I first heard about the massacre at Sandy Hook Elementary School on Twitter. In the flood of reactions, one stood out to me. “The children were killed execution style,” tweeted one woman.

“People are horrible.”

Are people horrible?

It’s a question we as a culture pose after every war and atrocity; it’s a question we as individuals ask ourselves after we experience personal betrayals or cruelty. The question certainly crossed my mind as the details of the massacre emerged; my immediate reaction was to think about the violence I’ve experienced in my life, and to look inside at my own capacity for violence. In the face of such horror, we feel overwhelmed. Optimism about our species seems out of place, perhaps even frivolous and offensive.

But that is exactly why it’s important, in the aftermath, to remind ourselves of human propensities for compassion, empathy, forgiveness, heroism, peacefulness, and altruism.

We can find evidence of human goodness in the event itself—in the actions of teacher Victoria Soto, school psychologist Mary Sherlach, and principal Dawn Hochsprung, who gave their lives in defense of the kids. Several friends have told me that they wept after reading the story of Soto, who died at age 27. I admit that I cried as well. We were crying over its tragedy, of course, but I believe we were also moved to tears by the example of primal human goodness that Soto now represents.

We can also look beyond this one event—to its context, and to what the science reveals about such violence. I like to say that science is essentially counting. That sounds like a cold activity, perhaps, but we humans count because it’s a tool that helps us create an accurate picture of reality. Emotions can be counted, and so can actions. And that natural human propensity for counting helps correct for our “negativity bias”—that is, our tendency to remember threats better than the good things.

Before we make room for counting and logic, we must allow ourselves to feel. To weep and to mourn, and to feel terrible about ourselves and humanity. But then comes the work of understanding what happened, and why, and what events like the one at Sandy Hook Elementary tell us about human nature, and what we can do to cultivate the good and diminish the bad. Here are four reminders that people are not, in fact, horrible—and that we can turn to each other in times of horror and need.

1. Compassion and forgiveness are everywhere.

I haven’t been able to stop thinking about this image, of one child comforting another. This image may be burned into my mind because the boy is just a little younger than my own son. But I am also struck by the maturity of the girl’s compassion. This girl (whose name I haven’t been able to discover) was probably frightened beyond all reason, and so the way she holds the boy seems to me to be an act of heroism.

And if you do an image search for Sandy Hook, you’ll find picture after picture of people holding and comforting each other. We shouldn’t be surprised. There is now a mountain of research showing that compassion and empathy are instinctive, defining human traits, ones that manifest themselves in children from a very early age. As Dacher Kelter writes in “The Compassionate Instinct,” the brain “seems wired up to respond to others’ suffering—indeed, it makes us feel good when we can alleviate that suffering.”

What happened in Sandy Hook is incomprehensibly horrific. But against the act of one mentally ill young man, we have to count the sacrifices of women like Victoria Soto. Let’s remember to count those children and parents who comforted each other. Let’s not forget the first responders—police, paramedics, firemen, doctors, nurses—who rushed to help, not knowing what they would face. Their work is part of an entire infrastructure of compassion, one supported by all of us through our tax dollars.

And we should remember the words of Robbie Parker, the father of one of the children who was killed. He offered comfort and forgiveness to the family of shooter Adam Lanza, saying “I want you to know that our love and support go out to you as well.” We should all take to heart Parker’s hope that the killings “not turn into something that defines us, but something that inspires us to be better, to be more compassionate and more humble people.”

2. Schools are safer than ever.

When I heard about the massacre, my first instinct was to rush to my son’s school. I gave in to that impulse, and I secretly spied on him and his classmates during recess. I didn’t go to him or pull him out of school, because I think that would have created questions and fear. I want school to feel safe for him.

And, in fact, Americans schools are safe. Yes, there has been violence. But believe it or not, school violence has been declining for almost 20 years, and your kids are safer at school than outside of it. According to the National Center for Education Statistics, the number of homicides in American schools fell by half in less than two decades, from a peak of 34 in 1993 to 17 in 2010, the latest figures available—this, despite the fact that enrollment skyrocketed during the same period.

