India and the origins of Zero

How the concept of 'shunya' emerged

It might seem odd to take a moment in our technology-driven lives to contemplate the humble and mysterious zero, the pivot upon which mathematics rotates upon.

At a time where zero underpins practically everything we do, being an essential part of the binary code which saturates our world, the origins of where it came from prove interesting.

The University of Oxford, which recently published research findings which have pushed back the first recorded use of zero to a 3rd century CE Indian manuscript, clearly thinks so.

The findings, involving the carbon dating of an ancient mathematical treatise, the Bakhshila Manuscript, have opened up the door in terms of revealing the provenance of the elusive zero.

Experts are clear that zero, as we know it, is an “Indian” invention — but how, why, and when it first emerged as a distinct mathematical concept is less a story of numbers, and more one of how different cultures look at the world, how information was disseminated across countries, and how fundamental aspects of different models of philosophy and religion informed our consciousness and interests.

Origins

The concept of zero, or nothingness, did exist before any South Asian hand penned it down, though not in a usable form, and so before delving into the history of it, it’s important to make a distinction between a placeholder and numeral.

In mathematics, the main difference between the two is that whether there is evidence that it was used in equations, and thus is a repeatable phenomenon.

Placeholder zeros have been present for thousands of years. According to Harvard math professor Robert Kaplan, they were first documented 5,000 years ago in Mesopotamia with the Sumerians using them.

Both the Chinese, with their mathematical model of counting sticks, and the Babylonians were clearly also aware of the concept of zero, but only as just that: a placeholder concept, something that could not be replicated with the same outcome each and every time a particular equation was used.

The concept then spread from Mesopotamia to places like China, Babylon, and India — but it was only the latter who made it more than just an idea.

India proved fertile ground for the evolution of zero from a placeholder to a numeral.

“Really the first place where zero was used as an equation was in India with the ancient Vedic mathematicians,” says Peter Gobets, secretary and leading member of ZerOrigIndia, or Project Zero, a collection of academics who are trying to determine the origin of zero.

“Indian mathematicians were able to conceive and fully invest in it because of their philosophical understandings of shūnya — the nothingness that is the natural counterpart to something,” he adds.

It’s difficult to overstate the importance of this. Mathematics at the time was more an expression of philosophical ideas and reasoning, and directed towards more abstract studies like astronomy, as opposed to commerce.

“Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world. But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics,” says Marcus du Sautoy, professor of mathematics at the University of Oxford.

“We now know that it was as early as the 3rd century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics have been in the Indian subcontinent for centuries,” he adds.

This explains why zero could never have been conceptualised in the West. The Greeks, whose astronomical models and mathematical equations certainly did influence their Indian counterparts, abhorred the very idea of nothingness.

Pre-Socratic schools of thought contended that there could be no such thing as nothing. “Nothing cannot be something,” as Aristotle famously once reasoned.

“This deeply ingrained aversion to emptiness prevented any mathematical equation involving zero — the very idea was offensive to the ancient Greeks,” says Gobets.

India, on the other hand, proved fertile ground for the evolution of zero from a placeholder to a numeral.

“The concept of shūnya is embraced completely, and is explored as being complementary to the concept of fullness,” Gobets explains. “It’s not just maths, or astronomy that it influences — you can see an evolution from the Vedas to being used in different cultural antecedents, in language, in dance, in music.”

“Indians actually utilised it in calculations — that’s what elevates zero from being a placeholder to a numeral. There’s no contention there. Where there isn’t a consensus is in when that first occurred.”

The first person to document zero as a number in its own right was the astronomer and mathematician Brahmagupta in 628 CE.

The Bakhshila manuscript was unearthed by a farmer in 1881 in a field near what is now Mardan in modern day Pakistan. It swiftly came into the possession of the Raj’s premier Indologist at the time, AFR Hoernle, before making its way to the Bodleian Library in Oxford.

Its age has been in contention for the past century. The most authoritative academic study on the manuscript, conducted by Japanese scholar Dr Hayashi Takao, placed its age from between the 8th and 12th Centuries.

Oxford’s research appears to suggest that the manuscript was far earlier than that thanks to carbon dating — which would make it’s dot the first recorded use of zero by the civilisation that made it a numeral.

Gobets, however, is unconvinced that zero began with the manuscript, which his team hopes to independently study, but he says it is possible.

