Chairman: Paulus Gerdes (Mozambique)
Secretary: Ahmed Djebbar (Algeria)
Treasurer: Salimata Doumbia (Côte d'Ivoire)
Members: Kgomotso Garegae-Garekwe (Botswana), Maassouma Kazim (Egypt), Cornelio Abungu (Kenya), Ahmedou Haouba (Mauritania), Mohamed Aballagh (Morocco), Ruben Ayeni (Nigeria), Abdoulaye Kane (Senegal), David Mosimege (South Africa), Mohamed Souissi (Tunisia), David Mtwetwa (Zimbabwe)


Objectives of AMUCHMA

2. Meetings, exhibitions, events

3. Notes and queries

4. Sources

6. Have you read? (#265-#277) --- 2nd web page

7. Announcements --- 2nd web page

8. Addresses of scholars and institutions mentioned in this newsletter --- 2nd web page


Do you want to receive the next AMUCHMA-Newsletter



Universidade Pedagógica (UP), Maputo (Mozambique), 06.25.1999



2.1 International Colloquium in Rabat (Morocco)

The Research Group on the History and Philosophy of the Sciences of the Faculty of Arts and Human Sciences of the Mohammed V in Rabat (Morocco) organised from 28 to 30 October, 1998, an international symposium on "Imagination in the global process of scientific knowledge". Academics from different countries (Algeria, Germany, Morocco, Portugal, USA) took part. The following themes were presented:
* Aballagh, Mohamed (Morocco): Aristotle versus the scientists from the Muslim west from the 12th to the 14th century;
* Abattouy, Mohamed (Morocco): Medieval Arab mechanics between real and imaginary;
* Alozade, Mohamed (Morocco): Imagination and science in the philosophy of al-Farabi;
* Bartuschat, Wolfgang (Germany): Imagination, understanding and aesthetic idea;
* Ben Maissa, Abdessalam: (Morocco): How imagination works: an empirical point of view;
* Cargon, Robert (USA): Model, analogy and the physical imagination: The case of the vortex atom;
* Carlos, Jacques (Portugal): Sokal's misreadings of philosophy;
* Chadli, Mostefa (Morocco): Space and its representations in the human sciences;
* Chaitin, Gilbert (USA): Reading Sokal's text: the right way to do science;
* Djebbar, Ahmed (Algeria): The place of imagination in the mathematical activities of the medieval Arabic tradition;
* El Bouazzati, Bennacer (Morocco): Imagination and reasoning;
* El Mesbahi, Mohamed (Morocco): The role of imagination in the view of the philosophers of the Islam;
* Haddad, Lahcen (Morocco): Sokal's imaginary philosophers;
* Herzenni, Ahmed (Morocco): Reality between unity and fragmentation;
* Levine, Amy (USA): A suspensing of fixity: A continuing debate between reason and madness in Derrida and Foucault;
* Molella, Arthur (USA): The electrodynamic world view an the frontiers of the scientific imagination;
* Moulay-Rachid, Mostefa (Morocco): The role of imagination in the progress of ancient geographic thought.

2.2 International Colloquium at the Dibner Institute, Boston (USA)

An international colloquium on "New perspectives on science in medieval Islam" was held (November 6-8, 1998) at the Dibner Institute (Boston, USA). The following papers were presented related to the history of science in the north of Africa:
* Djebbar, Ahmed (Algeria): Mathematical activities in the Muslim West (8th-16th Centuries): Present status and prospects;
* Folkerts, Menso (Germany): Arithmetic: From India through Baghdad to the West;
* Kunitzsch, Paul (Germany): The transmission of Hindu-Arabic numerals reconsidered;
* Langermann, Tzvi (Israel): Another Andalusian revolt?: Ibn Rushd's critique of Al-Kindi's Pharmacological Computus;
* Samso, Julio (Spain): The survival of Andalusian astronomy and the introduction of Eastern Zijes in the Maghreb until the 19th Century.

2.3a Visit of Ahmed Djebbar to Tunis

Invited by the Tunisian Ministry of Higher Education, Ahmed Djebbar visited Tunis from 19 to 25 November, 1998. He was invited in the context of creating (for the first time in the Maghreb) of a course of the History of Science and Epistemology. This one semester course (one hour a week), will be introduced at the beginning of the 98-99 academic year. It is compulsory for first year students of the 'Maîtrises' in Mathematics, Physics, Chemistry, and Computer Science and of the 'Maîtrises' in Life and Earth Sciences. In the first semester will have a course in the history of mathematics, of physics, of biology, of chemistry and of geology respectively. In the second semester, the history of these subjects will be continued by a more epistemological explanation.
During his visit, Ahmed Djebbar (Algeria) took part, with the lecturers of the history of science at the University of Tunis II (all volunteers), in meetings of evaluation of the new course in the history of science and in the preparation of a postgraduate program for these lecturers.
During his visit, Ahmed Djebbar gave three talks on the following themes:
* Mathematics in the Maghreb and in Andalusia and its transmission to Europe;
* Mathematics and cultural or game activities in the Maghreb;
* From al-Khwarizmi to Galois : a history of classical algebra.

2.3b National Seminar on the Teaching of the History of Science (Tunisia)

Following the visit of Ahmed Djebbar to Tunis, the Ministry of Higher Education organised a National Seminar on the Teaching of the History of Science with a duration of one week. Two conferences and one workshop on the history of mathematics were presented:
* Helène Gispert : Is it possible to speak of European mathematics in the 19th century ?;
* Ahmed Djebbar : Overview of scientific activities in the medieval Maghreb (11th-16th centuries).
* (Workshop) H. Abrougui, F. Bellalouna, A. Djebbar : Presentation and study of Arab algebraic texts.


2.4 Seminar in Paris on Mathematics in Africa south of the Sahara

At the initiative of Elikia M'Bokolo (CEAf) and invited by the Centre of African Studies (CEAf) at the "Ècole des Hautes Études en Sciences Sociales" (EHESS) of the French National Scientific Research Council (CNRS), Paulus Gerdes (Mozambique) conducted from January 20 to February 18, 1999, a research seminar entitled "Culture and mathematics in Africa south of the Sahara: History of mathematics and ethnomathematical research". In the seminar took part historians, anthropologists, sociologists, mathematicians and philosophers, from several African (Algeria, Angola, Congo-Brazzaville, Congo-Kinshasa, Mali, Senegal) and European countries (France, Germany, Italy).

2.6 Papers presented at recent meetings

During the 4th World Archaeological Congress (January 10-14, 1999, Cape Town, South Africa) a CASAS-CODESRIA Symposium on the Africanisation of Knowledge took place. It was coordinated by Kwesi Prah, the Director of the Centre for Advanced Studies of African Societies (CASAS) in Cape Town.
The following themes related to mathematics were presented:
* Gerdes, Paulus (Mozambique) : On the production of mathematical knowledge in Central and Southern Africa;
* Gnanvo, Cyprien (Benin) : African languages and the mastering of mathematical and scientific knowledge;
* Seepe, Sipho (South Africa) : Re-configuring African mathematics and scientific knowledge systems to meet the challenges of the 21st century.

At the International Colloquium on "Commerce and Mathematics" (Beaumont de Lomagne, France, May 13-16, 1999) the following papers were presented by researchers from the Maghreb:
* Ahmed Djebbar (Algeria) : The commercial transactions in Arab mathematical texts;
* Ezzaim Laabid (Morocco) : The proportional distribution in Maghrebian mathematical tradition;
* Mohammed Souissi (Tunisia) : Application of proportions in problems of commercial arithmetic.

About two hundred teachers and inspectors of mathematics from all regions of Morocco took part in the second International Colloquium on Didactics of Mathematics (Safi, Morocco, May 27-29, 1999). An important place was given to the history of mathematics, as three conferences and one workshop were dedicated to it. The conferences were the following:
* Ahmed Djebbar (Algeria) : Mathematics produced in the Maghreb and its place in the teaching of mathematics;
* Ezzaim Laabid (Morocco) : Use of the history of mathematics in the teaching of mathematics;
* Abdallah El Idrissi (Morocco) : Towards a historical perspective of mathematics education


This section is reserved for questions that readers would like to have answered; these are the 'queries'. The answers will be the 'notes'. If you have questions or answers about sources, dates, names, titles, facts, or other such matters related to the history of mathematics in Africa, frame them in clear and concise language and send them to the editors. If you are answering a question, make clear reference to that question. All readers may send both questions and answers. Each will be published with the name of the sender.

We received from Dr. Eluemuno R. Blyden (USA) the following query :
"I want to ask if you can tell me anything about the ways in which African cultures have formulated the problem of genetics and inheritance. What versions of the genetic code or Mendelian inheritance are known? It seems to me that the cultures based on cattle in which careful attention was paid to lineage and therefore to traits and their inheritance would be fertile places for such theories to develop".


Further sources on numeration in Africa south of the Sahara (1)
(Paulus Gerdes)

Several sources related to numeration (and/or numerology) in Africa south of the Sahara have been already presented in earlier issues of the AMUCHMA-Newsletter (in particular in #9). In addition to these, are the following sources - in alphabetical order -, I came across during my stay (January-February 1999) at the Centre of African Studies (EHESS-CNRS, Paris, France) and the Royal Museum for Central Africa (Tervuren, Belgium).

Casimir Agbo, La numération au Dahomey, Études Dahomeennes (Nouvelle Série), Porto Novo, 1969, Nos. 14-15, 59-110; 1970, No. 16, 5-112
Presents the numerals in several languages spoken in the Republic of Benin: Fon or Fongbé, Mina or Ghen, Ghin or Ghinbe, Nagot or Yoruba.

Nathalie Bonini, Numération et évaluation du temps dans trois sociétés d'Afrique orientale. L'exemple des Borana, des Chaga et des Maasai [Numeration and time measurement in three societies of Eastern Africa. The example of the Borana, the Chaga and the Maasai], Mémoire présenté en vue de la maitrise d'ethnologie, Université de Paris-X Nanterre, Laboratoire d'Ethnologie et de Sociologie comparative, 1989, 94 pp.
'Maitrise' thesis in ethnology.

Blandine Bril, Analyse des nombres associés à l'homme et à la femme en Afrique de l'Ouest [Analysis of the numbers associated with male and female in West Africa], Africa : Journal of the International African Institute, London, 1979, 49(4), 367-376
"The opposition and the complementarity of male and female have been brought out in different societies with the aid of pairs of symbols based on left-right, points of the compass, colour, etc. Number also appears to be an apt means of expressing this idea. By studying the rituals of birth and death in West Africa it has been possible to distinguish four pairs of numbers widely associated with male and female : (3,4), (4,3), (9,7) and (5,4). The geographical distribution of these pairs of numbers shows marked grouping. Explanations of the use of the different numbers are generally based on myths or on physiological differences between the sexes and are not very convincing. However, the pairs of numbers are widely used in the 'numerical system' of a society which determines the ritual calendar. These systems also make great use of the number 7 and the author contends that not only is this widely seen as the sum of 4 and 3 in areas using that pair but that some evidence can be found that the area using the pair (5,4) tends similarly to use the sum, 9, in its numerical system for the ritual calendar" (p. 376).

A. Burssens, Les numéraux en Amashi (Kivu) [The numerals in Amashi], Kongo-Overzee, XVIII, I, 1952, 66-76
Lists the numerals in Amashi, the language of the Abashi (Kivu, Congo / Zaire) and discusses grammatical aspects.

H. Burssens, Arithmétique, in: Les peuplades de l'Entre Congo-Ubangi (Ngbandi, Ngbaka, Mbandja, Ngombe et Gens d'Eau), International African Institute, London, 1958, 171-172
Presents brief information on the numeration systems among the Ngbandi, Ngbaka [7=6+1; 9=5+4], Mbandja [7=6+1; 9=8+1] and Ngombe (Congo / Zaire)

L. Bynon-Polak, L'expression des ordinaux dans les langues bantoues [The expression of ordinal numbers in the Bantu languages], Africana Linguistica II, Annales du Musée Royal de l'Afrique Centrale, Sciences Humaines, Tervuren (Belgium), 1967, #55, 127-160
Comparative linguistic study of the construction of the words for ordinal numbers in Bantu languages. Includes maps on the geographical distribution of the four basic methods of construction analysed by the author.

Jean-Pierre Caprile, Adoum Khamis & Ndjerassem Ngabot : Pour une terminologie de l'enseignement du calcul dans les langues africaines : la structure d'expression des nombres et des techniques opératoires dans deux langues "sara" du sud du Tchad, le "ngambay" et le "mango" [Towards a terminology for the teaching of arithmetic in African languages], Bulletin de l'AELIA (Association d'études linguistiques interculturelles africaines), 1983, 6, 273-287
Discusses the expressions used for numbers and operations in two "sara" languages from Chad : "ngambay" and "mango".

Jean-Pierre Caprile : Numérations orales et enseignement des mathématiques en Afrique [Oral numeration and the teaching of mathematics in Africa], LENGAS, revue de sociolinguistique, Montpellier (France), 1987, no. 21, 143-162
Paper presented at a session organised by the African Bureau of Educational Sciences in Kisangani (Congo / Zaire) in December 1984. It gives some information on systems of numeration in Africa (Sara-ngambay in Chad; Birom in Nigeria; Banda in Central-Africa) and outside Africa.

Chantal Collard, Les "noms-numéros" chez les Guidar [The "names-numbers" among the Guidar], L'Homme, revue française d'anthropologie, 1973, Vol. XIII(3), 45-59
Analyses the way the Guidar in North-Cameroon give names to their children. The first name indicates the order in which the mother gave birth (and also the sex in the case of the first four children); the second name is the name-number of the father of the child. E.g. the first of an individual called Tizi Dawaï expresses that he is a boy and the first child of his mother; his surname indicates that his father is the seventh child of his respective mother.

Sylvie Fainzang, Les sexes et leur nombres - Sens et fonction du 3 et du 4 dans une societé burkinabé [The sexes and their numbers. The meaning and function of 3 and 4 in a Burkinabe society], L'Homme, revue française d'anthropologie, 1985, Vol. 96, 97-109
"The author analyzes in sociological terms the widespread West-African tendency to associate the numbers 3 and 4 with man and woman respectively, practice usually attributed to certain aspects of male and female anatomy. An analysis of Bisa society (Burkina Faso) shows how the meaning and function of this symbolism are directly related to representations of the person on the one hand, and to social space as defined by residence rules on the other. The author suggests that the discourse implied by this symbolism serves to found social relations between the sexes and to legitimate male domination". (109)

Solange de Ganay, Graphie bambara des nombres [Bambara graphical representation of numbers], Journal de la société des africanistes, 1950, 20(2) : 295-305
Describes and displays graphical signs used by Bambara (Mali) to represent numbers.

P. Garnier, Les noms de nombre en bambara [The number words in Bambara], Notes africaines, 1954, 62, p. 50
Short comment on the words in Bambara (Mali) for 7, 9 (related to the duration of a pregnancy), 20 (related to the word for human being), and 40 (related to the word for mat). As 7 is a secret number, the author does not know an expression for it other than the indirect 'wuoron-fla', that is, the 'second six'.

Carlos Gonzalez Echegaray, Los sistemas de numeración y los numerales en los pueblos de la Guinea Española [The number systems and numerals among the peoples of Spanish Guinea (Equatorial Guinea)], Archivos del Instituto de Estudios Africanos, IV, 12, 1950, 19-29
Describes counting methods using fingers, knots, pebbles, etc., and number words (mostly decimal, some with auxiliary base five).

Marcel Griaule, Numération secrète [Secret numeration], in: Jeux Dogon, Institut d'Ethnologie, Paris, 1938, p. 222
In his book on children's games of the Dogon in Mali, Griaule presents two examples of a secret numeration (one to ten) used (and invented ?) by the children of the Pamyon and Guinna neighborhoods and often not understood by children from other neighbourhoods.

Karl Laman, Arithmetic, in: The Kongo, Upsala: Studia Ethnographica Upsaliensia, Vol. IV, 1968, 8-9
Describes briefly counting and measuring among the Sundi. Accounts are kept by means of stones, palm nuts, knots, tally sticks, etc. In games the score may be kept by putting aside certain objects, by tying knots in a string, or by chanting a jingle (examples are given).

Lucien Lévy-Bruhl, La numération chez les Bergdama, Africa, Journal of the International Institute of African Languages and Cultures, 1929, Vol. II, No. 2, 162-173
Compares aspects of (finger) counting of the Bergdama (Berg Damara) of South Africa and Namibia with the (verbal) counting of their neighbours, the Nama.

Guy Nicolas, Un système numérique symbolique : le quatre, le trois et le sept dans la cosmologie d'une société hausa (vallée de Maradi) [A symbolic numerical system : four, three and seven in the cosmology of a Hausa society (Maradi valley)], Cahiers d'études africaines, Paris, 1968, VIII(3), 566-616
The numbers four (hudu), three (uku) and seven (bakwai) play an important role in ritual, economic and social life among the Hausa in the Maradi valley (Niger). This role is described, analysed and discussed.

H. Sawyer & S. K. Todd, The significance of the numbers 3 and 4 among the Mende of Sierra Leone, Sierra Leone Studies : A Journal of the Arts and Sciences, 1970, 26, 29-36
Discusses "the significance and incidence of the use of the figure three to symbolise female activity, and of the figure four to symbolise male participation among the Mende" (p. 30).

Leo Stappers, Het hoofdtelwoord in de Bantoe-talen [The cardinal number in the Bantu languages], Africana Linguistica II, Annales du Musée Royal de l'Afrique Centrale, Sciences Humaines, Tervuren (Belgium), 1967, #55, 175-198
Compares the prefixes used in the Bantu languages in connection with the cardinal numbers one to five. The paper analyses also 'abstract' counting (i.e. without reference to the objects), and 'distributive' ('two by two', ...) and 'multiplicative' use of cardinals in the Bantu languages. Maps with information on the geographical distribution are included.

Placidus Tempels, De tel-gebaren der Bashila [The number-gestures of the Bashila], Congo-Overzee, 1938, IV. 2, 49-53
Describes the number-gestures among the (Ba)Shila in Congo / Zaire. There are two series, one for counting from 1 to 10, and one for indicating individually numbers (cardinal numbers).

Toussaint-Yaovi Tchitchi: Numérations traditionnelles et aritmétique moderne, in: Hountondji, Paulin (Ed.), Les savoirs endogènes: pistes pour une recherche, CODESRIA, Dakar (Senegal), 1994, 109-138
Discusses traditional numeration in "àjá" (Benin) and possibilities of and experimentation with a decimalisation

(to be continued)


6. Have you read? - 2nd web page


7. Announcements - 2nd web page


8. Addresses of scholars and institutions mentioned in this newsletter - 2nd web page






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