Posts Tagged ‘al-Khwarizmi’

History Debunked Refutes Ethnomathematics/Rehumanizing Mathematics

September 8, 2020

This is another video from History Debunked. In it, youtuber and author Simon Webb attacks Ethnomatics, sometimes also called Rehumanizing Mathematics. This is a piece of modern pseudo-scholarship designed to help Black children tackle Maths. The idea is that Blacks perform poorly compared at Maths compared to other ethnic groups. This is held to be because Maths is the creation of White men, and this puts Blacks off studying and mastering it.

The solution has been to scrutinise African societies for their indigenous Maths, especially the Dogon of Mali. They have been chosen as the chief model for all this, as they possessed extremely advanced astronomical and mathematical knowledge. In the 1970s there was a book, The Sirius Mystery by Robert K.G. Temple, which claimed that they owed this advance knowledge to contact with space aliens. Apparently this claim was subsequently dropped 10 – 15 years later, and the claim made instead that they were just superlative astronomers and mathematicians themselves. But Dogon Maths is held to be different from White, western Maths because it’s spiritual. History Debunked then goes on to demonstrate the type of pseudo-scientific nonsense this has lead to by providing a link to an Ethnomathematics paper and reading out its conclusion. It’s the kind of pretentious verbiage the late, great Jazzman, Duke Ellington, said stunk up the place. It’s the kind of postmodern twaddle that Sokal and Bricmont exposed in their Intellectual Impostures. It’s deliberately designed to sound impressive without actually meaning anything. There’s a lot of talk about expanding cognitive horizons and possibilities, but History Debunked himself says he doesn’t understand a word of it. And neither, I guess, will most people. Because it doesn’t really mean anything. It’s just there to sound impressive and bamboozle the reader into thinking that somehow they’re thick because they don’t, while the fault is entirely the writers.

I think History Debunked is a man of the right, and certainly his commenters are Conservatives, some with extremely right-wing views. He’s produced a series of videos attacking the pseudo-history being pushed as Black History, and apparently Seattle in America is particularly involved in promoting this nonsense. But he expects it to come over here in a few years. Given the way Black History month has jumped the Atlantic, I think he’s right.

There’s been a particular emphasis on find ancient Black maths and science for some time I know. For a brief while I got on well with a Black studies group when I was a volunteer at the slavery archives in the former Empire and Commonwealth Museum. That was before I read their magazine and got so annoyed with it and its attitude to Whites that I sent them a whole load of material arguing to the contrary, and pointing out that in places like the Sudan, Blacks were being enslaved and oppressed not by White Europeans, but by the Arabs. I also sent them material about the poor Whites of South Africa, who also lived in grinding poverty thanks to Apartheid. This was stuff they really didn’t want to hear, and I was told that if I wanted to talk to them further, I should do so through someone else. They were also interested in finding examples of Black maths and science. I sent them photocopies and notes I’d made of various medieval Muslim mathematicians. These were Arabs and Persians, like al-Khwarizmi, who gave his name to the word algorithm, Omar Khayyam, best known in the west for his Rubayyat, but who was also a brilliant mathematician, al-Haytham, who invented the camera obscura in the 12th century and others, rather than Black. But they were grateful for what I sent them nonetheless, and I thanked me. This was before I blotted my copybook with them.

I’m reposting this piece because, although it comes from the political, it is correct. And you don’t have to be right-wing to recognise and attack this kind of postmodern rubbish. Sokal and Bricmont, the authors of the book I mentioned early attacking postmodernism, were both men of the left. Sokal was a physicist, who taught maths in Nicaragua under the left-wing Sandinista government. They wrote the book because they took seriously George Orwell’s dictum that writing about politics means writing clearly in language everyone can understand. And even if you believe that Black people do need particular help with maths because of issues of race and ethnicity, Ethnomathematics as it stands really doesn’t appear to be it. It just seems to be filling children’s heads with voguish nonsense, rather than real knowledge.

