Wednesday, 22 April 2015


A Bakuba woman weaving a textile

Kuba Textiles

Kuba textiles are unique in the Democratic Republic of the Congo, formerly Zaire, for their elaboration and complexity of design and surface decoration. Most textiles are a variation on rectangular or square pieces of woven palm leaf fiber enhanced by geometric designs executed in linear embroidery and other stitches, which are cut to form pile surfaces resembling velvet. Women are responsible for transforming raffia cloth into various forms of textiles, including ceremonial skirts, ‘velvet’ tribute cloths, headdresses and basketry.

Raffia Cloth

In Kuba culture, men are responsible for raffia palm cultivation and the weaving of raffia cloth. Several types of raffia cloth are produced for different purposes, the most common form of which is a plain woven cloth that is used as the foundation for decorated textile production. Men produce the cloth on inclined, single-heddle looms and then use it to make their clothing and to supply foundation cloth to female members of their clan section. The cloth is coarse when it is first cut from the loom, so it is then pounded in a mortar, which softens it and renders it ready for the application of surface decoration, for which women are responsible. 


Many prestige weavings are dyed with twool, a deep red substance obtained from the heartwood of the tropical trees Pterocarpus sp. and Baphia pubescens. The Kuba believe that twool is imbued with magical and protective properties. When mixed with palm oil, it creates a pomade that is applied to the face, hair and body in a ritual context. According to oral tradition, the Pende were responsible for teaching the Kuba how to weave textiles; the Pende used twool to die their prestige clothes for death

"Bambala" Fabrics

Early 20th Century ethnographer Emil Torday acquired the oldest group of extant textiles from the Kuba tradition from the reigning king, Kot aPe. He called these textiles "Bambala" after the ruling clan. According to Joseph Cornet, these cloths were embroidered by Bushong women who were pregnant with the King's heirs for use in rituals surrounding the birth of the children.[5] They were also used as funerary regalia for noble women. The slight sculptural relief, elaborate geometric designs and technical cohesiveness of the textiles indicate that they were created by highly skilled elders. According to art historian Drake Moraga, "That Kuba embroiderers represented textile structures in their compositions underscores both the value of weaving to the culture and the prestige attached to women art." 

Women's Ceremonial Overskirts
Bushong woman's ceremonial
overskirt from the 20th century.

Kuba women traditionally wore overskirts during burial displays, but the overskirt was later adopted as part of many ceremonial ensembles worn during ritual dances, celebrations and masked performances. The wraparound skirt was secured with a belt and worn over a typically monochrome red or white embroidered skirt. These skirts exhibit a variety of design components; some skirts employ flat linear embroidery exclusively, while others employ this technique exclusive on the borders of the fabric, in which case the interior is executed with cut-pile embroidery, which lends the surface a "plush" appearance and feel. In the cut-pile embroidery technique, short raffia strands are individually inserted with a needle under one or more warps or wefts of a plain-woven raffia panel, then cut close to the surface at each end to produced the raised "pile." Textile weaving boasts a variety of motifs, such as guilloche interlace, which embroidery artists employed along with color, line and texture to yield varied compositions and visual effects. 

Pattern and Repetition: Kuba Textiles as they Relate to Mathematics and Music
Kuba cloth from early-mid 20th century, currently at the Honolulu
Kuba cloth from early-mid 20th century, currently at the Honolulu

Academy of Arts

Kuba textiles demonstrate a taste for interrupting the expected line; they compose through juxtapositions of sharply differing units and abrupt shifts of form.

Mathematician Donald Crowe has analyzed, in particular, the two-dimensional designs of Benin, Yoruba and Kuba arts and has shown the extent of the Africans' explorations into the formal possibilities of geometric variation. In their art, the Kuba have developed all the geometric possibilities of repetitive variations of border patterns, and of the seventeen ways that a design can be repetitively varied on a surface, the Kuba have exploited twelve. This exploration does not mean that they confine themselves to repetitive patterning in confronting a surface to be decorated.

The character of Kuba design accords with Robert Thompson's observation that some African music and art forms are enlivened by off-beat phrasing of accents, by breaking the expected continuum of surface, by staggering and suspending the pattern. In textile design, the Africans of the Kasai-Sankuru region do not project a composition as an integrated repetition of elements. Until recently, Euro-American attitudes on this point were so fixed that we called a textile design a "repeat," and expected to find a unit of identical imagery repeated over the surface. This kind of integration is not typical for African two-dimensional arts.

N.B. If we look at the Chief and what he is wearing and the designs he is seated on we would, if we were in the blazing sun, see him as floating above the earth. This is the power of the Kuba Designs.

Let Us Push These African Design Ideas To The MAX.

Here are some new works by Joe Pollitt from the UK, inspired by Kuba Designs from the Congo and Central Africa including Uglorious Ugandans. Here we see ideas that thread mathematics, knot theory, universal symbols that appear all over the world and the origins of African magic being introduced globally but what are all these powerful messages trying to teach us?

Kuba Shoowa Textile Kasai Velvet | POLLITT COLLECTION

Stage 1 | Uglorious Designs

Stage 2 & 3 | Uglorious Designs

Stage 4 & 5 | Uglorious Designs

Stage 6 | Uglorious Designs

The designs when layered take us into a different dimension. A two dimensional design when miss matched and crossed over send our minds into a sense of flying, uplifting movement so we see above and below. When lives are lived outside rather than inside the use of light or daylight can be harnessed to improve the mental state of all. These designs are key as the wearer twist and turn and do so next to similar designs so our eyes are tricked into a sense of three dimensional imagery that has never been seen before. Human movement coupled with complex designs is a source of visual alchemy. This is the true magic of Art and yet again coming out of Central Africa including Uganda.

Let us look at this from a Ron Eglash perspective of mathematics and the use of fractals at the heart of rural African village planning. 

Let us pick up on what Luke Dunn stated about the similarity of the Dogon people of Mali, they are well know to be the great mathematicians and astrologers with an in-depth knowledge of the cosmos. Their mapping of Sirius B is stuff of legends - Dogon People of Mali.

Dogon Designs

This lecture by Dr Van Sertima is enlightening and goes into areas of Africa that we are discussing with great depth and is a very useful resource for those interested in this area of intellectual debate about the importance of mathematics, design, primitive thought that is process even in today's standards and echoes much of what we have previously discussed.

*N.B. These are interesting articles sent to us by Joanne Muwanga.


The Ishango Bone: Evidence of the Congolese Invention of Mathematics

By Robin Walker

Mathematics was born in Central Africa at least 25,000 years ago.  The evidence comes from the Ishango bone, a prehistoric tool handle.

It was unearthed by archaeologists working in the Ishango region of Congo on the shore of Lake Edward. Jean de Heinzelin of Belgium's Royal Institute of the Natural Sciences discovered it in the late 1950s. Originally thought to have been over 8,000 years old, a more  sensitive re-dating by Alison Brooks of George Washington University has established that the bone tool is an astonishing 25,000 years old.

We would do well to ponder over this date. Civilisations as we know them did not exist. Africans had already developed fishing cultures by then and had already dug the world's first mines. They also began the observation of the heavens. Outside Africa, much less has happening. It must be remembered that the period of which we speak  was at least 22,000 years before the first Greek cities, the crowning achievement of the Europeans. This period was 20,000 years older than the first Middle Eastern kings. Even in Africa, where civilisation began, Ishango was an achievement. This artefact is at least 16,000 years older than the construction of the Great Sphinx  of the Giza desert, the crowning achievement of the African people of the Nile River.

So what is so special about this bone? On the tool are three rows of notches, two of which add up to sixty. The number patterns represented by the notches have been analysed by many scholars, most notably by Professor Claudia Zaslavsky, a European-American mathematician. She demonstrates that the number patterns show doubling, addition, subtraction, prime numbers and base ten. The patterns have also been analysed by brilliant and scholarly Charles Finch, one of Black America's best intellects.

