Smooth a patch of sand, press in a neat grid of dots with your fingertips, then trace one unbroken line that loops around every dot and ends where it began. For the Chokwe and Luchazi peoples of eastern Angola, northwestern Zambia and nearby parts of the Democratic Republic of the Congo, that is not a doodle. It is a lusona (plural sona), a drawing that holds a proverb, a fable, a riddle or an animal in memory.
The tradition is old enough that observers working independently found the same drawings among communities that had been separated for generations. In 2023 UNESCO added Sona to its Representative List of the Intangible Cultural Heritage of Humanity.
How a lusona is made
The drawing expert clears and flattens the ground first. According to the UNESCO listing, practitioners mark their reference points on a damp, sand-covered floor with the index finger and the little finger, then draw lines around them. The dots are evenly spaced, and each can stand for something in the story: a tree, a person, an animal. The lines become paths, rivers, fences, walls or the outline of a body.
The drawings work as memory aids. A storyteller draws while speaking, and the finished figure carries the tale. Sona are also passed on during initiation rites for young people preparing to take on adult roles in the community, and they are used as murals and as decoration.
The hidden math in the sand
Researchers who have studied the documented sona found striking regularities. About 80% of the drawings are symmetric, and about 60% are monolinear, meaning a single continuous line draws the whole figure. The researcher Paulus Gerdes identified six separate construction methods. The most common, which he called the “plaited-mat” algorithm, appears to borrow its logic from weaving mats.
Studies suggest the drawing experts worked out rules for “chaining” and “elimination” that let them build one-line figures on purpose, and that they understood why those rules worked. One clue points to a real number-theory insight: grids whose two side lengths share no common factor tend to produce single-line drawings. Of the 30 smallest such rectangular grids, 75% show up among the recorded sona.
Here is that rule in plain terms. Take a grid 3 dots by 4 dots. The numbers 3 and 4 share no factor except 1, so the rule predicts one line can weave through the whole thing. Now take 4 by 6. Both numbers divide by 2, so the grid falls outside the rule, and the drawer would need another trick to keep the line unbroken. The experts also seem to have known that adding a 2-by-2 block of dots to a one-line drawing keeps it one line.
Much of this knowledge was secret, and the tradition was fading by the time outsiders began recording it. That makes it hard to say how far the drawers generalized their findings.
A paper trail across 2,000 years
- 6th to 1st century BC: Rock engravings in the Upper Zambezi area and the Moçâmedes Desert share structural features with sona, though no direct link is proven
- 1650s: The Italian missionary Antonio Cavazzi paints watercolors of the Kingdoms of Matamba and Ndongo showing a basic lusona on trade goods, a scarf and a chest
- 1935: Hermann Baumann describes sona in his book Lunda, one of the first 20th-century studies
- 2023: UNESCO inscribes Sona as intangible cultural heritage of Angola
The drawings now have a second life in classrooms. UNESCO notes that schools and educational institutes have begun using sona to teach mathematics, ethnomathematics and anthropology. African scholars and makers keep turning up in our history coverage, from Benjamin Banneker’s survey of Washington, D.C. to the carved Swahili doors of Zanzibar’s Stone Town.
One of the most basic sona, katuva vufwati, is already visible on trade goods in those Cavazzi watercolors, painted more than 360 years ago.
Further reading
Image: Unknown author, Public domain via Wikimedia Commons
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