The Error of Being Earnest
Your Director has this week, a little mischievously, been asking students what 1 + 1 equals. The answer usually arrives before the question has had time to finish:
Two.
Not, probably two, or two in most circumstances, or even it depends. Just two. Certain, immediate, unquestionable. If there is one thing we feel we know beyond all doubt, it is that 1 + 1 = 2. Indeed, it is perhaps the first incontrovertible truth most of us ever learn. Before we know much about the world, we know that 1 + 1 = 2. It feels less like knowledge than certainty itself.
And you, dear reader, will know how your Director feels about certainty.
Enter, Harvard psychologist Ellen Langer. She has spent much of her career arguing that certainty is often less a sign of wisdom than of what she calls mindlessness: the tendency to stop paying attention because we think we already know. Her provocative claim that 1 + 1 does not always equal 2 is not an assault on mathematics. Rather, it is a reminder that context matters. Add one raindrop to another and you do not have two raindrops; you have a larger raindrop. Add your pile of laundry to that of your teenage offspring and you have one unnecessarily large pile of laundry, not two. The moment we move beyond a certain kind of classroom exercise, certainty starts to look rather less certain.
The trouble with certainty is not simply that it is sometimes mistaken. The greater danger is that it leaves no room for discovery. If I already know, why would I look more closely? If I am already right, why would I change my mind?
Much of education, despite what students sometimes would prefer, is not the accumulation of certainties but the gradual replacement of poorer ideas with better ones. To learn is, in a sense, to become aware of how often one has been wrong.
Yet being wrong has an unfortunate public relations problem. Somewhere along the way, we began to treat mistakes as evidence of inadequacy rather than evidence of growth. The red mark on the page, the incorrect answer, the unsuccessful attempt, the failed experiment or whatever, became things to be avoided rather than things from which understanding emerges.
This has always struck your Director as very odd especially when we consider how virtually every form of human progress actually occurs. Scientific discoveries are built upon hypotheses that turn out to be false. Writers produce drafts they later discard. Athletes spend countless hours getting things wrong before they get them right. Even toddlers, mercifully unconcerned with their reputations, learn to walk largely by falling over.
As a young Director I remember coming home from a long day at the chalkface and being greeted by my wife at the door. She was flushed with excitement and could not wait to bring me to its source. As I was gently dragged along the hall towards the drawing room, I had time to consider some possible reasons for her excitations. Had we won the Lottery? (difficult as we never participated), had my novel been optioned by a Hollywood studio? (difficult as I hadn’t written one), had our humble home been selected for a special episode of DIY SOS (not so difficult to imagine). No, it was none of these things. Upon arrival at said drawing room I was greeted with the sight of our youngest child teetering upright whilst being supported by one of his older siblings.
My wife then proceeded to sit at the far end of the room and called our youngest forwards. What followed would have looked, to an external observer, like a catalogue of failure. A few uncertain steps, a collapse, a recovery, another collapse, another recovery. Yet nobody in the room interpreted those events in that way. Each fall was greeted not with disappointment but encouragement, because every stumble was evidence that learning was taking place.
His first solo walk.
And we never stop falling down. The illusion of adulthood is that we eventually graduate from error, but the reality is simply that our mistakes become more sophisticated. We are all, if we are doing it right, perpetual toddlers in the eyes of a vast and complicated universe. Somewhere between infancy and adulthood, however, our attitude towards falling over changes and the very experiences that once attracted encouragement begin to attract embarrassment.
Failure is often imagined as the opposite of success. In reality, it is usually the opposite of certainty. Failure occurs when reality refuses to conform to our expectations. We attempt something, the world answers back, and we discover that things are not quite as we thought. The experience may be uncomfortable, but it is also profoundly informative. Failure is reality’s way of participating in the conversation.
Unsurprisingly, he ancient Greeks understood this well. Socrates, who as you know, spent much of his life irritating fellow Athenians by asking awkward questions, claimed that his wisdom consisted largely in knowing that he did not know. This was not false modesty. Rather, he recognised that awareness of one’s ignorance is often the beginning of understanding.
I am minded of the Koan of the scholar who visits a Zen master to find out more about Zen:
As the professor spoke, expounding his views and displaying his considerable knowledge, the master quietly poured tea. The cup filled, then overflowed, spilling onto the table. The professor finally exclaimed, “Stop! The cup is full!”
“Exactly,” replied the master. “Like this cup, you are full of your own opinions and certainties. How can I show you Zen unless you first empty your cup?”
Learning, it seems, requires space for something new to enter. Unfortunately, many of us arrive at education rather like the professor in the story: teacup full, saucer overflowing, and wondering why nobody can fit any more knowledge in.
And of course, it is also true that the person who believes they already possess the truth has little incentive to seek it. The person who suspects they might be mistaken remains open to discovery.
The philosopher Karl Popper built an entire philosophy of science upon a similar insight. Knowledge advances, he argued, not because we prove ourselves right but because we discover where we are wrong. He famously illustrated this with swans: you might have only ever observed white swans, millions of them maybe, but that does not prove the truth of the statement all swans are white. It only takes the observation of a single black swan to prove the statement false. A scientific theory earns its reputation not by being unquestionably true, but by surviving repeated attempts to show that it is false. Progress emerges from error corrected, not certainty defended.
