Five ways ancient India changed the world – with maths

Five ways ancient India changed the world – with maths

MENA-Forum is proud to reproduce Five ways ancient India changed the world – with maths with our compliments to the author as well thanks   to the publishers because of its obvious interest for its readers of the MENA region.
File 20170920 16437 hxdak9
Bakhshali manuscript.
Bodleian Libraries, University of Oxford

Christian Yates, University of Bath

It should come as no surprise that the first recorded use of the number zero, recently discovered to be made as early as the 3rd or 4th century, happened in India. Mathematics on the Indian subcontinent has a rich history going back over 3,000 years and thrived for centuries before similar advances were made in Europe, with its influence meanwhile spreading to China and the Middle East.

As well as giving us the concept of zero, Indian mathematicians made seminal contributions to the study of trigonometry, algebra, arithmetic and negative numbers among other areas. Perhaps most significantly, the decimal system that we still employ worldwide today was first seen in India.

The number system

As far back as 1200 BC, mathematical knowledge was being written down as part of a large body of knowledge known as the Vedas. In these texts, numbers were commonly expressed as combinations of powers of ten. For example, 365 might be expressed as three hundreds (3×10²), six tens (6×10¹) and five units (5×10⁰), though each power of ten was represented with a name rather than a set of symbols. It is reasonable to believe that this representation using powers of ten played a crucial role in the development of the decimal-place value system in India.

Brahmi numerals.

From the third century BC, we also have written evidence of the Brahmi numerals, the precursors to the modern, Indian or Hindu-Arabic numeral system that most of the world uses today. Once zero was introduced, almost all of the mathematical mechanics would be in place to enable ancient Indians to study higher mathematics.

The concept of zero

Zero itself has a much longer history. The recently dated first recorded zeros, in what is known as the Bakhshali manuscript, were simple placeholders – a tool to distinguish 100 from 10. Similar marks had already been seen in the Babylonian and Mayan cultures in the early centuries AD and arguably in Sumerian mathematics as early as 3000-2000 BC.

But only in India did the placeholder symbol for nothing progress to become a number in its own right. The advent of the concept of zero allowed numbers to be written efficiently and reliably. In turn, this allowed for effective record-keeping that meant important financial calculations could be checked retroactively, ensuring the honest actions of all involved. Zero was a significant step on the route to the democratisation of mathematics.

No abacus needed.

These accessible mechanical tools for working with mathematical concepts, in combination with a strong and open scholastic and scientific culture, meant that, by around 600AD, all the ingredients were in place for an explosion of mathematical discoveries in India. In comparison, these sorts of tools were not popularised in the West until the early 13th century, though Fibonnacci’s book liber abaci.

Solutions of quadratic equations

In the seventh century, the first written evidence of the rules for working with zero were formalised in the Brahmasputha Siddhanta. In his seminal text, the astronomer Brahmagupta introduced rules for solving quadratic equations (so beloved of secondary school mathematics students) and for computing square roots.

Rules for negative numbers

Brahmagupta also demonstrated rules for working with negative numbers. He referred to positive numbers as fortunes and negative numbers as debts. He wrote down rules such as: “A fortune subtracted from zero is a debt,” and “a debt subtracted from zero is a fortune”.

This latter statement is the same as the rule we learn in school, that if you subtract a negative number, it is the same as adding a positive number. Brahmagupta also knew that “The product of a debt and a fortune is a debt” – a positive number multiplied by a negative is a negative.

Negative cows.

For the large part, European mathematicians were reluctant to accept negative numbers as meaningful. Many took the view that negative numbers were absurd. They reasoned that numbers were developed for counting and questioned what you could count with negative numbers. Indian and Chinese mathematicians recognised early on that one answer to this question was debts.

For example, in a primitive farming context, if one farmer owes another farmer 7 cows, then effectively the first farmer has -7 cows. If the first farmer goes out to buy some animals to repay his debt, he has to buy 7 cows and give them to the second farmer in order to bring his cow tally back to 0. From then on, every cow he buys goes to his positive total.

