Apr 6, 2024

Fulani wedding blanket


One of the most suprising things I have learnt was the African origin of Fractals pls goto the vid and klik the link on the link ,think of how one would use your computer with out it.
The most interesting thing I found out about it was historical. In the 12th century, Hugo Santalia brought it from Islamic mystics into Spain. And there it entered into the alchemy community as geomancy, divination through the Earth. This is a geomantic chart drawn for King Richard II in 1390. Leibniz, the German mathematician, talked about geomancy in his dissertation called De Combinatoria. And he said, "Well, instead of using one stroke and two strokes, let's use a one and a zero, and we can count by powers of 2." Right? Ones and zeros, the binary code. George Boole took Leibniz's binary code and created Boolean algebra, and John von Neumann took Boolean algebra and created the digital computer. So all these little PDAs and laptops -- every digital circuit in the world -- started in Africa, and I know Brian Eno says there's not enough Africa in computers; you know, I don't think there's enough African history in Brian Eno.


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.

High in the mountains of Central Equatorial Africa, on the borders of Uganda and Zaire lies Lake Edward, a source of the Nile. It is a small lake (about 30 miles by 60 miles).



Though the area is sparsely populated today, approximately 25,000 (update from 9,000) years ago by the shores of the lake lived a small community that fished, gathered, and grew crops The settlement only existed a few hundred years before being buried in a volcanic eruption. The place where their remains were found (1960) has a name now given to these people - Ishango. Among their remains is the second oldest mathematical object (the oldest is here) in Africa.

Some say that the Ishango Bone is the oldest table of prime numbers. Marshack later concluded, on the basis of his microscopic examination, that it represented a six-month lunar calendar.

prime numbers or menstral calendar

The most interesting, of a large number of tools discovered in 1960 at Ishango, is a bone tool handle called the Ishango Bone (now located on the 19th floor of the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special demand). At one end of the Ishango Bone is a piece of quartz for writing, and the bone has a series of notches carved in groups (shown below). It was first thought these notches were some kind of tally marks as found to record counts all over the world. However, the Ishango bone appears to be much more than a simple tally. The markings on rows (a) and (b) each add to 60. Row (b) contains the prime numbers between 10 and 20. Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1. Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2) used more recently in Egyptian multiplication. Recent studies with microscopes illustrate more markings and it is now understood the bone is also a lunar phase counter. Who but a woman keeping track of her cycles would need a lunar calendar? Were women our first mathematicians?


The traditional Fulani wedding blanket is woven primarily from camel hair. The weavers who created it say that spiritual energy is woven into the pattern and that each successive iteration shows an increase in this energy. Releasing this energy is spiritually dangerous; the weavers say that if they were to stop in the middle (where the pattern is most dense, and hence the spiritual energy is greatest) they would risk death. The engaged couple must bring the weaver food and kola nuts to keep him awake until it is finished.
Note that the first iteration has only two diamond shapes on each side, but the second has four. How is that acheived in the simulation?


Fractals





Ron Eglash and Julian Bleecker
To appear in Science as Culture
DRAFT DRAFT DRAFT

The Race for Cyberspace: Information Technology in the Black Diaspora

Barbara Christian's seminal essay, "The race for theory," analyzed the ways in which the academic competition to create a theory of black women's writing had overshadowed the potent theoretical content of the writing itself. Similarly, this essay examines how the hype over application of new information technologies to racialized social problems has overshadowed the potent technological content of the communities themselves. Focusing on the black diaspora, we broaden the category of "information technology" to show how traditions of coding and computation from indigenous African practices and black appropriations of Euro-american technologies have supported, resisted, and fused with the cybernetic histories of the west, and provide a strong source for changes in reconstructing identity, social postition and access to power in communities of the black diaspora.

1) Cyberspace as Savior

In the early 1990s the internet was flooded with various versions of the "cyberspace manifesto," most of which contained something like this passage from John Perry Barlow:

Ours is a world that is both everywhere and nowhere, but it is not
where bodies live. We are creating a world that all may enter without
privilege or prejudice accorded by race, economic power, military
force, or station of birth.

It might be easy to write off such declarations as uninformed optimism, were it not continually echoed by computer experts such as the MIT Media Lab's Nicholas Negroponte: "While the politicians struggle with the baggage of history, a new generation is emerging from the digital landscape free of many of the old prejudices" (Negroponte 1995:230). To those gasping for breath in the ozone-rich atmosphere of superlative cyberspace promises, the crucial question is not necessarily why outrageous promises are offered, but rather precisely how do such promises sustain themselves against their own speculative appearance? How do the utterances of scientists, engineers, hucksters and marketeers literally move and shape worlds, channel flows of institutional funding, and exert enormous influence in shaping the meaning of life. How is it that such claims are offered and sustained?

Technoscience is considered in the science studies idiom to be that body of knowledge and practices that links representation to intervention, maps strategies for taking action, and encapsulates the skill and technique that evacuates the social and political from itself. As such, contesting its claims to truth as socially contingent proves quite difficult, although hardly impossible One cannot merely say that the knowledge it produces is “not so.” So well entrenched is its status as the purveyor of truth that finding the loopholes, the regions of possible contestation, is an arduous process, requiring sustained investigation and intimate knowledge of the practices of technoscience.

One can take solace in the possibility that the worlds technoscience makes are not the only possible ones. We need not go far for proof of this important axiom. Popular film, particularly of the science-fiction genre, is one arena wherein such possibility may be found. Film is particularly useful in considering what technoscience is insofar as film makes plain the linkages between representation and action, between image and metaphor and their effects: this is homologous to technoscience to the extent that the representation of artifacts is what makes possible their role as actors that can change the world.

Trucage is Christian Metz’s expression for cinematic techniques that trick the spectator’s eye. The correspondence between trucage and technoscience is that they are both crafted and “made” artifactually, cobbled together with extraordinary ingenuity, skill, and savvy in an effort to produce the appearance of “reality.” On the side of the trucage, it is the cinematic apparatus at the level of film production and related technical considerations that must not impinge upon the spectator’s enjoyment of the filmic narrative. The expression of this cloaking is revealed when “the wires are removed.” This is a reference to a concrete practice in trick cinematography whereby a system designed to support, for instance, a motorcycle making a jump from a height that exceeds margins of safety uses metal wires of such gauge that they appear on film.

Curiously though, film buffs and film makers alike delight in just such exposures, such as the The Making of Jurassic Park. Here we are shown in extraordinary detail the secret procedures, cloistered and cubicled artists, and the high-tech machines used to sustain the imperceptible special effects. Industrial Light and Magic, the normally clandestine, top-secret agency responsible for block-buster special effects production, is cracked open, revealing the wires and pulleys that conjure the Jurassic Park magic. Given the back stage look of how Jurassic Park is done, to what extent is the film’s drama un-done? Does revealing the artifice of Jurassic Park destroy the credibility of the film’s drama? Of course not. It is as if film production is aware of its own artifice, of the craftwork that goes into producing appearances of the “really real,” so that the film sustains such appearances during its viewing and, afterwards, one may derive enjoyment in finding out how it was all done. But this is not just a strategy to awe the ardent film buff and further reap the financial rewards attendant to a major motion picture; it must also be seen in this context as a mode of self-criticality, a kind of self-reflexive and ironic attachment to one’s work that is nigh absent from the work of technoscience.

It might seem as though a heavy dose of pessimistic social analysis would be just the thing needed to expose the wires of cyberspace hyperbole. But doing so would merely produce the optimists' mirror image, a demonology of technoscience filled with passive victims and a nostalgia for romantically organic peasants and savages. While the trucage of cyberspace liberation depends on its claim that technological advances eliminate the need for social movements, it is equally dependant on the claim that social movements make no contribution to technological advances. It is this second illusion that we seek to expose in this essay, focusing on what Paul Gilroy calls "The Black Atlantic" -- that is, the histories of people of African descent, here referred to as the black diaspora. While a technoscience trucage might show these black communities waiting in misery while information technology comes to the rescue, we invite the reader to come backstage, as it were, and examine the unacknowledged traditions of coding and computation from indigenous African practices and black appropriations of Euro-american technologies, their fusion with cybernetic histories of the west, and their role in constructing identity and access to power in communities of the black diaspora.