The thing is that when our scientists chums come up with a way of understanding the world that is successful and works, people tend to take it for granted and think that this is the way the world is. It invariably isn’t.
Take our old friend Isaac Newton sitting under his apple tree, reflecting on the nature of gravity. and ending up producing a description of the universe so successful that it dominated scientific thinking for more than two centuries. Newtton’s universe was orderly, predictable, and reassuringly sensible. Space was absolute. Time was absolute. Events occurred in a fixed cosmic framework that existed independently of those observing them.
And Newton was right. Or at least, right enough to predict the motions of planets, explain the tides, launch cannonballs, and eventually help us reach the Moon.
But of course, reality had not quite finished revealing itself.
As the nineteenth century progressed, the work of James Clerk Maxwell suggested that light behaved in ways Newton’s framework struggled fully to accommodate. Then, in the early twentieth century, Albert Einstein proposed something extraordinary: space and time were not fixed after all. They were woven together into a single fabric and could stretch, contract, and bend. Two observers moving at different speeds might disagree about the passage of time itself.
This was not merely surprising. It was absurd. At least, it sounded absurd. Yet experiment after experiment suggested Einstein was correct.
Then matters became even stranger. Just as physicists were beginning to adjust to relativity, quantum theory arrived to inform them that, at the smallest scales, particles behaved less like tiny billiard balls and more like probabilities. The universe, it seemed, was under no obligation to conform to common sense.
The pertinent thing here is that ‘Science’ did not collapse because Newton turned out to be incomplete. Nor did physicists gather together and lament that they had been getting things wrong for two hundred years. Instead, they probably celebrated. Each apparent failure was really a discovery. Every time reality contradicted an assumption, humanity learned something new about the world.
Karl Popper argued that this is precisely how knowledge advances. We learn not by proving ourselves correct once and for all, but by discovering the limits of our current understanding.
Science progresses because it allows itself to be wrong.
Indeed, one might argue that certainty, not failure, is the real enemy of discovery. Had physicists decided that Newton had explained everything worth explaining, relativity would never have emerged. Had Einstein regarded his own theories as beyond question, quantum mechanics might never have developed. Progress depends upon the willingness to say; This works remarkably well, but perhaps there is more to the story.
The history of science is therefore not a tale of geniuses getting everything right. It is the story of intelligent, curious people becoming progressively less wrong.
Literature offers much the same lesson. Tragedy, after all, rarely begins with a character admitting uncertainty. It usually begins with someone convinced they are right. Oedipus is certain he understands his situation. King Lear is certain he can measure love. Macbeth is certain he understands the witches’ prophecies. Their downfall does not arise from a lack of confidence but from an excess of it. The Greeks even had a word for this dangerous certainty: hubris.
Recent addition to the Column, Sherlock Holmes, that great champion of deduction, also recognised the danger of premature certainty. It is a capital mistake, he observes, to theorise before one has data. Yet how often do we do precisely that?
Many and often is the time that your Director will watch students construct their explanations first and then spend their time looking for evidence that confirms them.
The poet John Keats admired what he called negative capability: what he described as the ability to remain in uncertainties, mysteries, doubts, without any irritable reaching after fact and reason. Keats understood that some forms of insight require us to tolerate uncertainty for longer than feels comfortable. The rush to certainty can close doors that patience might have left open.
Indeed, one begins to wonder whether certainty and success are not opposites but uneasy companions. Success often belongs to those willing to revise, adapt, experiment, and occasionally abandon their most cherished assumptions. The entrepreneur who never changes course, the scientist who never questions a theory, the writer who never edits a draft, and the student who never admits confusion are unlikely to get very far.
This is not, of course, an argument for celebrating failure for its own sake. Nobody sets out hoping to fail an examination, lose a match, or drive a business into bankruptcy. Failure can be painful, discouraging, and sometimes costly. But neither should we imagine that a life without failure would be desirable. A life without failure would almost certainly be a life without challenge, without risk, and ultimately without growth.
The real danger lies not in being wrong but in becoming so attached to being right that we stop learning. Certainty can become a kind of intellectual comfort blanket. It shields us from embarrassment, but it also shields us from reality.
Perhaps that is why schools matter so much. At their best, they are places where young people can discover that being wrong is not a source of shame but an inevitable consequence of attempting something difficult. Every incorrect answer, every abandoned draft, every failed experiment, every missed shot, every awkward first attempt at a musical instrument is part of a conversation between expectation and reality.
And reality, as it turns out, is a remarkably patient teacher.
Until next time: Happy Reading / Failing!
Director’s Detritus #47
When Bertrand Russell and Alfred North Whitehead set out to prove all mathematical truths from scratch in their really big Principia Mathematica (1910–1913), they didn’t take 1 + 1 = 2 for granted. It took them until page 379 of Volume I to finally reach the proof. They accompanied it with the delightfully dry footnote: The above proposition is occasionally useful.