On Tuesday archaeologists reported that calculations made in building the Great Pyramid of Giza, one of the world’s oldest structures, were off by a measurement of several centimetres.
But to Glen Dash, the archaeologist and engineer who headed up the research, the discovery of that very slight miscalculation makes the 5,000-year-old structure that much more impressive.
Historians estimate that construction on the pyramid started around 2560 BCE. The tools the ancient Egyptians used were crude, their tasks were difficult and the construction was enormous. And yet “their accuracies were almost the same as with modern equipment,” Dash says. “It’s quite astonishing.”
Mark Lehner / Glen R. Dash Charitable Foundation / Ancient Egypt Research AssociationThe Dash Foundation and AERA team studying the Great Pyramid
The Great Pyramid, the largest in Egypt, poses a particular problem for archaeologists because its exterior has changed dramatically from its initial form: when the pyramid was first built it was covered in smooth white limestone casing. A few of these casing stones remain, but the majority were stripped away several millennia ago to be used as building materials. That makes it hard to extract much information from the rough rocks below.
Ancient Egypt is the primary focus of the Connecticut-based Glen Dash Foundation for Archaeological Research. Last year, the foundation teamed up with the Ancient Egypt Research Association to study the pyramid. Their joint report has just been released — seven dense pages of meticulously recorded calculations, graphs, observations, and analysis.
But media reports have largely fixated on one particular element, the pyramid’s base. The Dash Foundation’s study shows for the first time that the base of the Great Pyramid isn’t a perfect square: its west side is very slightly longer than its east side.
Glen Dash Archaeological Foundation / Ancient Egypt Research AssociationGlen Dash's calculations display that the base of the Great Pyramid of Giza is not a perfect square
“The Great Pyramid of Giza is lopsided,” read one headline. “There’s something not quite right about the Great Pyramid of Giza and it’s freaking people out,” said another. Few could resist “Leaning Tower of Giza” jokes.
But Dash doesn’t see it that way.
“I didn’t expect [the response] at all,” he said. “I was astonished by it. The story could have equally been written: ‘Study shows pyramid is near perfect.’”
It’s impossible to come up with exact measurements for the pyramid’s base — not enough of the baseline remains to confirm any calculation with certainty. And it’s certainly possible erosion or weather patterns have affected the structure over the last 5,000 years.
Mark Lehner / Glen R. Dash Charitable Foundation / Ancient Egypt Research AssociationGlen Dash measuring the southeast southeast socket, cleared of the sand that normally fills it.
But Dash and his team worked with the information they had.
In order to determine the pyramid’s length, Dash’s colleague Mark Lehner measured what remained of the pyramid’s baseline and members of the team plotted those points on a grid. Once they had those locations, they were able to use linear regression analysis, a statistical method that estimates the most likely lines between several points. That’s how they estimated the lengths of the pyramid’s base. They also took possible error bounds into account.
Dash’s team was able to determine with 95 per cent probability that the length discrepancy between the two sides falls somewhere between 0.6 and 14.1 cm.
Several news outlets have reported the higher number as fact — but Dash stresses that 14.1 cm is the highest possible length discrepancy between the pyramid’s east and west side. He believes a more accurate number is something close to 7 cm.
“It’s interesting how it gets re-reported,” Dash says.
To Dash, far from being a sign of failure, the discovery of an error this minimal re-affirms his belief in what he calls the “explosion of human ingenuity” in ancient Egypt.
Rebecca Dash / Glen R. Dash Charitable Foundation / Ancient Egypt Research AssociationGlen Dash, back, with a member of his team
“Today we look towards machines, but Egyptians didn’t do that,” he says. “They took what they had and used it in ever more clever says.”
Dash says the only tool ever discovered at the Giza pyramids is a plumb bob – a small vertical weight with a pointed tip that’s usually hung from a string to serve as a vertical reference line. Historians and archaeologists hypothesize that ancient Egyptians also used wood, rope, stones and possibly copper.
“It’s quite astonishing, all of the things they did with just those tools,” he says. “They had to be very patient and very clever.
“They had very primitive tools, but genius was there.”
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