The Berlin Papyrus: or when the Pythagorean Theorem was written 1000 years before the Birth of Pythagoras

Papyrus_Berlin_6619
Berlin Papyrus 6619

Is there a child on this planet who has gone to high school and not been taught the Pythagorean Theorem in some shape or form? I am not sure that many African children know that the so-called Pythagorean Theorem was written by their ancestors over 1000 years before Pythagoras was born, and on African soil. You heard me right: Pythagorean Theorem was written on the Berlin Papyrus or Berlin Papyrus 6619, a papyrus from ancient Egypt from the Middle Kingdom. This papyrus dates back from the second half of the 12th (c. 1990–1800 BC) or 13th Dynasty (c. 1800 BC – 1649 BC).

The papyrus is one of the primary sources of ancient Egyptian mathematical and medical knowledge, including the first known documentation concerning pregnancy test procedures. See our ancestors were already trying to test pregnancy! Amazing!

The first problem found on the Berlin Papyrus states, “You are told the area of a square of 100 square cubits is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other. What are the sides of the two unknown squares.” In modern terms, we would express this as x2 + y2 = 100 and x = (3/4)y, yielding to y = 8, and x = 6. Although the papyrus shows a solution using Egyptian multiplication and a somewhat different way of solving it today, it is understood that they most likely had a good knowledge of the Pythagorean Theorem. It is written in Hieratic script.

Next time you visit the Egyptian Museum Berlin, don’t just look at the bust of Queen Nefertiti which is next to the Berlin Papyrus and dwarfs it, but check it out also.

France returns 26 Artifacts from Behanzin’s Era to Benin

Behanzin, king of Dahomey
Behanzin, king of Dahomey

Last Wednesday, on November 11, 2021, artefacts that had been looted by France 130 years ago were finally returned to Benin. As you recall, on November 17, 1892, the colonel Alfred-Amédée Dodds led a French expedition into the Kingdom of Dahomey. The colonizing troops broke into the palace of King Behanzin at Abomey, and looted a huge number of royal objects, ancient statues, royal thrones, sacred altars, and much more. Upon the troops’ return home, Colonel Dodds donated the stolen objects to the Musée d’Ethnographie du Trocadero in Paris; they have been housed at the Musée du quai Branly – Jacques Chirac since the 2000s. It took 130 years for them to be returned to the homeland. So you can imagine the joy of the people and celebrations that followed. The collection – known as the Abomey Treasures – will remain in a room at the Benin presidency while the museum is in construction. As a slight note, only 26 colonial-era artefacts have been returned at this point, as you can imagine these represent only a fraction of the 90,000 artefacts from Sub-Saharan Africa still held in French museums. 

Benin_Fon statue symbolizing Behanzin Man shark
Benin Fon statue symbolizing Behanzin man shark (Musee du quai Branly – Jacques Chirac)

This is nonetheless a step forward, albeit small, and Benin President, Patrice Talon, said, “The stars have been aligning for Benin for some time now. The symbolism of the return to Benin is about our soul, our identity – to use a word that is easier to put on it to understand. This return is testimony of what we’ve been. The testimony of how we existed before.”

For more information, check out the articles on Euronews, and ABC. Enjoy!

 

Disputed Land Issues: The Case of the Khoi and San People and Amazon’s Headquarters

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Flag of South Africa
Flag of South Africa

The recent struggle faced by the Khoi and San people of South Africa over their land being used to build Amazon’s African headquarters brings back to light never ending issues: the appropriation of indigenous land by mega corporation, with the cooperation of local governments. While sometimes these local governments are powerless in the face of seemingly great deals that will “foster the local economy”, very often the governments are led by corrupt or ignorant individuals who seek immediate personal gains at the expense of the well-being of their communities (recent events in Sierra Leone). Lastly, why is it that it is always on “significant” indigenous lands that this occurs? Why not elsewhere? Of all places to build headquarters, couldn’t Amazon with its money find another piece of land in Cape Town? I am not against “development” or providing jobs to communities, but I wonder why these disputes are always recurrent. The excerpt below is from the BBC.

