Posts Tagged ‘Calendar’

A Treasury of Ancient Mathematical Texts

February 4, 2017

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

ancient-mathematics-cover

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.

babylonian-multipilication-table

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.

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Tariq Nasheed Corrects Alt-Right Fascist Lies about Black Civilisations

November 24, 2016

Yesterday I posted several pieces about Richard Spencer’s Nazi speech at the weekend, in which he celebrated Whites as a race of ‘strivers, explorers and conquerors’ whose civilisation and achievements keep improving. Spencer’s one of the founders and leaders of the Fascist Alt-Right, the Nazi nature of which was made chillingly explicit with the cries of ‘Hail Trump! Hail our race! Hail victory!’ with which he opened his vile little rant.

Spencer and his Nazi storm troopers, including another racist polemicist, Jared Tailor, claim that Blacks are inferior. Tariq Nasheed is a black blogger, who is clearly active attacking racism and pernicious claims against people of colour. In this video, he refutes Jared Taylor’s claims that Black people have invented nothing, and have a lower IQ than Whites. Taylor makes the claim that Blacks didn’t invent the wheel, and didn’t invent agriculture or domesticate animals. He also claims that Africans didn’t even have a calendar. This means that they are less intelligent than Whites. The White supremacists of the Alt-Right also maintain that Whites do not exploit Blacks and other ethnic minorities, and that they have benefited from contact with superior White civilisation.

Nasheed comprehensively trashes Taylor’s and his fellow Nazis’ claims that Blacks had no proper civilisation or achievements. He refuses to talk about the ancient Egyptian civilisation, which he feels strongly was Black, as this would be too easy. Instead, he talks about the lesser-known civilisations of West Africa. He mentions the work of Clyde Winters in documenting indigenous writing systems in the peoples of that part of Africa. Black people also very definitely had the wheel. Nasheed points to the rock pictures in the Sahara desert, which show Blacks driving chariots. The Black cultures in Africa also had agriculture and domesticated animals. They kept oxen, and their kings even had pet lions. As for buildings, they had houses and other structures that were two to three storeys tall. The Songhay empire had castles, and he rightly mentions, and ridicules, how the great fortress of Zimbabwe was so impressive, that its colonial discoverers tried to explain it as the work of space aliens. He also talks about the great university at Timbuktu, which was a centre of learning before Europe had universities. As for Black Africans lacking a calendar, he talks about how there is one monumental such device in Namibia.

He states that he’s offered to debate Taylor many times, but has never received an answer. His worry, however, is that now the Nazi Alt-Right have Donald Trump’s ear, Taylor, or an ignorant bigot like him, will get in charge of the educational system, and try to stop Black people learning about the achievements of their people in Africa.

Nasheed is also very much aware that many Whites also despise the Alt Right Fascists. He’s seen a group of White guys beat one of ’em up, and gives a shout out to Whites combating the Alt-Right.

I don’t condone unprovoked violence against the Nazis. They should have the same right not to be attacked as anybody else. But I’m well aware that they themselves are extremely violent, and have beaten and murdered people. I’m very aware that some people may have had to defend themselves, just as I’m also aware that their grotesque, vile opinions and racial insults may provoke others into violence against them, especially Blacks, Jews and others, who have been on the receiving end of their race hate and physical assault.

Nasheed is absolutely right about what he says, though I have some qualifications and additions to make. Black people certainly had the wheel. The rock paintings he mentioned are, I think, at Tassili N’Ajjer in the Sahara. They were painted when that part of the desert was green, many thousands of years ago. They show Whites from North Africa and Blacks from the south crossing and crisscrossing the desert, including people driving chariots. That said, convention historians believe that the wheel was probably invented somewhere in central Asia. So, not invented by Blacks, but arguably not invented by Whites either, or at least, not by Europeans. And yes, many Black nations and cultures certainly possessed agriculture, though again, the conventional explanation is that it spread to sub-Saharan Africa from ancient Egypt. As for the ancient Egyptians being a Black civilisation, they portrayed themselves as being lighter skinned than the peoples to their south, such as the Nubians, who are portrayed in ancient Egyptian papyri as being definitely Black. However, they were darker than their Greek and Roman conquerors. A few years ago New Scientist carried an article, which suggested that the seeds of ancient Egyptian civilisation was in a Black people from the south, whose religion centred around the worship of the cow. This was the ancestral version of Hathor, the Egyptian cow-goddess. These Black race migrated north, to what is now Egypt, as the Saharan desert dried out at the end of the last Ice Age, where they encountered and intermarried with White peoples.