The first row of patterns on the bone shows three notches carved next to six, four carved next to eight, ten carved next to two groups of five, and finally a seven. The numbers 3 and 6, 4 and 8, and 10 and 5, are believed to represent the process of multiplication by 2. Row 2 shows eleven notches carved next to twenty-one notches, and nineteen notches carved next to nine notches. This is thought to represent 10 + 1, 20 + 1, 20 – 1 and 10 – 1. Finally, row 3 shows eleven notches, thirteen notches,
seventeen notches and nineteen notches. 11, 13, 17 and 19 are the prime numbers between 10 and 20. A prime number can only be divided by itself and by 1 to produce a whole number.

The early mathematician(s?) responsible for the Ishango bone therefore understood multiplication, addition and prime numbers. Moreover, two of the rows add up to sixty. Row 2 consists of 11 + 21 + 19 + 9 = 60. Row 3 consists of 11 + 13 + 17 + 19 = 60. Our leading writer on ancient African science, Charles Finch of the Morehouse School of Medicine, believes that this represents an understanding  of base 60. This is, incidentally, the concept on which modern clocks and watches are based. For example, on a modern clock 60 seconds = 1 minute, and 60 minutes = 1 hour. Finally, the centrality of numbers ten and twenty for the calculations in row 2 and row 3, suggest an early understanding of base 10. This is the basis of the  decimal system of counting, the very one that we use today. For example, on a modern decimal ruler 10 millimetres = 1 centimetre, and 10 decimetres = 1 metre.

It is heartening to see that information about ancient African mathematics inspires people today. In England, for example, Elizabeth Rasekoala, a Manchester based chemical engineer, established the Ishango Science Clubs early in 1997. These clubs were part of an initiative by her charity The African-Caribbean Network for Science & Technology to promote mathematical and scientific excellence among Black school children in various  British cities. Their impact has already been felt.

We may never find out who the Congolese mathematician(s) was/were who carved the number patterns on the Ishango bone, but their list of distinctions are many. They presented the world's oldest known counting system. They were the first known people on the planet to present multiplication, addition, subtraction, prime numbers, base 10 and base 60 (if Charles Finch is correct). They did this sometime around 23,000 BC, that is 25,000 years ago! It is sometimes suggested that many Black school students are failures at mathematics and in the sciences. It is also suggested that teacher racism, broken families and the lack of role models are valid explanations for this shabby state of affairs. In all honesty, do these excuses stand up when Africans invented the subject 25,000 years ago?


Ancient African Mathematics

Source: Taneter |

Africa is home to the world's earliest known use of measuring and calculation, confirming the continent as the birthplace of both basic and advanced mathematics. Thousands of years ago, Africans were using numerals, algebra and geometry in daily life. This knowledge spread throughout the entire world after a series of migrations out of Africa, beginning around 30,000 BC, and later following a series of invasions of Africa by Europeans and Asians (1700 BC-present).

Measuring and Counting

Lebombo Bone (35,000 BC)

The world's oldest known measuring device, the "Lebombo bone
The oldest mathematical instrument is the Lebombo bone, a baboon fibula used as a measuring device and so named for its location of discovery in the Lebombo mountains of Swaziland. The device is at least 35,000 years old. Judging from its 29 distinct markings, it could have been used to either track menstrual or lunar cycles, or used merely as a measuring stick.

It is rather interesting to note the significance of the 29 markings (roughly the same number as lunar cycle, i.e., 29.531 days) on the baboon fibula because it is the oldest indication that the baboon, a primate indigenous to Africa, was symbolically linked to Khonsu, who was also associated with time. The Kemetic god, Djehuty ("Tehuti" or "Toth"), was later depicted as a baboon (also an ibis), and is usually associated with the moon, math, writing and science. Use of baboon bones as mathematical devices has been continuous throughout all of Africa, suggesting Africans always held the baboon as sacred and associated with the moon, math, and time.