I also remember the wild claims made about the Dogon and their supposed contact with space aliens. Part of it came from the Dogon possessing astronomical knowledge well beyond their level of technology. They knew, for example, that Sirius has a companion star, invisible to the naked eye, Sirius B. They also knew that our solar system had nine planets, although that’s now been subsequently altered. According to the International Astronomical Association or Union or whatever, the solar system has eight planets. Pluto, previously a planet, has been downgraded to dwarf planet, because it’s the same size as some of the planetoids in the Kuiper Belt. Lynn Picknett and Clive Prince discuss this in one their books,The Stargate Conspiracy (London: Little, Brown & Company 1999), which claimed that the American intelligence agencies were secretly preparing a fake UFO landing in order to convince everyone that the space gods really had arrived, and set up a one-world dictatorship. This hasn’t happened, and I’ve seen the Fortean Times and other weird magazines trying to explain their book as a high-level hoax which people took too seriously. I don’t believe this, as they seemed very serious at the time. The Dogon believe that the first human ancestors, and some of their gods, came from the sky. Hence Temple’s claim that they were contacted by space aliens. Picknett and Prince, however, sided with sceptics like Carl Sagan. They argued instead ithat the Dogon owed it to a French priest, anthropologist or colonial administrator, I’ve forgotten which, who visited them in the 1920s and who was extremely interested in astronomy. This seems to me to be far more likely than that they either got it from space aliens or that they far better mathematicians and astronomers than they could have been at their level of development.

The Dogon are fascinating as their homes and villages are laid out to be microcosms of the male and female human body and the universe. The book African Mythology by Geoffrey Parrinder, London: Hamlyn 1967, describes the layout of a Dogon house thus:

The shape of the Dogon house is symbolical. The floor is like the earth and the flat roof like heaven. The vestibule is a man and the central room woman, with store rooms at her sides as arms. The hear at the end is her head. The four posts are the man and woman entwined in union. So the family house represents the unity of man and woman and God and the Earth. This is accompanied by the elevation and ground plan of a typical Dogon house. (p. 49).

There’s also this diagram of an idealised Dogon village:

The caption for the diagrame reads:

Like the house, the Dogon village represents human beings. The smithy is at the head like a hearth in a house. The family houses in the centre and millstones and village represent the sexes. Other altars are the feet. (p. 51).

Truly, a fascinating people and I have no problem anybody wanting to study them. But it should be in anthropology, ethnography or comparative religion, not maths.

But it struck me that if teachers and educators want to enthuse and inspire young minds with what maths Africans were studying, they could start with ancient Egypt and the great Muslim civilisations of the Sahara and north Africa, like Mali. Aminatta Forna in one of her programmes on these civilisations was shown an ancient astronomical text from the medieval library of one of these towns, which she was told showed that Muslims knew the Earth orbited the sun before Copernicus and Galileo. I doubt that very much. It looks like a form of a combined helio-and geocentric system, first proposed by the ancient Greeks, and then taken up by some medieval astronomers not just in Islam, but also in Christian Europe. In this system, all the other planets when round the Sun, which orbited the Earth. Close to the modern system, but not quite. But it showed that the Black citizens of that civilisation were in contact with the great currents of Muslim science, and that they would have had learnt and taught the same kind of Maths that was being investigated and researcher right across the Muslim world, from India to Morocco and further south to Mali. One of the Black educationalists would like to translate one of these books from Arabic, the learned language of Muslim civilisation, and use it as an example of the kind of maths that was also taught in Black Africa.

Or you could go right back to ancient Egypt. Mathematical texts from the Land of the Nile have also survived in the Moscow and Rhind mathematical papyri. These have various maths problems and their solution. For example, problem No. 7 of the Moscow papyrus is about various calculations for a triangle. This runs

Example of calculating a triangle.

If you are told: A triangle of 2 thousands-of-land, the bank of 2 of 2 1/2;

You are to double the area: result 40 (arurae). Take (it) 2 1/2 times; result [100. Take its square root, namely] 10. Evoke 1 from 2 1/2; what results is 2/5. Apply this to 10; result 4. It is 10 (khet) in length by 4 (khet) in breadth. From Henrietta Midonick, The Treasury of Mathematics: 1 (Harmondsworth: Pelican 1965) p. 71.

It’s amazing to think that the boys at the scribal school were being taught all this millennia ago. It gives you a real sense of connection with the ancient schoolkids reading it. You can imagine them, hunched over with their pen and ink, busily cudgeling their brains while the teacher prowls about them. The Babylonians were also renowned as the pioneers of early mathematics. They even uncovered a school when they excavated Ur of the Chaldees in the 1920s, complete with the maths and other texts the schoolboys – female education didn’t exist back then, but I’m willing to be corrected – were required to learn. As a schoolboy character in the Fast Show used to say: ‘Brilliant!’ You don’t need to burden modern African societies like the Dogon with spurious pseudo-history and pseudo-science, when the real historic achievements of ancient Egypt and medieval Africa are so impressive.

