Atanu Dey On India's Development

Shunyata, Nirvana, and Zero

There is a persistent misconception in the English-speaking world that I have to every so often set right. It is this: because the numerals we use are called “Arabic,” the number system was invented by Arabs and by association, is Islamic in origin. This is as silly and illogical as claiming that potatoes originated in France since in the US we call them French fries.

Actually, two of the greatest inventions in mathematics arose in India: the positional number system and the number “zero.” Where else could zero have originated but in the land which has the concepts of Shunyata (emptiness, nothingness) and of Nirvana (complete, utter, and absolute extinction) embedded deep into its philosophy?

Of course, I claim no special insight into mathematics just because I was born in the same land as the ones who hundreds of years ago conceived of shunyata, nirvana, and zero. But I cannot deny myself a bit of pride that one of my ancestors’ mind created the bridge across which pre-numerate humanity walked to become numerate. Yet it fills me with profound sorrow to think that so many of the present-day descendents of those brilliant minds are innumerate. They were giants and we are really puny. C’est la vie and all that.

Let me conclude this one with Alfred, Lord Tennyson’s words from Ulysses

Though much is taken, much abides;
And though we are not now that strength
Which in old days moved earth and heaven
That which we are, we are:
One equal temper of heroic hearts
Made weak by time and fate but strong in will:
To strive, to seek, to find, and not to yield.

Notes:

A few selected references on the number system and zero.

1. The Concise Encyclopedia of Mathematics. W. Gellert, et al. Ed. 1975 Van Nostrand Reinhold:

Position Systems: Our present-day position system goes back to the Hindu from which it came to us by way of the Near East (Arabic Digits)…The introduction of zero is one of the greatest achievements of the Hindus (around 800 A.D.)

2. Beyond Numeracy. John Allen Paulos 1991 Alfred A Knopf:

…we note that about 2000 years ago Chinese invented a written positional numeration system based on the powers of 10. About 500 years later the people of southern India independently made the same discovery but soon thereafter went further and invented zero, a symbol that forever transformed the art of representing and manipulating numbers… The Chinese borrowed the notion of zero from the Indian, as did the Arabs, who eventually communicated the whole system to Western Europe. The invention can fairly be said to be one of the most important technical discoveries of mankind ranking with the invention of the wheel, fire, and agriculture.

3. Mathematics for the Millions. Lancelot Higben.WW Norton and Co:

… In the whole of history of mathematics there has been no more revolutionary step than the one which the Hindus made when they invented the sign ’0′… It makes alive the contents of the elements of mathematics.

4. The Columbia Encyclopedia 1993 Columbia Univ Press:

The introduction of zero was the most significant achievment in the development of the number system in which calculation with large numbers was feasible. Without it, modern astronomy, physics, and chemistry would have been unthinkable. The lack of such a symbol was one of the serious drawbacks of Greek mathematics. Its existence in the West is probably due to the Arabs, who, having obtained it from the Hindus, passed it on to European mathematicians in the latter part of the Middles Ages.

  • http://driveindia.blogspot.com Pranay Da Spyder

    Isn’t it a shame then that most of our past scientific and mathematical creed add up to nought when it comes to solving today’s issues!

    John Keay, in his book India: A History (page 8) quotes D.R Bhandarkar, the first archaeologist to survey Mohenjo-daro, as saying

    According to local tradition, these are the ruins of a town only two hundred years old …This seems not incorrect, because the bricks here found are of the modern type, and there is a total lack of carved terra-cottas amidst the whole ruins.

    Keay makes it a point to respond to this quote in his book,

    Wrong in every detail, this statement must rank amongst archaeology’s greatest gaffes … In assuming the bricks to be ‘of a modern type’, Bhandarkar was unwittingly paying the Harappan brickmakers a generous compliment.

    But like I have posted earlier, it is exteremly unlikely that the ASI, or any other body, will commit enough resources to make such fact more popular. Hell, why don’t we have a ‘Museum of Zero’, surely the story of how Indians invented the zero is as interesting as any other?

    Or for that matter, who will research the story behind this ancient wall in Mahabalipuram that I wrote about on my blog? Consider the ignominy this wall suffers when you compare it to the Hadrian Wall.

  • http://driveindia.blogspot.com Pranay Da Spyder

    I meant to say page 8 in my previous comment. But Atanu, your blog software automatically replaces with an emoticon! Perhaps we should have a preview page so we can see how our comments look? As usual I have made an ‘a href’ gaffe by not closing the tag properly!

  • http://www.coralfringe.com Rangachari Anand

    I have often wondered why Indians are drawn so strongly to the IT industry. When I am in a facetious mood, I sometimes think that this is because everyone in India aspires to a job in an airconditioned office. More seriously however, the ancestral remnants of this early achievement in mathematics also must play some role in the interest in computing.

  • Guru Gulab Khatri

    I have often wondered why Indians are drawn so strongly to the IT industry.

    The relative salary is high.

    …More seriously however, the ancestral remnants of this early achievement in mathematics also must play some role in the interest in computing.

    I’m not sure at all The bulk of IT jobs in india dont even require highschool level math. Its another thing that employers dont feel comfortable with graduates of other degrees. Their are sw engineering jobs which require a lot more knowledge of mathematics but i dont see them done in india. Take a company like mathworks its located in Boston MA thats where bulk of its developers and architects are. It has other offices in europe for some other stuff. But i doubt it that it has anything else but a sales and support team in india.
    (last time i checked it did not even have that in india).
    The Americans,Germans,Swiss can not say that they invented the indian numerals, but looking at the papers published in mathematics and the number of new algorithms being developed they are not coming in such large numbers from india as they are coming out of US, and europe.
    Most indians are interested in computing b/c it can help them earn a living. Its the same globaly.