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Campaigners in the South African city of Cape Town are trying to halt the building of the African headquarters for Amazon. It’s a battle that pits cultural concerns against economic interests, as the BBC’s Vumani Mkhize writes.

San (Basarwa/Bushmen) hunters
San (Basarwa/Bushmen) hunters

It is an overcast day in Cape Town and the scenic Table Mountain is shrouded in a ghostly cloud that silently cascades down the rocky green slopes. At the foot of this historic landscape, a small group of activists from the Khoi and San communities have gathered near the entrance of a huge building site known as the River Club. The communities are seen as some of the earliest inhabitants of southern Africa.

… Across the road from where the activists have gathered, construction is already under way. …

The first phase of the nearly $300m (£215m) development, which will include the Amazon offices, is set to be completed in two years. However the Khoi and the San are determined to stop it.

Tauriq Jenkins, of the Goringhaicona Khoena Council, a Khoi traditional group, says the land has profound historical and cultural value to his people. “This place for us is sacred because it’s on a confluence of Liesbeek and Black Rivers. These embankments are known as the birthplace of the Khoena [Khoi] people,”
he tells the BBC.

It is also where the European colonisers had their first battle with South Africa’s indigenous people, which is marked with a blue plaque.

The 150,000 sqm development will include residential properties and shops as well as offices.

The Amazon site, which is seen as key to pulling in other companies, is set to take up nearly half the space, from where it will run its bourgeoning operations across Africa.

… Jody Aufrichtig, who heads the project, says the development will provide a massive boost to Cape Town’s tourism-reliant economy, hit hard by the coronavirus pandemic. He said it would create 6,000 jobs during construction and about 13,000 indirect jobs. “It’s so desperately needed, especially post-Covid and some of the riots and troubles we’ve had in South Africa. It will give the people of Cape Town and South Africa hope and economic development.” [yeah right… so unless it is built on this specific site, there will be no jobs for South Africans? Of all the places to build, it had to be that one? Will elsewhere in Cape Town still not provide jobs to South Africans?]The tussle between the developer and the indigenous people of Cape Town comes amid the biggest unemployment crisis South Africa has ever faced.

… The site of the development is where the first conflict between the indigenous people and the Dutch colonisers took place in 1659.

This very place is where land was stolen for the first time in South Africa,” Mr Jenkins says. The dispossession of Khoi and San land set in motion centuries of land seizures across the rest of the country. The issue of land ownership, or the lack of it, remains a thorny issue.

… Mr Jenkins and members of the Khoi and San communities remain unmoved by the argument that the new development will bring much-needed jobs. “The reason why this development is so expensive is because it’s on a floodplain. If Amazon and the developer could take its money and build the same scale development off this flood plain, you’d find the size of the development three to four times bigger, which means you’d be able to employ exponentially more people.” [So Amazon is building on floodplains, and it costs more to build there?… so why is the government allowing it? Are there not better sites in Cape Town that will be cost-efficient to the parties involved? Or is there something missing in this information? … doesn’t this scream of corruption?]

The Ethiopian Festival of the True Cross or Meskel

Ethiopian religious leaders carrying crosses during the Meskel celebration (Ethiopiaonlinevisa.com)

September 27th this year marks another big Ethiopian celebration. An even bigger festival than Enkutatash the Ethiopian New Year, is the Meskel “True Cross” Celebration which takes place on September 27th or 28th in leap year. Meskel 2021 is on September 27th . The festival commemorates the discovery of the “True Cross” on which Jesus was crucified, and is held annually in Meskel Square in Addis Ababa.

The word “meskel” is from the Ge’ez language which translates to “cross.” The festival is basically a celebration of the finding of the cross. The festival is held at the iconic Meskel square in Addis Ababa and draws out a large number of religious and civil leaders as well as public figures and Christian faithful. Meskel has been celebrated in Ethiopia for more than 1,600 years as an outdoor religious festival and has been registered at UNESCO since December 2013 as an Intangible World Heritage.

Meskel celebration in Addis Ababa (Source: Wikipedia)

The legend goes that in 4BC, the Roman Empress Helena (Queen Eleni) was able to locate the important artifact in Jerusalem by using the smoke from a huge fire. The celebration is especially important to Ethiopians as it is alleged that a piece of the cross Helena discovered was brought to Ethiopia, and hidden away somewhere in the mountains of  Amba Geshen, which itself has a cross-shaped plan.

