# Tag: Play

## Learning Through Play

Play is an essential way of learning about the world. Doing things we enjoy without a goal in mind leads us to find new information, better understand our own capabilities, and find unexpected beauty around us. Arithmetic is one example of an area we can explore through play.

Every parent knows that children need space for unstructured play that helps them develop their creativity and problem-solving skills. Free-form experimentation leads to the rapid acquisition of information about the world. When children play together, they expand their social skills and strengthen the ability to regulate their emotions. Young animals, such as elephants, dogs, ravens, and crocodiles, also develop survival skills through play.

The benefits of play don’t disappear as soon as you become an adult. Even if we engage our curiosity in different ways as we grow up, a lot of learning and exploration still comes from analogous activities: things we do for the sheer fun of it.

When the pressure mounts to be productive every minute of the day, we have much to gain from doing all we can to carve out time to play. Take away prescriptions and obligations, and we gravitate towards whatever interests us the most. Just like children and baby elephants, we can learn important lessons through play. It can also give us a new perspective on topics we take for granted—such as the way we represent numbers.

***

## Playing with symbols

The book Arithmetic, in addition to being a clear and engaging history of the subject, is a demonstration of how insights and understanding can be combined with enjoyment and fun. The best place to start the book is at the afterword, where author and mathematics professor Paul Lockhart writes, “I especially hope that I have managed to get across the idea of viewing your mind as a playground—a place to create beautiful things for your own pleasure and amusement and to marvel at what you’ve made and at what you have yet to understand.

Arithmetic, the branch of math dealing with the manipulation and properties of numbers, can be very playful. After all, there are many ways to add and multiply numbers that in themselves can be represented in various ways. When we see six cows in a field, we represent that amount with the symbol 6. The Romans used VI. And there are many other ways that unfortunately can’t be typed on a standard English keyboard. If two more cows wander into the field, the usual method of counting them is to add 2 to 6 and conclude there are now 8 cows. But we could just as easily add 2 + 3 + 3. Or turn everything into fractions with a base of 2 and go from there.

One of the most intriguing parts of the book is when Lockhart encourages us to step away from how we commonly label numbers so we can have fun experimenting with them. He says, “The problem with familiarity is not so much that it breeds contempt, but that it breeds loss of perspective.” So we don’t get too hung up on our symbols such as 4 and 5, Lockhart shows us how any symbols can be used to complete some of the main arithmetic tasks such as comparing and grouping. He shows how completely random symbols can represent amounts and gives insight into how they can be manipulated.

When we start to play with the representations, we connect to the underlying reasoning behind what we are doing. We could be counting for the purposes of comparison, and we could also be interested in learning the patterns produced by our actions. Lockhart explains that “every number can be represented in a variety of ways, and we want to choose a form that is as useful and convenient as possible.” We can thus choose our representations of numbers based on curiosity versus what is conventional. It’s easy to extrapolate this thinking to broader life situations. How often do we assume certain parameters are fixed just because that is what has always been done? What else could we accomplish if we let go of convention and focused instead on function?

***

## Stepping away from requirements

We all use the Hindu-Arabic number system, which utilizes groups of tens. Ten singles are ten, ten tens are a hundred, and so on. It has a consistent logic to it, and it is a pervasive way of grouping numbers as they increase. But Lockhart explains that grouping numbers by ten is as arbitrary as the symbols we use to represent numbers. He explains how a society might group by fours or sevens. One of the most interesting ideas though, comes when he’s explaining the groupings:

“You might think there is no question about it; we chose four as our grouping size, so that’s that. Of course we will group our groups into fours—as opposed to what? Grouping things into fours and then grouping our groups into sixes? That would be insane! But it happens all the time. Inches are grouped into twelves to make feet, and then three feet make a yard. And the old British monetary system had twelve pence to the shilling and twenty shillings to the pound.”

By reminding us of the options available in such a simple, everyday activity as counting, Lockhart opens a mental door. What other ways might we go about our tasks and solve our problems? It’s a reminder that most of our so-called requirements are ones that we impose on ourselves.

