African Vernacular Architecture, Spatial organisation, Geometry and Justice

[Dante Monson]

The image you shared is the cover or headline of an essay by **Likam Kyanzaire**, published in *Aeon* magazine. The research explores the intersection of **ethnomathematics, architecture, and social justice**, specifically focusing on the use of **fractal geometry** in indigenous African societies.

Here is a deeper look into the core arguments of this research:

### 1. Fractals vs. Euclidean Extraction

The central thesis contrasts "centralised societies" (often Western or colonial models) with "African fractal systems."

 * **Centralised/Euclidean:** Western urban planning often relies on Euclidean geometry (straight lines, right angles, grids). Kyanzaire argues these structures are optimized for **extraction**—the efficient movement of resources out of a community toward a central power or global market.

 * **African Fractals:** Many indigenous African settlements (like the Ba-ila in Zambia or the Logone-Birni in Cameroon) utilize fractal patterns—shapes that repeat at different scales. These are described as systems of **circulation**. Instead of resources flowing "out," they flow "through," sustaining the internal community.

### 2. Social Justice through Geometry

The title "Justice is Geometric" suggests that the physical layout of a space dictates the social and economic justice of its inhabitants.

 * **Reciprocity:** In fractal villages, the "scaling" often mirrors social structures. A small family unit looks like a miniature version of the larger village. This physical mirroring reinforces mutual obligation; the wealth of the "center" (the chief’s house) is topologically connected to the smallest unit.

 * **Return:** Because the geometry is recursive rather than linear, it encourages "return"—the idea that what is given to the community eventually flows back to the individual, preventing the accumulation of wealth at a single point that never trickles down.

### 3. The Influence of Ron Eglash

Kyanzaire’s work builds significantly on the foundations laid by **Ron Eglash**, a pioneer in ethnomathematics who wrote *African Fractals*. Eglash discovered that while Western mathematics only "discovered" fractals in the 1970s (via Benoît Mandelbrot), African cultures had been using them for centuries in:

 * **Architecture:** Settlements designed as a "ring of rings."

 * **Art & Textiles:** Patterns in Kente cloth or hair braiding that use recursive scaling.

 * **Divination:** Systems like *Ifá* that use binary code and recursive modeling.

### 4. Application to Modern Problems

The research isn't just a historical study; it’s a critique of modern development. Kyanzaire suggests that:

 * **Education:** Traditional Western education often fails by imposing linear logic on students from cultures that intuitively understand complex, non-linear systems.

 * **Urban Planning:** By moving away from "extractive" grids and toward "circulatory" fractal models, we can design cities that are more resilient, biophilic, and equitable.

In short, Kyanzaire argues that **geometry is a form of technology**. By choosing fractal geometry over linear grids, African societies built "social safety nets" directly into the physical layout of their world.