{"id":86537,"date":"2017-02-06T12:00:53","date_gmt":"2017-02-06T12:00:53","guid":{"rendered":"https:\/\/www.transcend.org\/tms\/?p=86537"},"modified":"2017-02-06T14:00:29","modified_gmt":"2017-02-06T14:00:29","slug":"the-history-of-zero-how-ancient-mesopotamia-invented-the-mathematical-concept-of-naught-and-ancient-india-gave-it-symbolic-form","status":"publish","type":"post","link":"https:\/\/www.transcend.org\/tms\/2017\/02\/the-history-of-zero-how-ancient-mesopotamia-invented-the-mathematical-concept-of-naught-and-ancient-india-gave-it-symbolic-form\/","title":{"rendered":"The History of Zero: How Ancient Mesopotamia Invented the Mathematical Concept of Naught and Ancient India Gave It Symbolic Form"},"content":{"rendered":"

\u201cIf you look at zero you see nothing; but look through it and you will see the world.\u201d<\/em><\/p>\n

\"\"<\/a>If the ancient Arab world had closed its gates to foreign travelers, we would have no medicine, no astronomy, and no mathematics \u2014 at least not as we know them today.<\/p>\n

Central to humanity\u2019s quest to grasp the nature of the universe and make sense of our own existence is zero, which began in Mesopotamia and spurred one of the most significant paradigm shifts in human consciousness \u2014 a concept first invented (or perhaps discovered) in pre-Arab Sumer, modern-day Iraq, and later given symbolic form in ancient India. This twining of meaning and symbol not only shaped mathematics, which underlies our best models of reality, but became woven into the very fabric of human life, from the works of Shakespeare, who famously winked at zero in King Lear<\/em> by calling it \u201can O without a figure,\u201d to the invention of the bit<\/a> that gave us the 1s and 0s underpinning my ability to type these words and your ability to read them on this screen.<\/p>\n

Mathematician Robert Kaplan<\/strong> chronicles nought\u2019s revolutionary journey in The Nothing That Is: A Natural History of Zero<\/em><\/strong><\/a> (public library<\/em><\/a>). It is, in a sense, an archetypal story of scientific discovery, wherein an abstract concept derived from the observed laws of nature is named and given symbolic form. But it is also a kind of cross-cultural fairy tale that romances reason across time and space<\/p>\n

<\/a>

Art by Paul Rand from Little 1 by Ann Rand, a vintage concept book about the numbers<\/p><\/div>\n

Kaplan writes:<\/p>\n

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 \u2013 and all of their parts swing on the smallest of pivots, zero<\/p>\n

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.<\/p>\n

[\u2026]<\/p>\n

As we follow the meanderings of zero\u2019s symbols and meanings we\u2019ll see along with it the making and doing of mathematics \u2014 by humans, for humans. No god gave it to us. Its muse speaks only to those who ardently pursue her.<\/p>\n

With an eye to the eternal question of whether mathematics is discovered or invented \u2014 a question famously debated by Kurt G\u00f6del and the Vienna Circle<\/a> \u2014 Kaplan observes:<\/p>\n

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 \u2013 or only a little less than \u2014 the angels in our power to appraise?<\/p>\n

<\/a>

Art by Shel Silverstein from The Missing Piece Meets the Big O<\/p><\/div>\n

Like all transformative inventions, zero began with necessity \u2014 the necessity for counting without getting bemired in the inelegance of increasingly large numbers. Kaplan writes:<\/p>\n

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.<\/p>\n

[\u2026]<\/p>\n

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: \u201cWhere did you go?\u201d \u201cNowhere.\u201d \u201cThen why are you late?\u201d, you realize that 5,000 years are like an evening gone.<\/p>\n

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 \u00d7 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.<\/p>\n

Tug on each of these different systems and you\u2019ll 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 \u2014 and hence of monetary value \u2014 differed from their own.<\/p>\n

Having to reconcile the decimal and sexagesimal counting systems was a source of growing confusion for the Sumerians, who wrote by pressing the tip of a hollow reed to create circles and semi-circles onto wet clay tablets solidified by baking. The reed eventually became a three-sided stylus, which made triangular cuneiform marks at varying angles to designate different numbers, amounts, and concepts. Kaplan demonstrates what the Sumerian numerical system looked like by 2000 BCE:<\/p>\n

<\/a><\/p>\n

This cumbersome system lasted for thousands of years, until someone at some point between the sixth and third centuries BCE came up with a way to wedge accounting columns apart, effectively symbolizing \u201cnothing in this column\u201d \u2014 and so the concept of, if not the symbol for, zero was born. Kaplan writes:<\/p>\n

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 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?<\/p>\n

But zero almost perished with the civilization that first imagined it. The story follows history\u2019s arrow from Mesopotamia to ancient Greece, where the necessity of zero awakens anew. Kaplan turns to Archimedes and his system for naming large numbers, \u201cmyriad\u201d being the largest of the Greek names for numbers, connoting 10,000. With his notion of orders<\/em> of large numbers, the great Greek polymath came within inches of inventing the concept of powers, but he gave us something even more important \u2014 as Kaplan puts it, he showed us \u201chow 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.\u201d<\/p>\n

