The man from Lahore who discovered ‘zero’

By Majid Sheikh

Dawn, Sep 15, 2013

As one explores the history of ancient Lahore there are times when a major discovery leaves one amazed at just how little we know about our past. That is why any new information produces an excitement that leaves one aghast.

With my now pedantic knowledge of Sanskrit, thanks to the basic grammar book of the great Sanskrit grammarian Panini, new information keeps coming to the fore. One manuscript points to the work of his brother, also of Salatura, the ancient name of Lahore. The name of the brother was Pingala, the author of undoubtedly the greatest early treatise on mathematics in the fast declining Vedic Age. That he was from Lahore was enough for me to set off on his trail.

It seems, and this is not coincidental, that the history of great works being produced coincides with the decline of civilisations. Even the poets Mir and Ghalib, not to speak of others, bloomed once the Moghal decline was well under way. The same can be said of great English poetry, the Irish excluded. So it seems were placed in time Panini and Pingala as the Vedic Age ended. Mohenjo-Daro and Harappa were in decline and the rise and rise of Lahore was under way. Mind you Lahore is located at the eastern-most portion of the Indus Valley Civilisation; hence its rise is understandable.

Let me go over some significant events with a timeline that matters to us in Lahore. The ‘Mahabharata’, mythical some might say, and the wars that took place on the banks of the Ravi, especially the great battle of the Ten Kings, can safely be said to have taken place in 3125 BC or near about. By 3000 BC the Dravidians had developed the great Indus Valley Civilisation. By 2500 BC we know that the cities of Mohenjo-Daro and Harappa were thriving. The Aryans, of Kurgan-origin, had begun to move eastwards and by 1600 BC they had moved into the Indian subcontinent.

It was not, as is assumed, an invasion in one violent massive happening. Great migrations are spread over decades and centuries much in line with how modern migrations take place. The determinant is the ability to travel safety and the speed current transportation allows. As the Ice Age melted northwards and warmer lands emerged, agriculture took hold as forests were cut down to create space for it. In the subcontinent the Indus Civilisation came about much before the Ganges Civilisation for this simple very reason. The prosperity and the growth of urban spaces, richer than non-urban spaces as they are today, attracted people.

And so the Aryans came and the original natives, the Dravidians, were pushed further eastwards. In a way the continuous unrelenting push of modern-day Afghans into Pakistan is part of that very same ancient pattern. By 500 BC, almost 2,500 years ago, the Vedic Period was ending. The ruling classes spoke and worked in Sanskrit, and it was in this language that the great works of that age were written. Mind you variants of Punjabi were spoken by the people, depending on their location. Many linguists describe Sanskrit as “an amalgamation of old Punjabi in the main, and other Vedic languages”. Hence Punjabi was, and remains, the main spoken language of the people.

Now back to my excitement about Pingala the mathematician from Salatura, or Lahore. While Rishi Panini was travelling, researching and compiling his great ‘Ashtadhyayi’, his brother was also delving to advance the science of mathematics and logic. His immortal work is called ‘Chandahshatra’. Though considered a great contribution to the art of ‘prosody’, it contributes in its eight chapters on the very first known description of the binary numeral system. The deliberate use of Vedic meter comes through clearly.

What we today term ‘Pascal’s Triangle’ was first described in great detail in this great book written by the great mathematician from Lahore. One of his students, the great Halayudha, improved on this work and first use of (n-1) was seen, described and advanced. The origins of modern mathematics had been truly laid.

But Pingala was the very first man, so it seems, who came up with the concept of a ‘zero’. The use of the word ‘shunya’, meaning in Sanskrit “empty, or a void” came about. The empty space that emerged when the sum of anything was nothing was noted down by a small circle.

For simplicity let me trace the origin of the word ‘zero’. The Arab mathematicians who learnt the Sanskrit word ‘sunya’ termed it ‘sifr’, meaning ‘nothing, or empty’. From the word ‘sifr’ the Venetians who travelled the trade routes between Rome and the Arab word called it ‘zyphrus’, which is a Latin-Greek origin word. This is not surprising for the elite used Latin when writing. The word ‘zefiro’ was how they described it in their old texts, which went on to be called ‘zero’ once English influence prevailed.

Mind you the massive effort of Al-Mansur of Spain in 773 AD to translate all the old Sanskrit works formed the foundation of modern scientific research and thought. The influence of Greek thinking flushed with their scholars excited by the knowledge of India, and the translations of Sanskrit texts saw Muslim Spain enter into an ‘age of enlightenment’. Religious fundamentalism in Spain led to the beginning of the Inquisition led by the church. The end of religious plurality naturally bred intolerance and the Dark Ages set in Europe.

The greatest contribution of Pingala was the assertion, which Halayudha picked up and worked on, that negative zero and positive zero were one and the same thing. This assertion can be said to lay the foundation of modern mathematics, including the ‘zero’ or ‘one’ as used in binary bases of modern computing. That almost 2,500 years ago in our city this level of intellectual intercourse was taking place is an aspect that has never been explored.

By 900 BC the Aryans had pushed the Dravidians towards the Ganges, and the result was that by 750 BC the great Indo-Aryan states had come about, which formed the basis of the Punjab as it emerged over time. To gel power the Brahmins formed a caste system to consolidate their hold, a system that is very much, in essence if not in name, in existence today in the entire subcontinent. It is weakest in the west, but grows as we move eastwards.

As a reaction to these developments great thinkers like Gautam – the Buddha – and Mahavera the Jain emerged in northern India, especially in Punjab. Their influence in Lahore was very strong. It was in such circumstances that we see the great Panini and Pingala challenging the established order in their own spheres of work.

Can we own up to these inhabitants of Lahore? Our increasing move towards a non-plural society has seen growing intolerance to the very finest cultural symbols that we have. The curb by the Punjab Auqaf Department on placing mud-baked toy horses at the shrine of Ghorray Shah is one sad case in mind. It, therefore, comes as no surprise that great men like Panini or Pingala, both of Lahore, are unknown. That we do not have the guts to acknowledge them reflects our intolerance, let alone our march towards completely ending a plural dispensation.




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