Ethiopians commemorate the find by building their own massive bonfire, the Meskel, which they decorate with yellow flowers known as Adey Abeba before burning. Ethiopia’s religious leaders lead colorful processions and prayer around the fire, and attendees intently watch to see which way the bonfire will collapse, as it is believed to predict the future.

As you can see, the month of September is a month of cultural and religious celebrations in Ethiopia.

The Ethiopian Calendar

Flag of Ethiopia

As we talked about the Enkutatash or the Ethiopian New year, I thought that it will be awesome to talk more about the Ethiopian calendar. After all, we are in 2014 in the Ethiopian calendar while we are in 2021 in the Gregorian calendar. Where does this come from? Do months have 30 and 31 days in the Ethiopian calendar like in the current calendar used by most people?

Well, the Ethiopian calendar is derived from the Egyptian solar calendar but adds a leap day every 4 years without exception. Like the Egyptian Coptic calendar, the Amharic calendar comprises 12 months of 30 days each, with an additional month of just 5 or 6 days, depending on the year, i.e. in the Ethiopian calendar, there are 13 months, with 12 months which all have 30 days, and one month with only 5 or 6 days; no need for a song to keep track of which month has 30 or 31 days or even 28 days (February, I am looking at you). Ethiopian calendar months begin on the same days as Coptic calendar months but are instead named in Ge’ez, the ancient language of northern Ethiopia and southern Eritrea. Also a 6th day is added every four years to the 13th month, without exception, to indicate the leap year; this is placed 6 months before the corresponding Gregorian day.

The Ge’ez calendar is the principal calendar used in both Ethiopia and Eritrea.

Map of Ethiopia and Eritrea

The beginning of the calendar is based on the birth of Jesus. Ethiopians use the Incarnation Era to indicate the year, which places the Annunciation of the birth of Jesus on March 25, AD 9 in the Julian calendar. On the other hand, Europeans adopted a different calculation for the Annunciation which placed it eight years earlier, meaning that there exists a gap of 8 years between the start of the Ethiopian calendar and the Gregorian. Most of the major celebrated holidays such as Christmas occur on completely different days, so instead of December 25th, it is celebrated on January 7th which is considered by the Ethiopian orthodox church as Jesus birth day.

Lastly, the time of the day is such that the day starts at sunrise, and sunset is the end of the day: the sun and the moon that are used to count time each have 12 hours before setting… so 6:00AM in the morning in other places of the world will be 12:00AM, midday is 6:00AM, and when the sun goes down it is 12:00PM in Ethiopia. I just wonder how you would tell time if you lived in a different country, and were trying to call a friend in Ethiopia, how would you know when to call?

Wouldn’t it be difficult for a foreigner to tell the time and the year in Ethiopia? I must admit that the Ethiopian calendar does seem a lot simpler than what we have though!

Ethiopian New Year… A Look at the Ethiopian Calendar

Flag of Ethiopia

A few days back, yours truly was invited to the celebration of the Ethiopian New year. Yes… this year Enkutatash, or the Ethiopian New year, was celebrated on September 11th, and my friend went on to tell me more about it. Did you know that we are currently in the year 2014 in the Ethiopian calendar?

The Ethiopian calendar is a solar calendar based on the ancient Egyptian calendar. The first month of the year is September, called Meskerem in Amharic, the local language. One of the reasons given is that during the month of September, the number of daylight hours and nighttime hours happen to be exactly equal in every part of the globe. Moreover, during this time of the year, the sun and the moon that are used to count time each have 12 hours before setting. Another reason often given is that it could be derived from the Bible, where the creation of the Heavens and Earth are said to have taken place in September. Lastly as in many world calendars, harvests must have been key in the setting up of the calendar.