If we think back to being children, we often played with things in ways that were different from what they were intended for. Pots became drums and tape strung around the house became lasers. A byproduct of this type of play is usually learning—we learn what things are normally used for by playing with them. But that’s not the intention behind a child’s play. The fun comes first, and thus they don’t restrain themselves to convention.

***

## Have fun with the unfamiliar

There are advantages and disadvantages to all counting systems. For Lockhart, the only way to discover what those are is to play around with them. And it is in the playing that we may learn more than arithmetic. For example, he says: “In fact, getting stuck (say on 7 +8 for instance) is one of the best things that can happen to you because it gives you an opportunity to reinvent and to appreciate exactly what it is that you are doing.” In the case of adding two numbers, we “are rearranging numerical information for comparison purposes.

The larger point is that getting stuck on anything can be incredibly useful. If forces you to stop and consider what it is you are really trying to achieve. Getting stuck can help you identify the first principles in your situation. In getting unstuck, we learn lessons that resonate and help us to grow.

Lockhart says of arithmetic that we need to “not let our familiarity with a particular system blind us to its arbitrariness.” We don’t have to use the symbol 2 to represent how many cows there are in a field, just as we don’t have to group sixty minutes into one hour. We may find those representations useful, but we also may not. There are some people in the world with so much money that the numbers that represent their wealth are almost nonsensical, and most people find the clock manipulation that is the annual flip to daylight savings time to be annoying and stressful.

Playing around with arithmetic can teach the broader lesson that we don’t have to keep using systems that no longer serve us well. Yet how many of us have a hard time letting go of the ineffective simply because it’s familiar?

Which brings us back to play. Play is often the exploration of the unfamiliar. After all, if you knew what the result would be, it likely wouldn’t be considered play. When we play we take chances, we experiment, and we try new combinations just to see what happens. We do all of this in the pursuit of fun because it is the novelty that brings us pleasure and makes play rewarding.

Lockhart makes a similar point about arithmetic:

“The point of studying arithmetic and its philosophy is not merely to get good at it but also to gain a larger perspective and to expand our worldview . . . Plus, it’s fun. Anyway, as connoisseurs of arithmetic, we should always be questioning and critiquing, examining and playing.”

***

We suggest that playing need not be confined to arithmetic. If you happen to enjoy playing with numbers, then go for it. Lockhart’s book gives great inspiration on how to have fun with numbers. Playing is inherently valuable and doesn’t need to be productive. Children and animals have no purpose for play; they merely do what’s fun. It just so happens that unstructured, undirected play often has incredibly powerful byproducts.

Play can lead to new ideas and innovations. It can also lead to personal growth and development, not to mention a better understanding of the world. And, by its definition, play leads to fun. Which is the best part. Arithmetic is just one example of an unexpected area we can approach with the spirit of play.

## Descriptions Aren’t Prescriptions

When we look at a representation of reality, we can choose to either see it as descriptive, meaning it tells us what the world is currently like, or as prescriptive, meaning it tells us how the world should be. Descriptions teach us, but they also give us room to innovate. Prescriptions can get us stuck. One place this tension shows up is in language.

In one chapter of The Utopia of Rules: On Technology, Stupidity, and the Secret Joys of Bureaucracy, David Graeber describes his experience of learning Malagasy, the national language of Madagascar. While the language’s writing system came about in the fifteenth century, it wasn’t until the early nineteenth century that missionaries documented the rules of Malagasy grammar for the purpose of translating scripture.

Of course, the “rules” of Malagasy the missionaries recorded weren’t rules at all. They were reflections of how people spoke at that point in time, as far as outside observers could tell. Languages don’t usually come into existence when someone invents the rules for them. Instead, languages evolve and change over time as speakers make modifications or respond to new needs.

However, those early nineteenth-century records remained in place as the supposed “official” version of Malagasy. Children learned the old form of grammar in school, even as they spoke a somewhat different version of the language at home. For Graeber, learning to speak the version of Malagasy people actually understood in conversation was a challenge. Native speakers he hired would instruct him on the nineteenth-century grammatical principles, then turn and speak to each other in a whole other fashion.

