The requirements for producing such accuracy go beyond coincidental simplicity. I wasn’t expecting the corners of the sarcophagus to be perfectly square, for perfection is extremely difficult to achieve and to find it in an ancient artifact that was supposed to serve as a coffin would be a miracle. Yet I was not prepared for what I found: I was astonished as I slid my square along the top of the parallel (I used the top of the parallel to raise the square above the corner radius) and found it fit perfectly on the adjacent surface. The significance of the find came over me, and I pointed it out to others in the group. The film crew was busy capturing it on video as I went to each corner and performed the same test. On three corners, the square sat flush against both surfaces. The fourth corner had a gap that was detected by the light test, though its variance from being a true square may have been no more than 0.002 inch (0.0254 millimeter) (see plate 13).
What does this tell us about the methods used to create this box? The implications of my previous question about why the builders found it necessary to create a coffin with perfectly flat inside surfaces had just been raised exponentially. Why go to extreme trouble to create a box with perfectly flat inside surfaces as well as go to extraordinary lengths to make sure the inside corners are square—to within a tolerance normally expected of modern machinists and toolmakers?
Figure 6.7. Using an inside micrometer to measure between corners inside a box
In order to create a box with square corners, there has to be some way to measure them. The layperson who knows the ways of a carpenter may create square corners by measuring from corner to corner and making sure the distance is equal, but a solid granite box crafted to such exact specifications is a different class of work from that of cabinet making or squaring a structural frame.
There could be no adjusting Khafre’s granite box after the insides were finished to achieve perpendicularity. The only adjustment would be to lap the entire surface again and have a means to take measurements all along. To imagine creating this without orthogonal machine axes to guide a cutting tool is to imagine a task that borders on the impossible—or at least the hugely improbable considering the box’s stated purpose is a coffin.
Nonetheless, the diagonal measurement method could be used to verify what was already achieved using controlled mechanical axes, but we would need specialized equipment to do it. Before the introduction of laser metrology instruments, we might have employed two perfectly round bars in which the radius of the diameter is larger than the box’s corner radii. With them touching the adjacent flat surfaces, a means of measuring between the bars would be employed. Before the introduction of laser metrology instruments, we would have used a precision inside micrometer as seen in figure 6.7.
The method shown, however, only provides information at one point in the cavity, and the box in Khafre’s pyramid, as measured by Petrie, is 29.95 inches (76.073 centimeters) deep. In order to have a complete and accurate measure of the square corner down to the bottom of the box, there must be many measurements taken using this method.5 Moreover, a precision square would still need to be employed to assure that the adjacent surfaces were square and flat with the tangency point of the corner radius.
Figure 6.8. List of Petrie’s measuring instruments
Petrie did not address the square corners of the boxes when he performed his measurements. However, he did perform a detailed study of the inside and the outside of the box with a range of instruments—detailed in figure 6.8—that were quite sophisticated for his time and crafted by the finest engineers.
Not only, then, do we have an artifact with flat surfaces that are similar to a modern surface plate, we have one with inside corners similar to what we would find with a toolmakers square on a surface plate with the blade touching an angle plate (see figure 6.9). With the question of the orthogonal exactness now raised, along with one hundred and twenty years of advances in technology, any engineer, including Petrie himself if he were alive, would insist that the box in Khafre’s pyramid be measured again using the latest metrology instruments available. Petrie wrote about tolerable safe theories in his final chapter: “. . . others may by some further discovery be shown to have been intended, but most of these will probably bear the test of time, and certainly bear the test of exact measurement.”6
Figure 6.9. A surface plate, angle plate, and a precision square
If we were to inspect this box today, at the very least the inside measurements of the width and lengths should be taken with inside micrometers—or, preferably, special rods equipped with dial indicators. The examination could be performed, preferably, by an Egyptian engineer or an Egyptian architect. Even a layperson could perform these checks after receiving some training, as the level of skill necessary to use these instruments is not as difficult to attain as for the instruments Petrie was using—and the result would be more reliable.
What else is significant about this so-called sarcophagus? The corners themselves! After conducting the test with the parallel and the square in May, I pulled out my radius gauges to check the corner radius and thought about a documentary I had seen in March. In the 1999 Fox special Opening of the Lost Tomb, a dolerite ball was shown to the audience under one of the satellite pyramids next to Khephren’s pyramid and asserted to be the means by which the ancient Egyptians created granite artifacts. This method involved bashing the granite with a round ball until the desired shape was achieved.
I’m not disputing that this is a viable means of creating a box, and, indeed, there is evidence at Memphis near Saqqara that some boxes were created in this manner (see figure 6.10). This box has large corner radii and is extremely rough and tapered toward the bottom—exactly what you would expect to produce using a stone ball.