Adey Abeba flower (Source: WikiCommons)

Enkutatash is the name for the Ethiopian New Year and means “gift of jewels” in Amharic. The story goes back almost 3,000 years to the Queen of Sheba of ancient Ethiopia who was returning from her visit to King Solomon of Israel, as mentioned in the Bible in I Kings 10 and II Chronicles 9. She had gifted King Solomon with 120 talents of gold (4.5 tons) as well as a large amount of unique spices and jewels. When the Queen returned to Ethiopia, her chiefs welcomed her with enku or jewels to replenish her treasury. The name Enku may also refer to the countryside, which is covered by bright yellow flowers known as Adey Abeba as this time of the year also marks the end of the raining season. The appearance of the bright yellow flowers also indicates the impending harvest which is to be celebrated (see… harvest).

Doro wot on Injera (Source: cookingchanneltv.com)

The celebration is both religious and secular. The day begins with big church services, followed by the family meal. Young children will receive small gifts of money or bread after the girls gather flowers and sing, and boys paint pictures of saints. Families eat the famed national flat bread injera with the national dish doro wot (chicken stew), which takes at least half a day to prepare, and is rarely missed during these celebrations; families visit friends, and adults drink Tej, the national Ethiopian wine made out of honey… reminds me so much of King Lalibela (bees)… is this where the tradition comes from?

This year in particular, the hope is for peace and harmony… to a happy new year. Enkuan Aderesachihu!

Lucy: the Oldest Ancestor to Mankind?

Lucy_1
Lucy (Australopithecus Afarensis), approximately 3.2 million years ago (Replica of her skull at the Origins Museum)

How many of you have pondered upon the origin of humanity? Or who could have been the oldest ancestor to mankind? Or how we are all related to that ancestor?

I know some will say Adam and Eve… but what if it was Lucy and someone else instead? What if it was not somewhere in the Middle East but rather on the African continent?

Well, today, we will be talking about Lucy, the first human ancestor discovered in Ethiopia, in Africa, the cradle of humanity.

Lucy was discovered in 1974 in Africa, at Hadar, a site in the Awash Valley of the Afar Triangle in Ethiopia, by paleoanthropologist Donald Johanson of the Cleveland Museum of Natural History . In Ethiopia she is known as Dinkinesh, meaning the marvelous one in Amharic. The Lucy specimen is an early australopithecine and is dated to about 3.2 million years ago. At the time of the findings, it was the most ancient early human – or hominin – ever found. It was also the most complete: 40% of the skeleton had been preserved.

Reconstruction_of_the_fossil_skeleton_of__Lucy__the_Australopithecus_afarensis
Reconstruction of Lucy’s skeleton, cast from Musee national d’histoire naturelle, Paris (Source: Wikipedia)

Now, you might ask, why is she called Lucy? Well, because the Beatles’ song “Lucy in the Sky with Diamonds” was playing on the radio when the archaeologists found her remains. Thus the name Lucy. Lucy belongs to the species of Australopithecus afarensis; afarensis for the Afar region of Ethiopia where she was found. She is one of the most important fossils ever discovered. Her discovery helped solidify the idea that Africa was the cradle of humanity, and a crucial hub for human evolution. Before Lucy, the skeleton of the Taung child dated to about 2.8 million years old had been found in South Africa in 1924, but European archaeologists and scientists refused to admit (as always) that Africa could be important in the study of human evolution. As always, they thought that Europe and Asia were the centers. Aren’t we tired of this Eurocentric view of the world which pretends to give meaning to everything it does not understand? Oh Mama Africa, your beauty and splendor is truly too much for these people that they have to keep denying your place and importance in the world!

Lucy was an upright walker, i.e. she walked standing up, thus dating the bipedalism observed in humans to at least 3.2 million years. She was only about 1 meter tall (3.5 feet). Lucy was a full-grown adult, because she had wisdom teeth and her bones had fused. Unlike modern humans, it would seem that she had grown to full size very quickly, and was about 12 years old when she died. From a 2006 study, the findings of a 3-year-old Australopithecus afarensis suggested that their brains reached their full size much earlier than modern human’s does. Lucy was ape-like in appearance and brain size, but could walk upright like more advanced hominins that lived later like the Taung child (2.8 million years) or the Australopitecus sediba (2.2 million years old). She had powerful arms and long curved toes that paleontologists think allowed her to climb trees as well as walk upright.

