Bent Pyramid, Gordon Stein, 2019, Google maps

Mistake or Design? Was the Bent Pyramid angled on purpose?


The double-sloped pyramid may model the physics of light refraction in water illustration of the theory that the Bent Pyramid was intentionally double-angled in order to represent the way light bends as it emerges from water into air. Yellow bent pyramid, base angle 54 degrees, top angle 43 degrees. The bottom is submerged in water. The sun shines overhead. The Bent Pyramid may have been designed to commemorate the moment of creation when light first emerged from the primordial waters. Rays suggest the path of light. Illustration November 7, 2022 by Celeste Horner
Celeste Claire Horner, 2022. The Bent Pyramid may represent the primordial mound, and commemorate the first light of Creation.
The distinctive bend in the pyramid walls shows how light refracts as it crosses from water into air.

THE BENT PYRAMID was constructed circa 2600 B.C. by the Egyptian Old Kingdom Pharaoh Sneferu, father of Pharaoh Khufu, builder of the Great Pyramid of Giza. The kink in the angle of the pyramid is generally regarded to be the result of an engineering error. Apparently, the builders started a tower at a steep angle and having found it to be unstable, had to abruptly change course. It may be, however, that the bend might have been an intentional expression of something very important to Egyptian cosmology. Egyptians believed that at the beginning of time, a mound of earth emerged from Nun, the primordial Waters of Creation. This mound was symbolized by an object known as the Benben stone, which formed the top of pyramids. From this, life, and the all-important sun god Ra emerged. The Bent Pyramid may model the Mound of Creation with the lower stage representing what was hidden, like the bottom of an iceberg, below the primordial Waters of Creation.

The Bent Pyramid's angular design may both encode a perceptive observation about light and embody a resourceful engineering solution to a building weight support challenge When light crosses a boundary from one medium to another, for example, from water to air, its trajectory is bent, or refracted. It is possible that the angled profile of the Bent Pyramid represents light emerging from celestial waters.

The double angle pyramid structure might enable a modern scientist to compute the index of refraction of heavenly water, and infer something of its mysterious properties. As a solution pregnant with all possibility, it might be extremely dense. As etherial substance, spiritual water might be phantom-like and minimally dense. If equivalence with physical water is intended, the density would match physical water. Were the Primordial Waters of Nun envisaged as, more, less or equally dense as terrestrial waters?


HOW THE BENT PYRAMID ENCODES THE REFRACTION OF LIGHT


Bent pyramid photo by Ruth Shilling, Flickr. Refraction diagrams: Mortimer Abramowitz, Shannon Neaves, Michael Davidson, National High Magnetic Field laboratory, Florida State University


The bent edge of the pyramid traces the path light would take when emerging from water into air. The lower stage of the Bent Pyramid rises at an angle of 54°27'44" . The upper level has a decreased inclination angle of 43°22'00". The 1.3 ratio of these two angles with the vertical (36 °/47 °) matches the 1.3 ratio of the refractive indices of air and water.

The double angle of the Bent Pyramid is consistent with the way a ray of light bends when traveling from water to air. The Bent Pyramid angle thus may be a design feature, not a flaw. The pyramid should be envisaged with the lower part submerged in the Primordial waters of Nun. It would be like an iceberg, with a substantial part hidden below water. This design evokes the liminal moment, the crossing of the threshold, the first dawn, the moment of Creation. It re-traces the angular path of the first sunrise when land and life first emerged from eternally existing water, according to ancient Egyptian cosmology.

The Bent Pyramid offers a message of hope, resurrection, and resilience:

bent, part broken, but still standing;
after the night, there will be a new dawn;
despite a catastrophe like a flood, there is emergence, recovery and new life.

The lotus rises up through muddy water and opens an exquisite, fragrant bloom of enlightenment. Life, though messy and fraught with apparent failure at times, is a journey which leads to growth and ascension.


Substanceindex of refraction, n n(air)/n ratio
Diamond2.40.42
Glass1.50.67
Water1.30.77
Primordial Waters of Nun
(hypothesized from Bent Pyramid slope angle)
1.3 (47 °/ 36 ° )0.77
Air1.01.00

CCH draft 2022-11-6


AS ABOVE, SO BELOW. The ratio of the two incidence angles with normal vertical of the Bent Pyramid 36/47 matches the ratio of the index of refraction for water and air. (If the rise angle is 54, the angle from vertical normal is 90 ° - 54 ° = 36 °. The rise angle of the second stage is 43 °, a deviation from vertical of 90 ° - 43 ° = 47°). This ratio is equal to the ratio of the indices of refraction, and shows that the ancient Egyptians used the same value for earthly and the heavenly water. As above, so below, goes the Hermetic maxim. Hebrew scripture also records that God created the world by separating waters above and below.

Perhaps the pyramid with a reflecting pool or moat of water also made a statement about how life was refreshed, renewed, and emerged from the annual flood of the Nile. The Bent Pyramid might represent the Benben stone, the first reality within the turbulence of fluid primordial chaos; the first solid matter in the universe. It may be a metaphor set in stone for the first dawn; the emergence of light from the primordial waters of creation. This a durable and tangible representation of the double-angled path of light emerging from water may represent the rise to glory of an ancient Egyptian king who identified with the sun god.

