Chapter 7 Numeric systems. W: Ron Eglash: African Fractals: Modern Computing and Indigenous Design. Rutgers University Press, 1999, s. 100-101. ISBN 0-8135-2614-0, ISBN 978-0-8135-2614-0. Cytat: "The strong similarity of both symbolic technique and semantic categories to what Europeans termed „geomancy” was first noted by Flacourt (1661), but it was not until Trautmann (1939) that a serious claim was made for a common source for this Arabic, European, West African, and East African divination technique.The commonality was confirmed in a detailed formal analysis by Jaulin (1966). But where did it originate?
Skinner (1980) provides a well-documented history of the diffusion evidence, from the first specific written record, a ninth century Jewish commentary by Aran ben Joseph, to its modern use in Aleister Crowley's Liber 777. The oldest Arabic documents (those of az-Zanti in the thirteenth century) claim the origin of geomancy (ilm al-raml, „the science of sand”) through the Egyptian god Idris (Hermes Trismegistus), and while we need not take that as anything more than a claim to antiquity, a Nilotic influence is not unreasonable. Budge (1961) attempts to connect the use of sand in ancient Egyptian rituals to African geomancy, but it is hard to see this as unique. Mathematically, however, geomancy is strikingly out of place in non-African systems.
Like other linguistic codes, number bases tend to have an extremely long historical persistence. Even under Platonic rationalism, the ancient Greeks held 10 to be the most sacred of all numbers; the Kabbalah's Ayin Sof emanates by 10 Sefirot; and the Christian west counts on its „Hindu-Arabic” decimal notation.In Africa, on the other hand, base two calculation was ubiquitous, even for multiplication and division. And it is here that we find the cultural connotations of doubling that ground the divination practice in its religious significance.
The implications of this trajectory -- from sub-Saharan Africa, to North Africa, to Europe -- are quite significant for the history of mathematics. Following the introduction of geomancy to Europe by Hugo of Santalla in twelfth century Spain, it was taken up with great interest by the pre-science mystics of those times -- alchemists, hermeticists, and Rosicrucians (figure 7.9). But these European geomancers -- Raymond Lull, Robert Fludd, de Peruchio, Henry de Pisis and others -- persistently replaced the deterministic aspects of the system with chance. By mounting the sixteen figures on a wheel and spinning it, they maintained their society's exclusion of any connections between determinism and unpredictability. The Africans, on the other hand, seem to have emphasized such connections. In chapter 10 we will explore one source of this difference: the African concept of a “trickster” god, one who is both deterministic and unpredictable.
On a video recording I made of the Bamana divination, I noticed that the practitioners had used a shortcut method in some demonstrations (this may have been a parting gift, as the video was shot on my last day). As first taught to me, when they count off the pairs of random dashes, they link them by drawing short curves.The shortcut method then links those curves with larger curves, and those below with even larger curves.This upside-down Cantor set shows that they are not simply applying mod 2 again and again in a mindless fashion.The self-similar physical structure of the shortcut method vividly illustrates a recursive process, and as a non-traditional invention (there is no record of its use elsewhere) it shows active mathematical practice. Other African divination practices can be linked to recursion as well; for example Devisch (1991) describes the Yaka diviners' „self-generative” initiation and uterine symbolism.
Before leaving divination, there is one more important connection to mathematical history. While Raymond Lull, like other European alchemists, created wheels with sixteen divination figures, his primary interest was in the combinatorial possibilities offered by base-2 divisions. Lull's work was closely examined by German mathematician Gottfried Leibniz, whose Dissertatio de arte combinatoria, published in 1666 when he was twenty, acknowledges Lull's work as a precursor. Further exploration led Leibniz to introduce a base-2 counting system, creating what we now call the binary code. While there were many other African influences in the lives of Lull and Leibniz, it is not far-fetched to see a historical path for base-2 calculation that begins with African divination, runs through the geomancy of European alchemists, and is finally translated into binary calculation, where it is now applied in every digital circuit from alarm clocks to supercomputers.
In a 1995 interview in Wired magazine, techno-pop musician Brian Eno claimed that the problem with computers is that „they don't have enough African in them” Eno was, no doubt, trying to be complimentary, saying that there is some intuitive quality that is a valuable attribute of African culture. But in doing so he obscured the cultural origins of digital computing and did an injustice to the very concept he was trying to convey.”. (ang.).
buffalo.edu
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Dr. Scott W. Williams, Professor of Mathematics: Mathematics of the African Diaspora. Department of Mathematics, The State University of New York at Buffalo, 1997-05-25. [dostęp 2009-07-02]. Cytat: "Most histories of mathematics devote only a few pages to Ancient Egypt and to northern Africa during the 'Middle Ages´. Generally they ignore the history of mathematics in Africa south of the Sahara and give the impression that this history either did not exist or, at least, is not knowable, traceable, or, stronger still, that there was no mathematics at all south of the Sahara. In history, to Europeans, even the Africanity of Egyptian mathematics is often denied or suffers eurocentric views of conceptions of both 'history' and of 'mathematics' form the basis of such views. Contrary to the popular view, one can neither racially or geographically separate Egyptian civilization from its black African roots." (ang.).
Christopher M.Ch.M.KeltyChristopher M.Ch.M., Ramon Llull (1232-1316): Logic. Memory. Wacko., [w:] Anthropology 375/575: Abracadabra: Language and Memory in Science and Technology, Houston: Rice University, 17 marca 2003 [dostęp 2008-09-25](ang.).???