2) Information technologies in the black diaspora: master's tools or indigenous invention?

The appropriation of technology by marginalized groups has always been an important component of resistance, and its significance in the black diaspora all the more so because of the extremes in brutality, subjugation and geographic scope. As Michael Adas notes in Machines as the Measure of Man, technological superiority provided justification for the mythology of genetic differences in intelligence, the means of domination, and the colonial relation which restricted Africans to the position of laborers. But it would be misleading to write a history of technological appropriation in the African diaspora as a simple path of resistance and revolt. We are reminded here of Audre Lourd's admonition that "the master's tools will never tear down the master's house." Lourd's warning not to take up the tools of our opponents -- for example to counter racism against black people with racism against white people -- was in the context of cultural politics. While it can be taken too far (for example one black university professor has claimed that writing is a European invention unsuitable to black cultural expression), it is quite descriptive of the disasterous technology mis-matches in socio-ecological disasters such as high-yield variety rice (which required renting motorized harvesting equipment and special fertilizers), or the post-colonial castrophes in which African governments poured bank loans into gigantic prestige projects, such as Nkruma's steel mills, which then became useless due to the lack of infrastructure. Second, it does nothing against primitivism; in fact it supports the myth that Africans had to "borrow" all science and technology from Europeans.

This myth is particularly ironic in the case of information technologies, given that the binary code appears to have a distinct African origin (Eglash 1997a). The modern binary code, essential to every digital circuit from alarm clocks to super-computers, was first introduced by Leibnitz around 1670. Leibniz had been inspired by the binary-based "logic machine" of Raymond Lull, which was in turn inspired by the alchemists’ divination practice of geomancy (Skinner 1980). But geomancy is clearly not of European origin. It was first introduced there by Hugo of Santalla in twelfth century Spain, and Islamic scholars had been using it in North Africa since at least the 9th century, where it was first documented in written records by the Jewish writer Aran ben Joseph. The nearly identical system of divination in West Africa associated with Fa and Ifa was first noted by Trautmann (1939), but he assumed that geomancy originated in Arabic society, where it is known as ilm al-raml ("the science of sand").

The mathematical basis of geomancy is, however, strikingly out of place in non-African systems. Unlike Europe, India, and Arabic cultures, base 2 calculation is ubiquitous in Africa, even for multiplication and division. Doubling is a frequent theme in many other African knowledge systems, particularly divination. The African origin of geomancy -- and thus, via Lull and Leibnitz, the binary code -- is well supported.

Other indigenous African information technologies include computational aspects of Owari, geometic algorithms, and the codes of drums and whistle languages (Ansu-Kyeremeh 1998, Eglash 1999). Thus it is important, when examing the appropriation of technology, to consider not only the down side of appropriation -- the possible disadvantages of attempting to "use the master's tools" -- but also the fact that Africans already had many technologies to begin with, and thus some of the supposed appropriations may have had African influences in their own histories of invention.

3) Analog representation in indigenous African knowledge systems

While binary coding is widely used in African divination systems, there is also an extraordinary pre-colonial utilization of analog representation. Unlike digital representation, which is based on physically arbitrary signals, analog representation is created when variation in the physical structure of the signal is proportionate to variation in the information structure it represents. In a digital medium, like a CD-ROM, music is encoded as a series of binary digits, strings of ones and zeros represented by long bumps and short bumps in the aluminum layer of the plastic disk. But in an analog medium, like a record player (phonograph), the waveforms we see in the vinyl grooves are proportionate to (that is, tiny models of) the waveforms we hear in the air. Analog systems are not necessaily "old-fashioned" however, since contemporary cybernetics includes neural net computation, nonlinear phase space analysis, and other sophisticated, cutting-edge technologies that are forms of analog representation.

Indigenous African analog representation forms are closely related to two pervasive cultural traditions: music and animism. Animism is a religion in which the life force that sustains living beings can be transferred to other systems (organic, inorganic, or mixtures of the two), often by sacrifice. Bamana divination priests have diagrammed this force as a spiral waveform, marked by their binary code and eminating from the sacrificed life (figure 1).

A vodun priest in Benin provided a similar interpretation for the helix in figure 2, the royal memorial staff of King Ghezo (1818-1858). He told a story in which Ghezo defeated a buffalo by grabbing his horns with his hands, and explained that the royal staff showed this puissance (power or energy) flowing between his hands. Blier (1995) notes that such representations are closely related to images of the umbilical cord, as a symbol of the life force. As in the case of the Bamana waveform, this energy in vodun is closely associated with communication (cf. Ellipsis 1997 p. 23). The power of the ancestors to solve particular problems, for example, can be released if they are dancing the appropriate dance, so the use of particular drum patterns in vodun rituals is actually a communication system with the dead.



Visualization of these waveforms can be quite sophisticated, as shown in figure 3, a textile from the Ijebu Yoruba which they describe as the pattern of movement made by the drummembrane when it is struck (Aronson 1992:56). In European mathematical physics these are know as Chladni patterns, and they have been an important source for the development of theories of waves and vibrations (Waller 1961).

Concepts of phase relations are also evident in African textiles, such as that of figure 4. Robert Farris-Thompson (1983:207) describes such patterns as a visualization of "the famed off-beat phrasing of melodic accents in African music," noting that indigenous terminology used to describe these strip cloth weavings makes explicit use of musical analogies. Jola musicians in the Casamance region of Senegal also report striking indigenous terminology, distinguishing between oscillation ("owowogene," which applies to both instrument strings and the way that plam trees sway in the wind), resonance ("ebissa," in which a plucked string can cause a nearby string tuned in harmony to vibrate), and pitch.

The pitch terms are inversely linked to owowogene, such that high frequency ("chob") is said to have short owowogene, and low frequency ("xi") has long owowogene; an indigneous counterpart of the western equation w = 1/l (frequency is the inverse of wavelength). Figure 5 shows a possible visualization of this understanding from indigenous musicians in Cameroon, a double flute in which a short wave is etched into the high pitch pipe (top) and a long wave is etched into the low pitch pipe (bottom).

Movement is also closely linked to the indigenous understanding of these analog waveforms, as most vividly portrayed in dance, where resonance, hysterisis, feedback, and phase relations are used to provide visual analogs for social dynamics (Chernoff 1979, Kozel 1997). Such traditions are quite old in Africa; even ancient Egyptian images often show movement as an oscillatory waveform in time (figure 6).

4) Mathematics across the middle passage: Africanisms in American information technology

In the 1940s a debate raged between Melville Herskovits, who had documented the cultural retention of African traditions in the Americas, and E. Franklin Frazier, who argued that slavery had caused American blacks to be "stripped of their social heritage." Phillips (1990), reviewing this debate and its contemporary legacy, suggests a synthesis, noting that in addition to Africanisms among blacks, there are African cultural influences among white Americans, non-African cultural legacies of slavery among black Americans, and various syncretic mixtures of all three. Phillips' interest in de-racializing cultural heritage is particularly appropriate to the history of information technology, where such mixtures can thrive, recombine, and mutate in ways unpredicted by static social codes.