“Our biggest stumbling block is that there is very little evidence,” he says. “Most of the pertinent manuscripts were written on birch bark, which is pretty damn perishable, especially given the humid climate, and the ways they were stored.”

The precise moment when zero became a number may still be contentious, but how it spread from Sanskrit astronomical treatises to the rest of the world is fact.

The voyage of zero

Indian mathematical treatises began to be spread via trade and migration across the pre-Islamic empires of West Asia, particularly the Sasanian Empire in what is now Iran.

In 662, a Syrian Monophysite bishop named Severus Sebokht wrote approvingly about “the science of the Indians,” and “their subtle discoveries in astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians, and their valuable methods of calculation which surpass description.”

He wasn’t their only fan. During the reign of Caliph al-Mansur, an Indian scholar bearing Sanskrit astronomical works was recorded as a visitor to Baghdad in the 770s. Those works were subsequently translated and adopted as Zij-al sindhind andSindhind al-kabir - foundational mathematical treatises for Central Asian and Arabic scholars, based on Sanskrit models.

Take a moment to understand just how momentous a change this system would soon herald. Without zero, there would be no decimal system — and in turn no complicated equations suitable for commerce, for statistics, for figures.

The Arabs, in particular, began expanding and developing these ideas and concepts into what we now universally recognise as our numerals and our calculation system. The equations, and the methods that described them, were referred to as ḥisāb al-hind — literally, “Indian calculation.”

In the 9th century, an Arabic scholar and trader named Muḥammad ibn Mūsā al-Khwārizmī would set the stage for Indian calculation to travel to the West — albeit without much explanation or usage of zero specifically.

Without zero, and its many applications, everything from modern commerce, to banking, to statistics, to even coding would be hard to conceive of

His Al-kitāb al-mukhtaṣar fī ḥisāb al-jabr wa’l-muqābala (“The Compendious Book on Calculation by Completion and Balancing”) became so influential via Latin translations in the late 10th Century that its Latinised name gave us a new word to define a system calculation: Algebra. His own name in Latin, Algoritmi, would in turn give us algorithm.

The shūnya of ancient India became ṣifr in the Arabic works of al-Khwārizmī and his peers, which eventually became cipher,zero, and their respective cognates in European languages.

It wasn’t immediately adopted, however. This was the time of the Crusades, and information flowing from the East was considered to be inherently suspect by the most significant authority in Western Europe — the Church.

It’s also important to realise just how abhorrent an idea a void is, philosophically and spiritually, in the eyes of the Church. While the Greeks despised the idea on grounds of rhetoric, the Church was shocked due to a different dogma. After all, this was a religion founded with the end goal of there being a Heaven and a Hell — not a void.

Nonetheless, al-Khwārizmī’s works would later catch the attention of a certain mathematician named Fibonacci, who immediately saw the practical applications of this strange calculation method from the East in terms of commerce and banking.

Commerce, trade, and industrialisation led to the birth of new scientific concepts and practices, which in turn underscored how sublime ancient India’s usage of zero truly was as Western scientific thought became influenced by it. When Blaise Pascal, for example, first being exploring the idea of a vacuum, he was elucidating a type of void.

Endgame

It’s curious to realise that, in a sense, nothing has come to underpin a great deal. Without zero, and its many applications, everything from modern commerce, to banking, to statistics, to even coding would be hard to conceive of, let alone put into practice.

Oxford’s research has already come under academic criticism. In a rejoinder written in the History of Science in South Asian journal, several of the most prominent mathematical historians on the subject have argued that the age of the document has still not been determined due to factors outside of carbon dating, and that the zeros utilised in the Bakhshila Manuscript could potentially be more than a placeholder.

As the academic debate continues, the origins of zero continues to fascinate and confound us.

It’s history is that of ancient cultures, and of the intersection between philosophy, trade, and war, viewed through the oscillating tilt of civilisations on the axis of history. Even the outliers are fascinating to consider — what of the Mayans, who, isolated from other cultures, also independently conceived of a placeholder zero, only for that information to fade along with their empire into the jungles of the Yucatan?

More than just ancient however, these are also decidedly non-European histories. And the quest for zero’s origins provides an important opportunity to examine these cultures in a time of ever-increasing globalisation and uncertainty.

Something did come from nothing after all.

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