It struck me that even if you don’t use the original Egyptian maths texts to teach maths – which would be difficult, as their maths was slightly different. Their method of calculating the area of a field of four unequal sides yields far too high a figure, for example – you could nevertheless inspire children with similar problems. Perhaps you could do it with assistance of a child or two from the class. You could bring them out in front of everyone, give them and ancient Egyptian headdress, and then arranged the lesson so that they helped the teacher, acting as pharaoh, to solve it. Or else pharaoh showed them, his scribes, and thus the class. This is certainly the kind of thing that was done when I was a kid by the awesome Johnny Ball on the children’s maths and science programme, Think of a Number. And every week, as well as showing you a bit of maths and science, he also showed you a trick, which you could find out how to do by dropping him a line. It was the kind of children’s programme that the Beeb did very, very well. It’s a real pity that there no longer is an audience for children’s programmes and their funding has subsequently been cut.

Here’s History Debunked’s video attacking Ethnomathematics. He also attacks a piece of ancient baboon bone carved with notches, which he states has been claimed is an ancient prehistoric African calendar. He provides no evidence in this video to show that it wasn’t, and says its the subject of a later video. If this is the one I’m thinking of, then that is a claim that has been accepted by mainstream archaeologists and historians. See Ivor Grattan-Guinness, The Fontana History of the Mathematical Sciences (London: Fontana Press 1998) p. 24.

If you want to know more about ancient and medieval maths, and that of the world’s many indigenous cultures, see the book Astronomy before the Telescope, edited by Christopher Walker with an introduction by the man of the crumpled suit and monocle himself, Patrick Moore (London: British Museum Press 1998).

This has chapters on astronomy in Europe from prehistory to the Renaissance, but also on astronomy in ancient Egypt, Babylonia, India, Islam, China, Korea and Japan, North and South America, traditional astronomical knowledge in Africa and among Aboriginal Australians, Polynesia and the Maori. It can be a difficult read, as it explores some very technical aspects, but it is a brilliant work by experts in their respective fields.

A Treasury of Ancient Mathematical Texts

February 4, 2017

Henrietta Midonick, The Treasure of Mathematics: 1 (Harmondsworth: Penguin 1968)


I realise that the history of mathematics is an arcane subject, that few people will have much interest in, having struggled enough with the subject at school. But with Black History Month, there is immense interest amongst scholars of Black and Asian history about restoring Black and Asian scientists and mathematicians to their rightful place in history.

I picked up this book in one of the secondhand bookshops in Cheltenham about a year or so ago. It’s a collection of ancient and medieval mathematical texts from Ancient Egypt, Babylon, China, India, Islam, the Jews and, of course, the ancient Greeks. The blurb for it runs

Mathematics is the only true international language. men can communicate more directly, precisely and logically in pure mathematics than in any other tongue. Moreover we have much to learn from the achievements of past civilizations in this field: even modern computers have not fathomed all the intricacies of Stonehenge. In this fascinating collection of original sources (many of them published in a popular edition for the first time) Henrietta Midonick shows individual mathematicians grappling with varied problems – some practical, such as architecture, money valuation, mechanics, astronomy and calendar calculation; others verging on philosophy, such as the existence of zero and the concept of infinity. Her arrangement also demonstrates the growth of key ideas in geometry, arithmetic, logic and calculus.

Volume 1 documents the growth of mathematical science in the civilizations of Babylon, Ancient Egypt, the Mayas, India and China, and assesses the revolutionary discoveries of Plato, Archimedes and Euclid in classical antiquity.

Among the various extracts are pieces on Babylonian mathematics; four geometrical problems from the Moscow Papyrus, which dates from Ancient Egypt, c. 1850 BC; the Rhind Mathematical Papyrus, again from Egypt, c. 1650 BC; the Bakhshali Manuscript, from 4th century AD India; the Mayas – discussing their system of numbers, the calendar, arithmetic and chronology, and the Quipu, the method of keeping statistical records using knots, used by the ancient Incas in South America.

