About five weeks ago, I noticed the skin of our pet lizard (蜥蜴) was growing dusty. It worried me. I reported the strange surface on the skin of the lizard to my husband and children the next morning. Seconds later, our lizard emerged from its tank with its old skin flowing behind it.

I didn’t think about it much until a morning last week when I knocked my favorite teapot off the table. It burst into hundreds of pieces. As I swept up the mess, I wondered why we had been breaking so many things over the months.

The destruction started three months ago. It was my husband’s birthday. He had just lost his job. The uncertainty was starting to wear on us, so I wanted to do something special.

“Let’s make a cake for Dad!” I cried.

My kids screamed with joy. We baked, iced and sprinkled for most of the day. Candles on the cake! Balloons on the walls! Flowers on the table!

Two hours before my husband came back home from another job interview, my daughter climbed up to grab a glass vase from a high shelf. It fell and crashed beside the cake. Tiny pieces of glass were everywhere. She sobbed loudly as I threw the cake away. My husband had banana pudding for his birthday.

Three days ago, the light in our living room suddenly went out. After several frustrating hours of unsuccessful attempts to fix it, my husband suggested watching the Michael Jordan documentary (纪录片) series The Last Dance.

The poignancy (酸楚) of Jordan retiring from his beloved basketball to play baseball and what had pushed him to make such a tough decision took me by surprise. As I watched him take off his basketball uniform and replace it with a baseball uniform, I saw him leaving behind the layer that no longer served him, just as our lizard had. Neither of them chose the moment that had transformed them. But they had to live with who they were after everything was different. Just like us. I realized that we have to learn to leave the past behind.

Humans do not shed skin (蜕皮) as easily as other animals. The beginning of change is upsetting. The process is tiring. Damage changes us before we are ready. I see our lizard, raw and nearly new.

Jordan said that no matter how it ends, it starts with hope. With our tender, hopeful skin, that is where we begin.

By now you’ve probably heard about the “you’re not special” speech, when English teacher David McCullough told graduating seniors at Wellesley High School: “Do not get the idea you’re anything special, because you’re not.” Mothers and fathers present at the ceremony — and a whole lot of other parents across the Internet — took issue with McCullough’s ego-puncturing words. But lost in the uproar was something we really should be taking to heart: our young people actually have no idea whether they’re particularly talented or accomplished or not. In our eagerness to elevate their self-esteem, we forgot to teach them how to realistically assess their own abilities, a crucial requirement for getting better at anything from math to music to sports. In fact, it’s not just privileged high-school students: we all tend to view ourselves as above average.

Such inflated self-judgments have been found in study after study, and it’s often exactly when we’re least competent at a given task that we rate our performance most generously. In a 2006 study published in the journal Medical Education, for example, medical students who scored the lowest on an essay test were the most charitable in their self-evaluations, while high-scoring students judged themselves much more strictly. Poor students, the authors note, “lack insight” into their own inadequacy. Why should this be? Another study, led by Cornell University psychologist David Dunning, offers an enlightening explanation. People who are incompetent, he writes with coauthor Justin Kruger, suffer from a “dual burden”: they’re not good at what they do, and their very incapability prevents them from recognizing how bad they are.

In Dunning and Kruger’s study, subjects scoring at the bottom of the heap on tests of logic, grammar and humor “extremely overestimated” their talents. What these individuals lacked (in addition to clear logic, proper grammar and a sense of humor) was “metacognitive skill”: the capacity to monitor how well they’re performing. In the absence of that capacity, the subjects arrived at an overly hopeful view of their own abilities. There’s a paradox here, the authors note: “The skills that lead to competence in a particular domain are often the very same skills necessary to evaluate competence in that domain.” In other words, to get better at judging how well we’re doing at an activity, we have to get better at the activity itself.

There are a couple of ways out of this double bind. First, we can learn to make honest comparisons with others. Train yourself to recognize excellence, even when you yourself don’t possess it, and compare what you can do against what truly excellent individuals are able to accomplish. Second, seek out feedback that is frequent, accurate and specific. Find a critic who will tell you not only how poorly you’re doing, but just what it is that you’re doing wrong. As Dunning and Kruger note, success indicates to us that everything went right, but failure is more ambiguous: any number of things could have gone wrong. Use this external feedback to figure out exactly where and when you screwed up.

If we adopt these strategies — and most importantly, teach them to our children — they won’t need parents, or a commencement (毕业典礼) speaker, to tell them that they’re special. They’ll already know that they are, or have a plan to get that way.

I was in the middle of the Amazon with my wife, who was there as a medical researcher. We flew on a small plane to a faraway village. We did not speak the local language, did not know the customs, and more often than not, did not entirely recognize the food. We could not have felt more foreign.

We were raised on books and computers, highways and cell phones, but now we were living in a village without running water or electricity It was easy for us to go to sleep at the end of the day feeling a little misunderstood.

Then one perfect Amazonian evening, with monkeys calling from beyond the village green, we played soccer. I am not good at soccer, but that evening it was wonderful. Everyone knew the rules. We all spoke the same language of passes and shots. We understood one another perfectly. As darkness came over the field and the match ended, the goal keeper, Juan, walked over to me and said in a matter-of-fact way, “In your home, do you have a moon too?” I was surprised.

After I explained to Juan that yes, we did have a moon and yes, it was very similar to his, I felt a sort of awe at the possibilities that existed in his world. In Juan’s world, each village could have its own moon. In Juan’s world, the unknown and undiscovered was vast and marvelous. Anything was possible.

In our society, we know that Earth has only one moon. We have looked at our planet from every angle and found all of the wildest things left to find. I can, from my computer at home, pull up satellite images of Juan’s village. There are no more continents and no more moons to search for, little left to discover. At least it seems that way.

Yet, as I thought about Juan’s question, I was not sure how much more we could really rule out. I am, in part, an ant biologist, so my thoughts turned to what we know about insect life and I knew that much in the world of insects remains unknown. How much, though? How ignorant are we? The question of what we know and do not know constantly bothered me.

I began collecting newspaper articles about new species, new monkey, new spider…, and on and on they appear. My drawer quickly filled. I began a second drawer for more general discoveries: new cave system discovered with dozens of nameless species, four hundred species of bacteria found in the human stomach. The second drawer began to fill and as it did I wondered whether there were bigger discoveries out there, not just species, but life that depends on things thought to be useless, life even without DNA. I started a third drawer for these big discoveries. It fills more slowly, but all the same, it fills.

In looking into the stories of biological discovery, I also began to find something else, a collection of scientists, usually brilliant occasionally half-mad, who made the discoveries. Those scientists very often see the same things that other scientists see, but they pay more attention to them, and they focus on them to the point of exhaustion, and at the risk of the ridicule of their peers. In looking for the stories of discovery, I found the stories of these people and how their lives changed our view of the world.

We are repeatedly willing to imagine we have found most of what is left to discover. We used to think that insects were the smallest organisms, and that nothing lived deeper than six hundred meters. Yet, when something new turns up, more often than not, we do not even know its name.