimal system their
numbers are based upon.
The Pyramids, the System and the Cosmic Order:
There are direct parallels between the Giza pyramid complex and the System as introduced on
the website. The System as an expression of the cosmic order consists of a nested hierarchy of
subsumed higher Systems that all derive from requirements implicit in the nature of universal
wholeness. Each higher system is a discrete elaboration of the lower systems that precede it. The
lower systems thus transcend and subsume the higher systems such that the whole nested hierarchy
is a subsumed elaboration of System 1 and universal wholeness. Each higher system is
nevertheless complete unto itself as it relates to phenomenal experience. All possible structural
varieties of experience are thus encompassed. It is to this extent a Theory of Everything. It is not
possible to conceive of anything outside it. More accurately it is a Universal Methodology that must
find consistency with the living empirical evidence much like Ancient Egypt’s living insights. It is not a
Theory of Everything as an abstract construction distinct from a living reality such as the kind that
science currently seeks.
In System 2 there are only two ways that two circles can be drawn with respect to inside and
outside. One of the circles must be universal and unique and the other must be particular and many
in order for System 2 to be a consistent elaboration of System 1 and universal wholeness. The two
circles can be separate facing one another, or one circle can be inside the other. This implicitly
defines both a subjective and an objective basis to experience.
In System 3 with three circles there are four possible ways to draw them with respect to inside
and outside. Two of these Terms are universal and two are particular but they combine to work in
pairs as an elaboration of System 2. The pairs alternate between an objective and a subjective
orientation.
In System 4 with four circles there are nine ways to draw four circles, each called a Term, and
they interact as an elaboration of System 3. Three of the terms are universal and six are particular.
The six particular terms occur in alternating synchronous groups of three. One group has an
objective orientation. The other group of three has a reciprocal subjective orientation. So one
grouping is orthogonal or at right angles to the other, like the two groups of three small pyramids at
Giza. The six particular terms also relate in a subjective to objective orientation as polar pairs that
correspond to the three universal terms and the three large pyramids at Giza.
Summary:
These observations together with the stark geometry of the Khufu and Khafra pyramids that
correspond so accurately to the proportions of Earth and Moon make a powerful statement. These
two largest pyramids indicate the reconciliation of the living subjective dynamics of the circle that we
experience inside with the stark objective linearity of space and time that we experience outside.
These two perspectives must find reconciliation through living processes.
Menkaura’s pyramid did not have to be geometrically accurate to take its place as the third
member of the infinite triad. In fact it is rotated slightly as if on purpose to set it apart for this reason.
Its rotation together with its three orthogonal pyramids suggests a dynamic relationship between the
subjective and objective orientations implicitly represented in the other two pyramids.
Taken also in the context of the Weighing of the Heart as described in Part 1, it is a statement
that portrays life itself as the reconciliation of otherwise incommensurable elements between the
living subjective dynamics and the static objective regularities of the cosmic order.
| Ancient Egypt’s Theory of Everything Part 2 The Pyramids as Cosmic Temples Robert Campbell 2008 |
Squaring the Circle: