AMUCHMA-NEWSLETTER-22

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)

TABLE OF CONTENTS

2. Meetings, exhibitions, events

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. MEETINGS, EXHIBITIONS, EVENTS

**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**

**9. **SUGGESTIONS

Thanks to Scott Williams, the English language
edition of all issues of the **AMUCHMA Newsletter** is also
accessible on the following website: **http://www.math.buffalo.edu/mad/AMU/amuchma_online.html**

Please note the address of the above website
changed to the present with AMUCHMA 21.

The English version of AMUCHMA
22 is reproduced and distributed

with financial support from **SIDA**-**SAREC** (Sweden)