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The Untold Story Behind the real invention of Zero


Had the Arabs back in the days locked its borders down and had not accepted foreigners into their town, there would not have been astronomy or mathematics that we know today; it would have been different.

From Mesopotamia to Ancient India, The Story Behind Zero as mentioned by Robert Kaplan, an author of “The Nothing That Is: A Natural History of Zero”

There is the famous quote by Kaplan, “If you look at zero, you see nothing; but look through it, and you will see the world.” This concept of grasping nature and making sense of our own existence to be zero came from one of the most prominent shifts in human consciousness, the origin of which is said to be in pre-Arab Sumer, the modern-day Iraq, and later, a symbolic form was given in India back then. This not only brought us to mathematics and the concepts that developed further from it to investigate reality, but also brought us to the works of human life, from famous Shakespeare’s wink at zero in King Lear, calling it “an O without a figure”, to invention of our computer that has its base in 0 and 1.

In one of the famous works of the Mathematician Robert Kaplan, The Nothing That Is: A Natural History of Zero talks about the revolutionary changes that nought brought to the mankind. It’s a story about scientific discoveries, where abstract concepts are derived in nature and then given symbols. It’s a mixture of cultures, science and fairy tale that moves beyond the reasons in time and space.

His words:

If you look at zero you see nothing, but look through it and you will see the world. For zero brings into focus the great, organic sprawl of mathematics, and mathematics, in turn, the complex nature of things. From counting to calculating, from estimating the odds to knowing exactly when the tides in our affairs will crest, the shining tools of mathematics let us follow the tacking course everything takes through everything else – and all of their parts swing on the smallest of pivots, zero

With these mental devices, we make visible the hidden laws controlling the objects around us in their cycles and swerves. Even the mind itself is mirrored in mathematics, its endless reflections now confusing, now clarifying insight.

[…]

As we follow the meanderings of zero’s symbols and meanings we’ll see along with it the making and doing of mathematics — by humans, for humans. No God gave it to us. Its muse speaks only to those who ardently pursue her.”

Kaplan also talks about the general debate – if mathematics was discovered or invented – the debate by Kurt Godel and the Vienna Circle:

The disquieting question of whether zero is out there or a fiction will call up the perennial puzzle of whether we invent or discover the way of things, hence the yet deeper issue of where we are in the hierarchy. Are we creatures or creators, less than – or only a little less than — the angels in our power to appraise?”

As every invention, zero started with a necessity, the necessity for counting:

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Zero began its career as two wedges pressed into a wet lump of clay, in the days when a superb piece of mental engineering gave us the art of counting.

[…]

The story begins some 5,000 years ago with the Sumerians, those lively people who settled in Mesopotamia (part of what is now Iraq). When you read, on one of their clay tablets, this exchange between father and son: “Where did you go?” “Nowhere.” “Then why are you late?”, you realize that 5,000 years are like an evening gone.

The Sumerians counted by 1s and 10s but also by 60s. This may seem bizarre until you recall that we do too, using 60 for minutes in an hour (and 6 × 60 = 360 for degrees in a circle). Worse, we also count by 12 when it comes to months in a year, 7 for days in a week, 24 for hours in a day and 16 for ounces in a pound or a pint. Up until 1971, the British counted their pennies in heaps of 12 to a shilling but heaps of 20 shillings to a pound.

Tug on each of these different systems and you’ll unravel a history of customs and compromises, showing what you thought was quirky to be the most natural thing in the world. In the case of the Sumerians, a 60-base (sexagesimal) system most likely sprang from their dealings with another culture whose system of weights — and hence of monetary value — differed from their own.

It created a lot of confusion among the Sumerians to combine both the decimal and sexagesimal counting systems, especially since they used top of hollow reed to create circles and semi-circles to tabulate. This was what it looked like 2000BCE:

This mechanism lasted for thousands of years. Only when someone between 600 BCE to 300 BCE came up with a way to effectively symbolize and wedge accounting columns apart. This was perhaps how the symbol for zero was born. Kaplan writes in his work:

In a tablet unearthed at Kish (dating from perhaps as far back as 700 BC), the scribe wrote his zeroes with three hooks, rather than two slanted wedges, as if they were the thirties; and another scribe at about the same time made his with only one, so that they are indistinguishable from his tens. Carelessness? Or does this variety tell us that we are very near the earliest uses of the separation sign as zero, its meaning and form having yet to settle in?”

However, that zero almost got lost with the civilization that imagined it. It was unclear from Mesopotamia to Greek, when the necessity of zero awakens again. He talks about Archimedes used a numeric system for naming large numbers. For instance, they said “myriad” for their largest number, that was 10,000. The way he was developing orders of large numbers, he was close to developing the concept of power, which is a very important concept, according to Kaplan. He says, he showed us ““how to think as concretely as we can about the very large, giving us a way of building up to it in stages rather than letting our thoughts diffuse in the face of immensity, so that we will be able to distinguish even such magnitudes as these from the infinite.”