Lucy’s finding marked a turning point in our understanding of humanity, and the human lineage. She is a treasure, and although older skeletons have since then been found like the Kenyantropus platyops (3.5 million years) or the Ardipithecus (dated 4.4 million years), she remains a treasure. No wonder, Ethiopians call her Dinkinesh or “you are marvelous” or “marvelous one“, for Lucy truly is marvelous as she has allowed to place Africa back at the center as the cradle of humanity (Africa was always at the center, but some Eurocentric views would not let her shine). If you are ever in Addis Ababa, please do not forget to visit her (her cast) at the National Museum of Ethiopia . Enjoy!

For more, please check out the Institute of Human History at the Arizona State University (founded by Donald Johanson), the Smithsonian, and this very good article on The BBC website.

More on King Mkwawa and The Return of His Skull to Tanzania

King Mkwawa

I still don’t understand how a people can hold onto another people’s ancestors’ skulls, refuse to return it, and talk of partnership, friendship, among the people. Isn’t it ludicrous? Many of our ancestors’ skulls are still in museums in Europe, and to this date, Europeans refuse to return them, yet they talk of partnership. The information below shows all the obstacles met to find King Mkwawa’s skull, a skull which was included in the Treaty of Versailles, and return it, … As you read about all the hurdles, you wonder how hard it will be for the regular commoners. The excerpts below are from the article written by Dr. J. Desplat at the National Archives. For the full article, please go to the The National Archives, and see some of the correspondence quoted here, as well as the ones mentioning that the skull was said to have magical powers..

As a reminder, King Mkwawa’s skull’s return (King Mkwawa and the First German Colonial Forces’ Defeat in Africa) was stipulated in the 1919 Treaty of Versailles:

ARTICLE 246. Within six months from the coming into force of the present Treaty, … Germany will hand over to His Britannic Majesty’s Government the skull of the Sultan Mkwawa which was removed from the Protectorate of German East Africa and taken to Germany.

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King Mkwawa was the king of the Uhehe tribe in German East Africa (modern-day Tanzania), and was opposed to German rule. In 1895, he declared that ‘rather than submit to German rule he would fight them to the utmost limit, and rather than surrender he would die by his own gun’.

Sir Edward Twining returning King Mkwawa’s skull

In 1898, a bounty was placed on his head, which led to a manhunt. On 19 July, Sergeant Major Merkl and his party closed in on Mkwawa. Merkl reported that they heard a shot and hurried towards the camp, where they found ‘two natives lying down by the camp fire’. One of them was identified as Mkwawa himself. Merkl wrote: ‘I thought they were asleep, halted at about thirty yards and then fired. The bodies did not move. On reaching the spot, we found both men dead and cold (…). I ordered my askari to cut off Mkwawa’s head to take along to camp.’ (CO 822/770) …

[It took almost 40 years after the Treaty of Versailles to find the skull] … The [British] government of Tanganyika wasn’t too bothered. ‘This government does not now attach much importance to the question of Mkwawa’s skull’, they wrote, … The head mentioned was highly unlikely to be the right one as, by all accounts, it had been skeletonised rather than embalmed, but the German Foreign Ministry was asked to investigate again… The British embassy in Berlin commented: ‘it is of course possible that the German Government have made no very serious effort either to find out what truth there is in the story or to trace the skull.’ (CO 691/124/2)

… In January 1953, however, the German Foreign Ministry suddenly announced the skull might be among the large collection of the Museum für Völkerkunde in Bremen. As several skulls seemed to fit the description, they asked whether the skull had any marks by which it could be identified.

Twining [the Governor of TanganyikaSir Edward Twining] reported from Tanganyika that ‘nobody could be found still alive who remembered the Sultan’ (and if people had still been alive, they might have found it difficult to identify Mkwawa by simply looking at his skull anyway!) but Mkwawa’s cephalic index could be compared to that of his grandson Chief Adam Sapi, an apparently unusual 71%.

In June, Twining himself travelled to Bremen to identify the skull. Accompanied by the consul and the vice-consul, he went to the Museum.