Basis for calculus

This reluctance to adopt negative numbers, and indeed zero, held European mathematics back for many years. Gottfried Wilhelm Leibniz was one of the first Europeans to use zero and the negatives in a systematic way in his development of calculus in the late 17th century. Calculus is used to measure rates of changes and is important in almost every branch of science, notably underpinning many key discoveries in modern physics.

Leibniz: Beaten to it by 500 years.

But Indian mathematician Bhāskara had already discovered many of Leibniz’s ideas over 500 years earlier. Bhāskara, also made major contributions to algebra, arithmetic, geometry and trigonometry. He provided many results, for example on the solutions of certain “Doiphantine” equations, that would not be rediscovered in Europe for centuries.

The Kerala school of astronomy and mathematics, founded by Madhava of Sangamagrama in the 1300s, was responsible for many firsts in mathematics, including the use of mathematical induction and some early calculus-related results. Although no systematic rules for calculus were developed by the Kerala school, its proponents first conceived of many of the results that would later be repeated in Europe including Taylor series expansions, infinitessimals and differentiation.

The leap, made in India, that transformed zero from a simple placeholder to a number in its own right indicates the mathematically enlightened culture that was flourishing on the subcontinent at a time when Europe was stuck in the dark ages. Although its reputation suffers from the Eurocentric bias, the subcontinent has a strong mathematical heritage, which it continues into the 21st century by providing key players at the forefront of every branch of mathematics.

Christian Yates, Senior Lecturer in Mathematical Biology, University of Bath

This article was originally published on The Conversation. Read the original article.

The Conversation

Today’s Iraq eager to get back its antiquities

Today’s Iraq eager to get back its antiquities

Per the US Library of Congress, the world’s first civilizations grew up in the fertile valley between the Tigris and Euphrates rivers, the region of the Middle East long known as Mesopotamia (from the Greek meaning ‘between two rivers’), that roughly corresponds to the territory of present-day Iraq. These ancient civilizations included Sumer, the Babylonian Empire, and the Assyrian Empire. This modern map produced by the Directorate General of Antiquities of Iraq shows the locations of archaeological sites and rock monuments in the country. The table at the lower left lists chronological periods from the Paleolithic to the Islamic. The table at the upper right lists ancient place names such as Ashur, Babylon, and Nineveh, and their equivalents in modern Arabic. Today’s Iraq eager to get back its antiquities is covered by this proposed article of AlMonitor written by Adnan Abu Zeed with translation by Sahar Ghoussoub was published on August 3, 2017. It shows that the Middle East upheavals have amongst many other things consequences that are at best of times unpredictable. These normally include all sorts of rights but also duties such as those described here.

Recovered artifacts are seen at the National Museum of Iraq in Baghdad July 15, 2015. The U.S. handed back to Iraq on Wednesday antiquities it said it had seized in a raid on Islamic State fighters in Syria, saying the haul was proof the militants were funding their war by smuggling ancient treasures. The Iraqi relics were captured by U.S. special forces in an operation in May against an Islamic State commander known as Abu Sayyaf. They included ancient cylindrical stamps, pottery, metallic bracelets and other jewelry, and glass shards from what appeared to be a colored vase.[gallery ids="81735"]

Iraq eager to get back antiquities smuggled to US

BAGHDAD — Iraq is working to recover the thousands of ancient artifacts illegally imported into the United States by Oklahoma City-based arts-and-crafts retailer Hobby Lobby.

“Iraqi and US officials are in constant contact, and the smuggled artifacts are in safe hands now with the US Homeland Security and the US judiciary, which will issue a final verdict on the case,” Maysoon al-Damluji, a member of the Iraqi parliament’s Committee of Culture and Information, told Al-Monitor. “Meanwhile, the Iraqi Embassy is communicating with the US State Department to retrieve the artifacts.”

Hobby Lobby was fined $3 million in July for buying some 5,500 artifacts in 2010 that had been smuggled into the United States through a dealer based in the United Arab Emirates (UAE), according to the US Justice Department. The company paid $1.6 million for the items, which were sent to three different addresses of the company in Oklahoma City. The antiquities include clay cuneiform tablets, cylinder seals and ancient clay bullae that were used to place authenticating seals on documents.

