Perfect Information | The Open School

Perfect Information To find their own way in life, children must be told the whole story

by Tay Arrow, Open School staff
September 12, 2019

When I was a child, my family spent our summers in a pair of cabins in a forest on Mount Desert Island in Maine. Most of the time, I played in the woods, inventing tiny societies in the thick moss, or picking blueberries, or climbing on rocks. My mother would go for walks on the carriage roads, and write in her journal. And, for his part of our relaxing vacation, my father would do math.

My father is a mathematician. I mean that in the sense that he studied mathematics at MIT, and obtained a PhD in it, and before he retired that was his professional title — mathematician. But also in the sense that he was born to be a mathematician, and nothing else. I can not picture a single part of him existing without being rooted deeply in mathematics. It is in every fiber of his being, and when he looks at anything in the world, the first thing he sees is the mathematics of that thing. If you are painting, he sees the formulations of pigments, concentration percentages, the parabola of the paintbrush and the calculus of your revisions. If you are humming quietly to yourself, he hears the calculations of rhythm and tone. When you tell him, “I’ll meet you at the cafe on Dunster at 7,” he mentally plots that point in space and time on a multi-axis grid. In this way, he turns everything he does into a mathematical exercise, and gives his talent free reign to grow into every corner of his world. 

At times, he and I lose the thread of the translation. It can be frustrating — I see a different world from him. Mine is made of colors and words, linguistic theory, cadmium pigment from the desert, a curiosity about how one thing might be transformed into another thing. I write poetry, I paint. But I understand a little math, and sometimes, in Maine, we would talk about it.

My father loves to do math, but in occasional moments of debauch, he also loves to play solitaire. Not just the “usual” kind, but many different kinds. This was a kind of indulgent vacation activity, requiring lots of space and lots of time. For a long time, his favorite was a variety called Cloverleaf. In Cloverleaf, every card in the deck is placed, face up, in small stacks of three, except for the last four cards, which are placed face up in two stacks of two. Cards can only be moved, one at a time, on to an opposite color card of an adjacent number, and the maximum stack height is three. It can be frustrating, because you can’t backtrack. Once, I asked him why he liked it so much. 

“Well,” he told me, “because it’s a perfect information game.”

“What’s that?”

“You can see all the possible moves. Nothing is hidden. Theoretically, you could play the entire game in your head, without ever moving a single card.”

Sometimes I would watch him do just that. He would lay out the cards, examine them very intensely for a while, sigh, and sweep them up to deal again. 

“Why didn’t you play any moves?” I would ask.

“It wasn’t possible to win. It’s not always possible to win. After a while, you come across a block there’s no way around.”

Still, his inability to win was not a source of discouragement for him. He would deal another hand, playing a number of completely unwinnable games. He just enjoyed the mental exercise, even though it didn’t necessarily have a “point.” Chess, it turns out, is also a perfect information game — even though there is the unpredictable factor of your opponent’s decision making process, there are no secrets; no walls blocking your view of a portion of the board; no rules that will only be revealed later or made up on the spot. In his book “Two Person Game Theory,” mathematical psychologist Anatol Rapoport says, of games, 

If the best strategy available to Black and White respectively were ever found, the outcome of every game of Chess would be known in advance […] Poker, on the other hand, is not a game of perfect information, because no player knows with certainty what cards are held by the others. Formally speaking, no player knows the outcome of a move made by a fictitious player called Chance, who at the beginning of each deal chooses among all the possible arrangements of the deck.

Let’s not confuse the unpredictability of the future with a deck of cards that we have already shuffled, set in order, and are playing from: the randomness of the deck is in the past, and when we begin to deal the cards, we’re saying that we accept the completion of this past action. In a perfect information game, you know what you actually have, and you can knowingly make the best decision possible to meet your goals. This correlates to the difference between self directed education, which is a perfect information game, and set curriculum education, which functions like a game of chance. 

When I think of what kind of life I want to live, and what kind of things I want to do, I always come back to the idea of the perfect information game. I want real autonomy, even if that means that sometimes I make bad decisions — I want to keep being able to make decisions for myself anyway, and I want the freedom to try again until I figure out what kind of strategy will work. I want the ability to look at a game I can’t win in the “usual” way and decide to play it through to the end with my own, new goal, regardless of how unimportant that goal might seem to others.

