Ancient machinists

Kragen Javier Sitaker, 02020-10-08 (26 minutes)

YouTube keeps recommending me fringe-science videos with catastrophist theories of history, positing the existence of prehistoric high-technology civilizations terminated by a Younger Dryas impact event. I decided to watch one entitled, “Evidence for Ancient High Technology - Part 1: Machining”.

Sawing stone blocks

After the author, who goes by “UnchartedX” or “Ben”, spends 21 minutes complaining about how Wikipedia and the archaeological establishment are suppressing the theories he favors so they won’t lose tenure†, in between deprecating “savages”, he finally gets to explaining some actual arguments. He points out that some basalt blocks at what he says is the Old Kingdom Egypt site of Abusir are sawn: the cut surface has striations or grooves on it, with a characteristic spacing of a few millimeters and a height typically under a millimeter, and the block was broken off after being sawn most of the way through, showing that the kerf was a few millimeters thick. He says that it has “clearly been cut by a blade with a very distinctive circular arc to it”, but to me the striations look straight. He claims that the striations imply a “rapid rate of cutting”, which I don’t think follows at all; he doesn’t explain why he thinks this.

He says that the radius of the curvature of the striations suggests a circular saw of 8 or 9 meters.

(In passing it’s worth noting that, while Abusir does have Fifth-Dynasty Old-Kingdom pyramids, from around 2400 BCE, it also has the remains of a Ramesside temple from only about 1250 BCE, during the New Kingdom. Ben doesn’t mention why he thinks these blocks are from the Old Kingdom.)

To me it seems more likely that the cuts were made with an abrasive “wire saw”, as is commonly done in quarrying today, rather than a circular saw; but probably using plant-fiber cord, thin wood boards, or copper wire or sheet, to move the abrasive sand through the cut, since steel cable and synthetic diamond were unavailable. Quarrying stone with plant-fiber ropes, water, and sand is a well-documented technology in recent centuries, and could easily date back to the Neolithic. The block seems to be about a meter across, and a meter-long piece copper wire seems more likely to me than a circular saw of 8 or 9 meters in diameter. It would produce the observed kind of striations, but of course without a very consistent radius.

Wikipedia explains that abrasive sawing is the mainstream theory for how the Egyptians cut granite blocks, citing among other things Denys Stocks’s 2003 book on the subject. I wonder why Ben doesn’t mention this, or indeed abrasive cable sawing at all. He does say, “Until barely 100 years ago, the technique used in the field to cut through granite was far different, and far more primitive,” talking about wedge-wetting.

He points out that most of the blocks at the site do not have such striations, suggesting that they were polished smooth, which is clearly a thing that the Egyptians did with stone (see below about flatness).

The standard sawing technology for millennia has been a bow saw or bucksaw, where the blade is held in tension by a frame with some levers, usually tensioned with a twisted pair of ropes; although, with the recent advent of cheaper, stiffer, and harder steels, it’s become common to use blades that are just cut from sheet metal, often with the stiffness of the blade itself enabling the saw to be pushed through the cut. Even today you use a bow saw or hacksaw with an abrasive wire blade to cut materials that are too hard for metals to cut.

He points out that at Giza (Fourth Dynasty, Old Kingdom) there are stone blocks with similar saw marks that run only partway through the stone. To me some of these cuts are distinctly curved rather than planar, which is easy to achieve with a wire saw but very difficult with a circular saw — you’d have to make the saw blade accurately spherical (or cylindrical, like a hole saw or core drill) rather than a flat disc. Indeed, somewhat later he points out a sawn granite block at Abu Rawash whose surface is visibly concave, which to my mind clearly demonstrates that it was cut with something like a cable saw or bucksaw, not a circular saw.

You would think that if the Egyptians had 9-meter-diameter circular saws for cutting huge blocks with, they would also make much smaller saws for making the smaller cuts, which would leave circular striations with a much smaller radius as they moved through the cut.

Stocks, who doesn’t seem to have one of the academic positions so scorned by Ben, actually went to Egypt to try out abrasive cutting with copper tools; he has some 16 other academic publications from 1986 to 2013 on such subjects in addition to his 2003 book. Most of them are in the academic journals that won’t accept Ben’s work. However, Stocks doesn’t seem to be in favor of the cable-saw theory, instead advocating the use of 6-mm-thick copper sheets to drive the abrasive, using no lubricant — not only because water increased wear on his reed tube drills, but also because it slowed cutting in his tests with both saws and tube drills, rather than speeding it, and was more inconvenient to remove; however, it is known that the later Minoans used water or oil lubricants for abrasive cutting of stone with reeds. Ben attacks the copper-blade approach as impractical, I think rightly so — a cable saw would be more efficient, cheaper, and produce similar markings.

† This suggests that Ben doesn’t know what “tenure” actually is, seriously impairing his ability to understand the motivations of the opponents he demonizes.