Damluji said, “The course of things is in favor of Iraq to recover its archaeological pieces. It is only a matter of the time needed for administrative and legal procedures in the United States.”

She was confident when she told Al-Monitor, “There is an atmosphere of optimism regarding positive responses from the United States to this effect, given the existent law … whereby the trade in Iraqi artifacts and antiquities is not allowed, unlike the Gulf countries, including the UAE. A UAE-based dealer was involved in the [latest] smuggling operation because the UAE is not among the list of countries acceding to the UNESCO convention on smuggling of antiquities.”

The Iraqi Embassy in London and a legal team will work with the US Justice Department, “which has the final decision on the issue of returning the stolen artifacts to their rightful owners,” Damluji said. Moreover, under a 2015 UN Security Council resolution, countries are required to return smuggled or looted antiquities to their countries of origin.

The Justice Department said the Hobby Lobby acquisition “was fraught with red flags” and Hobby Lobby even ignored the warning of an expert it had hired who said the items might have been looted from Iraq. The company never met with the dealer who claimed to own the artifacts. Rather, a different dealer had the company wire payment to the personal bank accounts of seven other people, the Justice Department said.

Iraq has a history of fighting to retrieve its stolen antiquities and has recovered 4,300 artifacts smuggled out of the country since 2014 after Islamic State (IS) militants seized control of vast areas of the country’s north, east and west.

The United States pledged a year ago to protect and restore historic sites and museums in Iraq, according to the US State Department’s top adviser on Iraqi cultural heritage, John Russell.

A source at the US Embassy in Baghdad, who asked not to be named, said that “the embassy’s instructions regarding smuggling cases are very strict.”

Even before the Hobby Lobby case, government sources revealed that the Iraqi Embassy in Washington was following up on more than 5,000 antiquities smuggled from Iraq after 2003. The Iraqi Embassy in Cairo also has sought to restore manuscripts and other items smuggled to Cairo from Iraqi monasteries and churches in Mosul. In 2016, Iraq recovered the head of the King Sanatruq I statue, which is one the significant monuments registered in the Iraqi Museum of Antiquities. The statute was stolen in 2003.

Iyad al-Shammari, rapporteur of the parliamentary Committee of Antiquities, told Al-Monitor that the Public Authority for Antiquities in Iraq has contacted UNESCO “to urge the United States to hand over [any] stolen Iraqi artifacts,” and he expressed great hope of solving the issue soon. “Iraq has been preoccupied for years in trying to retrieve antiquities smuggled outside,” he said, adding that “some of the archaeological pieces were lost and sold on the black market.”

In 2016, artifacts smuggled from Syria and Iraq were being sold on eBay. Shammari stressed that the “Iraqi Ministry of Culture addressed the US Embassy in Baghdad to start the official and necessary procedures to recover the smuggled artifacts.”

Iraq also plans investigations to obtain the names of smugglers.

 Adnan Abu Zeed, Contributor,  Iraq Pulse is an Iraqi author and journalist. He holds a degree in engineering technology from Iraq and a degree in media techniques from the Netherlands.

Read more:

How has Palestinian traditional clothing changed over time?

How has Palestinian traditional clothing changed over time?

Quora requested me to answer this question of Mark L. Levinson and 3 others. How has Palestinian traditional clothing changed over time?  My answer is here below and I would be happy to have all views and comments, experts in the subject included.

I am no expert in anthropology neither in sociology but I shall endeavour to give what I learned from the multitude of friends I encountered whilst staying and working in the Gulf countries.

The Palestinians like all other peoples around the Mediterranean basin, dressed throughout their history in a wide range of cloths, fabrics and designs. These had variations according to the specifics of the region or town and were of course under the influence of every power that ruled them to date.

There were times of rebellion and times of conciliation and / or reconciliation. For instance, during the times of the presence of the Jewish tribes loitering around well before the advent of nation states, one could not tell a Palestinian from a Jew; they had the same accoutrement. And we are told that they do share the same DNA characteristics.

This went on for some centuries but after the people of the latter as mesmerized by the power and wealth left for Europe in pursuit of the retreating Romans, the fashion had reverted back to that of that of the pre-Roman times.