SMART PEOPLE IN ANCIENT TIMES. A number of researchers (Grant, CodeX ep1, 7:30) have observed that the Great Pyramid of Giza encodes advanced observations about mathematics (incorporating foot, meter, cubit, Euler, and pi), and science. There were great mathematical geniuses such as Pythagoras, Thales of Miletus, and Archemedes in ancient times. (Carl Sagan: How Erastothenes measured Earth). Geometry means measuring Gaia, the world. The height and perimeter are reportedly proportional to the earth circumference and polar radius; and earth moon diameter. * The 29.9792458 N latitude matches the 299,792,458 meter per second speed of light. The meter is one ten millionth the Earth's circumference from the equator to the north pole, the 29.9 N latitude of Giza is one ten millionth 10^-7 the speed of light. (counter-argument)| debunk 2 The ingenuity of ancient philosophers is a reason to study the knowledge that may be encoded in ancient monuments. Light is Truth. This is both metaphor and physical fact from the perspective of Relativistic physics. Light and time, expressed in mathematical and geometic code, are possible messages of ancient sacred geometry and architecture.

Pyramid of Giza coordinates: 29.9792458 N, 31.134658 E

Using the Cosmic Microwave Background as a reference, the Earth is moving toward the Leo Constellation at 3.9 x 10^5 meters per second. (Scientific American). The speed of light is 3 x 10^8 m/s. Earth speed / light speed = 1.3 x 10^-3. Earth speed around sun / light speed ~ 10^5 (Grant suggested pyramids may make a statement both about c and our velocity relative to light speed.).

PROPOSED EXPERIMENT

Construct model of bent pyramid and submerge in water up to the level of the bend. Observe if the double angle compensates for light refraction. Do the lines look straighter from above or below the water line?



POTENTIAL ASTRONOMICAL REFERENCE

Pyramids may represent beginning and resurrection. Leonardo Da Vinci recorded that the Giza pyramid was designed to glow brilliantly before dawn (Robert Grant, CodeX). Pyramids represent the Ben Ben, or Primordial Mound of Creation, which first emerged from Nu, the Primordial Waters of Chaos. If the Bent Pyramid refers to the Sagittarius Constellation, it could commemorate the new year, the return of the sun, following the shortest day of the year, the Winter Solstice. (This is the position of the sun currently, in the past, because of precession, the position would be different. Nevertheless, Sagittarius constellation marks the direction towards the center of the galaxy. Also, the Egyptian calendar was most concerned with rising of Sirius and the flooding of the Nile river.)


Comparison of Sagittarius constellation and the Bent Pyramid. (Star map withStellarium-web.org and Bent Pyramid image by Gordo Stein 2019). CCH 2022-12-26





Resources
Bent pyramid at Dahshur
Benben stone
transparent protractor image *
Bennu Bird
Wolframalpha.com scientific calculator, mathematical modeling suite
Bent Pyramid. In hieroglyphics, the name of the Bent Pyramid was "Sneferu shines." (If 𓈍 is interpreted the sunrise or dawn, the name becomes, " the sunrise of Sneferu. " This makes the primordial light emergence theory perspective quite relevant. It addresses exactly how the light rose from the water.)
Causal ocean o Hindu tradition
sacred thread tradition


The name of Sneferu is in the cartouche. 1. Folded cloth S. 2 nefer, good, beautiful, excellent, happy. 3. mouth R. 4. quail chick w. 5. N28 sunrise hieroglyph h'. 6. pyramid hieroglyph, with rectangular pool of water below. 7. hieroglyph for south.
Meisner, Gary (2016) Golden ratios in Great Pyramid of Giza site topography. Goldennumber.net



According to Egyptian cosmology, the Bennu bird was a presence which existed before Creation. It flew over Nun, the primordial waters. It was ba of Ra, soul of the Great Creator Spirit. When it landed on the primordial mound, the benben stone, it uttered a piercing cry which shattered the primeval silence *, triggering a cascade of creative events that determined the character of the world.

References

Davidson, Michael W. (2022)
Refraction of light. Molecular expressions: science, optics & you. Florida State University. Contributing authors: Mortimer Abramowitz, Olympus America, Inc.; Shannon H. Neaves and Michael W. Davidson, National High Magnetic Field Laboratory
Grant, Robert Edward (2022)
Code X. Gaia. {Polymath video series with intriguing investigation of the mathematical aspects of the pyramids, art, and the world.}
Greenberg, Ralph (2000)
The slopes of Egyptian pyramids. Sites.math.washingtonedu. pyramid angles table
Kinnaer, Jacques (2013)
Bent pyramid at Dashur. Ancient-Egypt.org. {Includes interactive 3D isometric diagram of Bent Pyramid.}
Nuzzolo, Massimiliano (2015)
The bent pyramid of Sneferu at Dahshur. A project failure or an intentional architectural framework? Studien Zur Altägyptischen Kultur, 44, 259-282. http://www.jstor.org/stable/44160232
Wukitsch, Tom (2021)
Egypt course Fall 2021 | Sneferu's bent pyramid | Ancient Egypt slides | Bent pyramid angle diagram. Encore Learning, mmdtkw.org



Celeste Claire Horner, celeste@DigitalThought.info, Draft updated 2022-12-26, 2022-11-18, 2022-11-6, 2022-11-5