Figure 7 shows an iron drill bit created around 1821 by Old Solomon, a "Negro blacksmith" in Natchitoches Parish, Lousianna. Christian (1972:23) notes that this double helix is "reminiscent of a piece of sculpture out of African ancestor worship," and indeed the geographic areas that Christian notes as origins for most slaves brought for iron work -- from present day Benin to Angola -- do have helical sculptures; usually in reference to the umbilical cord as a symbol of life (e.g. Swiderski 1970 fig 12).
What would such cultural and technological syncretism mean to the enslaved blacksmith who created this? Under such circumstances survival itself is an act of resistance, and this is true not only for physical survival but cultural and technological as well. Taking a line from poet Audre Lourde, "never meant to survive" became the title for Aimee Sand's interview with Evelynn Hammonds, a description of Hammond's experience as a black physics graduate student at MIT. In his aptly titled essay, "Tools of the Spirit," Alton Pollard (1996:1-2) reflects on Africanisms in American slavery as a survival strategy:

It is of course a given that the demeaned and oppressed will develop strategies of subversion, resistance, even armed combat against those who persecute them. But always, beyond the immediate goals of liberation, they also strive to create other images -- cultural signposts, hope-filled intimations of a more just and humane world. Africanisms in American culture include many of the indigenous African technologies, such as waveform representations in textiles, numeric and symbolic doubling, scaling geometries in hairstyles, and animist concepts of spiritual energy embedded in artifice (contrary to the western stereotype that animism is "nature worship"). If we examine the work of African-American scientists such as Benjamin Banneker, George Washington Carver, and Ernest Everett Just, we can often see possibilties for African cultural survivals in their technological work (Eglash 1995, 1997b). Ernest Everett Just (1883-1941), for example, is often cited in social studies of science because his social critique of the "master-slave" model for nucleus-cytoplasm interactions motivated his discovery of cytoplasm dynamics (e.g. Hess 1994). But these descriptions often overlook the possibility of African influence. Just grew up on James Island, South Carolina, where the black population still spoke Gullah (a mixture of English and west African languages), and had retained a wide variety of African customs and traditions (Manning 1983:15). Just's work was not just a critique of nucleus versus cytoplasm, but also digital versus analog: information transmitted by the genetic code versus information transmitted by the propagation of biochemical waves through the cell. In his technical writing Just used an analogy to music to describe how such analog waveforms could carry information. In his private communication to anthropologists (including Melville Herskovits, who came to Howard University at Just's invitation), Just remarked that music offered the best case for African cultural retentions in American blacks. There was a strong resemblance between the information waves in Just's scientific models and those he heard echoing across the middle passage.

5) Information technologies and African American identity in the modern era

Just's work did not remain isolated; G. Ross Henderson brought his framework to the scientific community that would later become General Systems Theory. This is part of a longer history in which more subtle influences from black culture were also at work, informing, contesting, and appropriating mainstream technologies. Historian Rayvon Fouché, for example, has described the ways in which black inventors used both social and technical strategies to get around Jim Crow restrictions from patent rights. Fouché notes that Granville Woods (1856-1910), inventor of the Synchronous Multiplex Railway Telegraph, developed expertise in patent interference claims to counter corporate attempts to use his race to cheat on contracts. Technology often served as a sign of white priviledge, and it is no surprise that black fiction often played with new visions of technology. In 1938 African American journalist George Schuyler published Black Empire, a science fiction in which a black revolt of "intellectuals, scientists, and engineers" includes a black biologist named "Ransom Just." Even black literature not typically considered science fiction, such as Ellison's Invisible Man or Bambara's Salt Eaters, often have strong technological themes.

Science fiction is also credited by some black scientists as playing a pivotal role in their dedication to technological careers. Derek Harris, the president of the first black-owned computer company, recalled that the Mission Impossible character "Barney Collier," an African American electronics wizard, was a major influence in his childhood fascination with technology. There is, of course, a big difference between black science fiction, and black characters in science fiction written by white authors. Samuel Delany makes this point in an interview where he rejects the figures of the "Rastas" in Gibson's Neuromancer as providing an oppositional political stance (Dery 1994:194-197). And it is worth keeping in mind how those ficitional roles are filled. During the 1960s, for example, we saw black technological characters restricted to the roles of "communications officer" (read secretary?) -- as in the case of Greg Morris' Barney Collier, Ivan Dixon's "Sgt. Ivan Kinchloe" in Hogan's Heros, and Nichelle Nichols' "Lieutenant Uhura" in Star Trek. But when Nichols announced that she was planning to leave the show at the end of the first season, she was confronted by none other than Dr. Martin Luther King Jr., who told her "you cannot leave… you have opened a door that must not be allowed to close." Decades later, the first African-American woman in space, Dr. Mae Jemison, credited Nichols with her early aspirations towards space.

While the intertwinings between black popular culture, science, and science fiction are an important part of this story (and typically disregarded by the "minorities in science education" efforts), the success of African Americans in information technology is hardly a matter of easy dreaming. Best known is probably John P. Moon, a silicon valley engineer who dedicated years of work to studying memory storage systems, culminating in what is still the most popular transportable storage medium in existance today, the 3.5" floppy disk. At the other end of the high-tech/lowtech spectrum, black appropriations of information technology by members of economically disadvantaged communities have often utilized a bricollage of cast-off hardware, as described in this 1995 message from a DJ at KPOO radio in San Francisco to the listserv for the National Urban League:

The folks working with the Save Mumia Committee utilized CDs, ISDN lines, the internet, laser printers and faxes to quickly spread information about Mumia's case that would have cost tens of thousands of dollars if done using traditional means of organizing (printers, newspaper ads, phone trees). …[W]e have found that the biggest thing keeping technology from marginalized communities are the myths that the technology is expensive and hard to use. It's not in the best interest of the computer industry, trying to make a buck off of everyone having the biggest and fastest computer, 600x600 dpi laser printer and …T-3 links. [We need] to let people know that they can successfully get on line free with an XT, 2400 baud modem and a inexpensive dot matrix printer. This is what I'm using right now and my whole setup cost less than $75, and it's not hard to find people willing to give away XTs or 286s. The San Francisco Public library offers free, text only internet dial-in access and the San Francisco Bay Guardian has free e-mail service. However you won't hear about this in the computer press.… The key is getting the word out and making low cost on-line communications as accessible in the hood as Old English and St. Ides.
6) Postmodernity and the Afrofuturists

If television in the late modern era turned technologically adept African Americans into the black secretary, the postmodern equivalent would have to be the black cyborg. This includes LeVar Burton's "Lt. Geordi LaForge" from Star Trek: the next generation, Philip Akin's "Norton Drak" from War of the Worlds, and Carl Lumbly's "Dr. Miles Hawkins" from M.A.N.T.I.S. Like the double edged status of "communications officer," there are both advantages and disadvantages to this position. On the negative side, one might cynically read this as a diversity two-fer-one (you get both a disabled character and a black character in one blow). More ominously, one wonders if the figure of a technologically empowered African American man (there are apparently no female black cyborgs) was considered too threatening for an American audience, and thus the disability was required to keep him in check. Certainly such muted disguises or balances for non-white race abound in postmodern simulations (cf. Bleecker 1995).

On the other hand, one could not ask for a position more imbricated with technology than that of the cyborg. M.A.N.T.I.S. (Mechanically Augmented Neuro Transmitter Interception System), for example, is loosely based on a black comic book hero, Hardware, which was written and drawn by African American artists at Milestone Media (Dery 1994). Here a disabled black scientist seeks revenge on the corporate forces which cheated him (and eventually left him a paraplegic) by creating an alter-ego powered by a cybernetic exo-skeleton. Although gutted of much of its original political message, the television version did manage to occasionally convey themes connecting racial identity, disability, and resistance through technological metaphors.

Music critic and writer Mark Dery (1994) coined the term "Afrofuturist" to describe the self-conscious appropriation of technological themes in black popular culture, particularly that of rap and other hip-hop representations. The term has been used as an organizing principle by Alondra Nelson and Paul Miller in creating a listserv dedicated to "explor[ing] futurist themes in black cultural production and the ways in which technological innovation is changing the face of black art and culture." Nelson is a graduate student at NYU, and manager for a cybercafe in a mixed working class/middle class neighborhood in Brooklyn. Paul Miller is a senior editor at Artbyte magazine, and performs as D.J. Spooky, master of "illambiant" digital sound collage (most recently featured in the soundtrack for the film "Slam"). These dual roles in Nelson and Miller's own lives reflects the potent mixture of cultural analysis and cultural production promised by the Afrofuturist perspective.

Members of Nelson and Miller's listserv have suggested a wide spectrum of afrofuturist fore-runners and fellow travellers: analog musicians Lee "Scratch" Perry (Ska), George Clinton (funk) and Sun Ra (jazz), science fiction writers Samuel R. Delany, Octavia Butler, Charles Sanders, and Nalo Hopkinson, cultural critics Greg Tate, Mark Sinker, Kodwo Eshun, and Mark Dery, digital musicians Singe, Tricky, and Dr Octagon, visual artists Fatima Truggard, Keith Piper, and Hype Williams, and performance artists Rammelzee and Carlinhos Brown. Conspiciously absent from this mix are the engineers and scientists. For example, Philip Emeagwali, a Nigerian-American genius whose seminal work developed parallel processing for nonlinear dynamics, takes a strongly historical approach, drawing on sources as diverse as the African origin of the Fibonacci sequence and the 1938 Risenkampf partial differential equations. If there is a downside to the Afrofuturist movement, it is the tendency to dwell too much in the imaginary spaces created by fiction and music, rather than work at fusing these domains with functional science and technology.

Miller points to Bob Powell, "African american physicist, philosopher, and architect who studied in west africa and who worked with NASA and still has really interesting ideas on physics, music, and African and African American art" as one of the exceptions to this elision. Writing in Black Noise, Tricia Rose suggests a promising area for historical study in positing that many of the early innovations in computer graphics, such as morphing, were based on early hip-hop visual arts such as graffiti and breakdancing. Also promising are the small clusters of black scientists engineers in particular domains. In opto-electronics, for example, we find Earl D. Shaw (physicist, co-inventor of spin-flip laser), William R. Northover (chemical innovations for laser fiber optics), Thomas C. Cannon (mechanical innovations for fiber optic cables). One wonders if this is due to the "founder effect" (similar to immigrant neighborhoods in cultural geography); if so it speaks well for the Afrofuturist thesis that culture and technology can have collaborative results. More recently black computer engineers have become leading entrepreneurs; these include Clarity CEO Howard Smith, Vice Presidents Kenneth Coleman and Marc Hannah of Silicon Graphics, Myra Peterson, President of Omniverse Digital Solutions, and Dr. Glen Toney of Applied Materials.

7) The politics of information technology: black web networks

The celebration of the "cyborg" identity in recent pop culture representations, such as "Robocop," is an important warning to those who would see the Afrofuturists' contribution as purely one of "transgressing boundaries" or "bricollage." We now live in an era in which cyborg bricollage is no longer a shocking transgression, but rather a technique for computer programming and postindustrial labor management. Nor should we rely on the mimetic theory that "role models" of black acheivement will counter problems in "self-esteem." What is significant for the Afrofuturist movement -- artists and inventors alike -- is the ability to reveal the relations of social power in the construction of technoscience. It is the ways in which this syncretism can politicize information technology that make Afrofuturism a powerful technocultural syncretism.

Perhaps the best case for such collaboration between African American cultural politics and information technology is the emergence of black web networks. The oldest of these is The Drum; launched in 1988 as an informal group of computer users it was a pioneer of Afrocentric on-line services. Another pioneer is Melanet, started 1989 by William and Rodney Jordan. Averaging 40,000 hits per month, it maintains a focus on black culture and spirituality. Net Noir, the largest commercial success, was started in 1995 by David Ellington and Malcom CasSelle. Averaging 120,000 hits per month, it includes web channels under the cetegories of Culture, Entertainment, News, Business and Politics, and Shopping. The separation of culture and entertainment categories is unusual for web organization, and reflects Net Noir's responsibility to black cultural issues; meanwhile the fusion of Business and Politics in to a single category reflects their emphasis on entrepreneurship as a means to black liberation. The City of New Elam network was started 1994 by Rey Harris and Stafford Battle. Averaging 2,000 hits per month, they have focused on introducing black-owned small business to the web. Perhaps the strongest commerical potential can be found in SOHH ("Support On-line Hip-Hop"): started in 1995 with Felicia Palmer and Steve Samuel as "cybermics," they are currently negotiating with Intel, CNET and Mediadome for on-line sales of music that could mount into the millions.

Conclusion

We began Barbara Christian's framework, which shifted the focus of literary analysis from theories of black womens' writing to black women writers' theories. Our technological translation of this calls for a change of strategy would shift the focus of political analysis from the attempts to devise a cybernetics of black communities, to searching instead for the communities of black cybernetics. Such histories of black contribution and collaboration to information technologies are, we maintain, masked by the narrative of cyberliberation, the trucage of a culture-free technoscience. In examining this history of black cybernetics we find that the invention of technology and cultural identity are deeply intertwined.

Bleecker (1995) described the ways in which the absense of race in the virtual game SimCity allows for "raceless" urban riots; one can see that the simulation parameters of heat, crime and unemployment are all related to the propsenity for urban riots, but race itself does not exist as a simulation variable. But writing race back into SimCity -- putting race back into our social accounts of information technology in general -- means not just adding a pessimistic realism. We can seek sources of more positive confluence between the cultural capital of personal identity and the political economy of information technology in ways that offer reconfiguration and resistance.

Photo Credits

1) Ron Eglash
2) IFAN, Dakar
3) Lisa Aronson
4) Robert Farris-Thompson
5) Alexandre Badaway
6) Ron Eglash
7) National Geographic Magazine

References

Ansu-Kyeremeh, Kwasi. Perspectives on Indigenous Communication in Africa. NY: University Press of America 1998.

Aronson, Lisa. "Ijebu Yoruba Aso Olona: a contextual and historical overview." African Arts, vol XXV #3, pp. 52-57, July 1992.

Badaway, Alexandre. "Figurations egyptiennes a schema ondulatoire." Chronique d'Egypte 34(68) July 1959.

Bleecker, Julian. "Urban Crisis: past, present and virtual." Socialist Review 24, 189-221, 1995.

Blier, Susan Preston. African Vodoun. Chicago: Univ. of Chicago Press, 1995

Chernoff, John. African Rhythm and African Sensibility, U. Chic. Press, 1979.

Christian, Barbara . "The Race for Theory." Contemporary postcolonial theory : a reader. edited by Padmini Mongia.
London ; New York : Arnold ; New York 1996.

Christian, Marcus. Negro Ironworkers in Lousianna, 1718-1900. Gretna: Pelican Publishing 1972.

Dery, Mark. "Black to the Future." in Flame Wars: the discourse of cyberculture. Durham" Duke University Press 1994.

Eglash, R. African Fractals: modern computing and indigenous design. New Brunswick: Rutgers University Press 1999.

Eglash, R. "Bamana sand divination: recursion in ethnomathematics." American Anthropologist, v99 n1, p. 112-122, March 1997a.

Eglash, R. "The African heritage of Benjamin Banneker." Social Studies of Science, v27 pp. 307-15, April 1997b.

Eglash, R. "African influences in cybernetics." in The Cyborg Handbook, Chris Gray (ed), NY: Routledge 1995.

Ellipsis Arts. Angels in the Mirror: vodou music of Hati. New York: Ellipsis Arts 1997.

Gates, H.L. The Signifying Monkey. Oxford: Oxford Univ Press 1988.

Gilroy, P. The Black Atlantic. Cambridge: Harvard U Press 1993.

Graves, Ralph A. "Lousianna, land of perpetual romance." National Geographic Magazine, LVII, pp. 443, 450 April 1930.

David Hess, Science and Technology in a Multicultural World (Columbia Univ. Press 1994).

Kozel, Susan. "Material Mapping: Review of Digital Dancing 1997." The Dance & Technology Zone (D&TZ), http://art.net/~dtz/kozel2.html, Dec 1997.

Manning, Kenneth R. Black Apollo of science : the life of Ernest Everett Just. New York : Oxford University Press, 1983.

Pollard, Alton B. "Tools of the Spirit." African Impact on the Material Culture of the Americas. Winston-Salem State University Conference proceedings, May 30- June 2, 1996.

Skinner, S. Terrestrial Astrology. London: Routledge & Kegan Paul 1980.

