Wednesday, November 11, 2015

Pyramids and Mounds Galore!


LONDON, ENGLAND—Sixteen pyramids sitting atop tombs have been unearthed since 1998 in a large cemetery near the ancient town of Gematon in Sudan. The largest was about 35 feet long on each side and would have stood some 43 feet tall. “So far, we’ve excavated six made out of stone and 10 made out of mud brick,” Derek Welsby of the British Museum told Live Science. Other tombs in the 2,000-year-old cemetery were topped with rectangular structures known as mastabas, or piles of rocks called tumuli. Most of the tombs at the site have been looted, but one yielded a royal tin-bronze offering table bearing a scene showing a prince or priest offering incense and libations to the god Osiris, ruler of the underworld. Osiris and the goddess Isis, who is also shown in the image, originated in Egypt, but they were also venerated in Kush. Gematon was eventually abandoned as trade routes changed and the economy of the Roman Empire deteriorated.

From here.


Jay Eppinga, an engineer, on the Kushite pyramids


I'm impressed. These Kushites had a lot going for them. I checked dimensions using a cad program. The claim about the tetrahedrons and the cube has also been verified for good measure. Here are the observations I recorded this morning:

The Kushite pyramid ruins with dimensions 35’ at the base, altitude 43’, has the following interesting properties:

The triangle formed by the isometric view of the pyramid has sides of length 49.5’ at the base, 49.6’ at the sides. The top apex angle is 59.85 degrees, and the base angles are 60.08 degrees each. It is not in the strictest mathematical sense, ‘equilateral’. When we factor in stochastic considerations, we see the equilateral triangle more clearly.

The shifting of any one of these edifices over time is probably greater than the “inexact” nature of ancient technologies with respect to geometric tolerances and dimensioning.

The more I think about it, the more I realize that the Kushites had to be going for the Equilateral Triangle:

1) Mathematically speaking, it really is an either/or type of thing. It's either the equilateral triangle of the 45/45/90;

2) The 45/45/90 thing lends itself to starting with a solid object, and then subtracting with an extrude operation, two directions (perpendicular to one another;

3) On the other hand, the 60/60/60 thing lends itself to -additive- construction techniques. Kind of like modern homeowners do when they stake out a garden or a shed in their backyard, starting with stakes and ropes (in this case, the Kushites would be working in 3d);

4a) How would they notice such a pyramid? There are two ways I can think of this. One way is starting with very small models (the size of one's hand, perhaps), and they would sort of 'hit' on the proportions eventually by playing around. 11th grade trig students might notice the 3/4/5 right triangle in similar fashion;

4b) Another way they might notice is more unusual, but not outside the realm of possibility. They might have noticed the (35x4)x43 pyramid by thinking about it. Stephen Hawking e.g., has trained his mind to work through physics equations without the benefit of something to keep track of the calculations. As for 3d thinking, Michelangelo demonstrated this ability in his work on the Statue of David (other examples of this abound);

5) How would they build such a pyramid? My guess is with rope. They could rope the sides the same way a homeowner would rope in a garden, and then they could build upwards until the hypotenuses are 'taut', something like that. Tricky. It would take some trial and error to perfect.

6) Ropes and construction sometimes go together. In my own ethnic background, there is a true about two competing towns in Medieval Friesland who wanted to have bragging rights to the larger church steeple. One town built a large steeple and then stuck up their noses about it. The other snuck in one night and measured the steeple, with the intent of using the measuring rope to help them build a larger steeple in their own town. The first town caught wind of the 'plot', and sent in some of their own spies late one night. The rogues cut the rope and made off with the remnant, causing the second town to build an inferior steeple. To this day, the residents refer to one another as, "Tower Builders," and the other side as "Rope Cutters." Alas, the rivalry persists to this day, and while it may be said that they are more civil to one another than spectators in South American soccer matches, it might not be saying much. Ropes .. might have helped the Kushites build their pyramids. They could easily copy pyramids this way (are the ones they just discovered all the same dimensions?). Just a theory.


4000 year Egyptian rope coils

Now I'm starting to wonder about the Hopewell thing over in Chillecothe. There are several of these in Ohio, very similar to one another and in very different places, in varied orientations. But that's a tangent.

END

Very  interesting, Jay. This is something to pursue.

The mound builders of Ohio continued down to Mississippi and Louisiana. Emerald Mound, built and used during the Mississippian period between 1250 and 1600 AD,was a ceremonial center for the local population, which resided in outlying villages and hamlets. Its builders were the ancestors of the Natchez Indians. Na'Tchez is a Nilotic word. Na means no, and T refers to crossing or crossing over. (Na sometimes designates a female name.) We know that the Nilotic Ainu came to North America. In eastern Canada they are called Mi'kmaq. Their word for house was chis/chisei. Perhaps Na-T-Chez means something like "No crossing through this land."

Lots to think about!



2 comments:

J Eppinga said...

An unexpected honor. :)

Interesting about the Natchez name. It does give more to think about.

DManA said...

There are mounds all over Mn. Some go back to 200 BC, the so called woodland culture. A golf course up north uses one for the tee box for the 4th hole. The Grand Mound up on the Canadian border is shaped like an otter. Current thinking is it had something to do with commemorating one of their myths. There was a great flood and brother otter kept diving to the bottom to bring up mud until he built up land for the people to live on.