<\/a>

\u201cArchimedes Thoughtful\u201d by Domenico Fetti, 1620<\/p><\/div>\n

This concept of the infinite in a sense contoured the need for naming its mirror-image counterpart: nothingness. (Negative numbers were still a long way away.) And yet the Greeks had no word for zero, though they clearly recognized its spectral presence. Kaplan writes:<\/p>\n

Haven\u2019t 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 \u2014 1 with 100 zeroes after it \u2014 is a large and living friend, as is a googolplex (10 to the googol power, in an Archimedean spirit).<\/p>\n

[\u2026]<\/p>\n

By not using zero, but naming instead his myriad myriads, orders and periods, Archimedes has given a constructive vitality to this vastness \u2014 putting it just that much nearer our reach, if not our grasp.<\/p>\n

Ordinarily, we know that naming is what gives meaning to existence<\/a>. But names are given to things, and zero is not a thing \u2014 it is, in fact, a no-thing. Kaplan contemplates the paradox:<\/p>\n

Names belong to things, but zero belongs to nothing. It counts the totality of what isn\u2019t 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 \u2014 or now six \u2014 apples. Then what does zero name? It looks like a smaller version of Gertrude Stein\u2019s Oakland, having no there there.<\/p>\n

Zero, still an unnamed figment of the mathematical imagination, continued its odyssey around the ancient world before it was given a name. After Babylon and Greece, it landed in India. The first surviving written appearance of zero as a symbol appeared there on a stone tablet dated 876 AD, inscribed with the measurements of a garden: 270 by 50, written as \u201c27\u00b0\u201d and \u201c5\u00b0.\u201d Kaplan notes that the same tiny zero appears on copper plates dating back to three centuries earlier, but because forgeries ran rampant in the eleventh century, their authenticity can\u2019t be ascertained. He writes:<\/p>\n

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 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.<\/p>\n

But if zero were to have a high priest in ancient India, it would undoubtedly be the mathematician and astronomer \u0100ryabhata, whose identity is shrouded in as much mystery as Shakespeare\u2019s. Nonetheless, his legacy \u2014 whether he was indeed one person or many \u2014 is an indelible part of zero\u2019s story.<\/p>\n

<\/a>

\u0100ryabhata (art by K. Ganesh Acharya)<\/p><\/div>\n

Kaplan writes:<\/p>\n

\u0100ryabhata wanted a concise way to store (not calculate with) large numbers, and hit on a strange scheme. If we hadn\u2019t 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 \u2018thousand\u2019, H for \u201chundred\u201d and Te for \u201cten\u201d (in fact, this is how we usually pronounce our numbers, and how monetary amounts have been expressed: \u00a33.4s.2d). \u0100ryabhata did something of this sort, only one degree more abstract.<\/p>\n

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)\u2026<\/p>\n

There is clearly no zero in this system \u2014 but interestingly enough, in explaining it \u0100ryabhata says: \u201cThe nine vowels are to be used in two nines of places\u201d \u2014 and his word for \u201cplace\u201d is \u201ckha\u201d. This kha<\/em> 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 \u201cnamed\u201d to a purely positional notation, from an empty place where a digit can lodge to \u201cthe empty number\u201d: a number in its own right, that nudged other numbers along into their places.<\/p>\n

Kaplan reflects on the multicultural intellectual heritage encircling the concept of zero:<\/p>\n

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 \u2014 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.<\/p>\n

In the remainder of the fascinating and lyrical The Nothing That Is<\/em><\/strong><\/a>, Kaplan goes on to explore how various other cultures, from the Mayans to the Romans, contributed to the trans-civilizational mosaic that is zero as it made its way to modern mathematics, and examines its profound impact on everything from philosophy to literature to his own domain of mathematics. Complement it with this Victorian love letter to mathematics<\/a> and the illustrated story of how the Persian polymath Ibn Sina revolutionized modern science<\/a>.<\/p>\n

_________________________________________<\/p>\n

\"\"<\/a>Brain Pickings<\/em> is the brain child of Maria Popova, an interestingness hunter-gatherer and curious mind at large obsessed with combinatorial creativity who also writes for <\/em>Wired<\/em> UK and <\/em>The Atlantic<\/em>, among others, and is an MIT Futures of Entertainment Fellow. She has gotten occasional help from a handful of guest contributors<\/a>.<\/em><\/p>\n

Go to Original \u2013 brainpickings.org<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u201cIf you look at zero you see nothing; but look through it and you will see the world.\u201d –Mathematician Robert Kaplan. If the ancient Arab world had closed its gates to foreign travelers, we would have no medicine, no astronomy, and no mathematics \u2014 at least not as we know them today. <\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[145],"tags":[],"class_list":["post-86537","post","type-post","status-publish","format-standard","hentry","category-science"],"_links":{"self":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/posts\/86537","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/comments?post=86537"}],"version-history":[{"count":0,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/posts\/86537\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/media?parent=86537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/categories?post=86537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/tags?post=86537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}