## building the pyramids -- 1/3/23

Today's selection -- from Numbers Don't Lie by Vaclav Smil. How many people were required to build the pyramids?:

"Given the time elapsed since the completion of Khufu's Great Pyramid (nearly 4,600 years), the structure -- ­albeit stripped of the smooth white limestone cladding that made it shine from afar -- stands remarkably intact, and hence there is no argument about its exact shape (a polyhedron with regular polygon base), its original height (146.6 meters including the lost pyramidion or capstone), and volume (about 2.6 million cubic meters).

"However, we may never know how it was built, because every common explanation is problematic. A single long ramp would have required an enormous amount of material to construct, and moving stones up shorter, wraparound ramps would have been tricky -- as would lifting and jacking up more than 2 million stones into position. But just because we do not know how it was erected does not mean that we cannot say with some confidence how many people were required to build it.

"We must start with the time constraint of two dec­ades, the length of Khufu's reign (he died around 2530 BCE). Herodotus, writing more than 21 centuries after the pyramid's completion, was told during his visit to Egypt that labor gangs totaling 100,000 men at a time worked in three-month spells to finish the structure. In 1974, Kurt Mendelssohn, a German-born British physi­cist, put the labor force at 70,000 seasonal workers and up to 10,000 permanent masons. But these are large overestimates, and we can come close to the real num­ber by resorting to inescapable physics.

"The Great Pyramid's potential energy (what is required to lift the mass above ground level) is about 2.4 trillion joules. Calculating this is fairly easy: it is simply the product of the acceleration due to gravity, the pyramid's mass, and its center of mass (a quarter of its height). Though the mass cannot be pinpointed because it depends on the specific densities of the Tura limestone and mortar used to build the structure, I am assuming a mean of 2.6 tons per cubic meter and hence a total mass of about 6.75 million tons.

 The three main pyramids at Giza, together with subsidiary pyramids and the remains of other structures

"People are able to convert about 20 percent of food energy into useful work, and for hard-working men that amounts to about 440 kilojoules a day. Lifting the stones would thus require about 5.5 million labor days (2.4 tril­lion divided by 440,000), or about 275,000 days a year during the 20-year period, and about 900 people could deliver that by working 10 hours a day for 300 days a year. A similar number of workers might be needed to emplace the stones in the rising structure and then smooth the cladding blocks (in contrast, many interior blocks were just rough-cut). And in order to cut 2.6 mil­lion cubic meters of stone in 20 years, the project would have required about 1,500 quarrymen working 300 days per year and producing 0.25 cubic meters of stone per capita by using copper chisels and dolerite mallets. The grand total of the construction labor would then be some 3,300 workers. Even if we were to double that in order to account for designers, organizers, and over­seers, and for the labor needed for transport, repair of tools, the building and maintaining of on-site housing, and cooking and clothes-washing, the total would be still fewer than 7,000 workers.

"During the time of the pyramid's construction, the total population of Egypt was 1.5-1.6 million people, and hence the deployed force of less than 10,000 would not have amounted to any extraordinary imposition on the country's economy. The challenge would have been to organize the labor; to plan an uninterrupted supply of building stones, including the granite for internal struc­tures (particularly the central chamber and the massive corbeled grand gallery) that had to be delivered by boats from southern Egypt some 800 kilometers from Giza; and to provide housing, clothing, and food for labor gangs on-site.

"In the 1990s, archeologists uncovered a cemetery for workers as well as the foundations of a settlement used to house the builders of the two later pyramids at Giza, indicating that no more than 20,000 people lived at the site. The rapid sequence of building two additional pyra­mids (for Khafre, Khufu's son, starting in 2520 BCE; and for Menkaure, starting in 2490 BCE) is the best testimony to the fact that pyramid-building had been mastered to such a degree that the erection of those massive struc­tures became just another set of construction projects for the Old Kingdom's designers, managers, and workers."

Vaclav Smil

#### title:

Numbers Don't Lie: 71 Stories to Help Us Understand the Modern World

Penguin Books