Core-drilling stone

Ben makes much of spiral grooves found in cores drilled out of stone using core drills, saying these are “machining marks not explainable by the tools and techniques in the archaeological record”. Wikipedia claims that core drills date to 3000 BCE in Egypt, so he seems to be in accordance with the “establishment” he so bitterly attacks. He even shows a museum tag saying, “UC.44985: Basalt tube drill core from enlarged hole. Tools & Weapons, LII, 61; p.45. ?Dyn. IV,” so I guess he knows this is already the mainstream theory. Nowadays of course we use metal or cermets for our core drills, but hollowed wood or bamboo would probably also work, because what cuts is the abrasive.

Stocks did some experiments using Egyptian hollow reeds, very similar to bamboo, as bow-driven tube drills, with some success, but he thinks these were displaced by copper tube drills not long after 3600 BCE, resulting in a “rapid increase in the manufacture of hard and soft stone vessels” at that time, and mentions that in Minoan Crete (around 2000 years later) emery has been found adhering to drilled-out cores. He was not able to drill granite with the reeds. Emery is impure corundum, or sapphire, which is the major abrasive used today in industry and is dramatically more effective than quartz; Stocks believes, however, that emery was not available in Egypt.

I suspect that if you needed to cut basalt or granite with a reed tube drill, you might have more success after fire-hardening it, a technology 400,000 years old, predating stone weapons, though not stone tools. Using an oil abrasive would have avoided softening the reed with water, and probably would improve the efficiency of the process.

Beaten copper tubes from the Fifth Dynasty have been found, and would be much harder than either reeds or cast copper tubes. They can also be much thinner, also improving the efficiency of the process by reducing the kerf width. Despite this, Stocks believes that cast copper predominated, in part because in his tests soft metal worked better for abrasive cutting.

Ben claims that the evidence of the spiral groove on Petrie’s UC 16036 tapered red granite core is suppressed by mainstream archaeology textbooks that tilt photos of it to make it appear non-spiral. However, Stocks’s book — my reference for mainstream archaeology — discusses this groove as an established fact, mentioning Petrie’s resulting hypothesis that it demonstrated the use of tube drills with jeweled teeth firmly fixed to the tube, rather than abrasive cutting; Stocks rejects this as impractical. He also points out that Petrie found verdigris in tube-drill holes as well as saw cuts, suggesting sawing with copper or bronze, and in one case even bronze particles in a New Kingdom tube-drilled hole.

Another non-mainstream theory is that the Egyptians used sound vibrations to drive their tube drills, rather than bow drills; modern loudspeaker-driven experiments have demonstrated that this is a practical approach. Stocks points out that in his experiments, the tapering observed in many ancient Egyptian tube-drilled holes and cores was only observed with bow drills, which tend to rock the drill back and forth in the hole. Also, tomb paintings show woodworkers with bow drills.

Flatness

Ben makes much of the “flatness” of the various surfaces he observes. However, it’s easy to see that many of the masonry walls he admires are made of stones tightly fitted together upon installation, rather than by using the flat surfaces that a circular saw would easily produce. Corners are curved, and hollows are cut into the corners of stones (presumably by grinding away the points of contact), to enable the blocks to fit together despite the extremely visible non-flatness of their mating surfaces.

Some of the surfaces are indeed quite flat and well-polished, with in many cases parallel scratches from the grinding and polishing process.

I have a vague memory that the technique of grinding three trial surfaces against one another pairwise to achieve flatness, refined by Henry Maudslay with hand scraping of metal, dates to ancient Sumeria, however, I can’t find my source for this. Clearly it wouldn’t require any technology or materials unavailable at the time, though. Sandstone or fired clay pottery with sand can easily achieve 100-micron flatness in this way, and fired clay tempered with silt instead of sand can reach 10 microns.

In modern machining practice, once you have a flat surface, a standard way to transfer this flatness to a new surface is by “lapping”: putting a piece of sandpaper on your flat granite surface plate, then moving the part to be lapped around on the sandpaper in order to grind it flat. This technique has been routinely used in optics for centuries to achieve surfaces perfect to within a fraction of the wavelength of light, though without interferometric inspection, roughness of several microns is more commonly achieved.

A very similar process allows you to produce surfaces that are perpendicular to very high precision, once you have a surface plate; three trial squares are tested against one another on the surface plate, being ground at their high spots.

In the sequel video, Ben claims that Christopher Dunn‡ has used a modern straightedge to measure some surfaces in some kind of stone box in the Serapeum as being flat to within one thou, 25 microns, strongly suggesting the use of the three-surfaces grinding method; the perpendicular surfaces examined were also perpendicular to within measurement precision (claimed to be much better, but he shows a photo of the measurement being taken with a machinist’s square not capable of such precision). Ben does not mention why Dunn didn’t use a dial indicator to examine flatness to micron precision, and indeed describe’s Dunn’s method as “relative rudimentary testing”.

