Art by Paul Rand from Little 1 by Ann Rand, a vintage concept book about the numbers
“If you look at zero you see nothing; but look through it and you will see the world.”
BY MARIA POPOVA
If the ancient Arab world had closed its gates to foreign travelers, we would have no medicine, no astronomy, and no mathematics — at least not as we know them today.
Central to humanity’s 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 — 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 by calling it “an O without a figure,” to the invention of the bit that gave us the 1s and 0s underpinning my ability to type these words and your ability to read them on this screen.
Mathematician Robert Kaplan chronicles naught’s revolutionary journey in The Nothing That Is: A Natural History of Zero (public library). 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
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.
With an eye to the eternal question of whether mathematics is discovered or invented — a question famously debated by Kurt Gödel and the Vienna Circle — Kaplan observes:
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?
Like all transformative inventions, zero began with necessity — the necessity for counting without getting bemired in the inelegance of increasingly large numbers. Kaplan writes:
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…