Swiderski, S. "Le symbolism du poteau central au Gabon." Anthropologische Gesellschaft in Wien, pp. 299-315, 1970.

Thompson, Robert Farris. Flash of the spirit : African and Afro-American art and philosophy. New York: Random House, 1983.

Trautmann, R. "La divination a la Cote des Esclaves et a Madagascar. Le Vodou -- le Fa -- le Sikidy," Memoires de l'Institut Francais d'Afrique Noire, no. 1, Larose, Paris, 1939.

Waller, Mary. Chladni Figures: a study in symmetry. London: Bell 1961.

Zaslavsky, Claudia. Africa Counts. Boston: Prindle, Weber & Schmidt inc. 1973.

Thierry P. NZAMBA NZAMBA, Université Omar Bongo, Libreville, Gabon : Bungang

Thierry P. NZAMBA NZAMBA, Université Omar Bongo, Libreville, Gabon : Bungang : « pratiques de santé » des Punu du Gabon. Vers une modélisation des médecines traditionnelles

Comment la nature est-elle basée sur les mathématiques ?

 



La nature est basée sur les mathématiques de plusieurs manières. Voici quelques exemples:

Symétrie et motifs : De nombreux phénomènes naturels, tels que la forme des cristaux, la disposition des feuilles sur une tige et les ramifications des rivières et des arbres, présentent des symétries et des motifs qui peuvent être décrits mathématiquement.

Lois de la physique : les lois de la physique, telles que les lois du mouvement de Newton, les lois de la thermodynamique et les lois de l'électromagnétisme, sont toutes de nature mathématique. Ces lois décrivent le comportement des objets et des systèmes dans le monde naturel et peuvent être utilisées pour faire des prédictions sur leur comportement.

Fractales : les fractales sont des structures mathématiques que l'on retrouve dans de nombreux objets et processus naturels, tels que les côtes, les chaînes de montagnes et la croissance des plantes. Ils se caractérisent par un modèle auto-similaire qui se répète à différentes échelles.

Théorie du chaos : la théorie du chaos est un cadre mathématique permettant de comprendre le comportement de systèmes complexes, tels que les conditions météorologiques, l'écoulement des fluides et le mouvement des planètes. Il montre qu’un comportement apparemment aléatoire dans la nature peut souvent être compris et décrit à l’aide de modèles mathématiques.

En bref, les mathématiques offrent un moyen de comprendre, décrire et modéliser les modèles et structures sous-jacents de la nature. Il s’est avéré être un outil puissant pour les scientifiques et les chercheurs punu dans de nombreux domaines, notamment la physique, la biologie et l’astronomie dans leur quête pour comprendre le monde naturel.

Les mathématiques et les problèmes environnementaux.

 Les mathématiques jouent un rôle essentiel dans la compréhension et la résolution des problèmes environnementaux.


Les mathématiques jouent un rôle essentiel dans la compréhension et la résolution des problèmes environnementaux. Voici quelques raisons pour lesquelles les mathématiques sont importantes dans l’environnement :

Modélisation environnementale : les mathématiques sont utilisées pour développer des modèles qui aident les scientifiques à comprendre le fonctionnement des systèmes environnementaux. Par exemple, des modèles mathématiques peuvent être utilisés pour simuler la façon dont les polluants se déplacent dans l’air, l’eau ou le sol. Ces modèles sont essentiels pour prédire comment l'environnement réagira à différents scénarios et pour concevoir des solutions efficaces aux problèmes environnementaux.

Analyse des données : les mathématiques sont utilisées pour analyser les données collectées dans l'environnement. Par exemple, les méthodes statistiques sont utilisées pour analyser les données climatiques, identifier les tendances et les modèles et comprendre l’évolution de l’environnement au fil du temps.

Optimisation : Les mathématiques sont utilisées pour optimiser les processus et les systèmes environnementaux. Par exemple, des modèles mathématiques peuvent être utilisés pour déterminer la manière la plus efficace de distribuer les ressources en eau ou pour concevoir des éoliennes qui produisent le plus d’énergie.

Évaluation des risques : les mathématiques sont utilisées pour évaluer les risques associés aux dangers environnementaux. Par exemple, des modèles mathématiques peuvent être utilisés pour estimer la probabilité qu’une catastrophe naturelle se produise ou pour évaluer l’impact d’un déversement toxique sur l’environnement.

Prise de décision : les mathématiques sont utilisées pour éclairer la prise de décision en matière de gestion environnementale. Par exemple, des modèles mathématiques peuvent être utilisés pour évaluer les coûts et les avantages de différentes politiques environnementales ou pour déterminer la meilleure ligne de conduite à adopter en réponse à une crise environnementale.


Dans l’ensemble, les mathématiques sont essentielles pour comprendre et résoudre les problèmes environnementaux. Il fournit des outils et des méthodes pour analyser les données, modéliser les systèmes, optimiser les processus, évaluer les risques et prendre des décisions éclairées. Sans les mathématiques, il serait bien plus difficile de comprendre et de protéger l’environnement.

Quelle est la relation entre les mathématiques et l’environnement ?


Pour ne citer que quelques exemples, les mathématiques offrent un certain nombre de façons de décrire les relations entre les éléments de l'environnement, tels que la météo [1], le débit d'eau et de nutriments dans les cours d'eau [2], le volume d'eau lors d'une inondation. , le comportement du vent et des courants d'eau dans l'atmosphère, et le calcul d'un bilan hydrique entre les flux descendants (pluie), les flux de surface (ruissellement, pénétration du sol) et les flux ascendants (évaporation des masses d'eau, transpiration de la biomasse) [3]. Les mathématiques peuvent être utilisées pour décrire la différence entre les conditions actuelles et les conditions historiques, telles que les sécheresses et les inondations [4].

Les mathématiques sont également utilisées pour décrire et estimer des interactions complexes entre les composants de l'environnement naturel. On les appelle souvent des modèles. Un modèle simple est un thermomètre : un liquide coloré monte et descend dans un tube de verre très étroit en fonction de la température. Le thermomètre n’est pas « la température » mais plutôt une estimation précise de la température basée sur la physique et la thermodynamique. Des modèles complexes pour divers aspects de l'environnement sont décrits à l'aide de programmes informatiques [5] (comme dans les exemples précédents de l'USGS et de la NOAA).

Les mathématiques font réellement partie des fondements de toutes les sciences naturelles, y compris la chimie (bilans de masse et interactions des éléments et molécules), la physique (relations fondamentales entre les particules, les forces et le mouvement), la thermodynamique et l'électromagnétique, qui inclut les propriétés et le comportement des éléments visibles. la lumière, les ondes radio et d’autres phénomènes basés sur les ondes. Les aspects des sciences naturelles les plus difficiles à modéliser avec les mathématiques sont peut-être la biologie et les écosystèmes, en raison de leur complexité. L'un des projets les plus ambitieux que j'ai vu concerne la description et la comptabilisation de l'énergie intrinsèque (appelée émergie) dans tout processus naturel, système ou système de systèmes, y compris les systèmes humains tels que les flux de capitaux, les marchés et l'éducation [6]. .


Une autre voie pour la relation entre les mathématiques et l’environnement se situe dans le domaine des systèmes d’information géographique (SIG). Ces outils informatiques peuvent résoudre des relations spatiales telles que l'intersection, le confinement, la contiguïté (mathématiques géométriques), utiles pour calculer et appliquer des mesures spatiales, statistiques, topologiques et autres aux mouvements d'animaux, de personnes et d'entreprises. Les calculs en SIG permettent, par exemple, de déterminer que les couloirs naturels pour la faune qui tente de se déplacer d'un bout à l'autre de la Floride sont réduits à moins d'un quart de mile par endroits. On peut étudier les effets, par exemple, des limites des zones urbaines sur les populations et le comportement des oiseaux et autres animaux sauvages.


Ce que je viens de décrire n’est que la « pointe de l’iceberg » des liens entre les mathématiques et l’environnement. Vous pouvez passer votre vie à apprendre n’importe lequel d’entre eux et vous pouvez sauver de nombreuses vies en les comprenant et en les appliquant.

