Lost Technologies of Ancient Egypt: Advanced Engineering in the Temples of the Pharaohs

by Christopher Dunn

  As we discovered earlier, the Fibonacci spiral is based on the number series 1, 1, 2, 3, 5, 8, 13, 21, and so forth (see figure 2.5). Figure 2.16 illustrates how the spiral corresponds to the drawing of the Ramses’ face and the grid.

  Figure 2.15. Ramses’ outline drawing

  Figure 2.16. Ramses, Pythagoras, and Fibonacci

  Figure 2.17. Ramses with four Fibonacci spirals

  Figure 2.16 illustrates the construction of the Fibonacci spiral using the Fibonacci series 1, 1, 2, 3, 5, and 8. As we can see, the spiral has been sized to touch the right jaw and to circle the eye. We can note other correspondences to the bottom line of the grid and the top of the oval that was created from the outline of Ramses’ jawline.

  Figure 2.17 was created using copies of the spiral that are mirrored horizontally and vertically. The vertically flipped pair was aligned with Ramses’ mouth. We can see correspondences where the spirals cross and where they end on grid lines at the top and the bottom.

  LEONARDO MEETS RAMSES

  The Golden Ratio, or Greek Phi φ, expressed as the mathematical constant 1.6180339887, has been used in art and architecture, including in such Renaissance masterpieces as Leonardo da Vinci’s painting of the Last Supper and in the Notre Dame Cathedral in Paris. Its proportions are said to be embodied in the human form and can also be found in nature, but certainly it is used deliberately by those who strive to achieve aestheticism in their work. The proportions of the Golden Ratio, also known as the Golden Section, are expressed using both triangular and rectangular shapes.

  Figure 2.18. The Golden Ratio

  Figure 2.19. The Golden Rectangle

  Figure 2.20 illustrates four Golden Rectangles of equal proportion. The rectangles that frame the width of the nose look narrower than the other two, but this is an optical illusion caused by two overlapping and offset rectangles. The rectangle was generated using the width of the nose as the base square multiplied by 1.618033, the Golden Ratio, to achieve the height ratio. The rectangle was then positioned under the nose, where we see it lined up with the eyebrow grid line.

  Figure 2.20. Ramses’ Golden Rectangles

  Three copies of this Golden Rectangle were then made, and two were then fitted to the bottom corners of the Golden Rectangle that frames the oval shape of Ramses’ face, with one Golden Rectangle on the left bottom corner rotated 90 degrees. The third Golden Rectangle was then shaded differently and placed with the bottom surface aligned with the Ramses’ mouth. As figure 2.20 illustrates, the top of this Golden Rectangle corresponds with the grid line that is tangent to Ramses’ eyebrows.

  It would seem reasonable at this juncture to suggest that the key to Ramses’ geometry has been discovered. The face, grid, and Golden Rectangle working in unison strongly imply that all three were used in the placement of the different features of the face. This geometry and the circles seem to give us enough information to explain the two-dimensional drawing of Ramses. However, while this is a compelling argument, the testimony of the famous architect I. M. Pei may cast doubt on the intentional application of the Golden Section by the ancient Egyptians. His design of the pyramid at the Louvre in Paris is considered to be a masterpiece and incorporates the Golden Section in its design. During an interview with Ekwanim Productions of Paris he was asked if he was inspired by the same proportions that are found in the Great Pyramid. Pei claimed that he came by the Golden Section naturally and that he has abandoned strict adherence to measurement, preferring to arrive at his designs through his intuitive and artistic eye for what is pleasing, and the Golden Section appeals to a more right-brain approach to shaping the architectural landscape. The question should be asked, therefore, whether the ancient Egyptians were similarly influenced. Regardless of what their answer might be, however, engineers working under the direction of Pei, as well as those involved with the designers of Ramses, had to apply measurement to convey to the craftspeople the information they needed in order to bring what may have been inspired creativity into physical manifestation.

