Viewing Formal Mathematics from Yoruba Conception of the Sky Aimé Dafon Segla Université d’Abomey-Calavi Abstract: social science take place, they only operate Yoruba Cosmology resembles a generative system at the in terms of furtive descriptions of ideas and foundation of concepts. The traditional thought, which achievements that have been superseded. derives from the reality of the identical pair incorporated In such studies, described achievements from cosmology into real life, exemplifies all kind of ex- and thoughts are best understood as histor- isting knowledge, culture and practices. Previous studies ical markers and anthropological guides; by the author show in some detail the scientific interests in Yoruba cosmology. The present paper aims to view rarely are they logical, well portrayed, dy- formal mathematics through the interpretation of Yoruba namic transformations. For the substance sky knowledge. It attempts to demonstrate that linguistic of the state of the debate, we first recall the codes elaborated from the Yoruba conception of the sky status of Western Science, which is identi- are binary and hexadecimal codes that imply Algebraic fied by reference to its theories and system- Boolean structure or Group Structure. The system is in atic and dynamic character, as opposed to accord with classical mathematical properties of Group non-Western Science, which is associated Structure. Finally, the review and interpretation of Yo- with traditional practices, has no theory, ruba cosmology may suggest the possibility of formal rea- and has a static character. soning without any writing system in human history. The problem that has always been raised is that of To challenge and differentiate the dis- knowing if symbols and configurations in the Yoruba in- tinction between static and dynamic sys- terpretation of the sky are the result of implicit premedi- tems of thought, we need to give and show tated mathematical development. It is clear that behind sufficient parameters. What orthodox or the implicit oral discourse described hereafter lies a cor- positivist critiques say is not only that there responding semiology elaborated with the corresponding is no dynamic trend of knowledge in non- formal mathematical reasoning that we claim. Western Science, but that there is a lack of visibility and an impossibility of demon- Keywords: history: concept and logic; alge- strating the presence of tangible outward bra: Boolean-group structure; astronomy: in- terpretation; formal mathematics; Yoruba cos- signs and key concepts like objectivity, cau- mology; knowledge: tacit-implicit sality, deduction and induction. While on the Western side, the practices—symbols Introduction and cosmological as well as social back- As Abiola Irèlè observed in The African grounds—are cut out, making knowledge Scholar (1991) and further in The African Im- there appearing thoroughly instrumental, agination (2001), scientific and technical systematic and dynamic; on the African achievements of Classical African Cultures side the practices are still reduced to their are under-studied. The focus of scholar- cosmological and social backgrounds, fre- ship in African Studies is directed only to- quently narrowed down to the symbolic di- wards the humanities and the social sci- mension. In these conditions, for modern ences. Hountondji (1990) also argues in anthropology, it is, for example, impossible Scientific Dependence in Africa Today (1990) to sort out from African belief accurate sci- that, even when studies on humanities and entific knowledge and techniques like Journal of Astronomy in Culture 1(1), 2016, pp. 9-21 Copyright © International Society for Archaeoastronomy and Astronomy in Culture 10 mathematics. This makes Western Science art, Nok iron civilization and technology. look like it arrives at speculative and mod- It is well known that Yoruba art, together ern theorizing mysteriously from nowhere. with that of Benin, originated in the Ifè Yet, science in Europe also originated from classical period (1000 to 1400 CE), had a myth and rituals and moved from magic tradition of excellence, and is comparable and religion only progressively; theoretical to the works of art of classical Greece and constructions in Western cultures logically Rome (Willet 1967). also started from basic human traditional knowledge. Beliefs and Knowledge In the present essay, using founda- As Lawal (2008) points out, in “Ejiwapo: tional archaeology of concepts taken from the dialectics of twoness in Yoruba art and Yoruba history and culture, we try again to culture,” the concept of “twoness—ejiwapo make clear the dynamism of African tradi- meaning ‘our two(s) are many’; the idea of tional thought by bringing a case study of the reality of an identical pair derived from formal knowledge extracted from folk be- cosmology”—exemplifies the idea of the lief. By the way, included here is a demon- reality of nature, constantly characterized, stration again that African science can in faith, by two aspects: “spirit/matter, vis- prove the accuracy of the stock of tradi- ible/invisible, male/female, good/evil, es- tional knowledge and technologies (Sègla, sence/existence.” About Yoruba’s cosmo- 2015a, 2015b). We first present the Yo- logical vision, studies by Morton-William ruba cosmological model and its elements. attest to a “twoness mental model.’’ Mor- We then show their scientific interests and ton-William (1964) reported from the Yo- further, we present our mathematical in- ruba Oyo country: “…The House of the terpretation of the Yoruba conception of Sky is the domain of the supreme God, the universe and the sky. Olorun or Olodumaré (Olorun means ‘Sky – Owner’)… The Earth is the domain Yoruba Ethnoastronomy of the Goddess Onilè, Earth-Owner, who Who are the Yoruba? is sometimes simply called Ile...” This ob- The Yoruba are about 50 million people servation from the Oyo Yoruba, apart living in West Africa, Nigeria, Benin Re- from some variability, is available for all public and Togo. Millions of others in the other Yoruba. Cuba, Brazil (Bahia) and the United States From these observations, the Earth are descendants of Yoruba slaves. The or- Goddess is recognized to be the conceptual igins of the Yoruba are lost in history. counterpart of the Sky God, since Earth Their ancient history, sometime between and Sky are in relation of a Female/Male 3000 BCE and 500 CE (Horton 1979; duality. They are coeval, each of them be- Obayemi 1979), is well known by the study ing characterized by four correspondent of the pre-dynastic (pre-Oduduwa) Yoruba spirits: matter, water, air and fire. Between linguistic groups now mainly in Benin Re- them is the World of the humans (Ilé Aiyé), public, Togo or in the eastern parts of Yo- governed by the Orisha in Yoruba history ruba land in Nigeria (Sègla 2003, 2006). and culture. Thus, Orisha are the Su- Their recent history began with the foun- preme God functionaries and ministering dation of Ifè between 500 and 800 CE, and spirits in the World /Ilé Aiyé/ (Awolalu later with the foundation of Oyo. Heritage 1979). This means that the Orisha are in- is widespread with strong knowledge of so- termediary deities between the Supreme cial organization, agriculture, medicine, God and humans. The Orisha, who are Segla, A. 11 Figure 1. Yoruba cosmological model reproduced from Morton-William (1964). sent by the Supreme God to govern hu- tory lead us to the main proposal for a uni- man life, thus constitute socially con- versal scientific theory because they show structed institutions for scientific practices how a people’s conception of the sky con- (Sègla 2015a). structed science (Sègla 2015a), whereby Most prominent social institutions, un- Orisha (or Vodun, as named by the Yo- der the authorities of the intermediary Or- ruba’s neighbors, the Fon) is conceived as isha, that enable humans to penetrate nat- a variant of several existing world views. ural phenomenon and establish their inner They give evidence of a “science of the lo- laws are: Obatala, the knowledge of form- cal” within a common universal scientific ing a child in womb (fertility); Shango, thun- theory (Sègla 2015a). However, a detailed der and lightning; Ogun, use of iron; Oko, study of the Orisha is not our concern fertility of farm, forest and environmental here. This article aims to concentrate on science; Shapona or Sapata, curing of small- mathematical interpretations of the Yo- pox; Esu, philosophy, part of the divine ruba cosmological model. It is therefore in- which tests and tries out people; and Orun- teresting to ask why and how the original mila/Ifa, the whole encyclopedia that gath- coders count sixteen most important inter- ers all oral knowledge produced within mediary deities (the Orisha)—also called every existing Orisha (Sègla 2015a). There the Primordial Deities—and why and how are many Orisha; scholars count thou- the Sixteen Primordial Deities have under sands and thousands of them, but accord- their control the other Two Hundred and ing to oral tradition and very well devel- Forty Secondary Deities. oped studies (Bascom, 1969; Abimbo 1975, 1977), the most famous Orisha are Scientific Interests the Sixteen (16) so-called Fundamental or We propose that the study of the Yoruba- Primordial and the Two Hundred Forty Idààcha Divinatory Calendar (Sègla 2006, (240) Secondary Orisha. The total gives 2008) gives evidence of a pre-Ifa (Encyclo- two hundred and fifty-six Orisha. pedia of Yoruba Knowledge) divination Studies of the Orisha in Yoruba his- system that remained immune from to- JAC, Vol. 1, No. 1, 2016 12 day’s ‘confusing’ and permuted Ifa hegem- world, one must take into consideration ony, which has already been observed by the Two Masters of the Universe, that is Maupoil (1943). In modern days, semantic Eeji Oni-Ilè or ‘the Two who own the truthfulness from the original Ifa World’ (or ‘two possessors of the universe’) knowledge system’s coding still shares as Morton reported (i.e. the Sky or Su- claims of aboriginal status with a cluster of preme God and the Earth Goddess), the associated cults.