Likewise, it would be impossible to create the corner radius of the box inside Khafre’s pyramid with such a primitive method. While inspecting the inside of the granite box in Khafre’s pyramid I checked the corner radius with my radius gauges. I started with a half-inch radius gauge and kept working my way down in size until I selected the correct one. The inside corner radius of the box inside Khafre’s pyramid revealed a 0.09375-inch (1.009-millimeter) radius. There is, however, a rise in the material toward this radius and a cusp where another rise, presumably from the tool that cut the adjacent surface, meets the corner. The radius at the bottom, where the floor of the box met the wall, had an approximately 0.4375-inch (11.1125-millimeter) radius. Clearly, an 8-inch ball will not fit into a corner with a radius this size or even one five times larger.
So what kind of tool may have been used to cut the inside corners of these boxes? In 2001, I was able to take wax impressions of the south-west corner inside the box. Figure 6.11 shows that the corner reveals the geometry of the tool and may lead us to determine the method of manufacture. While other engineers may provide their own ideas to the puzzle, one possible reason for the corner profile is not uncommon in machining today. A grinding wheel may start out cutting a surface with a sharply defined radius on its edge. Through use, over time the corners become worn and the wear will appear as a taper from the edge. It appears that the cutting tool used to finish the inside of the box in Khafre’s pyramid became worn, and we are left to study its profile on the inside corner of the box where the tool cut the north to south surface and then the east to west surface, leaving a cusp there the shape of the tool overlapped.
Figure 6.10. Granite box at Memphis (Photograph courtesy of Stephen Mehler)
It is an incredible piece of work that speaks of a higher technology in its creation and perhaps even in its use. Even if we put aside the question of how it was manufactured, it still shouts the question: For what non-technological purpose might it be necessary to have such precision and accuracy? If we understand what it takes to perform such work, we are left with no alternative but to acknowledge a high level of technological prowess on the part of the ancient Egyptians.
Artifacts such as these fly in the face of any previous explanations of the ancient Egyptians�
� stonecutting methods. Egyptologists are now abandoning their previous assertions that these marvelous granite artifacts were cut using copper chisels. Moreover, though Denys Stocks and Mark Lehner have recently demonstrated how the ancient Egyptians may have cut granite using primitive methods,7 these demonstrations do not come close to explaining the remarkable exactness, geometry, and tool marks cut into the stones found on the Giza Plateau and at other sites in Egypt.
Figure 6.11. Wax impression of the inside corner
As we wander around the Giza Plateau, we find this precision in the most unlikely places. For instance, a single diorite block in the southeastern wall of the Valley Temple duplicates the accuracy found on the inside of Khafre’s pyramid box. In the Valley Temple there are several places where the inside corners comprise blocks that wrap around to create a part of the adjacent wall. This suggests that the blocks were positioned and then the inside walls were cut to specific dimensions. The diorite block is the finest example of precision, but there are sections of the granite pillars that are similarly precise, perhaps due to being buried in sand and protected from wind erosion, unlike much of the rest of the granite.
Figure 6.12. Valley Temple diorite wall block
Though there is now no doubt that accuracy and symmetry were part and parcel of the ancient Egyptians’ manufacturing and building scheme, there is a vast difference between a simple, precise flat surface and the complex geometry of a symmetrical Egyptian statue. As viewed orthogonally along a specific axis, we have an impression of precision, but examining a three-dimensional object with a two-dimensional photograph does not provide complete information: though it looks as if the right side of Ramses’ head is precisely mirrored on the left side, there are myriad points on the surface of each side that must be inspected to determine exactly how similar they are. The outline of the major features provides us with sufficient information to allow us to see just this, and we can hope this work will be performed in the future, preferably by experts in the field of metrology using 3-D photography and computer analysis.
Fortunately, I have inspected less complex surfaces that were created using the same geometric protocol of describing simple tangent circles. Yet instead of the tangent circles morphing into different shapes, as in face of Ramses or the wire frame that binds the geometry to create the surface and tool path of MadCam’s head (see plate 11), these tangent circles are projected along a precise axis that can be measured.
In 1995, I inspected a block on the Giza Plateau that caught my attention because of its smooth surface and what appeared to be machined corners and a rounded surface. I presented my findings in my book The Giza Power Plant. As time and technology progressed, I found myself examining the block again each time I returned to Egypt. On some occasions, I invited witnesses to examine the block with me. In February 2006, I invited John Anthony West. In May 2006 I was accompanied by Judd Peck, whereas Arlan Andrews and Randy Ashton joined Judd and me in November 2008.
John West is very good at reaching the heart of an issue using simple analogies. In summarizing the evidence of precision at Giza, he said, “It’s like finding a Porsche where only a wheelbarrow should be.”
This is a great analogy! To discover precision normally found only on modern artifacts in artifacts from a period of time when the wheel was not supposed to have existed raises eyebrows, many questions, and an overarching sense that such accuracy was the result of a period of technological development of tools that were capable of nothing less.