  Unfortunately, the question of Ramses’ head is much more complicated, because it involves three-dimensional geometry, not just lines and circles on a flat piece of paper.

  RAMSES BOUQUET

  While working in my CAD program, my wife suggested that I see how the Flower of Life fit with the geometric scheme that was crafted into Ramses’ face. I didn’t think much of the idea (probably a typical left-brain engineer response), but nevertheless, I set about drafting a Flower of Life in my computer. The results are fascinating to look at, but far be it from me to suggest that the designers were dropping flowers all over their plans! Yet this superimposition illustrates, in an analogous way, the complexity of the three-dimensional geometry of Ramses.

  The Flower of Life symbol is considered to be sacred among many cultures around the world and is seen as symbolic of the connectedness of all life and spirit in the universe. It is found inscribed in some temples in Egypt—most notably at Abydos, where it is drawn, with meticulousness, in red ochre on a giant granite support column in the Osirian. The temple contains several of these drawings, and they are believed to have been placed there when the Osirian was filled with sand, for they are located high on the column.

  Figure 2.21. Ramses bouquet: the Flower of Life

  The geometry of the flower consists of intersecting circles that create six equally spaced petals. The arrangement of the flowers in a mandala is supposed to symbolize unity with the cosmos and aspiration for harmony and perfection. It is a powerful icon in the Indian culture, and it commands profound philosophical and religious reverence.

  Though I am not arguing that the use of these geometric elements were necessary to create Ramses’ head, the correlations with the statue of Ramses do illustrate the reality of a greater sophistication than what two-dimensional images can convey.

  FROZEN MUSIC

  The mathematical principles of musical harmony are directly related to geometry. Pythagoras brought these concepts to the Western world and inspired the orderly and disciplined understanding of objects we observe and create. Leonardo da Vinci used geometric archetypes, sometimes called sacred geometry, in his art. The German writer Goethe and the English expatriate Oscar Wilde, as well as the philosopher A. W. Schlegel, considered architecture to be “frozen music.”

  Grand musical events are planned with the accompaniment of the imposing grandeur of frozen music. To celebrate the inauguration of Cairo’s Theatre de l’Opera in 1869, Ismail Pasha, Khedive of Egypt, commissioned Guiseppe Verdi to write an opera. Inspired by ancient Egyptian architecture and with the help of Auguste Mariette, he produced Aida, which has played for large audiences at Luxor and more recently on a large, specially built stage at the foot of the Giza Plateau. Egyptologist Zahi Hawass pleaded for the set to be removed, because it detracted from the archaeological value of the area.5

  Though we don’t normally consider objects around us to be musical, as a carefully designed and crafted geometric shape, a musical instrument that sits quietly in the corner of the living room could be considered frozen music. In this respect, the analogy between architecture and music can be considered correct—but it may also pose the question of whether there is such a thing as frozen music at all. It could be argued that when an observer is introduced to and interacts with a geometric structure, whether it is an instrument to play or a building within which to pray, it has an effect on the senses. Without the presence of people, the building responds to subtle energies from the earth and the environment through seismic or thermal movement of its structural components. An instrument adds its own voice, responding in resonance to weak forces, but the output cannot be discerned by the human ear. The grand piano sitting in the corner of my living room plays a faint encore after all sources of sound are turned off and nothing but quiet reigns.

  Scottish composer Stuart Mitchel discerns frozen music in the design of the Rosslyn Chapel in Scotland. His analysis of the architecture of this structure reveals archetypal design
s that are associated with certain frequencies that affect membranes that have been dusted with fine sand or powder. The powder organizes itself into patterns on the membrane according to the acoustic wave pattern generated by the frequency on the surface of the membrane. Stuart’s music can be sampled at www.tjmitchel.com.

  The geometric proportions of the Temple of Amun Mut Khonsu (commonly known as the Temple of Luxor, though it is not the only temple in Luxor) were measured by Schwaller de Lubicz and were found to have been designed with harmonic proportions encoded in the dimensions of their architecture. To experience the temples of Egypt is to become absorbed in harmonic proportion, and they have influenced many travelers.

