# An Ancient Superpyramid

One of the last pyramids to survive to the present day was the Pyramid of Giza. Its longevity was no miracle. First and foremost, it was built on the Sahara Desert, a vast stretch of land that seldom--if ever--sees water. Then there was its shape--a triangle with a wide base and a narrow peak, ideal for durability. Finally, there was its size--139.5 meters, or 457 feet, tall. It took maybe 20 or so years just to build that particular pyramid.

In this scenario, let's say that Giza was as tall as the proposed Shimizu Mega-City Pyramid in Tokyo--2004 meters, or 6575 feet, tall. How long would it take to construct such a monstrosity?

For anyone who asks who this hypothetical pyramid is for, it's a pharaoh's astrologically-aligned palace, not his tomb. Because seriously, it's not practical to spend more than a few months building a tomb. By then, the corpse would have decomposed beyond hope.

• What technology level did you have in mind for answers? – Frostfyre Nov 6 '15 at 4:34
• Yeah, I'm concerned that the sheer weight (if it's the same material) would be an issue of some kind, as well as @Frostfyre's concern of technology level. – Mikey Nov 6 '15 at 4:42
• Pharoahs' tombs were typically constructed well before death, and construction halted shortly after death if they were incomplete to allow the interment to take place. – Monty Wild Nov 6 '15 at 4:48
• "Because seriously, it's not practical to spend more than a few months building a tomb" How long do you think it took to build the pyramids, a couple of weeks each? – Antrim Nov 6 '15 at 13:08
• By then, the corpse would have decomposed beyond hope. - Um, mummification solves that problem. And in the desert, it's possible for natural mummification to occur under certain conditions. Your corpses have nothing to worry about (besides being dead). – HDE 226868 Nov 6 '15 at 13:25

The volume $V$ of a pyramid of height $h$ and width $a$ is $V = a^2 * h / 3$

For the Cheops pyramid we get $(230.33\,m)^2 * (146.59\,m) / 3 = 2592293\,m^3$

Assuming we scale the base length with the same factor as the height, we get:

$(3148.79\,m)^2 * (2004\,m) / 3 = 6623139000\,m^3$ or a volume factor of $2554.93$

According to Wikipedia, it took 200,000 men 20 years to build it.

That means, if you use the same technology and the same 200,000 men you would get a construction time of $20\,years*2554.93 = 51098.6\,years$.

Or, in other words: you need more men or better technology.

An interesting factoid is that, if the figures from Wikipedia are right, an average worker apparently moved only $0.64\,m^3$ per year. So, obviously, your best vector for improving building time is increasing this factor, i.e. use (better) machinery to move the material.

And one more thing: At the time (~ 2500 B.C.E.) there were fewer than 50 million people in the world.

That also means: if you found a way of getting everybody to help, you could manage building the pyramid in 204.4 years. Feeding the people, with no one left to help, there might be a bit of a problem, though...

Egypt at the time apparently had something between 2 and 7 million inhabitants. All those together would still need 1,460 - 5,110 years. Frankly, that is still a bit on the long side to be considered feasible. Even if you hand waved feeding problems away.

• It wouldn't be entirely this bad, because as the size of the base grows, you can add more workers to the task. So providing enough workforce the time would be closer to linear, rather than cubic growth. – SF. Nov 6 '15 at 13:14
• See my last edit, @SF.: you have to have those people first. – Burki Nov 6 '15 at 13:19
• @Burki A minor edit turned into a large one due to some calculation and factual errors. For instance, it's clear that with only 20 times the workers to build something 2,500 times larger will take more than 20 times as long. – Samuel Nov 6 '15 at 18:58
• I'm curious how much weight would come into play with that too. The pyramid at Maidum collapsed under it's own weight at some point, which caused Egyptian architects to change their designs right in the middle of building the Bent Pyramid in order to avoid the same fate. When increasing the size that much, at some point the stone blocks are going to simply break under all that weight... – AndyD273 Nov 6 '15 at 20:40

Well, I can't say how long it would take, because frankly it would depend not only on available resources, but also on how much the builders would be able to cut down on labor. As Burki notes in his answer, any naive approach would require impossible amounts of labor. Which given available population and the fact that most of your labourers would only be available for a short time every year they are not busy producing food, would make the time far too long.

I can how ever give some pointers about how to build it.

First, start with an actual mountain of the correct height and roughly the correct shape. No ancient civilization is going to build something of that height from scratch. Why would they? The pyramids and the great lighthouse are about the maximum people of that level of technology might want to build. Anything more would be pointless waste.

There is no useful distinction between "overwhelmingly huge" and "even more overwhelmingly huge". And this goes especially for height. Some temple areas were ridiculously extensive since scaling up in the horizontal plane is fairly easy. Scaling up height in contrast is a major engineering problem that gets increasingly bothersome and pointless as height is increased.

Second, there must be an actual reason to use the mountain as a core instead of simplifying your logistics by building on level ground close to navigable river or safe harbour.

So make the mountain holy. The top of mountain is where gods once stepped on Earth and the ancestors of the ruling dynasty received their blessing, wisdom, or whatever. In many cases the rulers were considered descendants of the gods, in which case the peak would be the place where the first king stepped down from heavens and gave up his immortality to adopt human guise so he could guide the mortals.

In such case it would make sense to have a shrine on the sacred spot and have the royal family live on a palace built on top of the mountain. And then have a court where they receive people and arrange official functions built on a terrace slightly lower on the mountain so that the king does not need to travel up and down the mountain too often. And once you get started building lower terraces, you'll end up having multiple levels for high officials and nobility, for slightly less important officials and nobility, the servants, the guards and so on. You might need a separate level for clergy and temples for sacred rituals and secular matters. You might need a separate level for every level of officials and nobles and such people have infinite ability to discern differences in status.

After you have done such extensive modification to the mountain and its shape to create all those levels, it becomes only natural to do landscaping and architecture so that the overall shape of the mountain is pleasing. In practice, if the mountain roughly resembled a pyramid to begin with, it would be sculpted and filled with masonry until it actually is shaped like a huge pyramid. The process would be gradual one taking multitude of generations.

This is the only way I can think of to get the mega-pyramid with ancient technology and logistics. And obviously since there is no continuous, planned construction, just a constant evolution of form, there is no way to estimate the time needed. In some ways you could consider it a pyramid created by the gods to begin with. That is probably the actual reason it was sacred.

• Nice answer! i would like to give you another +1 just for "even more overwhelmingly huge". – Burki Nov 6 '15 at 14:39