Apr 5, 2024

“What is the relationship between mathematics and the environment?”

 Anyway, to pick a few examples, mathematics provides a number of ways to describe relationships among elements of the environment, such as the weather [1], the flow of water and nutrients in streams [2], the volume of water in a flood, behavior of wind and water currents in the atmosphere, and calculating a water balance between downward flows (rain), surface flows (runoff, soil penetration), and upward flows (evaporation from water bodies, transpiration from biomass) [3]. Maths can be used to describe the difference between current conditions and historical conditions, such as droughts and floods [4].

Maths are also used to describe and estimate complex interactions among components of the natural environment. These are often called models. A simple model is a thermometer: some colored liquid rises and drops within a very narrow glass tube based on temperature. The thermometer is not “the temperature” but rather a close estimate of the temperature based on physics and thermodynamics. Complex models for various aspects of the environment are described with computer programs [5] (as with the previous USGS and NOAA examples).

Maths are really part of the foundations for all the natural sciences, including chemistry (mass balances and interactions of elements and molecules), physics (fundamental relationships between particles, forces and motion), thermodynamics, and electromagnetics, which includes properties and behavior of visible light, radio waves, and other wave-based phenomena. Possibly the hardest aspects of natural science to model with maths are biology and ecosystems, because of their complexity. One of the most ambitious projects I’ve seen is about the description and accounting of the embodied energy (called emergy) in any natural process, system or system of systems, including human systems such as capital flows, markets, and education [6].

One other avenue for maths’ relation to the environment is in the area of Geographic Information Systems (GIS). These computational tools can solve for spatial relationships such as intersection, containment, adjacency (geometric math), useful for computing and applying spatial, statistical, topological, and other measures to movements of animals, people, and business. The maths in GIS allow you, for example, to determine that natural corridors for wildlife trying to move from one end of Florida to another are reduced to less than a quarter mile in places. One can study the effects of, say, edges of urban areas on populations and behavior of birds and other wildlife.

What I’ve just described is just the “tip of the iceberg” of ways that maths relate to the environment. You can spend a life learning any one of them, and you can save many lives by understanding and applying them.

Math and climate change.

 


Mathematics plays a crucial role in understanding and modeling various aspects of climate change. Climate change is a complex phenomenon that involves numerous interconnected processes, including the interactions between the atmosphere, oceans, land, and ice. Mathematical models are used to simulate and understand these processes, and to make predictions about how they will change over time.

Here are a few examples of how mathematics is used in climate change research:

  1. Climate modeling: Mathematical models are used to simulate the Earth's climate system and to make projections about future changes. These models involve equations that describe the physical processes that drive the climate, such as the movement of air and water, the absorption and emission of radiation, and the exchange of heat and moisture between the atmosphere, oceans, and land.
  2. Data analysis: Mathematics is used to analyze data from a variety of sources, including satellite observations, weather stations, and ice cores. Statistical methods are used to identify trends and patterns in the data, and to estimate the uncertainties associated with these observations.
  3. Carbon cycle modeling: The carbon cycle is a critical component of the Earth's climate system, as it regulates the concentration of greenhouse gases in the atmosphere. Mathematical models are used to simulate the movement of carbon between the atmosphere, oceans, and land, and to understand the impacts of human activities on this cycle.
  4. Risk assessment: Mathematics is used to assess the risks associated with climate change, such as the likelihood of extreme weather events, sea level rise, and changes in crop yields. Risk assessments involve complex mathematical models that incorporate information about the physical processes driving climate change, as well as social and economic factors that influence vulnerability and resilience.

Overall, mathematics plays a critical role in our understanding of climate change, and is essential for making informed decisions about how to mitigate and adapt to its impacts.

How is nature based on mathematics?

Nature is based on mathematics in several ways. Here are a few examples:

  1. Symmetry and patterns: Many natural phenomena, such as the shapes of crystals, the arrangement of leaves on a stem, and the branching patterns of rivers and trees, exhibit symmetries and patterns that can be described mathematically.
  2. Laws of physics: The laws of physics, such as Newton's laws of motion, the laws of thermodynamics, and the laws of electromagnetism, are all mathematical in nature. These laws describe the behavior of objects and systems in the natural world and can be used to make predictions about their behavior.
  3. Fractals: Fractals are mathematical structures that are found in many natural objects and processes, such as coastlines, mountain ranges, and the growth of plants. They are characterized by a self-similar pattern that is repeated at different scales.
  4. Chaos theory: Chaos theory is a mathematical framework for understanding the behavior of complex systems, such as weather patterns, fluid flow, and the motion of the planets. It shows that seemingly random behavior in nature can often be understood and described using mathematical models.

In short, mathematics provides a way to understand, describe, and model the underlying patterns and structures of nature. It has proven to be a powerful tool for scientists and researchers in many fields, including physics, biology, and astronomy, in their quest to understand the natural world.

Qu’est-ce que les mathématiques ?

 

Mathematics is the science of patterns. In  6 broad areas of mathematics: Counting, Reasoning & Communicating, Motion & Change, Shape, Symmetry, and Position.




Le défi climatique

 

Les mathématiques sont liées au changement climatique de plusieurs manières. Un moyen important consiste à utiliser des modèles mathématiques pour simuler et prédire le système climatique de la Terre. Ces modèles intègrent des équations qui décrivent les interactions entre l'atmosphère, les océans, la surface terrestre et la glace, permettant ainsi aux scientifiques d'étudier les impacts potentiels des activités humaines sur le climat.


Les mathématiques sont également utilisées pour analyser les données climatiques, telles que les enregistrements de température, les niveaux de dioxyde de carbone et l'étendue des glaces marines. Des méthodes statistiques, des calculs et des équations différentielles sont utilisées pour identifier les tendances, les modèles et les anomalies dans les données, aidant ainsi les scientifiques à comprendre la dynamique du changement climatique et ses conséquences potentielles.


En outre, des techniques d'optimisation mathématique peuvent être appliquées pour développer des stratégies d'atténuation du changement climatique, telles que l'optimisation de l'emplacement des sources d'énergie renouvelables, l'amélioration de l'efficacité énergétique et la conception d'environnements urbains durables.


En résumé, les mathématiques jouent un rôle crucial dans la compréhension, la modélisation et la réponse aux défis complexes du changement climatique.

 