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While infinity was on extreme, the mirror-image counterpart was required; the nothingness. [Back then, the negative number not even thought of.] But they didn’t have any word for zero, but they had realized its presence:

Haven’t we all an ancient sense that for something to exist it must have a name? Many a child refuses to accept the argument that the numbers go on forever (just add one to any candidate for the last) because names run out. For them, a googol — 1 with 100 zeroes after it — is a large and living friend, as is a googolplex (10 to the googol power, in an Archimedean spirit).

[…]

By not using zero, but naming instead his myriad myriads, orders and periods, Archimedes has given a constructive vitality to this vastness — putting it just that much nearer our reach, if not our grasp.”

We need names to be assigned to bring something into existence. Otherwise, how do we really say that it exists? Zero is, however, not a thing. Instead, it’s no-thing. Kaplan seems to be interested in this paradox:

Names belong to things, but zero belongs to nothing. It counts the totality of what isn’t there. By this reasoning it must be everywhere with regard to this and that: with regard, for instance, to the number of humming-birds in that bowl with seven — or now six — apples. Then what does zero name? It looks like a smaller version of Gertrude Stein’s Oakland, having no there-there.”

This odyssey continued to travel across the world during those days until finally it was given its name. From Babylon and Greece to India, this concept saw its material rise. The first written appearance of zero is on a stone tablet dated back to 876 AD, where the measurement of the garden is written: 270 by 50. It was written as “27°” and “5°”. The same tiny zero appears copper plates that is said to be 300 years before that. But since the 11th-century era was filled with forgery, the authenticity of the copper plates is in question. Kaplan says:

We can try pushing back the beginnings of zero in India before 876 if you are willing to strain your eyes to make out dim figures in a bright haze. Why trouble to do this? Because of every story, like every dream, has a deep point, where all that is said sounds oracular, all that is seen, an omen. Interpretations seethe around these images like froth in a cauldron. This deep point for us is the cleft between the ancient world around the Mediterranean and the ancient world of India.”

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That was when zero was attributed with the high priest in India – Aryabhata, who is undoubtedly one of the best mathematician and astronomer of those days. Kaplan says:

Āryabhata wanted a concise way to store (not calculate with) large numbers and hit on a strange scheme. If we hadn’t yet our positional notation, where the 8 in 9,871 means 800 because it stands in the hundreds place, we might have come up with writing it this way: 9T8H7Te1, where T stands for ‘thousand’, H for “hundred” and Te for “ten” (in fact, this is how we usually pronounce our numbers, and how monetary amounts have been expressed: £3.4s.2d). Āryabhata did something of this sort, only one degree more abstract.

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He made up nonsense words whose syllables stood for digits in places, the digits being given by consonants, the places by the nine vowels in Sanskrit. Since the first three vowels are a, i and u, if you wanted to write 386 in his system (he wrote this as 6, then 8, then 3) you would want the sixth consonant, c, followed by a (showing that c was in the units place), the eighth consonant, j, followed by i, then the third consonant, g, followed by u: CAJIGU. The problem is that this system gives only 9 possible places, and being an astronomer, he had need of many more. His baroque solution was to double his system to 18 places by using the same nine vowels twice each: a, a, i, i, u, u and so on; and breaking the consonants up into two groups, using those from the first for the odd-numbered places, those from the second for the even. So he would actually have written 386 this way: CASAGI (c being the sixth consonant of the first group, s in effect the eighth of the second group, g the third of the first group)…

There is clearly no zero in this system — but interestingly enough, in explaining it Āryabhata says: “The nine vowels are to be used in two nines of places” — and his word for “place” is “kha”. This kha later becomes one of the commonest Indian words for zero. It is as if we had here a slow-motion picture of an idea evolving: the shift from a “named” to a purely positional notation, from an empty place where a digit can lodge to “the empty number”: a number in its own right, that nudged other numbers along into their places.”

Kaplan talks about the cultural and multicultural heritage that revolves around this concept of zero:

While having a symbol for zero matters, having the notion matters more, and whether this came from the Babylonians directly or through the Greeks, what is hanging in the balance here in India is the character this notion will take: will it be the idea of the absence of any number — or the idea of a number for such absence? Is it to be the mark of the empty or the empty mark? The first keeps it estranged from numbers, merely part of the landscape through which they move; the second puts it on a par with them.”

In his explanatory uncovering The Nothing That Is, Kaplan also attributes the influences of other cultures – from Mayan to Roman – in the creation and value of zero that has made a significant impact in the after years of its inception, and how it affects the modern age too. It’s not just the mathematics side of things, it has affected other disciplines such as philosophy, literature and art, all which he talks about in his work.

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