In 2004, I walked with Stephen Mehler, author of Land of Osiris and From Light into Darkness, across the plateau to show him the block I had described in my book when he turned in the wrong direction. The block I had written about was about one hundred yards east of the southeast corner of Khafre’s pyramid, but Stephen was heading down to the Valley Temple. As it turned out, on a previous trip to Egypt, he had looked for the block that I described in my book and had mistakenly identified another block south of the Valley Temple. Because I had not yet seen the block Stephen had found, we headed down the causeway toward the Sphinx and the block.
I was curious to see this example of ancient Egyptian stonework, and my curiosity was rewarded: it provides an excellent example of what could be described as an evolutionary step from a simple flat surface to the more complex geometries of ancient Egyptian statuary. In other words, if we consider a flat surface as the projection of a flat vertical line along a horizontal line, then the block on the south side of the Valley Temple is the projection of a profile composed of tangent radii and straight lines along a perpendicular horizontal line.
What is remarkable and important about the Valley Temple contoured block is that it shows that the ancient Egyptians crafted not only flat surfaces, but also contoured surfaces, with uncommon precision. As any engineer can tell you, a customer’s specifications regarding the accuracy of their product will determine its final cost. When considering the significance of this contoured block, therefore, we must keep in mind that it was obviously an architectural element that at one time was positioned on the top of a wall—beyond the close examination of passersby. If the contour varied slightly from its path, it would not be noticed, nor would it affect the purpose it served.
There is an even greater mystery to this forgotten piece of Egyptian architecture. If we discount the smaller piece nearby as originally a part of the piece we are studying, there is only one piece that has survived. If the entire wall of the temple was capped by dozens of these elements (see figure 6.14) that weigh approximately 17 tons each, where did the rest of them go? It seems that more of them would have survived if such a large number of pieces had been manufactured. A clue that provides a possible answer to this question comes from an unlikely place.
Figure 6.13. Granite block outside the Valley Temple
Sliding the 12-inch straight edge along the crown of the convex radius there, I could not detect any variation, which would be revealed by light showing through the straight edge’s interface with the stone. At several locations around the arc I repeated the inspection with the gauge coaxial with the centerline of the radius and found remarkable consistency.
From a photograph taken of the end of the cornice, we discovered that the ancient Egyptians applied the geometry of tangent circles in building three-dimensional form (see figure 6.16). I tried to detect a variation in the smoothness of the transition between the large concave radius and the small convex radius, but I could detect nothing but perfection of form. There are no ripples on the surface. There are no ridges or bumps or depressions. The precision and geometry of the piece cause it to stand apart from many other artifacts lying around it. It surpasses the columns and wall blocks that make up the construction of the temple, and I cannot help but wonder what important purpose it served.
Figure 6.14. Cornice on top of Valley Temple wall
Figure 6.15. Inspecting the accuracy of the cornice
Because the block was broken off at the end on an angle, the large circle (see figure 6.16) does not fit close to the end. It should also be noted, that the large circle is approximate, given the unevenness of the end. The radius at the far end, however, represents with reasonable accuracy the concave arc that begins at the bottom and ends tangent to the top convex radius. With this information, we can be reasonably certain, especially following what we have learned of the design protocol on the statues and crowns, that the piece was crafted to conform to exactness using true arcs as the design elements.
Figure 6.16. Cornice geometry
But, the question still remains: Why go to such trouble for an architectural detail that goes into a building? From a distant epoch in time, it would not be surprising to find a cornice that had been bush hammered and then given a polish without regard to a high level of precision. But to discover not only strict constraints in the design, but also the adherence to machinelike precision on a granite block that is destined merely to look elegant and attractive provides more evidence in the emerging picture of lost tech
nology in ancient Egypt.
The answer to the mystery of how the Valley Temple cornice block may have been used may be at the place where Stephen Mehler and I were heading before he diverted my attention. I described this granite block as being similar to a couch. In 2008, while I was on the Giza Plateau with Judd Peck, Arlan Andrews, and Randy Ashton, we walked over to the block and found it being used for just that purpose by a young Egyptian woman and her boyfriend.
This piece of granite has all the hallmarks of machining. Cut into the piece are characteristics that experienced machinists and designers use to allow a more rigid, stronger tool to be used to machine it. But, you may say, there were no machines in ancient Egypt! Why, then, would these features exist? We could say that there have been no machines found in the archaeological record that we can argue were responsible for this kind of work. This presents a bit of a conundrum, for there are no tools whatsoever in the ancient Egyptians’ toolbox that can be used to replicate what has been crafted in igneous rock, and which imposes its majesty on our consciousness. But before we begin discussing what tools might have been responsible for cutting Egyptian stone in antiquity, let us take a look at what is machinelike about this block.
Lost Technologies of Ancient Egypt: Advanced Engineering in the Temples of the Pharaohs Page 15