Why? Most criminologists agree it’s not tighter school security or zero-tolerance policies, which more and more school districts are rejecting. As Claudia Anderson, director of Student Support Services for San Francisco Unified, once told me: “For a decade we went through this zero-tolerance era. And quite frankly it didn’t work. It didn’t make one bit of difference.”

That’s why San Francisco and hundreds of other school districts around the country are turning from punitive policies to ones that are designed to foster empathy for victims and to provide mental health support for families. The data are still coming in, but so far these policies seem to have contributed to reducing school violence. Today, parents can send their kids to school confident that they will be safe.

3. Children (and adults) are resilient.

Much of the attention has focused on trauma, and some press coverage has looked to divorce, Asperger’s Syndrome, and video games for explanations of Adam Lanza’s violence.

The trauma is real. And it may well be the case that elements of Lanza’s personal life fed the rampage. But tragedy can feed speculation, which, if unchecked, can lead to scapegoating and stigmatization. What are the facts?

As Christine Carter regularly discusses in her Greater Good blog about raising happy kids, children of troubled families can struggle—but divorce is often a solution to, not a cause of, these troubles. Most school shooters have come from intact homes; quite a few have come from seemingly happy, stable homes, though parental conflict and neglect are huge risk factors. People on the autistic spectrum, such as those with Asperger’s, can be treated and can manage their own difficulties, and autism is not at all linked to shooting rampages. Most kids today play video games without ever physically harming others—and the best evidence we have does not reveal a link between mass shootings and video game play.

It’s critical in the wake of tragedy to not go to the easy answers—and to remind ourselves that divorce does not create homicidal killers, people with Autism should not be viewed as threats, and the data on video games remains inconclusive. If we allow these unsupported explanations to flourish, we risk blaming and marginalizing people who happen to share Lanza’s traits and experiences without actually changing one thing for the better—and we risk making things even worse for people who might need help.

We have good reasons to have faith in ourselves and each other. People are built to survive and rebound from life’s difficulties and tragedies, including divorce, illness, and encounters with violence. In What Doesn’t Kill Us: The New Psychology of Posttraumatic Growth, psychologist Stephen Joseph argues that treatment for trauma must highlight strengths, reframe horrible experience in a more positive way (by, for example, focusing on being a survivor rather than a victim), and taking positive steps in your life.

As childhood trauma expert Dr. David Schonfeld told the New York Daily News, “The one thing to remember is that while these experiences are life-changing and traumatic, it doesn’t mean these kids are damaged for the rest of their lives.”

4. Peace is the rule, not the exception.

“Believe it or not,” writes psychologist Steven Pinker, “violence has declined over long stretches of time, and today we may be living in the most peaceable era in our species’ existence.” His 2011 book The Better Angles of Our Nature assembles an impressive array of evidence for this startling argument.

But again, we shouldn’t be surprised—the evidence has been mounting for decades. “The study of killing by military scientists, historians, and psychologists gives us good reason to feel optimistic about human nature, for it reveals that almost all of us are overwhelmingly reluctant to kill a member of our own species, under just about any circumstance,” writes Lt. Col. Dave Grossman in his Greater Good essay, “Hope on the Battlefield.”

Anthropologist Douglas P. Fry studied violence in hundreds of societies—and found that it is peace, not war and violence, that characterizes most human lives. “Our daily observations may seem to contradict the idea that peacefulness predominates in human affairs, especially when we have become accustomed to Hollywood films and daily newscasts that depict unrelenting violence. In actuality, the vast majority of people on the planet awake on a typical morning and live a violence-free day—and this experience generally continues day after day.”

That’s easy to forget when confronted by horrors like the one at Sandy Hook Elementary School. Of course, peace is never a given. It’s something we have to work for every day, in every interaction with other people. As a result of Sandy Hook, we are now engaged in national discussions about mental health, guns, and education, much of which is shaped by trauma and fear. In that discussion, it’s critical that we follow Robbie Parker’s example—and speak out for the good in people.