Skull on display at the Mkwawa Memorial Museum

They went to a storeroom where there was a large cupboard full of skulls, and it was arranged for those which had originated in German East Africa to be put together on a table and for their cephalic indexes to be measured. There were two in the 71 group which were selected, and one of these had a hole where a bullet had entered towards the back of the head and come out in front.’ (CO 822/566)

Twining had this skull examined by a German police surgeon who confirmed the hole was consistent with a 25mm rifle of the typed used by German troops in East Africa. Besides, Twining explained, ‘the skull was bleached, which probably happened when they boiled the meat off it’ – someone at the Colonial Office noted in the margin: ‘Ugh!’

[On the return trip], Twining’s irritation might actually have been due to the skull itself which ‘continued to behave very badly’[it was reportedly said to have magical powers]. He reported: We had a series of mishaps which cannot otherwise be accounted for. Our poor old Bandmaster, Gulab Singh, died on the train. My A.D.C. collected a sinus and had to go to hospital. The head boy had a soda water bottle burst in his face, and the cook was struck in the face by a flying saucer. We all got hay fever and we all got very irritable!(CO 822/770)

Benin Bronzes: Horniman Museum to consider returning looted artefacts

Benin City Bronzes at Horniman Museum (Source: Horniman Museum)

Yet another one! Isn’t it odd that there seems to be an avalanche of “proposals” to return looted artifacts? Is it real? Are these museums really going to relinquish these artifacts? or is it just a publicity stunt? Excerpts below are from an article on the BBC website. The article dates from April, but it is still worth mentioning. Enjoy!

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A London museum will consider [seriously?] returning artefacts obtained by “colonial violence” – including Benin Bronzes – to their countries of origin.

Collections at the Horniman Museum in Forest Hill include plaques, figures and ceremonial items taken from the Kingdom of Benin in 1897 [Benin City: the Majestic City the British burnt to the ground].

The decision follows a consultation with London’s Nigerian community.

There has also been mounting political pressure for the return of objects taken in the 19th Century.

Since 2017the Benin Dialogue Group, which brings together the current Oba (state leader of Edo), the Nigerian government and museums across Europe, has been working on a plan for some Benin Bronzes to return to Nigeria. If returned, Nigeria plans to house repatriated bronzes in the Edo Museum of West African Art set to open in 2025.

Campaign group Topple the Racists recently added the Horniman to an interactive map detailing the statues in the UK that have links to colonialism.

The Horniman’s collection includes 15 Benin Bronze plaques depicting Obas (kings) and legendary figures, a brass cockerel called an Ebon which would be placed on the altar of a dead Lyoba (queen mother), and a ceremonial paddle called an Ovbevbe used by priests to ward off evil.

A brass bell, typical of those worn around the necks of Benin’s warriors, is also in the collection, along with an ivory staff of office.

Blombos Cave and the GPS?

Oldest Drawing by Homo Sapiens, dated to be 73,000 years old, found in the Blombos Cave (Wikipedia)

As we said earlier, a lot of new discoveries were made at the Blombos cave [Blombos Cave: Earliest Known Drawing by a Human found in Africa old of 73,000 years] in South Africa. In 2002, Henshilwood and his team had found 2 ocre rocks as old as 100 000 to 80 000 years, which had particularly special graphic inscriptions. On some of these rocks, there are very clear graphic designs in shapes of triangles, revealing a triangulation system similar to that of the modern-day GPS. Is it possible that our ancestors, 80 000 years ago already had already imagined a triangulation system?

There are three major tiling systems: the square (which is simplistic as a reflection), the hexagonal (used by bees) and the triangle (non-existent in nature). But out of these three, only the triangle does not occur naturally in nature. Interesting that out of those three, our ancestors chose the triangle, the most complex. Not only that, but imagine the mathematics required to make that happen, very advanced, almost 100,000 years ago. This pattern on the piece of red ochre displays the hexagon of  Sacred Geometry. The triangles, diamonds, or the red ochre of this object were not randomly chosen. The triangle refers to the principle of divine creation (Trinity). It is possible that the geometric patterns found in Blombos were used to define the ideal model for the triangulation of surfaces, and thus laid the fundamentals for today’s triangulation found in the GPS. So, next time you use the GPS on your phone, remember the Blombos cave and your African ancestors!

Findings from Blombos Cave, South Africa