Chinese mathematicians include Wan Wang, from the 12th century BC, Chou Kung, c. 1100 BC; Chang Tsang, died 152; Liu Hui, 3rd century AD; Sun-Tsu, from the same century; Hsia-Hou Yang, 6th century AD; Wang Hs’iao-T’ung, 7th century AD, Li Yeh, c. AD 1178-1265; Ch’in Chiu-Shao, c. AD 1250; Yang Hui, c. AD 1275; Chu Chi-Chieh, c. AD 1300.

The Indian scholars collected include Aryabhata the Elder, c. AD. 476; Brahmagupta, AD 598; and Bhascara Acharya, AD 1114-c. 1185.

It also includes the Algebra of Mohammed ben Musa al-Khowarismi, who founded much of modern algebra, including giving it its modern name.

The two Jewish mathematicians collected include the Mishnat ha-Middot of Rabbi Nehemiah, from c. AD 150; and the Method of Division of Immanuel Ben Jacob Bonfils, c. AD 1350.

The ancient Greeks include Hippocrates of Chios, 5th century BC; an extract from Plato’s Dialogues; the Elements of Euclid of Alexandria, c. 300 BC; Apollonius of Perga’s Conic Sections, from the same period; Archimedes’ On Spirals, Mechanical Problems, and Quadrature of the Parabola, Pappus, c. AD 300, and Proclus, AD 410-485.


Ancient Babylonian Multiplication Table for X 10.

For the non-mathematician like myself these texts aren’t easy reading. There are diagrams to help, but many of them, as the pioneering works of their time, are trying to express difficult mathematical ideas without the modern language of Maths, and so it can be difficult understanding what they are trying to describe. Nevertheless, this is an important collection of some of the classic texts of ancient mathematics on which the structure of modern maths has been built.

Peace, Love and Lebanese Rockets

October 22, 2014

The Lebanese Rocket Society

Joana Hadjithomas and Khalil Joreige
Soda Film + Art
Arabic with English, French and Arabic subtitles
Running time 95 minutes.

Lebanon Rocket 1

With the news full of the horrors of ISIS and their genocidal war in Iraq and Syria, I thought I’d turn to a far more optimistic and inspiring episode of recent Middle Eastern history: how a group of Lebanese students in 1962 were inspired to join the nascent space race and begin building their own rockets. It’s a piece of history that has been all but forgotten. The film not only documents the rise and fall of the Lebanese space programme, but the film makers’ own attempts to jog people’s memories of it on Lebanese radio. They then turned the rocket programme into an art project, constructing a full-scale statue of one of the rockets, which they presented to the Lebanese Armenian college at the centre of the rocket programme. They also made their own version of the Golden Record, the disc containing the sounds of Earth, which was carried into space on the Voyager 2 probe destined to leave the solar system for the depths of interstellar space and possible contact with aliens. In the hands of the film’s producers, the record held the sounds of Lebanon.

They also created an animated film, by Ghossein Halwa, depicting what Lebanon might be like in 2025, if the programme had continued. In Halwa’s film, the Lebanon of the near future is a prosperous, bustling space age state. Space technology has given the country security by allowing it to guard its borders against foreign invasion. It has also contributed to the country’s material wealth by discovering oil reserves off its coast. Beirut and its suburbs are a true, futuristic city like the vast megalopolis’ in Japanese manga films and the SF classic, Blade Runner. Vast space craft, Arab versions of the Space Shuttle, are launched to explore the depths of space. But it’s also a fun a place, where you can trip the light fantastic in zero-gravity nightclubs.

Lebanon Rocket Cartoon

One of the new generation of spacecraft from the alternative Lebanon of 2025.

The Founder, Manoug Manougian

The programme was the brain child of Manoug Manougian, a professor of mathematics at Haigazian college, an Armenian college in Lebanon. Manougian’s interest in space travel seems to have been sparked, like many a child’s, by reading Jules Verne. Now teaching maths at university in Tampa, Florida, he says during one interview that it may not be accident he ended up there. Verne made it the location for his astronaut’s journey into space in his Voyage to the Moon as it was at the right latitude for launching a flight to the Earth’s companion world. Inspired by the achievements of the Americans and Russians, Manougian was inspired to begin his own experiments. He and a group of his students began making and launching a series of rockets. At first these were tiny ‘baby rockets’, not much larger than fireworks and about the same size as some of the model rockets hobby rocketeers enjoyed by hobby rocketeers. The rockets became increasingly larger and more sophisticated, until they reached the end of what could legally be built. The fuel used by the rockets was strictly limited to the armed forces. Furthermore, there was a problem with funding as any further increase in size would make the rockets prohibitively expensive for a small, civilian project. Manougian’s group had caught the interest of the Lebanese army under Captain Wehbe, who stepped in to give the young rocketeers the money and equipment they needed.