  In The Beginner’s Guide to Constructing the Universe, Michael Schneider writes, “Earthly Music was seen as a mirror image of the heavenly ideal descending from above.”6 After working with a Ramses’ head and discovering the correlation between its features and well-known geometric shapes, I decided to draw the example that Schneider gives in his lavishly illustrated book of the harmonic sequence of an Apollo Zeus harp. One of the sequences given includes the notes B flat, E flat, A flat, D flat, and G flat (the five black notes on a piano). The notes were played on the harp covering three octaves, from high notes to low notes, and are described as overlapping circles with nodes that represent the length of a string.

  Figure 2.22. Harmonic scale of Apollo Zeus harp

  I then overlaid the image of Ramses with the Flower of Life with the geometry of the head, rotating it 90 degrees and scaling it so that the small circles were the same size as the flowers. The top circle was then placed over the uppermost flower. The correspondences that flowed from this arrangement are shown in plate 6.

  RAMSES’ HARP CORRELATION TABLE

  Musical Note Flower of Life Face and Grid

  B Center of three flowers Bottom eyelid

  E Center of three flowers Tip of nose

  A Center of two flowers Parting of lips and lower lip profile/Vertical lines on grid

  D Perimeter of flower Vertical and horizontal lines on grid

  G Center of two flowers Horizontal line on grid

  With the Flower of Life, the face takes on a more three-dimensional appearance, which is necessary in order for us to appreciate fully what was accomplished. The geometry is more complicated, but not as complicated as what is necessary to create two identical, mirrored, three-dimensional surfaces in granite. The intricate web of correspondences among the face, the harmonic sequence, the flower, and the grid seems to establish a physical manifestation and integrated expression of art, mathematics, music, and engineering.

  In chapter 1, we saw the perfection of the Hedjet and the Pschent. They presented us with a hint of techniques in ancient Egypt that have been unknown until now—techniques whose application required workers with both the knowledge of absolute accuracy in manufacturing and the tools to accomplish it. We are leaving Ramses’ face with a greater understanding of the difficulty involved in manufacturing the head. Though we have worked thus far with only a two-dimensional view, our results have yielded enormous implications. In the next chapter, we will examine the third dimension of Ramses’ head: a 90-degree view of its profile from both left and right. We will then examine other Ramses figures to compare their geometry to the one we have been studying and examine some ideas as to how these mammoth objects could be created today.

  3

  The Ramses Challenge

  An answer brings no illumination unless the question has matured to a point where it gives rise to this answer which thus becomes its fruit. Therefore learn how to put a question.1

  ISHA SCHWALLER DE LUBICZ, HER-BAK: THE LIVING FACE OF ANCIENT EGYPT

  Figure 3.1. Nefertari, Ramses’ guiding hand

  RAMSES’ SMILE

  As I pondered the features of Ramses’ face, I found it quite curious that his mouth was turned up in an exaggerated smile (see figure 3.2). Though some might argue that having a wife with the attributes of Nefertari would give any man cause to smile, visitors to the temple are faced with what seems to be a synthetic smile that gives the face of Ramses a rapturous countenance. Examining the mouth closely, there appears to be anomalous geometry that does not blend with the contoured surface of the face. In fact, it appears that the face was cut first and then a separate tool shaped the mouth—and that this tool followed a contour that left a sharp cusp along the upper vermilion border (the junction between the mouth and the facial skin) of the mouth. It is particularly pronounced at the philtrum (the trapezoid-shaped indentation that joins the nose with the mouth) and forms a sharp, triangular point.

  Figure 3.2. Ramses’ smile at Luxor

  The triangular point where the philtrum meets the vermilion border on the Ramesseum Ramses is even more pronounced. The smile, though, does not appear as exaggerated as on the Ramses at Luxor.

