The ‘Zero’ Puzzle – What an itinerary for a nought — and impetus for abstract thinking.
That BBC documentary had drawn a pensive smile from me. It revealed that the IndoArabic numerals would have been more complicated to all of us had the zero denotation not been gifted to that system.
It seems that the first record of this “0” was on the wall of a temple in India – as revealed by the mathematician from Oxford. The first known use of special glyphs for the decimal digits that includes the indubitable appearance of a symbol for the digit zero, a small circle, appears on a stone inscription found at the Chaturbhuja Temple at Gwalior in India, dated 876 AD.
I was most tickled by the mention of that digit, because there was a time when it had given me a lot of ‘food for thought’, much hesitation, and doubt. Many of you would be visualizing a student at secondary school trying to grapple with mathematics where the zero was the hub of the problems. Well, you would be far from the mark.
‘Ti l’ecole’
In the 50s, I was at what is now called a preprimary school; in those days it was known as “L’ecole Payer” or “Ti L’ecole”. At that time in Dupéré Street, Beau Bassin, there was such a PPS run by a Miss Gisele at her place. Whereas most people had thatched houses, like the one I came from, this “Ti L’ecole” of ours had a tin sheet roof, which in itself would draw more than ordinary respect and wonder from the young inmates of that establishment. The flooring was not earthen like ours at home, but had paved stones; there were even benches to sit on – plastic chairs were things of the future, and still unheard of.
That was where we had first learnt to write, and to draw our circle with a tail; at that time pictures and images were lacking, so that we children had to conjure up and dream of things that went through our ears, as the brave Miss Gisele tried her best to drive her lessons home.
So, many slates and many more “crayons l’ardoise” later, we were introduced to arithmetic; we had mastered copying 1, 2, 3… hundred times over and now it was time for addition and all its attending cronies.
I think it was at that time that I experienced a sense of discomfort. As far as I can remember I had no problem to follow my classes – but addition was a different baby; oh well, adding 1+1, 1+2 was easy; however, the crunch came when our Miss gave us 1+0, 2+0, 3+0 to calculate. I remember, in spite of my young age, that in those years of early 50s I really had a mental block. I can still recall my complete embarrassment for not knowing just what this “0” represented.
It was possible that when the numbers 1, 2, 3 were written on the blackboard the corresponding number of objects were shown to all of us, so there was no problem to visualize what 1, 2, 3 stood for, but as to zero – I do not remember that anything, or any object was connected to it. The gentle Miss might have said that “0” stood for nothing, for things that could not exist. But how could I visualize nothing – it’s possible that it was too abstract for me, and that was where my embarrassment came from.
My friends seemed to be doing better than I, because they were having the ‘yes’ nod of Miss Gisele when she examined their work; as for me, there was a bit of adult, comprehensive tolerance to my irrational answers, followed by the teacher rubbing them off and writing the right ones.
I had a vague feeling that on some days I did cast a furtive glance on my neighbor Dinesh’s answer before writing my own.
Adding 1+0 or 2+0 were my nightmares. That zero stuff Miss Gisele had introduced into our curriculum was my bête noire and complete Greek to me. But I did remember that I came up with a bright, though unparalleled, conception. It was childish, but now that I look back I wonder whether I was not given a sort of raucous laughter by Miss Gisele.
For me 1+0 = 2… 2+0 = 3… 3+0 = 4; how on earth did I come to this modern mathematics and physics? – the reader may ask. Well it was simple. Take the “0” squeeze it on both sides – so it becomes thinner and thinner, leaner and leaner until the opposite sides coalesce and, lo, one ends up with a “1” on the slate. At that age I had invented a new method, unknown to mathematicians. I had reduced the insoluble theorem of 1+0 into that of 1+1 and discovered my answer, maybe much to the despair of the teacher. The ‘0’ and ‘1’ affairs were engaging my mind even in that distant past, possibly when Alan Turing was already dreaming of a computerized world; little did I know that one day they’ll become the bases for a new science.
I have no inkling as to when that queer concept was forgotten, or how it got corrected; but years later mathematics became my favorite.
Centuries Ago
Going deeper into the issue later, I read that someone had suggested seriously that some of our ancestors had started counting by picking pebbles from the ground or shores of rivers and the sea; then someone noticed that when a pebble had been picked – and there was ‘nothing’ on the sand – there was a roundish pock mark left behind on the sand. Could this have had inspired someone to think of a ‘O’ for ‘nothing’? Who knows?
We understand that some 3500 years ago, the Sag Giga (“Black Headed”) Sumerians were the first to conceive of a symbol for zero; many other civilizations – in China, Egypt, South Americas, and in Babylon had the same idea of using a symbol to represent ‘nothing’, but it was never used as an integer proper. Centuries later even the Greeks, for whom the universe was fixed, with the earth at its centre, would utter, on learning about zero ‘how could nothing be something’. It was left to the Indians, not only to invent the modern symbol ‘O’, but to use it as a number – with positional sense.
Indians invent the zero
Around the 2nd century BC the Indian scholar Pingula was the first to use the Sanskrit word ‘sunya’ (‘a void, or ‘nothing’) to denote zero. Gradually it would be used by others in their calculations, but when did it first assume its present round symbol is not sure. About 450 AD the Jains were dealing with the decimal place – value system, including the zero, in their mathematics. By 498 AD, Aryabhata, another mathematician and astronomer (the very one who first described that the earth does rotate on its own axis) came up with — “sthānāt sthānam daśagunam syāt”, meaning ‘from place to place each is ten times the preceding’ which is the origin of the modern decimalbased place value notation.
By 628 AD Brahmagupta, another great astronomer, was already using the zero in his maths, along with negative numbers. In his book ‘The Opening of The Universe’, he showed how to add numbers to zero; to subtract it from another integer; how ‘a – a = 0’; how to multiply by zero. It was a real exercise into abstract thinking. However, he had no clear answer when he tried dividing a number by zero: he thought that a/0 = 0 (which would be disproved later). And that would be left to Newton and Leipzig, many centuries later, to solve and propel calculus to the fore and help Newton to discover his constant of gravity, G.
As culture and trade moved West, the Arabs produced great mathematicians, and algebra flourished. They translated the word ‘sunya’ (empty) into safira or sifr. By 1202 Fibonacci, also known as Leonardo of Pisa, travelled back from the shores of the Mediterranean and brought the concept of zero to Italy. But by 1299, the IndoArabic numerals and its zero were banned from Florence, it was thought that it was an invitation to fraud — abstract views were not coinciding with the fixed immovable concepts of the universe of that time. But in due time the Italian called it zefiro, which went to Venice and became zevero – contracted to zero; the French made it their zero with an ‘accent aigu’, from where it reached the English who conveniently forgot the accent – and by 1598 zero came to be used for the first time in the British Isles. In the 17th century Descartes in France used it extensively as he tried to combine geometry and algebra.
And the rest is history.
What an itinerary for a nought — and impetus for abstract thinking.
* Published in print edition on 12 June 2015
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