Involvement with the Army

The alliance with the army brought its own problems, however. Manougian and his students were only interested in peaceful research. The college’s founder, a Protestant pastor, was very much afraid that the rocket would be used as a weapon, and was initially strongly opposed to the research. He resolved to put a stop to it when he saw his own 12 year old daughter come out of one of the campus’ laboratories, her forearms grey from mixing the rocket fuel. He decided to go round and tell Manougian to put a stop to it.

He was persuaded otherwise by the massive publicity the programme was giving Lebanon and his college. The newspapers were full of stories about Manougian and his band of space cadets. Other, similar groups sprang up elsewhere in Lebanon. One such was a group of 13-15 year old boys, who launched their own baby rockets. The Lebanese also received international assistance and co-operation from France and America. Col. Wehbe attended a course on rocketry and the American space programme in Florida. He also attended the launch of a French experimental rocket in North Africa.

International Tensions and War

The programme was doomed by the political tensions in the Middle East. The film makers point out that the 1960s was a period of tension and conflict between the superpowers, America and Russia, and their allies and clients in the Arab world. Against them was Arab nationalism, led by the Egyptian president Abdel Nasser, which briefly resulted in the union of Syria and Egypt, and the anti-imperial forces. Lebanon was buzzing with spies and political intrigue. One of the speakers recalled how one frequent drinker at a hotel bar in Beirut was none other than Kim Philby, the notorious British traitor. The Lebanese’s success in building larger and more sophisticated missiles attracted attention and alarm from other nations. Their last missile was to have a projected range of 500 km, bringing into range Cyprus, Syria and Israel. Manougian’s rocketeers received a sharp message from their diplomatic staff in Cyprus. The British authorities were understandably annoyed after they made a mistake with one of their rocket’s trajectory, so that it almost landed on a Cypriot fishing boat.

Other Arab nations were also keen to acquire Lebanon’s success and expertise. Manougian recalled how he was approached at an official party by another Armenian, whom he didn’t know. The man asked him if he was looking for funding. When Manougian said he was, the unknown man replied that he knew someone who wanted to meet him. And so Manougian found himself driving through Beirut with the man at 2.30-3.00 O’clock in the morning, before ending up at hotel, in front of which was a crowd of people. He was then approached by the heir of one of the other Arab states, who asked him if he’d like to come and do the same in his country as he’d done for Lebanon. Manougian states that he felt it would have been impolite to refuse the offer, and so simply replied that he’d have to think about it. He then fled back to Texas to complete his education, explaining that at the time he only had a B.A., and not even an M.A.

The Army’s Takeover and End of the Project

With Manougian absent, the rocket programme began to experience a series of disasters. Three of the rocketeers were badly burned in an accident when the perchlorate rocket fuel being mixed exploded. The College decided the rocket programme was too hazardous, and so had them removed from campus. it was then gradually taken over by the Lebanese army. Manougian, Joseph Sfeir and the other leading rocketeers were peaceful visionaries, but the army made it clear that they had always been interested in developing it as a weapon. They just didn’t tell the project’s civilian leaders. Well, said one of the officers, if you told Manougian it would be all over Haikazian college, and if you told Sfeir, it would be all over his home province. Under the army’s control, the tests became more secret and closed to the public, unlike the earlier launches. Eventually the project was closed down due to international pressure. One of the rocketeers identified the French as responsible. Another recalled how he knew the then-president personally, and asked him, which country was responsible. ‘Was it from the north?’ he asked. ‘From the north, from the south, and elsewhere’, came the reply. Clearly Lebanon’s success at creating such a missile had made a lot of people understandably very nervous.

