The Setting Model

Setting influences how art is developed and interpreted. Within the context of a piece of art itself, such as a novel or film, it makes no sense to talk of a story without setting. All stories must take place somewhere. Where and when that place is located impacts the story told. Settings introduce constraints and parameters that help a story hold together. Within a story, everything the characters do, every event that carries the plot, must respect the construct of the setting. A setting can be completely made up, but it will still have rules.

Art is also constructed and consumed in a setting. In the arts, setting matters for more than stories. Where people will hear your music can change what you write or how you play. The dialogue you write for the stage is unlikely to be the same dialogue you write for a film, even if both depict the same story. Where people will interact with your art guides choices about the art itself.

Some stories are just not possible in some settings. If there are logical inconsistencies between the plot of a story and where it occurs, your art isn’t going to go very far. People will tune out if it doesn’t make sense. A chase scene presented as realistic in present-day Tokyo creates different expectations from one set in a fantasy world. The place where an audience encounters art matters too. Dim light can hide a painting’s detail, and reading a symphony’s score offers a different experience from hearing it performed.

As a mental model, setting prompts us to ask which conditions shape an activity and what would change if we moved it elsewhere.

The First Zero

The concept of zero is now a ubiquitous component of our understanding. It is taught early in school and is central to positional notation. Its familiarity can hide the conceptual work required to develop it. The zero is a relative newcomer to the number set, because what it represents is not intuitive to most people. We can easily understand the idea of three deer in a field, but it’s much harder to get our head around the idea that no deer in a field can be represented by a symbol describing the number of deer.

Zero has appeared in different numerical traditions, including the Maya number system. The account here follows Amir Aczel’s search for early zero symbols in Indian-influenced cultures around present-day Cambodia and Indonesia.

A lot of ancient math was done without the zero. Pythagoras’s famous conclusion—that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides—was achieved without a zero, as was Euclid’s entire Elements. In Number: The Language of Science, Tobias Dantzig offers as a possible explanation: “The concrete mind of the ancient Greeks could not conceive the void as a number, let alone endow the void with a symbol.” This explanation hints that you must first understand the concept of the void before you can name it.

As mathematician Amir Aczel explains, the key function of a zero is that it grants “the ability of the numbers to cycle so that the same signs could be used over and over again to mean different things.” It was thought that the number zero was invented in the pursuit of ancient commerce. Something was needed as a placeholder; otherwise, 65 would be indistinguishable from 605 or 6,050. The zero represents “no units” of the particular place that it holds. So, for that last number, we have six thousands, no hundreds, five tens, and no singles. The need for a placeholder helps explain zero’s usefulness, but it does not by itself settle when or why people first developed it.

Aczel’s account focuses on an early surviving zero in an Indian-influenced culture in what is now Cambodia. “In the ruins of the temple of Trapang Pei at Sambor on Mekong, in 1891 [a French archaeologist] found two stone inscriptions written in Old Khmer.” These were eventually translated by French scholar George Coedès. The zero “was clearly discernible and only slightly different in form from Indian zeros: instead of a circle, it was a dot” on an old stone table Coedès labeled K-127.

In his book Finding Zero, Aczel describes his journey to Cambodia to find K-127 and understand its origins. What he learns propels him to argue for the invention of zero being dependent on the characteristics of the place in which it was invented. He claims that the people who discovered the zero must have had an appreciation of the emptiness that it represented. They were labeling a concept with which they were already familiar.

Aczel connects this zero with philosophical and religious ideas in the region. He contrasts an openness to emptiness with familiar binary distinctions, such as good and evil or mind and body. This is his interpretation of the intellectual setting, rather than a description of every person or tradition in those cultures. If something is “A,” then it cannot be “not A.” The very definition of “A” is that it is not “not A.” A thing cannot be both.

Aczel writes that this duality is not universal. He describes the catuskoti, found in early Buddhist logic, that presents four possibilities, instead of two, for any state: that something is, is not, is both, or is neither. It may seem hard to grasp, but actually, our world and words are full of events and expressions that defy binary categorization. A dinner at a fancy restaurant may just be average, which is a way of saying it is neither good nor bad. Your child leaving home may be something you consider both great and devastating.

Aczel quotes Buddhist writer Thich Nhat Hanh, writing, “Emptiness is the Middle Way between existent and nonexistent.” Reflecting on this statement, Aczel explains, “I came to believe that I could even read the quoted verses as saying: existence = 1, non-existence = -1, and emptiness = 0. Emptiness was the door from nonexistence to existence, in the same way that zero was the conduit from positive to negative numbers.” Innovations are extensions of the world in which they originate. They use pieces of what already exists to build something new. Aczel proposes that concepts such as emptiness and the void helped make a symbol for zero conceivable.

The idea of nothing being something is harder to process in binary thinking. A thing is something and is not nothing. Nothing is, by definition, not something. No thing can be both.

In conversations with a Buddhist monk, Aczel is told, “When we meditate, we count. We close our eyes and are aware only of where we are at the moment and of nothing else. We count breathing in, 1; and we count breathing out, 2; and we go on this way. When we stop counting, that is the void, the number zero, the emptiness.” Aczel concludes, “Here was the intellectual source of the number zero. It came from Buddhist meditation.”

A symbol can represent the absence of a quantity without creating a logical contradiction. Aczel’s argument is that the philosophical setting of Cambodia circa the sixth century CE made people comfortable treating that absence as something they could represent.

Since Aczel found the zero in Cambodia, zeros predating that one by a few years have been found in Indonesia. They are artifacts of the Srivijaya empire. Srivijaya too was Buddhist and therefore familiar with exploring the concept of the void. When it comes to history, the oldest thing found is only the oldest until the next oldest one is found. We’ll never know if we’ve found the very first zero. A surviving inscription can establish that a symbol was in use; it cannot by itself establish who first conceived it or whether a particular philosophy caused the invention.