Although this video claims to be about “precision”, Ben doesn’t provide a single metric of precision in the whole video; he never says, “The interior of this vase is spherical to within 100 microns,” or “The two sides of this statue’s face vary from one another by no more than one millimeter.” He only says things like “basically perfect” and “identical”.

Ben makes much of the fact that incised hieroglyphs are not polished, even when cut into flat polished stone surfaces, claiming that this demonstrates that a much later and more primitive culture cut the hieroglyphs than that which made the flat surfaces themselves. To me it seems more likely that hieroglyphs are unpolished to improve the visual contrast with the surrounding stone.

‡ Christopher Dunn is author of The Giza Power Plant, a book claiming that the Great Pyramid was actually a power plant harnessing “harmonic resonance” to convert seismic energy to hydrogen and microwave energy. Ben promotes this book in the video.

Lathes

Bow lathes are well-attested from ancient Egyptian drawings. Ben is puzzled about how ancient Egyptian stone vessels were made (“I’d like to see anyone try and make these by hand with copper chisels and the known techniques of ancient Egypt,” he says in his second video), but a glance shows that they were made on lathes — not continuous-rotation lathes like modern lathes, but reciprocating lathes like bow lathes and pole lathes, which allow you to, for example, leave handles on the side of your jug, though those handles don’t enjoy the precise circularity of the lathe-cut surfaces. Bow lathes and pole lathes were the common form of the lathe until the 18th century.

However, it must be admitted that the oldest surviving Egyptian depictions of lathes date only from 1300 BCE, only 3300 years ago. It hardly seems surprising that the ancient Egyptians had lathes another 1000 years before that. Ben does eventually mention lathes, explaining that Petrie believed these pieces to be lathework. As far as I know, this is also the current mainstream academic archaeological opinion as well; Ben claims that it is not, because the wheel was not known at this date. But a lathe does not require wheels any more than a tube drill does.

Immediately after quoting Petrie talking about alabaster vases, Ben starts talking about how amazing this is, particularly in “these very hard materials”. But alabaster is the second softest stone of all; it’s gypsum, also known as plaster of Paris or sheetrock; you can carve it with your fingernails. (Some archaeological “alabaster” is actually calcite, which is harder than gypsum, but only slightly. Chalk is calcite.)

Perhaps Ben doesn’t know what alabaster is and didn’t think it was worth looking it up, just like he seems to not know what “tenure” is. But at some point the evidence starts to suggest that Ben is not just misinformed or deluded but deliberately deceiving people.

Of course, lathework on such brittle materials would need to be carried out by abrasion in the last stages, not cutting with gouges or chisels.

Stocks in his book points out that the interiors of many of these jars and vases were bored out using stone and wood boring tools, which are clearly depicted in hieroglyphs.

The schist disc

Ben is also mightily impressed (in his second video) by a beautiful schist disc in the Cairo museum with three graceful thin hyperboloids symmetrically carved around a wheel; it’s usually known as the Egyptian Tri-Lobed Disc. He perhaps is not aware that you can make such hyperboloids by cutting a series of straight lines between evenly marked points along two curves.

Again Ben lies about the nature of a stone in order to persuade the ignorant: he calls schist “this very hard stone”, but the defining characteristic of schist is that it is very friable due to high phyllosilicate content, which is in fact where its name comes from: σχίζειν, to split.

Sometimes the artifact is described as “metasiltstone”, described as a weakly metamorphosed form of siltstone or silty shale favored by Egyptian sculptors for its suitability for thin carvings like this.

Weight

Ben makes much of the fact of moving stones that weigh tens of tonnes. But if one person can lift 50kg, then, without levers, you only need 200 people to lift ten tonnes, which is a small number compared to the population of Egypt at the time. And if they can get 5:1 leverage with some logs, then you only need 40 people.

Moreover, most of the process of moving a large stone like that doesn’t involve actually lifting it; it’s much less effort to slide it horizontally or on a seked-2 ramp, and you can do that with just ropes rather than having to stick stuff underneath it. And a fellow in Canada has demonstrated his proposed stone-manipulation technique with a several-tonne chunk of concrete: you balance it horizontally on a small number of stone pivots near its center of mass, push down on one end to lift it off all but one pivot, rotate it around that one pivot, possibly position pivots anew, then release its weight so that it settles on the pivots again. Then you can start again from the other end, allowing you to move the pivot you were using previously. He was able to move this slab entirely by himself, using the slab itself as the lever.