When I look back on my childhood, I feel very clear that top-down, instruction based education was not such an environment. I made almost no decisions, and if I did, they had no real substance. As a child, most of the tapestry of life was hidden from me, systematically and deliberately. I was constantly reminded that I was preparing for the “real world” — and that, implicitly, I was not at that time a part of anything real. I did not get to set any goals, except within aggressively structured frameworks made by some invisible person who decided what my curriculum options could be: did I want to read eleven books about cats or eleven books about dogs? (Not really allowed: eleven thousand books about dragons, read in a tree). The assumption was that, if left to my own devices, I would never do anything of value, or ever be enough. 

I was constantly reminded that I was preparing for the “real world” — and that, implicitly, I was not at that time a part of anything real. Click To Tweet

In addition, knowing too much about some particular subject would somehow make me become damaged. Often we are most aware when this takes the form of censorship, such as protecting kids from swearing, or nudity, or depictions of violence. But even more than that, young children in controlled “educational” environments are denied access to things like: post-structuralist literary theory, particle physics, the history of the discovery of Pluto, unexpurgated Classical Athenian theater, endangered indigenous languages, 17th Century cabinetry craftsmanship, and molecular gastronomy. There is neither depth of exploration, nor is there breadth. And yet it is among these kinds of things that children will find what I (a language person) think of as their “language,” which, for my father, is mathematics. Where one person looks at the stars and sees their chemistry, another will see their poetry, and another will see the color of their light. In this way, once we have our “language”, or our “mathematics,” the world becomes a customized textbook that focuses on our favorite subject.

When I watch my children playing, I see them taking symbols and themes, and adapting them to the maps they have begun to build in their internal worlds. They are searching for the thing that causes life to resonate, and come together as a cohesive whole. If you are not looking closely, what they are doing may seem rudimentary and silly. They might be running around with a stick, or dressing up as a villain, or scribbling on a piece of paper, or playing video games. But, in fact, this is the beginning of life, and of the perfect information game we call “having a self.” They are picking up pieces of the world and turning them into their own dreams and experiments. These dreams and experiments are a kind of adventure that leads them to the kind of self understanding and self acceptance they will need to survive and thrive. They use all the information at their disposal to try to understand the world so they can build whatever kind of life it is they have in mind. Maybe many of their experiments will fail — I know that many of mine have failed, even when my information was good. But soon the scribble becomes a composition, the costume becomes an elaborate gown sewn by hand, and the stick is cut into an intricately carved chair. 

As adults, we can become impatient, and try to control the narrative. We want to “make sure” of the outcome of the game: the carved chair, the composition, the gown. But when we refuse to give children access to the full scope of possibility, we are creating a game of imperfect information. From this, we get disengagement, which comes from a sense of powerlessness. We get random, lackluster outcomes, where kids end up following paths that didn’t really speak to them and that they often regret later in life. When we control kids, and don’t let them make decisions, what they do doesn’t actually matter. We know it — and in fact this is why many people chose this track specifically — but, more importantly, children know it. And they know there is absolutely nothing to be gained by “trying hard” in such an environment, other than exhaustion, and despair. 

In our obsession with making sure kids get exposed to the “right” things, we are demanding that they accept the erasure of the real world. And we all have our different visions of this “rightness” — a specific religion, or, a specific diet, or, only stories written in a certain tone, or, no toys we think are tacky, or, no subject matter we think is frivolous or weird. Usually our sense of what that most essential thing is, is governed in some way by whatever has resonated for us: language, or mathematics, or song, or color, or chemistry, or structure. And usually it is also informed by what we have learned to fear and struggle with: language, or mathematics, or song, or color, or chemistry, or structure. We need to recognise these biases as our own individual battlegrounds and not compound them in our children. To some extent, we see this, but our solution is misguided. In our alleged best efforts to avoid bias, we attempt to “standardize” the “rightness” and come to a massively multiplayer consensus on what is right for children. And with every new effort to make everyone happy all the time and force people to learn to be “good enough”, the scope of our national curriculum tightens like a noose. 

Children who are given the full story are able to make real, informed decisions. If we allow them to both accelerate and ruminate at their own pace, they have the space to find the one thing that connects them to everything around them, the way that my father connects to everything through mathematics. And it is in this space where our consciousness is consumed by that which speaks to us most deeply that genius is born. 

It is part of our educational ethos to offer children at The Open School a perfect information game. We have the time, and the space, to let them explore the breadth and choose the depth. When children are presented with set curriculum, they are simply made busy with a series of compliance tasks. In our school, they can manufacture their own curriculum — or, as I like to call it, their own life. And, in manufacturing their life, they have the chance to find that thing that a photographer might call a lens, that I call a language, and that my father sees as a field of numbers flickering across the world.