The following Byzantine period shone little bit in the same way but in a much sterner extravagance. This was soon to be followed by the successive Arab Kalifates with a total departure from the above through a more oriental vista onto the world.

More recently, it is the Ottomans that left an indelible mark on the men and women of the region with their floating robes, headdresses, shoes, etc.

The British didn’t have time to bear any pronounced mark but they did influence the rich and the wealthy in opening the routes of emigration to Europe and later on to America.

The Israelis today being themselves from as diverse an origin cannot imprint a definite style. Could this be at the root of the on-going conflict? Europe is not that far off and its eastern and central regions from which most of these originate from come second to their western counterparts in terms of numbers. Hence a more adversarial attitude that is not conducive to a more effective influence.

Asia with all its ICTs is just around the corner. Social media carry the load in the latest fashion in investment ideas swaps.

America is on the other hand on the other side of the world, but Hollywood isn’t, with all those brave action films heroes in fatigues, baseball caps and all, lambasting each other mercilessly with oversized machines. Closer to us still, there is this multitude per the above, that is housed, looked after relatively well in all GCC countries, but that is another story that could be told on a different occasion.

Greater Cairo Region (GCR) many Challenges

Greater Cairo Region (GCR) many Challenges

Of all the MENA countries capital cities, the Greater Cairo Region (GCR) with a present population well over the 20 million mark is a vast agglomeration with many challenges.  It is a place of unique political and cultural significance for the world.  It has always and still is the prime engine of economic growth and the main population centre in Egypt.  The newly settled leadership facing enormous challenges has wisely decided to involve two of the many influencing factors of the country, i.e. its youth and transportation.

Prior to diving the thick of the subject, and as highlighted in an article of the UN HABITAT, Cairo lives with many key challenges; most importantly planning, infrastructure and service delivery which has been managed to barely keep up with the very rapid urban growth over the past four decades, we would like to propose in this context, this article of Centre for Mediterranean Integration of Marseille, France, titled:

Promoting Public Private Partnership “PPP” to Include Transportation Start-ups in Greater Cairo


October 3, 2016

Transportation has direct impact on the economy, the environment and people’s mobility. On one hand, the air quality is getting worse and there is pollution due to vehicle emissions resulted from the increasing fuel consumption. On the other hand, the large number of people working in places far away from their residence directly affect traffic negatively.

Due to the poor performance of the public transport system, there have been major changes in the methods of travel in Greater Cairo. Private cars have become the favourite mode of transport for a large percentage of Cairenes, and among the public transport users there has been a move from the formal public transport services (Metros, buses, minibuses and rails) to the informal and private services (taxis, microbuses, minibuses and three wheeled rickshaw) which have a great impact on urban transportation as it is filling the gaps of the formal public transport services in terms offering accessibility, speed, and route flexibility.

As a result of the challenges that the government faces in meeting the transportation and mobility needs; solutions have been more complicated and untraditional, that is why citizen-based innovation and initiatives are strongly encouraged to take place in solving the problem. Few years ago, new private initiatives in Egypt have offered diverse solutions to alleviate transportation problems in Greater Cairo, such as crowdsourcing mobile applications and customized ride sharing platforms, promoting fewer car usage and ownership; besides other flexible routing transit services that facilitate commuters’ trips.

Although the emergence of transport start-ups and the solutions they provided might help in solving the transport complications, and might have a great contribution to the community if successful, some of them had a short life span for various internal and external reasons (as shown below), and might be terminated at any phases of the start-up’s life cycle. It has been noticed that there is no one-size-fits-all; the start-ups that survived are the ones that are most adaptable to change, cope with the transformations and keep offering what people want. Perseverance as well as agility are core features in the success of any start-up. The question is how to keep the transport start-ups, having solutions to the severe transportation problem, to sustain?

According to some conducted researches, below are some recommendations for the Transportation Start-ups to help them survive for some time:

Since the objective of the transportation start-ups is to solve community problems, they should have a clear strategy on how they would expand in the market and affect a larger segment to attract the attention and to be sustainable.

For the transport industry, Business to Customer (B2C) service needs a large amount of funding, as it needs a quick market spread. Money will be generated when many vehicles are operated and more clients opted for the service.