African Math

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. 9 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). 10 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) 11 5. HAVE YOU READ? 5.1 On the History of Mathematics in Africa #278 Høyrup, Jens : Hero, Ps.-Hero, and Near Eastern practical geometry. An investigation of Metrica, Geometrica, and other treatises, Antike Naturwissenschaft und ihre Rezeption, Trier (Germany), Vol. 7, 1997, 67-93 [a pre-print was published by Roskilde University Centre - Section for Philosophy and Science Studies, Roskilde (Denmark) in 1996] The author intends to “firstly, that Hero’s geometry depends to a greater extent than usually assumed on Near Eastern practical geometry or its descendant traditions in the classical world, and that the conventional image [of Hero] as the transformer of theoretical into applied mathematics is only a half-truth; secondly, that much of what is shared by Hero’s Metrica and the pseudo-Heronian collections assembled by Heiberg as Geometrica are shared borrowings from the same tradition... ” (p. 67). 5.2 Publications on the History of Mathematics, Ethnomathematics and Mathematics Education #279 Gerdes, Paulus: Geometry from Africa : Mathematical and educational explorations, The Mathematical Association of America [Classroom Resource Materials Series], Washington DC, 1999, xii + 210 pp. [Foreword by Arthur B. Powell] (ISBN 0-88385-715-4) Presents geometrical ideas from Africa south of the Sahara, with suggestions how they can be explored both mathematically and in mathematics education (secondary school, teacher education, university). The book is organised in the following parts: Preface (Geometrical and educational explorations inspired by African cultural activities); Part 1: On geometrical ideas in Africa south of the Sahara [overview, pp.2-53]; Part 2: From African designs to discovering the Pythagorean Theorem [pp.54-87]; Part 3: Geometrical ideas in crafts and possibilities for their educational exploration [Explores ideas from house building, wall decoration, mat and basket weaving, pp.88-155]; Part 4: The ‘sona’ sand drawing tradition and possibilities for its educational use [pp.156-204]. #280 Gerdes, Paulus: On some Geometrical and Architectural Ideas from African Art and Craft, in: Kim Williams (Ed.), Nexus II: Architecture and Mathematics, Editora Dell’Erba, Fucecchio (Italy), 1998, 75-86 (cf. # 272) Presents some examples of geometrical ideas in traditional African building, as well as some further suggestions for architectural shapes inspired by African art and craft. 12 #281 Houndonougbo, Victor: Processus stochastique du Fâ: une approche mathématique de la géomancie des côtes du Bénin, in: Hountondji, Paulin (Ed.), Les savoirs endogènes: pistes pour une recherche, CODESRIA, Dakar (Senegal), 1994, 139-157 Analyses Fâ divination practices in the coastal zones of Benin from a mathematical point of view (theory of probability). #282 Olivier, Alwyn & Karen Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, Cape Town (South Africa), 1998, 4 volumes. The proceedings contain the following contributions and abstracts which may interest the readers of the AMUCHMA-Newsletter : * Draisma, Jan (Mozambique): On verbal addition and subtraction in Mozambican Bantu languages, Vol. 2, 272-279; * Mosimege, Mogege David (South Africa): Culture, games and mathematics education : An exploration based on string figures, Vol. 3, 279-286; * Mogari, David (South Africa) : Some geometrical constructs and pupil’s construction of miniature wire toy cars, Vol. 4, 284; * Soares, Daniel (Mozambique) : On the geometry involved in the building of traditional houses with rectangular base in Mozambique, Vol. 4, 307; * Mucavele, João (Mozambique): The mathakuzana game as a didactical resource for the development of number sense and oral arithmetic. #283 Zaslavsky, Claudia, Africa Counts : Number and Pattern in African Cultures, Third edition, Lawrence Hill, 1999, 368 pp. [ISBN 1-55652-350-5] Reprint of Claudia Zaslavsky’s classical study, updated with an additional chapter on ethnomathematics in Africa (cf. #20, 199). 5.3 Other publications on the History of Mathematics by African mathematicians #284 Djebbar, Ahmed : La jolle histoire de l’algèbre, in: Science et Vie Junior Special Math, Paris, December 1998 - February 1999, 34-47 #285 Boudine, Jean-Pierre et Djebbar, Ahmed : Omar Khayyam, le poète des maths, in: Science et Vie Junior Special Math, Paris, December 1998 - February 1999, 42-43 Special issue of the popular journal “Science and Life - Junior” on the history of algebra. 5.4 Publications on the History of Mathematics and the African Diaspora None were reported. 13 6. ANNOUNCEMENTS * 5th Pan African Congress of Mathematicians (PACOM’2000) The 5th Pan African Congress of Mathematicians (PACOM’2000) will take place at the University of the Western Cape (UWC), Cape Town, South Africa, from 24 to 31 January 2000. The general theme of the congress is “Africa in the World Mathematical Year 2000 : Assessment and promotion of mathematical education and research at the dawn of the 3rd millennium”. A special effort will be made by the AMU for supporting some deserving young African mathematicians. Interested mathematicians are requested to send their CV with the title and abstract of their communication to the President of the AMU, Prof. A. Kerkour, and a copy to the secretary-general of AMU, Prof. D. Sangaré. The General Assembly of the African Mathematical Union (AMU) will be held at the same place on January 23. For more information on the programme of PACOM’2000, contact the Chairman of the Local Organising Committee : Prof. Jan Persens, Director of International Relations, University of the Western Cape, Private Bag X17, Bellville, 7535 South Africa (Tel: +27-21-959-2884/3340; Fax: +27-21-9592655; E-mail: jpersens@uwc.ac.za) Mogege Mosimege and Paulus Gerdes will coordinate the session on mathematics and culture / ethnomathematics / history of mathematics in Africa. If you like to presen a paper in this session, please contact with the coordinators. * 10th Pan African Mathematics Olympiad (PAMO) The 10th Pan African Mathematics Olympiad will take place at the University of Cape Town (UCT), Cape Town, South Africa from January 17 to 24, 2000, that is in the week preceding PACOM’2000. For more information, contact the Chairperson of the AMU Commission on Mathematical Olympiads : Prof. Nouzha El Yacoubi, Department of Mathematics and Informatics, Faculty of Science, P. O. Box 1014, Rabat, Morocco [Fax : +212 7 77 30 44; E-mail : elyac-sb@fsr.ac.ma] or the convener, Local Organising Committee : Prof. John Webb., Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, South Africa [Fax : +27 21 686 0476; E-mail : jhwebb@maths.uct.ac.za] 14 * Proceedings of the 3rd and 5th Maghrebian Colloquia on the History of Arabic Mathematics The Proceedings of the 3rd and 5th Maghrebian Colloquia on the History of Arabic Mathematics have been published. Detailed information on the contents will be given in issue 23 of the AMUCHMA-Newsletter : * Actes du 3e Colloque maghrebin sur l’histoire des mathématiques arabes, Alger, 1-3 Decembre 1990, Office des Publications Universitaires, Alger, 1998, 280 pp.; * Actes du 5e Colloque maghrebin sur l’histoire des mathématiques arabes, Hammamet, 1-3 Decembre 1994, A.T.S.M. / Impression IMPAK, Tunis, 1998, 357 pp. * XXIst International Congress of History of Science (ICHS) The XXIst International Congress of History of Science will take place in Mexico City from the 8th to the 14th of July, 2001. The general topic for this congress is “Science and Cultural Diversity”. “A limited number of grants will be available for participants from selected regions in order to assure the more possible participation of researchers from all parts of the world”. For further information, please contact: Prof. Juan José Saldaña, Chairman of the Organizing Committee of the XXIst ICHS, Apartado Postal 21-873, C.P. 04000 México, D.F., Mexico (e-mail : xxiichs@servidor.unam.mx), or visit the web-site of the International Union of History and Philosophy of Science / Division of History of Science (IUHPS/DHS): www.cilea.it/history/DHS * New international journal “Board Games Studies” “Board Games Studies is an academic journal for historical and systematic research on board games, Its object is to provide a forum for board games research from all academic disciplines in order to further the understanding of the development and distribution of board games within an interdisciplinary