Indigenous Mathematics of the Hunt in Southern Africa
Documenting the embodied geometric, probabilistic, and astronomical knowledge encoded in traditional foraging practices
Archival Context
This document archives a sophisticated system of **applied, embodied mathematics** developed by Southern African foraging communities—including the San, Zulu, Xhosa, Venda, Tsonga, Hadza, and BaAka. It examines how abstract concepts of geometry, probability, and astronomy were not theoretical abstractions but **essential technologies for food procurement**, distilled into memorable rules and rituals. The analysis reveals that the hunt was a **pedagogical field** where the human body was the primary measuring instrument, environmental patterns were the textbook, and success—a meal—was the proof of concept. This entry preserves these algorithms of survival as a cornerstone of indigenous STEM knowledge.
Archival Visual: Knowledge transfer in context. This image captures the pedagogical moment where abstract environmental relationships—angles, distances, timing—are conveyed through gesture, observation, and story, not formal notation.
Decoding the Algorithms: Six Principles of the Hunt
Long before chalkboards, African children learned trigonometry with a slingshot, probability with three snares, and astronomy by watching bushbaby eyes shine under the moon.
1. The Three-Branch Rule – Predictive Trigonometry
The Rule: "Do not shoot until the squirrel crosses exactly three branches."
The Algorithm: This is a **predictive model for projectile motion**. By observing the squirrel's leap *angle* and *distance* across three consecutive branches, the hunter subconsciously calculates its **average velocity vector**. The prescribed pause on the fourth branch is the moment the animal's velocity drops to near zero, transforming a chaotic moving target into a near-stationary one. The rule encodes: Observe three consistent data points to extrapolate the fourth position and time your release.
Modern Corollary: Projectile motion calculation and reaction latency modeling.
2. The Marula Triangle – Optimized Probability
The Rule: Place three identical snares in an equilateral triangle under a fruiting marula tree.
The Algorithm: This is **applied probability theory for resource optimization**. The geometric arrangement assumes the squirrel's movement from tree to ground is random but constrained to the fruitful area (the canopy's drip-line). An equilateral triangle is the configuration that **maximizes coverage and interception probability** while minimizing material (three snares). It applies a uniform probability distribution to a symmetric field.
Modern Corollary: Optimal foraging theory and uniform probability distribution in a bounded area.
3. Bushbaby Moon Fractions – Applied Astronomy & Optics
The Rule: Hunt galagos (bushbabies) only when "the moon is half a hand above the horizon after full dark."
The Algorithm: This is a **multi-variable optimization rule** for visibility. The "half a hand" (roughly 8–12°) is a **consistent angular measurement** using the body as a sextant. This specific lunar altitude maximizes two factors: 1) sufficient moonlight to create eye-shine (tapetum lucidum reflection) in the bushbaby's eyes, and 2) a low enough angle to cast long shadows that silhouette the animal against the ground or trees.
Modern Corollary: Angular measurement in spherical astronomy and optics of light reflection.
4. BaAka Net-Hunt Semicircle – Cooperative Spatial Logic
The Rule: Form a hunting semicircle with a radius equal to 1.7 times the tallest tree height.
The Algorithm: This is **applied geometry for group coordination and optimal search**. The radius is calibrated to the forest's vertical scale (tree height), which correlates with animal dispersal. The semicircle shape allows beaters to drive game inward while minimizing escape routes, effectively creating a closing, human-made topography. The specific multiplier (1.7) likely represents an empirically derived optimum between coverage and maintainable formation cohesion.
Modern Corollary: Optimal search theory and geometric coordination in collective action.
5. Dassie Parabola – Iterative Ballistics
The Rule: Adjust your launch angle by "one finger width" per 10 meters of distance to a dassie (hyrax) target.
The Algorithm: This is **iterative, empirical ballistics**. Without concepts of gravity or velocity, the rule establishes a **linear correction factor** ("one finger width") for a **non-linear parabolic path**. Through constant practice from varying distances, the learner internalizes the relationship between angle, distance, and impact point. The "finger width" is a portable, scalable unit of correction derived from direct sensory feedback (miss/hit).
Modern Corollary: Empirical derivation of parabolic trajectories and iterative learning.
6. Sharing the Kill – Modular Arithmetic & Social Code
The Rule: "One portion for every five net-holders, plus one portion returned to the forest."
The Algorithm: This is **applied modular arithmetic ensuring fair distribution and ritual respect**. The rule works for any number of hunters (n). It can be expressed as: Portions = (n // 5) + 1, where the extra portion is a ritual offering. This algorithm guarantees equitable sharing regardless of group size, embeds a social/spiritual tax, and operates without needing to count or divide the actual meat into precise fractions beforehand.
Modern Corollary: Division with remainder (modular arithmetic) and algorithmic fairness protocols.
The Integrated Knowledge System & Its Fragility
These six principles are not isolated tricks but interconnected components of a **coherent knowledge system** for interacting with the environment to secure food. This system is acutely vulnerable to the forces documented in other AGFA collections:
- Displacement (`AGFA-FW`): Loss of ancestral hunting grounds doesn't just remove a food source; it **destroys the classroom and the curriculum**. The "Squirrel's Curriculum" cannot be taught in a settled village or urban setting.
- Ecological Change (`AGFA-IE`): The replacement of marula trees with invasive species or commercial plantations collapses the **"Marula Triangle" probability model**. Changing climate patterns can desynchronize the animal behaviors and lunar cycles that the rules predict.
- Legal Restrictions: Bans on traditional hunting methods legally proscribe this entire **mathematical and pedagogical tradition**, rendering it a theoretical artifact rather than a living practice.
Did You Know? The First Peer Review
The most rigorous form of peer review in these knowledge systems was **collective survival**. If a young hunter's interpretation of the "Three-Branch Rule" consistently failed, the group went hungry. His "thesis" was disproven by reality. This created an unforgiving but incredibly efficient feedback loop that refined these algorithms over generations into models of stunning empirical accuracy. The "journal" that published these findings was the shared meal.
The same little tree squirrel raiding your mango tree this morning once carried the entire mathematics curriculum of a continent on its back.
No textbooks.
No rulers.
Just sharp eyes, hungry bellies, and ancestors who understood that
to feed the body, you must first learn to measure the world.
