Lusona

Lusona ideograph illustrating the story of the beginning of the world

Sona(sing. Lusona) drawings are an ideographic tradition known across eastern Angola, northwestern Zambia and adjacent areas of the DRC, and is mainly practiced by Chokwe and Luchazi people.[1]. Those ideographs function as mnemonic devices to record and transmit knowledge, proverbs, fables, games, riddles, animals, etc...[2]

Origins

According to Gerhard Kubik, this tradition must be ancient, and certainly pre-colonial, as observers independently collected the same ideographs among people who have lived separately for generations. In addition to this, early petroglyphs from the Upper Zambezi area in Angola and Citundu-Hulu in the Moçâmedes Desert exhibit similarities with the structural aspects of the lusona ideographs.[3]. Those petroglyphs have been dated from a period between the 6th century BC and the 1st century BC[4]

Usage

Sona ideographs are sometimes used as murals, and most of the time executed in the sand. To make them, drawing experts, after cleaning and smoothing the ground, would impress equidistant dots, and then draw a continuous line between them. The dots can represent trees, persons, or animals while the lines can represent a path, a river, a fence, a wall, contours of a body, etc.[5]

Mathematical properties

The mathematical ideas exhibited by those ideographs are transformational geometry, abstract algebra, and linear algebra. 80% of them are symmetric, and 60% are mono-linear.[6] They are also an example of the use of coordinate system and geometric algorithms.[2]

Geometric algorithms

Sona drawings can be classified by the algorithms used for their construction. Paulus Gerdes identified 6 algorithms, the most common one being the "plaited-mat" algorithm, which seems to have been inspired by mat weaving.[7]

Chaining rules and theorems

Various studies suggests that the drawing experts knew specific rules of "chaining" and "elimination" relating to the systematic construction of monolinear figures. Studies suggest that the "drawing experts" who invented these rules knew why they were valid, and could prove in one way or another the validity of the theorems that these rules express.[8]

It is difficult to find accounts of theorems developed by the drawing experts to generalize specific patterns relating to dimension and monolinearity/polylinearity,[6] as this tradition was secret and in extinction when it started to be recorded.

However, there is a strong possibility that the drawing experts knew that rectangles with relatively prime dimensions give one-line drawings. This idea is supported by the fact that of the 30 smallest relatively prime rectangular shapes, 75% appears among the documented drawings. Also, it is possible that they knew that if a square of dot is added to a one-line lusona, the lusona would still be mono-linear. It seem clear that they had experimentally discovered this fact for 2 X 2 squares.[9]

References

  1. ↑ Gerhard Kubik 2006, p. 1.
  2. 1 2 "On mathematical elements in the Tchokwe "Sona" tradition Gerdes, Paulus. 1990. For the Learning of Mathematics10(1), 31–34". Historia Mathematica. 18 (2): 198. 1991. doi:10.1016/0315-0860(91)90542-6. ISSN 0315-0860.
  3. ↑ Gerhard Kubik 2006, p. 229.
  4. ↑ José Redinha 1948.
  5. ↑ I. Hodder (12 November 2013). The Meanings of Things: Material Culture and Symbolic Expression. Routledge. p. 210–213. ISBN 978-1-317-76232-4.
  6. 1 2 Daniel Ness; Stephen J. Farenga; Salvatore G. Garofalo (12 May 2017). Spatial Intelligence: Why It Matters from Birth through the Lifespan. Taylor & Francis. p. 56–57. ISBN 978-1-317-53118-0.
  7. ↑ Paulus Gerdes 1999, p. 163-167.
  8. ↑ Gerdes, Paulus (1994). "On mathematics in the history of Sub-Saharan Africa". Historia Mathematica. 21 (3): 355. doi:10.1006/hmat.1994.1029. ISSN 0315-0860.
  9. ↑ Chavey, Darrah. "Sona Geometry".
  • Gerhard Kubik (2006). Tusona: Luchazi Ideographs : a Graphic Tradition of West-Central Africa. LIT Verlag Münster. ISBN 978-3-8258-7601-2.
  • Paulus Gerdes (2006). Sona Geometry from Angola: Mathematics of an African Tradition. Polimetrica. ISBN 978-88-7699-055-7.
  • Paulus Gerdes (30 September 1999). Geometry from Africa: Mathematical and Educational Explorations. MAA. ISBN 978-0-88385-715-1.
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