The transportation field needs to be managed in a way that protects the passenger from both the road hassles and drivers harassments. Developing monitoring and evaluation system would help in that sense.

To offer a transportation service to be used by the public, it is all about developing IT. In this era, investing in a strong IT platform will distinguish one service provider from the other.

Since many governmental entities are looking at the benefit they will get in return of their provided support, the transportation start-ups have to cater to the needs of the Ministry of Transportation in solving the transportation problems. Upon the applicability of the service, and how much it aligns with the Ministry’s needs, the start-up might be supported.

Transportation start-ups that deliver almost the same service have to coordinate with each other to cover a big range and get a large number of users. The transportation start-ups should be implemented in a bigger scale to make a real difference and get the needed support.

Moving to the concept of Public Private Partnership (PPP), the role of the public sector is always needed for the progress and the development of the community services. The public sector believed in innovation and entrepreneurship and noticed that those two components play a significant role in the economic growth, thus, several governmental entities launching centres to incubate start-ups and Small and Medium Enterprises (SMEs), few years ago, to help them build their companies professionally, yet these entities are not well marketed and their capacities are not fully utilized.

Focusing on the transportation services, the government has to encourage people and give them incentive to leave their own cars and go for the public transport as an initiative to reduce traffic jam. To achieve so, things should be prioritized, for instance: developing a good infrastructure, managing traffic properly and handling parking management. At the same time the government has to encourage and facilitate the operations of the private sector that offers solutions in the transportation domain and provides services to the public that decrease the congestion such as ride sharing in the form of carpooling, bus pooling and car-hailing services.

Finally, the first step to solve a problem is to tackle its roots. To do so, there should be cooperation between different sectors, the private sector, the public sector as well as the social community; all these segments must play a role in developing the country. Solving transportation problem is a strategic project and if all sectors worked together to solve this problem, it will be solved.

Passant Fakhr El-Din, MPA

Passant is a Faculty Affairs Officer at the American University in Cairo (AUC). She has a Master’s degree in Public Administration from the AUC, School of Global Affairs and Public Policy, and a B.Sc. in Business Administration from Ain Shams University, Faculty of Commerce, the English Section. Her research analyses the Egyptian start-ups and entrepreneurs; she is trying to highlight the crucial role of the public sector in the entrepreneurial domain and promoting the concept of Public Private Partnership “PPP”.

Great Giza Pyramid’s Construction Details

Great Giza Pyramid’s Construction Details

The 4,500 years old papyrus has just been displayed in public in Cairo Museum as reported by the International Business Times on July 21, 2016 in an article written by Léa Surugue.  it is about the Great Giza Pyramid’s Construction Details. 

Oldest papyrus ever found reveals details of Great Giza pyramid’s construction

Ancient documents described as the oldest papyruses in existence have been put on display at the Egyptian Museum in Cairo. The 4,500-year-old documents, unveiled at the museum last Friday (15 July 2016), appear to detail the steps of the Great Pyramid of Giza’s construction as well as the daily lives of workers.

The pyramid is believed to have been completed between 2560 and 2540 BC under Pharaoh Khufu’s reign – during the Fourth Dynasty of Egypt. Some scholars believe the King’s Chamber at the heart of the pyramid contains his royal remains, but this has not yet been proven.

Analysing these papyruses may solve a number of other mysteries regarding the construction of the pyramid.

The documents were unearthed three years ago during excavations led by the French Institute for Eastern Archaeology at the Wadi el-Jarf archaeological site.

After years of careful examination, the rare documents have been publicly displayed for the first time.

Allusion to the construction

Wadi el-Jarf is situated on the coast of the Red Sea, and is the oldest-known artificial harbour in the world. It served as major communication corridor between the Nile Valley and the Red Sea. In 2013, during excavation works, 300 fragments of papyri were recovered from ancient boat storage facilities.

Most of the documents, which date back to Egypt’s fourth (2613 to 2494 BC) and fifth (2494 to 2345 BC) dynasties, are ‘bureaucratic’ account books – with records of monthly food deliveries from various regions, including the Nile Delta. But the most interesting find was a personal logbook providing details of the construction of the pyramid – which dates back to 4,500 years ago. For the first time there is written evidence directly alluding to the building of this ‘wonder of the world’.