When asked why they couldn’t teach him the version of the language they spoke, Graeber’s Malagasy teachers responded that they were just using slang. Asked why no one seemed to speak the official version, they said people were too lazy. Graeber writes, “Clearly the problem was that the entire population had failed to memorize their lessons properly. But what they were actually denying was the legitimacy of collective creativity, the free play of the system. ” While the official rules stayed the same over the decades, the language itself kept evolving. People assumed the fault of not speaking “proper” Malagasy lay with them, not with the outdated dictionary and grammar. They confused a description for a prescription. He writes:

It never seems to occur to anyone—until you point it out—that had the missionaries came and written their books two hundred years later, current usages would be considered the correct ones, and anyone speaking as they had two hundred years ago would themselves be assumed to be in error.

Graeber sees the same phenomenon playing out in other languages for which grammars and dictionaries only came into existence a century or two ago. Often, such languages were mostly spoken and, like Malagasy, no one made formal records until the need arose for people from elsewhere to make translations. Instead of treating those records as descriptive and outdated, those teaching the language treat them as prescriptive—despite knowing they’re not practical for everyday use.

***

## Why don’t people talk “proper”?

So why can’t people just speak a language per the official rules? If someone has gone to all the effort of identifying and recording the rules and people received instruction on them in school, why not follow them? Why keep changing things up?

If languages didn’t evolve, it would make life a lot easier for historians looking at texts from the past. It would also simplify matters for people learning the language, for those coming from different areas, and even for speakers across generations. Yet all languages change all the time.

Graeber suggests the reason for this is because people like to play. We find it dull to speak according to the official rules of our language. We seek out novelty in our everyday lives and do whatever it takes to avoid boredom. Even if each person only plays a little bit once in a while, the results compound. Graeber explains that “this playing around will have cumulative effects.”

Languages still need conventions so people can understand each other. The higher the similarity between the versions of a language different people speak, the more they can communicate. At the same time, they cannot remain rigid. Trying to follow an unyielding set of strict rules will inevitably curtail the usefulness of a language and prevent it from developing in interesting and necessary ways. Languages need a balance: enough guidance to help everyone understand each other and provide an entry point for learners, and enough flexibility to keep updating the rules as actual usage changes.

As a result, languages call into question our idea of freedom: “It’s worth thinking about language for a moment, because one thing it reveals, probably better than any other example, is that there is a basic paradox in our very idea of freedom. On the one hand, rules are by their nature constraining. Speech codes, rules of etiquette, and grammatical rules, all have the effect of limiting what we can and cannot say. ” On the other hand, no rules whatsoever mean no one can understand each other.

Languages need frameworks, but no amount of grammar classes or official dictionaries will prevent people from playing and having fun with their speech.

***

## The dictionary is not the language

“The map is not the territory” means that any representation of reality has to be a simplification that may contain errors, become outdated, or reflect biases. Maps remove details that aren’t necessary for their intended use. Representations of complex systems may show expected behavior or ideal behavior. For example, the London Underground map doesn’t reflect the distances between stations because this information isn’t important to most commuters. If a map represented its territory without reducing anything, it would be identical to the territory and therefore would be useless. In fact, the simplest maps can be the most useful because they’re the easiest to understand and remember.

Sometimes maps are descriptive, and sometimes they’re prescriptive; often they’re a bit of both. We run into problems when we confuse one type for another and try to navigate an idealized territory or make the real territory fit an idealized image.

A language’s grammar and dictionary are a sort of map. They take a complex system—a language spoken by what could be tens of millions of people—and aim to represent it with something which is, by comparison, simple. The official rules are not the language itself, but they provide guidance for navigating it. Much like a map of a city needs periodic updates as parts are torn down, built up, renamed, destroyed, added, and so on, the official rules need updating as the language changes. Trying to learn Malagasy using grammar rules written two hundred years ago is like trying to navigate Antananarivo using a street map made two hundred years ago.

A map of a complex system, like a language, is meant to help us find our way by giving us a sense of how things looked at one point in time—it’s usually descriptive. It doesn’t necessarily tell us how that system should look, and we may run into problems if we try to make it conform to the map, ignoring the system’s own adaptive properties. Even if the cartographer never intended this, we can end up treating a map as a prescription. We try to make reality conform to the map. This is what occurs with languages. Graeber calls this the “grammar-book effect”:

People do not invent languages by writing grammars, they write grammars—at least, the first grammars to be written for any given language—by observing the tacit, largely unconscious rules that people seem to be employing when they speak. Yet once a book exists, and especially once it is employed in schoolrooms, people feel that the rules are not just descriptions of how people do talk, but prescriptions for how they should talk.

