A key principle in African philosophy is that what is first is sacred; and that by imitating what is sacred, we too become sacred. In African geometry, we mimic nature in order to know the deepest truths of our universe. Take for instance the spiral.
Spirals are found throughout nature. In geometry, the sacred (golden) spiral is a logarithmic spiral with a growth factor equal to 1.61803…the golden ratio! We find this ratio embedded in African architecture from Cameroon to the ancient Nile Valley civilizations going back as far as 2580 BCE.
Let’s start with the golden ratio and work our way back to the golden spiral. The sacred ratio occurs when the ratio of two numbers is equivalent to the ratio of their sum to the larger quantity. Mathematically it looks like this:
When this occurs, the ratio is always the same:
The ratio is conventionally represented by the Greek letter φ (phi), but since the Greek alphabet had not yet been invented when this ratio was first being embedded into ancient African architecture, we choose to break with that convention.
Ipet-Isut (the most select/holy of places) is an ancient Nile Valley temple that housed shrines to Amun-Ra, Mut, and Montu. Known today as the Karnak Temple Complex, it sits on the east bank of the Nile River facing west in such a way that the central corridor when it was first built in 1700 BCE was directly aligned to the western hills such that on June 21st (the summer solstice) when the sun set behind the western hills, just as it was setting would send a flash of light directly down the corridor and it would shine on a metal apparatus in the sanctuary for 2 – 5 minutes. This was how these ancient Africans knew that it was the first day of summer. In this way, the central corridor of Ipet-Isut was designed with such precision that it functioned both as an architectural masterpiece and as a solar calendar.
These images show the size and scale of the Ipet-Isut Temple Complex and it’s interior – we can see that it is essentially a small town. Ipet-Isut is located in the ancient city of Waset (Thebes) – the land of the scepter.
Something else that’s special about Ipet-Isut is that the sacred ratio is embedded into it’s architecture.
If we look at a plan view of the site we’ll see numerous sacred (golden) rectangles that form a self-repeating pattern:
Sacred rectangles have dimensions that are of the sacred ratio.
If you research the golden ratio in ancient architecture you’re likely to read about the Greek Parthenon as the earliest example of the golden ratio being embedded into ancient architecture. But that is inaccurate. While the Parthenon was constructed in 490 BCE, keep in mind that the Ipet-Isut Temple Complex was constructed around 1700 BCE. As in all things mathematical, the numbers don’t lie! Remember what is first is sacred, and being the first humans on our planet, it stands to reason that Africans would be the first to advance mathematics and the sciences.
Now let’s travel over to West Africa. The photo below shows an aerial photo of the Palace of the Chief in Logone-Birni, Cameroon which is built using fractal geometry. The palace also incorporates the sacred rectangle – see if you can spot the pattern.
Logone-Birni (Fort Logone) is the capital of the Kotoko people and was founded around 1700 ACE. At the center of the palace is a sacred shrine. To get to the shrine you have to travel through a passage which is a rectangular spiral. As you get closer to the center, the size of the compound shrinks accordingly. And as you enter each progressively smaller room you are required to behave more politely. By the time you have arrived at the throne you must behave with impeccable manners and cultured formality.
In addition to sacred rectangles we also have sacred triangles. The Great Pyramid of Giza (2580 BCE) is the earliest example of the sacred triangle being embedded in architecture. The images below show some of the basics, but we’ll save the breakdown for another post.
Now, let’s break down the golden spiral. Earlier we said that the golden spiral is a logarithmic spiral with a growth factor equal to the golden ratio (1.61803…). So first, what is a logarithm? A logarithm is a function that is used to undo an exponent. Similar to how we use division to undo multiplication and we use subtraction to undo addition, we can use logarithms to solve for the variable when it is an exponent. For example, if you were given the equation 3x = 19,683 you can use a logarithm to solve for x. One of the properties of logarithms states that log(ax) = x·log(a) so we can transform the equation in the following manner and use the log function on our calculator to solve:
3x = 19,683
x·log(3) = log(19,683)
x = log(19,683) ÷ log(3)
x = 9
So, back to spirals. Spirals can be found in shells, the cochlea of the ear, and the movement of whirlpools and hurricanes. Spirals are one way nature packs a lot of space into a small area. Ancient mathematicians and engineers chose to use what works in nature for their human designs. The field of permaculture encompasses these ideas today. For example, we can use natural patterns – such as spirals – in designing a compact garden.
The spiral is also an important symbol in African cosmology. Take a look at these excerpts from both the Big Bang Hypothesis and the Dogon’s description of the origin of the Universe.
|Big Bang Hypothesis (1920s ACE)||The Dogon (3200 BCE)|
|About 15 billion years ago, the entire universe was compacted into a single point called a singularity. |
The sphere/singularity exploded in all directions, and a giant cloud was formed. Some parts of the cloud moved faster than others, and many parts condensed into galaxies. Billions of these galaxies were formed. Within these galaxies, dust and gases spiraled around, collecting other pieces of gas and dust.
Gravity pulled the gas and dust together into a flat disk as it spiraled around. These eventually became stars and planets.
|When Amma (the supreme being) began the new creation Amma formed the germs of the new seeds, which would be used to make the second world. The first and most important, but smallest, of all seeds was the Po.
The spiral at the center of the first yala (thought image) represents the movement of the po seed. But the spiraling po, which moves inside of Amma’s egg/womb reversed its direction and exploded out of Amma’s womb. This is symbolic of the “opening of Amma’s eyes” and the bursting forth from the hole of a light that lightened up the universe and revealed the existence of all things.
These eyes also created the potential for the coming into being of space. The spiral of the po represents the spiral shape of the milky way galaxy, which includes the entire stellar world of which our earth is a part.
Finally, sacred spirals are self-similar. That is, they form an infinite pattern as the spiral is magnified.
With these secrets that we’ve just shared with you hopefully you understand better why the ancient mathematical textbook – the Iahmesu Mathematical Papyrus – was titled: Correct method of investigating nature to know all that exists, all mysteries and all things secret. This knowledge was sacred to our Ancestors. How will you use it today?