academic context. Articles are accepted in English, French, and German”. The journal is published by the Research School CNWS, Leiden University, Netherlands. For more information, contact the managing editor Alex de Voogt. The first issue (1998) contains a review (pp. 112-113) by Philip Townshend of the book by Elisio Silva on mancala type games from Angola (cf. AMUCHMA 18: #217). On p. 67, appear the following references to papers by Philip Townshend on board games in Africa: * Autour du jeu de Mankala, Zaire-Afrique, 105: 287-297, 1976; * Les jeux de Makala du Zaire, du Rwanda et du Burundi, Cahiers du CEDAF, Brussels, 3: 1-76, 1977; * Mankala Games, Bulletin of the International Committee on Urgent Anthropological and Ethnological Research, 19: 47-54, 1977; 15 * The South West African game of Illhus in the wider context of African Mankala, Journal of the South West African Scientific Society, 31: 85-98, 1977; * Mankala in Eastern and Southern Africa: a Distributional Analysis, Azania, 14: 108-138, 1979; * Bao (Mankala): The Swahili Ethic in African Idiom, Paideuma, 28: 175-191, 1982; * Games in Culture: A Contextual Analysis of the Swahili Board Game and its relevance to Variation in African Mankala, Ph.D. thesis, University of Cambridge, 1986. The following references to publications by Richard Pankhurst are presented on page 67: * Gabata and related Board-games of Ethiopia and the Horn of Africa, Ethiopia Observer, 14(3): 154-206, 1971; * Gabata and other Board-Games of Ethiopia and the Horn of Africa, Azania, 17: 27-41, 1982. The managing editor, Alex de Voogt, published two books on mancala board games : * Limits of the mind : towards a characterisation of Bao mastership, Research School CNWS, Leiden (Netherlands), 1995, 169 p. Ph. D. thesis in which the Bao game as played on the island Zanzibar (Tanzania) is analysed (cf. # 276); * Mancala board games, British Museum Press, London, 1997, 80 p. The book looks briefly at the social and cultural context of the game, but focuses mainly on the boards themselves. It also contains a catalogue of the 105 boards (many from Africa) in the British Museum’s collection. 7. ADDRESSES OF SCHOLARS, INSTITUTIONS AND PUBLISHERS MENTIONED IN THIS NEWSLETTER * Blyden, Eluemuno R. : President, Genetic Designs, Maine, USA [E-mail: eblyden@khepera.com] * CODESRIA (Council for the Development of Social Science Research in Africa) : B.P. 3304, Dakar, Senegal (Fax : +221-241289; E-mail : codesria@sonatel.senet.net) * Draisma, Jan : Departamento de Matemática, Universidade Pedagógica, C.P.2025, Beira, Mozambique (E-mail : draisma@upb.uem.mz, draisma@zebra.uem.mz) * Editora Dell’Erba : piazza Garibaldi 3, 50054 Fucecchio FI, Italy (Fax : +571-242093, E-mail : EdErba@leonet.it) * Folkerts, Menso : Institut für Geschichte der Naturwissenschaften der Univertsität München, Postfach, D-80306 München, Germany * Gnanvo, Cyprien : Département de Mathématiques, Faculté des Sciences et techniques, Université Nationale du Bénin, 04 BP 0440, Cotonou, Benin 16 * Houndonougbo, Victor: Directeur de l’Ecole normale intégrée de Parakou, Parakou, Benin * Hountondji, Paulin : Directeur, Centre Africain des Hautes Etudes, BP 1268, Cotonou, Benin (E-mail : hountond@syfed.bj.refer.org) * Høyrup, Jens : Institute of Communication Research, Educational Research and Theory of Science, Roskilde University, P.O.Box 260, DK-4000 Roskilde, Denmark (E-mail : jensh@frode.ruc.dk) * Kerkour, Ahmed : President of the AMU, Zankat Ait Rkha, Dar Yamina - Bir Kacem - Rabat, Morocco (E-mail : akerkour@mis.net.ma) * Mathematical Association of America, P.O.Box 91112, Washington, D.C. 20090-1112, USA (Tel: 1-800-331-1622, +301-617-7800; Fax: +301-206- 9789; Webpage: www.maa.org/books) * Mogari, David : Department of Mathematics and Science Education, University of Venda, Private Bag X5050, 0950 Thohoyandou, South Africa (E-mail : dmogari@caddy.univen.ac.za) * Mosimege, David Mogege: Manager Indigenous Technologies CSIR, Building 41, P.O.Box 395, Pretoria 0001, South Africa (E-mail: mmosimeg@csir.co.za) * Mucavele, João : Departamento de Matemática, Universidade Pedagógica, C.P.2025, Beira, Mozambique (E-mail : ....) * Persens, Jan: Director of International Relations, University of the Western Cape, Private Bag X17, Bellville, 7535 South Africa (Tel: +27-21-959- 2884/3340; Fax: +27-21-9592655; E-mail: jpersens@uwc.ac.za) * Powell, Arthur: Academic Foundations Department, Rutgers University, 175 University Avenue, Newark, New Jersey 07102, USA (Fax: 201- 648 5700; E-mail: abpowell@andromeda.rutgers.edu) * Samso, Julio : Dep. Arabe, Facultad Filologia, Universidad Barcelona, Gran Via 585, 08007 Barcelona, Spain * Sangare, Daouda : Secretary-General AMU, 1409 Quartier de la Grande delle, F-14200 Hérouville Saint Clair, France (Tel/Fax : +33 2 31 53 71 88; E-mail : daouda@math.unicaen.fr) * Seepe, Sipho : Department of Mathematics and Science Education, University of Venda, Private bag X5050, Thohoyandou 0950, South Africa * Soares, Daniel : Departamento de Matemática, Universidade Pedagógica, C.P.2025, Beira, Mozambique (E-mail : upbeira@lemep.uem.mz) * Souissi, Mohamed : 7 Rue de Teheran, 2000 Le Bardo, Tunis, Tunisia * Tchitchi, Toussaint-Yaovi : Centre national de linguistique appliquée (CENALA), Université Nationale du Bénin, Cotonou, Benin * Voogt, Alex de: Board Games Studies, Onderzoekinstituut CNWS, Rijksuniversiteit leiden, Postbus 9515, NL-2300 RA Leiden (Fax: +31 3554 30697; E-mail: boardgames@iname.com) * Webb., John : Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, South Africa [Fax : +27 21 686 0476; E-mail : jhwebb@maths.uct.ac.za]17 * Yacoubi, Nouzha El : Department of Mathematics and Informatics, Faculty of Science, P. O. Box 1014, Rabat, Morocco [Fax : +212 7 77 30 44; E- mail : elyac-sb@fsr.ac.ma] * Zaslavsky, Claudia : 45 Fairview Av. #13-1, New York, NY 10040, USA 8. SUGGESTIONS What are your suggestions for improving the AMUCHMA Newsletter? What are your suggestions for other activities of AMUCHMA? Send your suggestions, comments, information, questions and any other contributions to the chairman or secretary of AMUCHMA. Send articles, books and manuscripts for the AMUCHMA Documentation Centre to the Chairman or Secretary. 9. DO YOU WANT TO RECEIVE THE NEXT AMUCHMA- NEWSLETTER? The AMUCHMA Newsletter, published in Arabic, English and French, is available free of charge upon request. Send requests to the Chairman Paulus Gerdes: Universidade Pedagógica, C.P. 915, Maputo, Mozambique (Fax: 258-1-422113; E-mail: pgerdes@virconn.com) for the English version; or to the Secretary Ahmed Djebbar: Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, 91405 Orsay Cedex, France (Fax: 33-1- 47015917; E-mail: Ahmed.Djebbar@wanadoo.fr) for the French and Arabic versions. Readers who would like to receive the AMUCHMA Journal in Portuguese should contact the chairman, C.P. 915, Maputo, Mozambique. 10. AMUCHMA-NEWSLETTER website 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/amuchma_online.html The English version of AMUCHMA 22 is reproduced and distributed 17 * Yacoubi, Nouzha El : Department of Mathematics and Informatics, Faculty of Science, P. O. Box 1014, Rabat, Morocco [Fax : +212 7 77 30 44; E- mail : elyac-sb@fsr.ac.ma] * Zaslavsky, Claudia : 45 Fairview Av. #13-1, New York, NY 10040, USA 8. SUGGESTIONS What are your suggestions for improving the AMUCHMA Newsletter? What are your suggestions for other activities of AMUCHMA? Send your suggestions, comments, information, questions and any other contributions to the chairman or secretary of AMUCHMA. Send articles, books and manuscripts for the AMUCHMA Documentation Centre to the Chairman or Secretary. 9. DO YOU WANT TO RECEIVE THE NEXT AMUCHMA- NEWSLETTER? The AMUCHMA Newsletter, published in Arabic, English and French, is available free of charge upon request. Send requests to the Chairman Paulus Gerdes: Universidade Pedagógica, C.P. 915, Maputo, Mozambique (Fax: 258-1-422113; E-mail: pgerdes@virconn.com) for the English version; or to the Secretary Ahmed Djebbar: Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, 91405 Orsay Cedex, France (Fax: 33-1- 47015917; E-mail: Ahmed.Djebbar@wanadoo.fr) for the French and Arabic versions. Readers who would like to receive the AMUCHMA Journal in Portuguese should contact the chairman, C.P. 915, Maputo, Mozambique. 10. AMUCHMA-NEWSLETTER website 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/amuchma_online.html The English version of AMUCHMA 22 is reproduced and distributed with financial support from SIDA-SAREC (Sweden)