  • Pardeshi

    Atanu,
    Parmentier made potatoes popular in France brought from America at the time of Louis XIV ; regarding french fries, you can actually give credit to the Belgian menu moules-frites-bière( a mussel based national dish).
    According to my Arab friends, the numerals used now are in fact referred to as an Indian system in their countries.In the western nations, every high school maths teacher knows that zero is the fundamental contribution of India.It is well known through popular science books that positional numeration system is another big achievement.We may feel proud of it as Arabs do about algebra.
    That’s past ;we need more Eulers, Fouriers,Fermats etc

  • http://cafeda.blogspot.com DA

    As far as I can remember we were told that it originated from India but the Indian people expressed zero as a big dot – to mark the absense of a number. When Leonard Pisano (a.k.a. Fibonacci) translated the Arabic writing into Latin he created the dot with the hole, the “0″

  • Uday

    “We may feel proud of it as Arabs do about algebra.”

    Like ’0′, the Arabs did not invent algebra either. Al Khwarizmi was a reputed Persian mathematician and astronomer. While many Arabs view his contributions as fundamental, many other western scientific historians credit him only with compiling the work of previous mathematicians in his “Al-Mukhtasar fi Hisab Al-Jabr Wa’l-Muqabala” from which the term Algebra was derived. There is no doubt that translation of his book to Latin in the 12th century AD allowed Europe to become familiar with earlier work on the topic. Hence both he and his text became famous.

    The Wikipedia entry on Algebra does not credit him with the invention either.

    Interestingly:
    “Al-Khwarizmi also wrote a treatise on Hindu-Arabic numerals. The Arabic text is lost but a Latin translation, Algoritmi de numero Indorum in English Al-Khwarizmi on the Hindu Art of Reckoning gave rise to the word algorithm deriving from his name in the title”. (From http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html)

  • Sahil

    Your reference to “Beyond Numeracy” by Paulos reminded me of another quick read by the same author: Innumeracy. Although you might not agree with everything therein, it does make for an interesting — and oftentimes funny — read.

  • http://pnarula.com Pankaj Narula

    The concept that amazes me about zero is the concept of abstraction. This was a major leap in human thinking. In normal way of life we don’t have zero kg jalebi or zero meter of land.

    For more read “Against the Gods”

    Pankaj

  • http://pb-intel.blogspot.com/ Nath

    Yet it fills me with profound sorrow to think that so many of the present-day descendents of those brilliant minds are innumerate. They were giants and we are really puny.

    I’m not sure I agree with that. Most people have always been innumerate; a good education is a luxury that’s always been available only to a small percent of the population. If anything, the proportion of people without basic mathematical skills has probably decreased over the centuries.

    Our education system is a mess, but it’s not accurate to say that it was ever much better.

    Atanu’s response: I don’t see where I claimed that our education system is not a mess, or that it used to be much better at an earlier time. So your last statement is a bit of a non sequitur.

    Besides, I do agree that a good education is a luxury and like all luxuries, only available to a select but growing few.

  • http://www.nachiketa.org/ Nachiketa Version 0.1

    There is something wrong with a nation where it needs to romanticize the past to feel good. Even a brilliant person like Amartya Sen off late has been running too many precious brain cycles on how wonderful India was.

    It does not matter if Harappa/Mohanjedaro had wonderful sewage system, if our rural folks are still going to behind bushes with tumbler for toilets. What is the use if we could design such advanced space projects if we could not design a cheap shit pot for our poor ? Let us talk about the current problems. Let us talk about a grander future. And then let us plan a bridge from here to there.

    Sorry, I sounded skeptic but I am only alerting to the fact that “I love Atanu’s writings and I want him to write on real problems/solutions”.

    Atanu’s response: I agree that it is not helpful to romanticize a mythical golden past. Those who indulge in doing so are laboring under a delusion for psychological reasons. If you read what I wrote, I did not doing that. My point was that some minds in the distant past in the land now called India made an astonishing invention in arithmetic. The extrapolation of that fact into some imagined golden age is not my intention. Any such misreading could be due to the reader’s prejudices.

    Thanks for the words of appreciation for my writings. I appreciate them. I also try to highlight real problems and suggest solutions as much as I am able to.

  • http://www.cfdvs.iitb.ac.in/~amv Abhijat

    At the end of feeling proud of the achievements of our ancients must lie an introspection of why we – the present – fail to build on their work.

    The achievement of the creation of the number 0 and the place order system is no mean feat! As an example, consider the ease with which addition of two numbers is performed using the position system against, say, the Roman system.

    It is an error to imagine that this faculty of invention must have resulted in the interest in computing. On that grounds, it is the Chinese who must be most adept at computing for their ancients invented the ABACUS. Of course, the Chinese are better than us at computing, but not only because their ancients invented the ABACUS.

    Atanu’s response: There is a distinction between the scientific discoveries as opposed to technological discoveries, though the latter depends on the former. Scientific discoveries are not sufficient for inducing a macro change in society; the benefits of technological innovations can diffuse through society.

    Unfortuntately, we are still unable to see our reality of ourselves until the white man tells us. And we immediately believe him without a thought!

    Just a comment that attempts to give an insight into the beauty of the invention, and take a little space to lament!