  Why is the curve of the Luxor Ramses’ smile so exaggerated? Further, as we’ve seen, only the mouth is smiling; the rest of the face is at rest. Even if the muscles of the cheeks were pulled up, as they would be if anyone tried to smile this big, it is doubtful such curved lips could be achieved.

  I puzzled over Ramses’ unnatural smile, but it seemed to me that it wasn’t shaped this way merely to achieve a Pythagorean triangle; perhaps there was another reason for its appearance. Creating a line drawing from the features of the face and then removing the photograph revealed an image that was uncomplicated and distinct (see figure 3.3). Then it dawned on me that I was studying a face that was not in situ, but close to eye level—originally, the head was connected to a statue that was approximately 40 feet tall.

  The seated Ramses figures at Luxor tower above the tourists at the temple. The proportion of both the people and their interaction with the statues has some bearing on the design of the statue, as we can dis-cern from the face. Ramses’ smile appears exaggerated only when we view the head at the same elevation. When viewed from the ground, the smile from the shortest to the tallest statue, 40 to 60 feet (13 to 18 meters) high, appears more natural. We can see one illustration of this effect when we look at our own mouth in the mirror, then notice that when we raise our head, our mouth appears downturned. To understand this effect even further, we can hold an egg vertically by the ends and draw a straight line horizontally from one side to the other. When we rotate the egg either toward or away from ourselves, the straight line appears curved. Obviously, when the ancient Egyptians visited the temple, they preferred to meet with a beneficent-looking king, rather than one who had a frown frozen on his face. Thus, the seemingly unnatural smile of Ramses when we view it straight on was calculated to appear natural via the perspective of someone at ground level. This is why the Ramesseum Ramses’ smile looks natural: the photograph was taken looking up at the statue.

  Figure 3.3. Ramses’ iconic features.

  We can note another example of geometric warping for visual effect in the fluted Doric columns of the Parthenon. The Greeks developed a technique known as entasis to avoid an optical illusion caused by the shaft’s fluting (parallel vertical lines): In a tall structure such as the Parthenon, these lines appear concave. To compensate, the Greek architects made the columns slightly convex, so that to the viewer they seemed straight.

  Modern architects and engineers are still trying to understand how the ancient Greeks were able to build the Parthenon in ten years when the restoration of the monument has continued for more than three decades and is still not complete. What they have learned and shared along this arduous path of rediscovery is that the Greeks were highly skilled at building visual compensations into their structures. Columns were crafted and positioned to compensate for how the eye interprets what it sees at a distance. Subtle variances in the surfaces of platforms, columns, and colonnades provide the appearance of geometric proportion, whereas if they had worked from the perspective of a flat datum surface, the brain would interpret the results as being slightly skewed.2

  In the face of Ramses, we see that such compensatory c
oncepts did not originate with the Greeks, but instead were used by the Egyptians at Memphis and Thebes more than a thousand years earlier. If a normal mouth had been crafted onto Ramses’ face, it would appear from the ground to be turned down in a frowning shape. To confirm this, we can look at the image of the statue of Ramses at Memphis, near Saqarra.

  The statue of Ramses at Memphis is estimated to have originally weighed more than 300 tons. Though it once stood upright, the statue now lies on its back in the open-air museum at Memphis. It is crafted of fine limestone and, as the photograph taken from the viewing mezzanine illustrates (see plate 7), is manufactured using the same inexplicable precision and product value as the Ramses statues at Luxor. The symmetry is maintained between both halves of the face, and the exact surface of both sides of the face of the statue is composed of curves of varying dimensions that flow together. The Memphis Ramses provides us with information that we are able to infer by viewing the front and side views of the Luxor Ramses, because the photographs of the front and side of Ramses’ head at Luxor provide two-dimensional views of three-dimensional geometry. The Memphis Ramses, on the other hand, provides us with information that clearly shows that the features on both sides of the face are mirrored in not just two dimensions (x and y), but three (x, y, and z).