As we’ve seen, one reason the map is not the territory with language is because people feel compelled to play and experiment. When we encounter representations of systems involving people, we should keep in mind that while we may need rules for the sake of working together and understanding each other, we’re always pushing up against and reshaping those rules. We find it boring to follow a rigid prescription.

For instance, imagine some of the documents you might receive upon starting a role at a new company. Process documents showing step by step how to do the main tasks you’ll be expected to perform. But when the person you’re replacing shows you how to do those same tasks, you notice they don’t follow the listed steps at all. When you ask why, they explain that the process documents were written before they started actually carrying out those tasks, meaning they discovered more efficient ways afterward.

Why keep the process documents, then? Because for someone filling in or starting out, it might make sense to follow them. It’s the most defensible option. Once you truly know the territory and won’t change something without considering why it was there in the first place, you can play with the rules. Those documents might be useful as a description, but they’re unlikely to remain a prescription for long.

The same is true for laws. Sometimes aspects of them are just descriptive of how things are at one point in time, but we end up having to keep following them to the letter because they haven’t been updated. A law might have been written at a time when documents needed sending by letter, meaning certain delays for shipping. Now they can be sent by email. If the law hasn’t been updated, those delay allowances turn from descriptions into prescriptions. Or a law might reflect what people were permitted to do at the time, but now we assume people should have the right to do that thing even if we have new evidence it’s not the best idea. We are less likely to change laws if we persist in viewing them as prescriptive.

***

## Conclusion

Descriptions of reality are practical for helping us navigate it, while also giving us room to change things. Prescriptions are helpful for giving us ways of understanding each other and providing enough structure for shared conventions, but they can also become outdated or end up limiting flexibility. When you encounter a representation of something, it’s useful to consider which parts are descriptive and which parts are prescriptive. Remember that both prescriptions and descriptions can and should change over time.

***

The FS team were saddened to hear of David Graeber’s passing, shortly after we completed this article. We hope his books will continue to inspire and educate new readers for many years to come.

## The Value of Play As a Driver of Innovation

Innovation does not always have to be the result of serious study and agonizing progress. As Steven Johnson so eloquently argues in Wonderland: How Play Made the Modern World, many of the activities and endeavors we have undertaken for pleasure have fueled an exceptional amount of innovation and discovery.

The story of play, of how it fits into the human experience, can teach us how to embrace the possibilities that can come of being frivolous. Initially, play might seem like an indulgence, but it can lead to some amazingly consequential developments. As Johnson writes:

History is mostly told as a long fight for the necessities, not the luxuries: the fight for freedom, equality, safety, self-governance. Yet the history of delight matters, too, because so many of these seemingly trivial discoveries ended up triggering changes in the realm of Serious History.

## Play and Technological Innovation

The desire to both amuse and be amused can lead to the development of technology that has wide-ranging applications.

Johnson traces a direct line between devices described in The Book of Ingenious Devices, by three brothers known as the Banu Musa in Baghdad in 760 CE, and the programmable software that drives our computer-based culture. Play is the connection that links the inventions from ancient pictures of self-playing instruments to the relatively recent development of the internet.

Some of the devices described in the book were programmable in a very rudimentary sense. And it was this idea that contained the seeds of the future. “Conceptually, this was a massive leap forward: machines designed specifically to be open-ended in their functionality, machines controlled by code and not just by mechanics.”

These machines were designed to entertain, but for this entertainment to come alive, some significant technological advancement needed to happen. We had to develop the working parts, the engineering know-how, the language to create machines that could move on their own, and a whole host of other innovations. Johnson traces “how long the idea of a programmable machine was kept in circulation by the propulsive force of delight” until the skills and technology developed gave us such things as the typewriter, the frequency hopping technology used on navy ships, and Bitcoin.