Front and rear of Ishango Bone in the Museum of Natural Sciences, Brussels
Ishango Bone (20,000 BC)

The world's oldest evidence of advanced mathematics was also a baboon fibula that was discovered in present-day Democratic Republic of Congo, and dates to at least 20,000 BC. The bone is now housed in the Museum of Natural Sciences in Brussels. The Ishango bone is not merely a measuring device or tally stick as some people erroneously suggest. The bone's inscriptions are clearly separated into clusters of markings that represent various quantities. When the markings are counted, they are all odd numbers with the left column containing all prime numbers between 10 and 20, and the right column containing added and subtracted numbers. When both columns are calculated, they add up to 60 (nearly double the length of the lunar or menstrual cycle).

A Gebet'a carving on the base of an Aksumite tekhen (stela), courtesty of Indech

Rwandans playing Omweso, a more advanced version of Gebet'a
Gebet'a or "Mancala" Game (700 BC-present)

Although the oldest known evidence of the ancient counting board game, Gebet'a or "Mancala" as it is more popularly known, comes from Yeha (700 BC) in Ethiopia, it was probably used in Central Africa many years prior. The game forces players to strategically capture a greater number of stones than one's opponent. The game usually consists of a wooden board with 2 rows of 6 holes each, and 2 larger holes at either end. However, in antiquity, the holes were more likely to be carved into stone, clay or mud like the example from Medieval Aksum, shown at right. More advanced versions found in Central and East Africa, such as the Omweso, Igisoro and Bao, usually involve 4 rows of 8 holes each.

Fractions, Algebra and Geometry

A copy of the so-called "Moscow" papyrus in "hieratic" text, with a clearer rendering below in "hieroglyphs".
"Moscow" Papyrus (2000 BC)

Housed in Moscow's Pushkin State Museum of Fine Arts, the so-called "Moscow" papyrus, was purchased by Vladimir Golenishchev sometime in the 1890s. Written in hieratic from perhaps the 13th dynasty in Kemet, the papyrus is one of the world's oldest examples of use of geometry and algebra. The document contains approximately 25 mathematical problems, including how to calculate the length of a ship's rudder, the surface area of a basket, the volume of a frustum (a truncated pyramid), and various ways of solving for unknowns.

"Rhind" Mathematical Papyrus (1650 BC)

Purchased by Alexander Rhind in 1858 AD, the so-called "Rhind" Mathematical Papyrus (shown below) dates to approximately 1650 BC and is presently housed in the British Museum. Although some Egyptologists link this to the foreign Hyksos, this text was found during excavations at the Ramesseum in Waset (Thebes) in Southern Egypt, which never came under Hyksos' rule. Written by the scribe, Ahmose, in the "Hieratic" script, the text reads as follows:

"Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries...all secrets... This book was copied in regnal year 33, month 4 of Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy..."

The first page contains 20 arithmetic problems, including addition and multiplication of fractions, and 20 algebraic problems, including linear equations. The second page shows how to calculate the volume of rectangular and cylindrical granaries, with pi (Π) estimated at 3.1605. Tere are also calculations for the area of triangles (slopes of a pyramid) and an octagon. The third page continues with 24 problems, including the multiplication of algebraic fractions, among others.

A page from the so-called "Rhind" Mathematical Papyrus in "Hieratic" text.

Timbuktu Mathematical Manuscripts (1200s AD)

Timbuktu in Mali is home to one of the world's oldest universities, Sankore, which had libraries full of manuscripts mainly written in Ajami (African languages, such as Hausa in this case, written in a script similar to "Arabic") in the 1200s AD. When Europeans and Western Asians began visiting and colonizing Mali from 1300s-1800s AD, Malians began to hide the manuscripts in basements, attics and underground, fearing destruction or theft by foreigners. This was certainly a good idea, given Europeans' history of stealing and/or destroying texts in Kemet and other areas of the continent. Many of the scripts, such as the one shown below, were mathematical and astronomical in nature. In recent years, as many as 700,000 scripts have been rediscovered and attest to the continuous knowledge of advanced mathematics and science in Africa well before European colonization.

A famous example of a mathematical and astronomical manuscript from medieval Timbuktu

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