The Songhay and Malinka peoples, who founded the great Muslim empire of Mali, were rich and powerful, and the university of Timbuktu was one of the major centres of Islamic learning and civilisation in West Africa. There have been documentaries exploring the priceless intellectual heritage preserved in the books from its library. Unfortunately, this has been threatened by Islamism. You may recall that a few years ago, Islamist barbarians allied to Daesh tried to set the university on fire in order to destroy its vast repository of the area’s indigenous Muslim culture. The Songhay did indeed have castles. They also had cavalry troops, who have been described in European textbooks as ‘knights of the Sahara’. And yes, in this part of Africa there are multi-storey buildings and extensive palaces. These are of mud brick, but then, so were ziggurats of ancient Babylon. The great Swahili civilisation of East Africa, however, built cities made from coral, which were coated with a lime wash made from burning the same substance. Their cities are as impressive and as richly carved as any others in Islam. The great fortress of Zimbabwe, which is also in east Africa, is also spectacular. It seemed such a contrast to the architecture of the indigenous peoples, who now live in wooden huts, that the Europeans who discovered it tried to explain it as the work of the Chinese, Arabs, or indeed, anyone other than indigenous Africans, including space aliens. In actual fact, its method of construction is very much the same type of building techniques as the mud huts of the local peoples. It seems it was built by the Razwe people, but then during some disruption in the 19th century, it was abandoned.

As for his statement that Black Africans didn’t have the calendar, he is most definitely, monumentally wrong. They definitely had the calendar, and from a very early period. There’s a piece of notched bone, found in a cave in South Africa by archaeologists, which appears to have been a counting device of some kind. The bone dates from 70,000 years ago, and it has been suggested that it may have been a portable calendar. This is about 40,000 years before modern men, Homo Sapiens Sapiens, moved out of Africa to colonise Europe. If it is true that this is a calendar, then clearly Taylor in this regard couldn’t possibly be more wrong.

Regarding Nasheed’s fears of the intellectual damage Alt-Right Fascism could do to the American educational system, I think Taylor and his squadristi will have severe problems if they true to impose a White supremacist curriculum at the universities. I think the liberal traditions of many American universities are simply too strong. No reputable historian, anthropologist or archaeologist specialising in researching African culture and heritage is going to stand for the denigration of African civilisation or the attack on their academic disciplines. I also anticipate considerable resistance from Black Studies professors and their students. And this is quite apart from professors, intellectuals and students, who wish to defend American academia as seats of genuine learning and liberal culture.

However, I recognise that there is a real danger that the Nazis will try to undermine this aspect of the American education system, either by depriving it of funding, or demanding that other courses be introduced to ‘balance’ it.

In my opinion, the real danger is much lower down the educational system, at school level. A little while ago one of the left-wing news shows I watch on YouTube reported that the state educational authority in Arizona decided that the existing school curriculum and its textbooks were too left-wing. I think they objected to them, because they didn’t just present American civilisation as absolutely wonderful, with no defects or shameful episodes. It taught students about slavery, Jim Crow, segregation, institutional racism and civil rights, as well as the other, better aspects of American history. So the right-wingers in power got rid of it.

What did they insist school students learn instead of the complexities, shame and achievements of American history? Ronald Reagan’s speeches.

I kid you not. Ronald Reagan’s speeches. Which weren’t even written by him. I think this should count as a crime against education. Mind you, I think the Tories over here would like to inflict something equally stupid and sinister on our youngsters. Remember when Michael Gove was ranting about children being taught the ‘Blackadder’ view of the Great War in history? He and his fellow Tories would like to do the same, presenting a sanitised version of British history consonant with turning our children into earnest Thatcherites. In fact, I’m surprised they aren’t demanding that school pupils aren’t learning her speeches, like the poor souls in Arizona’s classrooms.

The Alt-Right are a threat to Blacks and other people of colour, and a threat to genuine history and learning. They shouldn’t be allowed anywhere near power, or the young minds they want to poison and keep in ignorance.