The film laments how very, very few Lebanese now remember the programme, despite the massive publicity it had at the time. They feel that the 1967 War and the losses of Arab territory to Israel and subsequent conflicts have blotted out all memory of the programme, and made Arabs afraid to dream and strive for utopias. There is very little Science Fiction in the Middle East, they opine, because there’s always the danger that someone in the future will consider it subversive.

Peaceful Idealism

What actually comes out of the film, in contrast to the militarism and political intrigue, is the peaceful idealism and patriotism of the projects leaders and founders. Manougian states that Lebanese Armenians are very loyal to their adopted country for taking them in after the Armenian massacres that occurred throughout the Turkish Empire and the Middle East. It’s a situation the film’s producers strongly sympathise with. One of them has an Armenian grandparent, while the other is part Palestinian. They see the space programme as what their country, and the Arab peoples themselves, can achieve if only they dare to dream and look for utopias. The film was made in 2009-10, during the Arab Spring, which they hail as the Arab people once more daring to dream of better societies without tyrants or despots. As for Manougian, he is still very much a visionary and campaigner for peace. He’s active in a project, ‘Peace through Education’. The film makers hoped by making the film they would restore its memory. The sculpture of the rocket was painted white to show that it wasn’t a real missile, and taken through the streets of Beirut to Haikazian College to show what Lebanon had achieved peacefully, through idealism.

The Lebanese Rocketeers – The Arab ‘Mice that Roared’

The film and its rocketeers remind me somewhat of the Ealing comedy, the Mouse on the Moon. This was the successor to the comedies about the minuscule state of Little Fenwick, an English village that manages to gain independence from the rest of the UK, Passport to Pimlico and The Mouse that Roared. The Mouse on the Moon chronicles the events as Little Fenwick joins the space race, rushing to land on the Moon ahead of the Americans and Russians. Apart from well-known Ealing stars like Margaret Rutherford, it also has Bernard Cribbins, known to grown-up children of a certain age as the narrator of The Wombles, and to a new generation of children as one the friends of David Tenant’s Doctor. It shows what small nations and ordinary people can do with skill, vision and military backing. Sadly, from the perspective of 2014 the film’s optimistic embrace of the Arab Spring seems misplaced. The despots throughout the Middle East have either successfully clamped down on the civil rights movements, or else the dissident movements themselves have led to the raise of dangerous and unstable Islamist militias. Egypt’s brief experiment with the democracy and the rule of the Muslim Brotherhood has collapsed, and the country is once more under the control of the army. Nevertheless, for a brief moment another world of peace and freedom seemed possible.

Human Progress Made when Peoples and Cultures Come Together

The other point that comes out of the film is the amazing advances in science and civilisation when difference peoples and cultures come together in peace to try to learn from one another. Lebanon was known as the Switzerland of the Levant. It’s a mosaic of different peoples and religions, including Christians, Muslims and the Druze, a highly unorthodox form of Islam. Islam was able to make great strides in science in the Middle Ages, because the early caliphs were keen to draw on the knowledge and expertise of their empire’s subject peoples. The caliph Al-Ma’mun founded a bayt al-hikma, or House of Wisdom dedicated to science and medicine. They drew on Greek, Persian and Indian science and mathematics, and employed Christians, Zoroastrians and Hindus, as well as Muslims, to translate scientific and medical works into Arabic. Al-Ma’mun himself sent a scientific mission of scholars, including the pioneering mathematician al-Khwarizmi, who gave his name to word ‘algorithm’, to acquire scientific knowledge and texts from the Byzantine Empire, the Greek Empire of the East. Western science, in its turn, because massively enriched from the 12th century onwards when European scholars acquired copies of the lost Greek classics and Arabic scientific and medical texts. Peaceful contact between nations and cultures, and the great advances they could make by learning from each other, is now threatened today by the rise in militant xenophobia and, in the Middle East, by the genocidal Islamism of groups like ISIS.

Bill Hicks’ Vision – ‘We Can End World Hunger and Colonise Space’

This film shows the opposite, of what can be achieved through peaceful co-operation. It goes some way to proving the point the late comedian, Bill Hicks, used to make at the end of his gigs. Hicks used to state that if the world spent the amount of money it spends on arms instead on developing, we could feed the world. ‘Not one person would starve. Not one. And we could go and colonise space, in peace, together.’

Bill Hicks sadly died of cancer, but the dreams lives on.

Here’s the great man in action, taken from Youtube.