The Zeno's Paradox in Somali Culture

Every community that is ruled by a traditional culture has its own ways of using mathematics. These methods could be open to everybody or hidden, and the mathematical concepts used by that community could be used for sorting out basic necessity of the day-by-day life such as counting, measuring, memorizing, estimating, etc. It can also be used for sorting out more complicated tasks that require advanced competencies in calculation such as buildings, resolving hidden riddles or traditional games.  Nowadays, a revival of this typical traditional usage of mathematics can facilitate the learning of conventional mathematics in schools. In fact, researchers in education support the concept that teaching mathematics must be related to the cultural context where it takes place.

For example: Looking at the math school textbooks in different parts of the world, it is noticeable that it has became the norm to use the game of dice to introduce the notation of probability, with the classical example being, “throw a dice, and calculate the probability that the face with 6 comes out”. Consider now if this mathematics class is taking place in a culture where the game of dice is not totally known. The lesson is that the teacher will need to first teach the game of dice to the students, and then use it for the probability lesson, or vice versa i.e., to teach mathematical notion of probability first, and then the game of dice. Is it not important to look at the traditional games and tales from any culture to introduce mathematical concepts in a homebred way?

The aim of this note is to present a well known fable in the Somali culture and demonstrate how it could be used as an appropriate tool for introducing abstract notions of mathematics like limit and infinity.

In Somaliland, the thorn is also the tree under which Somali children, in the rural areas, receive their first educational approaches: Quranic lessons, fables, tales and behaviour rules. Among the fables it is well known - and mathematically rich - Qayb Libaax (lion's share) or sometimes known also as Qayb Dacawo (fox apportionment), whose interest for Somalis have little to do with mathematics; it is instead told to the children only for moral purpose. This is the story:

One day, the wild animals family killed a she-camel for prey and the lion, the king of the family, assigned the hyena, which was considered the most idiotic member of the family, the task of distributing the prey to the beasts. The hyena divides the meat into two equal parts, one half for the lion and the other half for the rest of the family. The lion, displeased with this decision, punishes the hyena, injuring its eye by striking him with his front leg. The fox (considered the most intelligent and opportunist member of the family) is then assigned the task of dividing the prey amongst the family. The fox observes the situation and glances at the lion, which replies by striking his canine teeth together sharply; the fox says: "One half of the camel is for the king, the lion; from the remainder, again one half is for the king; again from the remainder one half is for the king; and so on." The lion, satisfied for this statement, asked the fox.

"Where did you learn this fairness and justice?" 

"Here! When I saw the injured eye of the hyena," fox replied.

Somali children listening at this plane fable are hardly persuaded by the narrator that the lion got the whole camel. The narrator guesses that adding, [times by times], one half of the previous half to this one, without stopping the procedure, the result will be the unit, but he has no mathematical formula and demonstration procedure to explain that fact mathematically to the children. They cannot understand the underlying notion of infinity and the narrator is unable to give a theoretical frame to his intuitions. He or she may say, for the sake of Allah, the lion finally takes all the meat (bal Ilaahay amarkii, ugu danbayn libaaxu wuu wada qaadan hasha!)

The Zeno's paradox, the sum of the geometrical series of ratio ½; the limit of a sequence are so deeply involved in this fable. The Greek philosopher Zeno (5th century BCE) devised several “paradoxes of motion” that baffled mathematicians, scientists and philosophers for millennia. His first and most famous paradox involves a race between Achilles—a very fast runner, and a lowly tortoise. The tortoise is allowed to have a head-start. Zeno gives a simple but surprisingly plausible argument that Achilles could never catch up. It needed years and years of mathematical analysis to demonstrate mathematically what Zeno affirmed: “In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. – as recounted by Aristotle, Physics VI:9, 239b15”. As a related situation that involves the same issues, the sum of the geometrical series of ration ½ is the unit. 

 The use of this fable as an example to introduce geometrical series is a nice way to be culturally sensitive and to be beneficial for students and approach mathematics with ease. While it is still necessary to tell Zeno's paradox, for historical and philosophical purpose, however, traditional Somali story would support hugely the learning of abstract mathematics concepts, which often are wrongly considered alien to the Somali culture.  

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