As I mentioned a few weeks ago, I’ve been reading The Outline of History, published in 1920 by H. G. Wells. I’m still at it — I tend to have several books going at once, and this two-volume item is about 1,200 pages long.

I’ve just read the brief entry on the conquests of Timurlane (Tamerlane) — who, as I’m sure you know, was very good at conquering, but not so much at anything else.

We read:

[I]n the fifteenth century a last tornado of nomadism arose in Western Turkestan under the leadership of a certain Timur the Lame, or Timurlane. He was descended in the female line from Jengis Khan. He established himself in Samarkand, and spread his authority over Kipchak (Turkestan to South Russia), Siberia, and southward as far as the Indus. He assumed the title of Great Khan in 1369. He was a nomad of the savage school, and he created an empire of desolation from North India to Syria. Pyramids of skulls were his particular architectural fancy; after the storming of Ispahan he made one of 70,000. His ambition was to restore the empire of Jengis Kahn as he conceived it, a project in which he completely failed. He spread destruction far and wide; the Ottoman Turks — it was before the taking of Constantinople and their days of greatness — and Egypt paid him tribute; the Punjab he devastated; and Delhi surrendered to him. After Delhi had surrendered, however, he made a frightful massacre of its inhabitants. At the time of his death (1405) very little remained to witness to his power but a name of horror, ruins and desolated countries, and a shrunken and impoverished domain in Persia. The dynasty founded by Timur in Persia was extinguished by another Turkoman horde fifty years later.

It’s a dreary story, and I think we should all be glad not to have lived through it. One thing in particular, though, stuck in my mind. In case you missed it:

Pyramids of skulls were his particular architectural fancy; after the storming of Ispahan he made one of 70,000.

My word, I thought to myself, what a thing to have to assemble. I decided to do some calculations.

Let us assume that the pyramid in question is square, and not triangular, and not based on some other polygon. (I can’t confirm this, but it seems likely, as the square pyramid was by far the most popular kind in the ancient world.) If that’s so, then the total skull-count would have to fit in somewhere along the square-pyramid number series, which begins with 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650… (This sequence, by the way, is item A000330 in the On-Line Encyclopedia of Integer Sequences.)

The general formula for the nth item is (n (n+1) (2n +1)) / 6.

The 58th entry in this sequence is 66,729, while the 59th is 70,210. (Timurlane himself, by the way, may not have been familiar with this formula. I would hate to have been standing around watching this thing go up if he got close to the end and realized he was a few skulls short.)

We’ll go with the closest approximation, and say that the pyramid Timurlane built in Ispahan used 70,210 skulls, which means it was 59 skulls on a side, and 59 layers high.

How big is that? Well, we’ll need to simplify, I think, by assuming spherical skulls. (I hate to do it, but I don’t have all night here, and at least it isn’t as bad as this. And no Cromwell jokes, please.) The average male human skull has a circumference of 22 inches or so. Dividing by pi, we get a diameter of 7 inches.

So now we need to calculate the height of a square pyramid of stacked 7-inch spheres 59 layers high. The formula for that, where d is the diameter of the spheres, and n is the number of spheres on each side of the square base, is: d + d(n-1)âˆš1/2.

The result? Timurlane’s pyramid of 70,000-odd skulls at Ispahan was 24.5 feet high. The base was 34.4 feet on a side (59 x 7″).

Now comes the tough part: how the hell do you build such a thing? How do you climb up that slippery mess, neatly piling skulls, without knocking the whole thing down? The only way I can imagine would be to have built some sort of superstructure from which people could dangle as they dropped the skulls into place. What an effort!

I have a feeling Timurlane himself didn’t hang from ropes placing skulls; if I know anything about Army work, this would be the sort of thing he’d have delegated. Did he have a skull-pyramid team that traveled with him? I bet he did. It’s pretty specialized work.

For some reason, Mr. Wells is silent on this important historical question, so I decided to look on Google just now. I didn’t find much of anything about how Timurlane did it, but I did find this.