Geometry of statues

Ben, quoting Dunn, is very impressed with the geometric precision of the heads of the Rameses statues at Luxor and the Ramesseum, claiming that the only way to make such shapes nowadays is with CNC machining; in 1970, he claims, it would have been impossible. But he show Dunn’s diagrams demonstrating that the heads’ shapes are mostly composed of simple circular arcs and convex solids of revolution, carefully planned to be tangent to one another. (Dunn claims you’d need NURBS, but his diagrams demonstrate the opposite.)

I do think it’s clear that the statues, like Tibetan sand paintings and like pyramids since the time of Djoser, are laid out geometrically, using precise procedures and measurements. But I don’t think this requires 18th-century technology, much less 21st-century technology. The Romain du Roi typeface was thus laid out in two dimensions on a regular grid with circles and arcs in 1692.

The simplest brute-force approach would be to simply measure out a large number of points in space. Since we’re presumably talking about enormous numbers of workmen sawing and grinding granite for decades, the hard part is not the stone cutting; it’s knowing which stone to cut and which to leave. That is, the problem is measurement, or sensing, not actuation.

A point in open space can be precisely located by its distance from three reference points, which can be measured out precisely by metal chains. (Aside from the reflection ambiguity, of course, which would not have presented the problem for sculptors that it does for GPS.) Copper’s linear coefficient of expansion is 16–17 ppm/K; a five-meter-long copper chain will thus lengthen and shorten by some 800 microns with a 10° temperature change, less than a millimeter. The lengths of pieces of wood, clay, or plaster are even more precisely constant, and even plant-fiber rope would probably be good enough. Distances measured with tiny copper chains on a small plaster scale model of a sculpture can thus be scaled up to a full-scale megalithic sculpture with submillimeter errors.

Ben, as usual, never quotes a tolerance, but he does include some measurements from one of Dunn’s books, which are given to only four significant figures, which would not be enough to detect millimeter-scale errors.

Moreover, the Egyptians seem to have understood the Pythagorean Theorem by the time of the Berlin Papyrus 6619 (12th or 13th Dynasty, around 1800 BCE), several centuries before Ramesses, and it was in widespread use in Mesopotamia at that time as well. So you wouldn’t have needed to make a scale model; you could have calculated.

Drawing tangent arcs and tangent lines on sand (or paper, or papyrus) is easily done with compass and straightedge, both of which are ropes stretched thin over sand until the Hellenistic period. This may not be appreciated by those who have never done it.

To make an arc tangent to another arc at point P, draw a line through P and the center of the arc. Any arc through P centered at any point Q on this line will be tangent to the other arc there. They form a beautiful smooth curve.

Given a point P on a line L, select a point Q on L. L and the circle through Q centered at P have two intersections; one is Q; call the other R. The circle through Q centered at R and the circle through R centered on Q have two intersections; the line through them is perpendicular to L at P.

To make an arc tangent to a line L, and choose a point P on L. Draw a line M through P perpendicular to L. For any point Q on M, an arc centered at Q starting at P will be tangent to the line at P.

To make a line tangent to an arc at a point P on the arc, draw a line M from the center of the arc through P. The line perpendicular to M through P is tangent to the arc at P.

Solids of revolution are most easily produced by a series of circles around their axis, each circle produced by swinging two chains around the axis from two reference points on it. Given a smooth curve in one plane containing the axis, you can use it to repeatedly set the distances on the two chains to a point on the curve, then generate the rest of the circle. However, this will not work for convex surfaces to be cut out of a solid material, because the chains would have to be inside the material.

However, there are many other contrivances that can be put to the same use, one of them being the lathe, which was already in use, as we have seen. But a wooden board that rotates around two pivot points, like a door, would work just as well; the curve to generate the solid of revolution can be cut into the board, allowing it to be accurately cut into a plaster model. To directly apply the method to the full-size statues without a scale model, you probably need a different way to swing your pattern points around your axis.

(To be continued?)

Backward progression

One of the few things Ben says that I agree with, in his second video, is that there seems to be a “backward progression of technological capability” in ancient Egyptian technology, with Old-Kingdom artifacts being often more finely made than Middle-Kingdom artifacts, which are more finely made than New-Kingdom artifacts, which are more finely made than Hellenistic-period artifacts. The Egyptians themselves at the time are known to have made similar comments, and of course the Bronze Age Collapse loomed large in Classical Greek mythology and popular culture.

I think the reason for this is relatively easy to understand: technological progress is created by innovators like Imhotep, Djoser, Champollion, and Feynman, not by conservative traditionalists. Innovators must constantly struggle against conservatism to make any progress. But it’s easy to see, looking at the development of hieroglyphic writing, ancient Egyptian art, and ancient Egyptian metallurgy, that for millennia Egypt was a very traditionalist, conservative society, even for its time; 1200 years after Imhotep, they deified him and thus halted progress. Even the adoption of iron smelting in Egypt took from 2000 BCE until the neo-Assyrian conquest in 671 BCE, several centuries after neighboring kingdoms.

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