This power of play to inspire technology that does more than entertain reminds us that there is no specific prescription for innovation. New ideas can come from a chain of thoughts and circumstances that are not obvious in terms of what they produce. Take the story of Charles Babbage, considered one of the fathers of modern computers. His mother took him to a Mechanical Museum, a place to be entertained by artistic, whimsical devices. He was taken up to the attic to see rare specimens, the most captivating of which was a mechanical dancer.

The encounter in [the] attic stokes an obsession in Babbage, a fascination with mechanical devices that convincingly emulate the subtleties of human behavior. He earns degrees in mathematics and astronomy as a young scholar, but maintains his interest in machines by studying the new factory systems that are sprouting across England’s industrial north. Almost thirty years after his visit to [the Mechanical Museum], he publishes a seminal analysis of industrial technology, On the Economy of Machinery and Manufactures, a work that would go on to play a pivotal role in Marx’s Das Kapital two decades later. Around the same time, Babbage begins sketching plans for a calculating machine he calls the Difference Engine, an invention that will eventually lead him to the Analytical Engine several years later, now considered to be the first programmable computer ever imagined.

“Because play is often about breaking rules and experimenting with new conventions,” Johnson explains, “it turns out to be the seedbed for many innovations that ultimately develop into much sturdier and more significant forms.”

For most of us, play is a special time away from the ordinary tasks we undertake every day. It can open us up to possibilities because it requires an atypical engagement with our surroundings. Sometimes, this openness provides a space for innovation.

## Play and Social Innovation

Johnson also demonstrates how play led to social innovation. Certain types of recreation, like attending theater performances, seeing exhibits of the weird and wonderful, or visiting amusement parks, are play experiences that we partake in as a group. When we started doing this, it was revolutionary because those groups were made up of equals. The usual social hierarchies were temporarily suspended, as all audience members were there to have the same experience of entertainment, diversion, and wonder. It was equally thrilling for rich and poor, women and men.

This shared play experience set up new possibilities for social interaction. The ability to come together in a leisure environment with no particular agenda other than to enjoy it unleashed collaboration. “Escaping your lawful calling — and your official rank and status in society — not only created a new kind of leisure, it also created new ideas, ideas that couldn’t emerge in the more stratified gathering places of commerce or religion or domestic life.”

Take, for example, the development of the bar. “The birth of the drinking house also marked the origins of a new kind of space: a structure designed explicitly for the casual pleasures of leisure time. The tavern was not a space of work, or worship; it was not a home. It existed somewhere else on the grid of social possibility, a place you went to just for the fun of it.” Johnson argues that these spaces, these places we went to just for fun, gave birth to movements of democracy, of equality. In an interesting example, he describes how taverns were directly responsible for the colonists’ success in the American Revolution.

The pursuit of play gave us the ability to organize ourselves differently, to make connections with people we would not normally have interacted with. Not that this ability necessarily transformed each individual, but it changed our ideas of what was proper and right, gradually allowing the concept of the common space to become critical to how we design our cities and organize our societies.

## A Final Musing on Play

Why is play so powerful? Johnson explains that “humans — and other organisms — evolved neural mechanisms that promote learning when they have experiences that confound their expectations. When the world surprises us with something, our brains are wired to pay attention.”

And the whole point of play is to be surprised. The unknown factor is part of what entertains us. Play is a gateway to possibility. Whether it’s through new music, a new spectacle, or a new round of a board game, play can get our senses tingling as we wonder what we will experience in the coming minutes. This is why Einstein called play the essential feature of productive thought. Seneca was also a fan of combinatorial play.

Play can transport us out of the realm of “things we already know” (the route to work, the importance of saving money and of brushing our teeth) and into the realm of “things we haven’t yet figured out.” And it is here that innovation happens.

It is in this sense of the concept that Johnson suggests that play is a gateway into the future. “So many of the wonderlands of history offered a glimpse of future developments because those were the spaces where the new found its way into everyday life: first as an escape from our ‘lawful calling and affairs’ and then as a key element in those affairs.”

Exploring play is about understanding that innovation can happen when we are driven by enjoyment. Innovation doesn’t always have to be a serious pursuit. So if you are in a creative funk, fresh out of good ideas, try playing.