The pyramids of Giza are impressive Ancient Egyptian constructionsGetty

According to archaeologists Pierre Tallet and Gregory Marouard – who led the team that discovered the papyri – this logbook was written in hieroglyphics by a man named Merer, who was in charge of a team of about 200 workers. In a paper published in 2014, Tallet and Marouard explain that Merer used the papyrus to transcribe the details of many operations related to the construction of the Giza pyramid, and to describe the work at the limestone quarries on the opposite bank of the Nile.

The papyrus reveals that the limestone was brought from the site of Tura, near Cairo, by boat along the Nile river. The logbook also says that in Khufu’s 27th year, the construction of the Great Pyramid was being overseen by the vizier Ankhaf – a high-ranking official and half-brother of Khufu.

This papyrus thus allows archaeologists to discover detailed information about the history of the pyramid and better understand how the 139-metre-tall structure (originally almost 147 metres tall) was constructed. Now, the public can access this unique relic to the Ancient Egyptian civilisation.

World Cities and Tourists’ Destinations

World Cities and Tourists’ Destinations

There are an increasing number of World Cities and Tourists’ Destinations studies in dedicated websites with eye opening reports generously provided on Cost of Living, Telephone and Taxi charges, etc.   We propose 2 websites with excerpts of each reproduced here.  The sites are and  .  Interestingly, the cost of a picnicking day out throughout the world cities was reviewed and the resulting ranking proposed for everyone’s enlightenment.  According to data collected by Expatistan’s Cost of Living Index, a picnic for two will cost just $22.14 in Dubai, a little over half of that of Paris’ $34.02. 

We propose here only the first 5 cities of the Ucityguides and a short introduction to the Expatistan.

The Top 10 Cities and Tourist Destinations in the Middle East

Although plagued by religious and social tensions, the Middle East is one of the most fascinating parts of the world, with some of the most breath-taking places and wonders anywhere.  Contrary to what may be believed by many in the West, it is perfectly safe to travel to large parts of the region (particularly Turkey, Jordan, United Arab Emirates and Israel), and most of it really is a must-see destination at least once in a lifetime.



Although it’s currently a place to avoid, at some point the social and political turmoil will die down and Cairo will once again be one of the world’s must-go destinations. There’s the beautiful setting by the Nile, and amid all the chaos is faded grandeur in Paris-like architecture downtown. But it’s as a gateway to the Giza pyramids and the spectacular treasures of the Egyptian Museum that should place Cairo on anyone’s travel list.


IstanbulIstanbul, Turkey

It’s in Europe and in Asia and it’s the place that mostly mixes East and West in the Middle East. A great imperial capital for almost sixteen centuries, this is old Constantinople, still filled with architectural splendor. There’s the Blue Mosque and Hagia Sophia and other great cultural attractions, but today Istanbul is also a cosmopolitan city that mixes tradition and modern sophistication. End your visit by overlooking the Bosphorus and the entire city from a rooftop bar.


PetraPetra, Jordan

All of Jordan (with the exception of the unattractive capital  ) is filled with magic and wonder, culminating in Petra. This ancient city hewn from rock is unlike anywhere else on earth, with great sculpted temples created by desert tribes. This is one of the most remarkable cities ever built, and it’s especially spectacular as the sun sets and at night.


DubaiDubai, Emirates

The city of the future is already a city of the present. It’s all about the new and the newer, the big and the bigger, and trying to outdo itself and the competition. Hoping to become the great modern metropolis, it’s now one of the world’s main city destinations, home to the world’s grandest hotels on a magnificent waterfront location. Visiting Dubai is getting a glimpse of the future.



Being in this fascinating city is going back 3000 years in history. It’s the spiritual centre of the world, holy to the three great monotheistic faiths, Judaism, Christianity and Islam. Whatever your religion (and even if you don’t have one), you can’t help becoming intrigued by the life and architecture of the place, as you go through a maze of alleys and bazaars.

The rendition of its findings follow; the costs of a romantic picnic were calculated for a couple of people, in cities around the world and as you can see, below, differences are quite obvious in the infographic picture.