Given the off-center alignment of the photographs of Ramses’ head, it became clear that I had to return to Egypt. When I examined the photographs I took of Ramses’ head in February and began to compare the symmetry from one side of the face to the other, I realized that in the photographs I took when my camera was handheld (as opposed to on a tripod), the central axis of the camera frame was not quite in alignment with the central axis of the statue. I knew that I could not capture an image that was perfectly in alignment without trial and error, and what I had produced had errors, so I determined that I could do better if I was able to use a tripod stand and take a series of photographs while moving the stand incrementally around the head and keeping the nose in the center of my viewfinder. To understand why this tripod setup is so important, we can consider the following series of sketches that represent a view from above looking down on the head.
The ideal camera setup is illustrated in figure 2.9. To achieve this, the camera axis is oriented exactly along the central axis of the head, which is a theoretical line that bisects the features of the head. If an image of the head is then taken, flipping the image on its horizontal axis would make for an identical image.
Figure 2.10 shows the head rotated 1 degree from center. What this means is that when the image is copied and flipped and compared to the original, some features will not match.
The arrangement we see in figure 2.11 is the same one that was captured by my camera with my first set of photographs of Ramses’ head— when I copied, flipped, and overlaid a transparency onto the original. As we saw in figure 2.3, the mouth, nose, and eyes do not match, but the jaw outline matches perfectly. This is because the outline of the face is used to establish the central axis of the photograph and the nose is rotated slightly off-center.
As depicted in figure 2.7, by making the mouth the center point, the outline of the face is thrown off axis and the nose is thrown off axis. The eyes, because they are approximately at the same distance from the camera as the mouth, then come into alignment.
Even with a less than perfect alignment, however, I was elated by this discovery. The implications were immediately clear to me—and they were enormous. My preliminary studies indicated that the statue was crafted so that the left side was a mirror image of the right side. I realized then what was needed: I had to take another series of photographs and hope that one of them presented a closer alignment with the central axis of the head.
The photographs I took in May 2006 were certainly an improvement
Figure 2.9. Top view of camera setup. The central axis is identified with an L overlapping a C, which is the standard notation engineers use in their drawings to denote a centerline.
Figure 2.10. Rotated head
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Figure 2.12. Ramses’ symmetry, taken in incremental steps while moving the camera in an arc around the statue
Upon those I took in February. However, I was still not quite satisfied with the results and returned in 2008 with a better camera that resulted in figure 2.12, which is photograph 70 of a series of 94 photographs that I took while moving the camera in action mode while panning in an arc around the statue, keeping the nose in the center of the viewfinder. I then duplicated the image and mirrored it and made a transparency, then positioned this over the original to match the features of the face.
As we can see, the match is much closer, but not perfect. Figure 2.12 shows that the jawline, mouth, and eyes match, but the nose is slightly off center. Figure 2.13 shows a close-up of the nose and mouth with the nose in alignment. It should be noted that the amount of error in the orientation of the camera is actually half of the width of the shad-
Figure 2.13. Ramses’ nose symmetry
Ows revealed when different features are brought into alignment. If the camera was adjusted by half the amount of the error shown, then all shadows may disappear.
As we can see from studying figure 2.13, the jawline, mouth, and eye from the right side appear to line up perfectly with the left, but it appears that the nose is slightly off center. In figure 2.14, the nose is brought into alignment and a shadow appears around the jaw and the lips. The shadow is quite useful for our study, because it actually provides a reference line with which to calculate the percentage of error from one side of the face to the other. These results are stunning— beyond anything I had imagined.
Though visually the comparison between the two sides of the face is remarkably similar, dimensionally it requires further examination with metrology equipment to measure exactly the differences between the two sides. From a manufacturing perspective, the dimensional variation from a perfect form (i. e., the tolerance band) on the contoured surface of a form die depends on the ultimate function or purpose of the piece. Today’s machine tools can produce complex contoured surfaces to a level of accuracy that was not within the capability of machines forty years ago. When we compare Ramses’ head and modern machined surfaces, the analogy does not register as relevant or fitting, because the end products are created for completely different reasons, and a statue does not require the same precision as a contoured surface for, say, a rocker panel, a trunk lid, or a hood for a car body. Nevertheless, the comparison using a digital photograph compelled me to try to determine some kind of dimensional reference so that we can say with a reasonable amount of certainty that I was not influenced by an optical illusion.
To this end, and in order to draw from the photograph a relative dimension from one cheek to the other, I enlarged the photograph to approximately five times that of a human head and applied dimensions (measured in inches) from a vertical centerline to the outline of the jaw. In this way, there was no interference with an overlying transparency and the resulting shadow; thereby there was less uncertainty as to exactly where the edge of the face was.
The results in figure 2.14 show that the camera’s axis was shifted to the left of the axis of the head, and the dimensions of the nose and the ears indicate that a mere 0.l40-inch (3.55-millimeter) rotation of the camera to the right would bring these dimensions closer to being the same. On a human scale, the amount of error in the orientation of the camera would be 0.028 inch (0.711 millimeter), just slightly more than the thickness of a thumbnail. The dimensions of the jaw line are within a tolerance band of plus or minus 0.010 inch (0.254 millimeter), which on a human scale is plus or minus 0.002 inch (0.0508 millimeter). Close to the ears the tolerance band increases to plus or minus 0.065 inch (1.65 millimeters), which on a human scale is plus or minus 0.013 inch (0.33 millimeter).
Though they do not achieve perfection—but are much closer to the central axis of the head than those I had taken in February and May of 2006—the photographs featured in figures 2.12, 2.13, and 2.14 taken in November 2008 illustrate that slight variations in the camera angle can yield different results. Without specialized equipment and special permission, it is impossible to achieve the laboratory-type analysis that I am convinced must be achieved in order to quantify exactly the accuracy to which these statues were crafted. With the aid of two-
Figure 2.14. Ramses precision
Dimensional computer software, though, we can extract some basic geometric information about the artifacts and compare one half of each face against the other. In this manner, we can glimpse, through the fog of millennia, the minds of the designers of the sculpture, and we can conclude that a sophisticated geometric protocol was used. Designers, engineers, and craftspeople in the modern era may relate to the complex sculpted surfaces that have been proven here to create both sides of the face in mirror image.
The contoured surfaces of Ramses’ symmetrical face would be familiar to designers of everyday products that are created routinely today with computer algorithms known as non-uniform rational B splines (NURBS), which allow them to smoothly morph one shape to another with unbroken perfection. By using NURBS, computer-aided design programs create contours of airplane wings, turbine blades, and even the computer keyboard at your fingertips. Surfaces are now routinely designed and manufactured to the apparent precision of Ramses’ head. Incredibly, the ancient Egyptians were also able to routinely craft Ramses’ head and achieved the same results again and again from the north to the south of their linear, Nile-based empire.
The stunning implications are analogous to looking through the static interference pattern of time and confusion and seeing the elegance and precision that is normally built into a Lexus in a place where only the most rudimentary techniques of manufacturing are thought to have existed. The techniques that the ancient Egyptians are supposed to have used—those taught us in school—would not produce the precision of a Model T Ford, let alone a Lexus or a Porsche.
World History
