IT often befalls presidents to be most criticized in office for what later turn out to have been their particular strengths. Disparaged at the time as simplemindedness, timidity, and slickness, Ronald Reagan’s firmness, George H. W. Bush’s caution, and Bill Clinton’s adaptability look in hindsight like features, not bugs. (Unfortunately, George W. Bush’s bugs still look like bugs.) President Obama catches flak for his supposed underreaction to crises in the Middle East, Ukraine, and elsewhere. Instead of leading, the professorial president lectures the American public not to be so darned worried. “If you watch the nightly news, it feels like the world is falling apart,” he said last August. “I promise you things are much less dangerous now than they were 20 years ago, 25 years ago, or 30 years ago. This is not something that is comparable to the challenges we faced during the Cold War.” Blame social media, he tells us, for shoving so much upsetting stuff in our faces.

Naturally, Obama’s pontifications draw protests. “I strongly disagree with the president’s assertion last night that America is safer,” said Senator John McCain. “By no objective measurement is America safer.” Danger abounds! In 2012, General Martin Dempsey, the chairman of the Joint Chiefs of Staff, pronounced the world “more dangerous than it has ever been.” That was before the Islamic State, or ISIS, took over swaths of Iraq. Senator Lindsey Graham has warned that failure to defeat ISIS “will open the gates of hell to spill out on the world.” Obama appears to have his doubts: a few months after Chuck Hagel, then the defense secretary, pronounced ISIS an “imminent” threat, not just to the United States but “to every stabilized country on Earth,” Obama sacked him.

The American people deserve to hear complex, multifaceted debates about any number of complex, multifaceted matters. This is not one of them. Obama is simply right. The alarmists are simply wrong. America is safer than it has ever been and very likely safer than any country has ever been, a fact that politicians and the public are curiously reluctant to believe.

Danger is a broad category. In principle, it includes everything from workplace accidents and natural disasters to infectious diseases and pollution. In pretty much all of those categories, we’re doing well, although we have much work to do. For present purposes, however, let’s limit ourselves to threats in the usual political sense: malevolent violence against Americans. The major menaces here would be warfare, crime, and terrorism.

Historically, warfare has been the biggest violent killer of humans. According to Steven Pinker, the author of The Better Angels of Our Nature: Why Violence Has Declined, today is probably the most peaceful time in human history. By the numbers, he writes, “the world was a far more dangerous place” in the 1960s, ’70s, and ’80s. According to the Uppsala Conflict Data Program, armed conflicts have declined by almost 40 percent since right after the end of the Cold War. “Today,” write Micah Zenko and Michael A. Cohen in Foreign Affairs, “wars tend to be low-intensity conflicts that, on average, kill about 90 percent fewer people than did violent struggles in the 1950s.” War between major nation-states has dwindled to the verge of extinction. In the context of human evolution, this is an astounding development.

Of course, the world remains turbulent, but most of today’s military conflict, as in Syria right now, takes the form of civil war rather than war between nations, and implicates American interests but not American lives (unless America enters the fighting). The United States faces no plausible military invader or attacker. All we are really talking about, when we discuss threats from Iran or North Korea or ISIS, is whether our margin of safety should be very large or even larger. “No great power in world history comes close to enjoying the traditional state security that the United States does today,” writes Stephanie Rugolo in A Dangerous World? Threat Perception and U.S. National Security, a new collection of essays from the Cato Institute.

Here at home, criminal violence is, as ever, a serious problem. But its reduction over the past couple of decades is one of the great success stories of our time. The violent-crime rate (which excludes homicides) has declined by more than 70 percent since the early 1990s. The homicide rate has declined by half, and in 2011 it reached the lowest level since 1963. According to the National Crime Victimization Survey, between 1995 and 2010 the rate of rape and sexual assault fell from five per 1,000 females to two.

And how do Americans celebrate this extraordinary success? By denying it. Every year Gallup asks whether crime has gone up or down since the previous year. Every year, rain or shine, the public insists, usually by overwhelming margins (63 percent to 21 percent in 2014), that crime has risen. “Most Americans Unaware of Big Crime Drop Since 1990s,” announced the Pew Research Center in 2013; only 10 percent of those surveyed knew that gun crimes had gone down since the 1990s. Criminologists say that many people get angry when told that crime is decreasing.

Perception is even more skewed where terrorism is concerned. “Terrorism Worries Largely Unchanged,” ran another Pew headline, also in 2013. That year, 58 percent of the public was worried about another terrorist attack in the United States, a rate not all that much lower in October 2001, immediately after the 9/11 attacks, when 71 percent of the public was worried. A few months ago, perhaps influenced by ISIS’s atrocities, a large plurality of respondents told NBC News/Wall Street Journal pollsters that the country is less safe than it was before 9/11.

Reality, once again, tells us otherwise. State-sponsored international terrorism, writes the intelligence analyst Paul R. Pillar in Cato’s A Dangerous World?, “is today only a shadow of what it was in the 1970s and 1980s.” As for the risk posed by terrorism inside the United States, to characterize it as trivial would be very generous. Americans are about four times as likely to drown in their bathtub as they are to die in a terrorist attack. John Mueller of Ohio State University and Mark G. Stewart of Australia’s University of Newcastle estimate the odds of such deaths at one in 950,000 and one in 3.5 million, respectively.

Surely we can at least agree to worry about a nuclear Iran, or nuclear terrorism, or ISIS? All are indeed worrisome, but Mueller persuasively argues that none merits the alarm it begets. Since Nagasaki in 1945, the few countries that have obtained nuclear weapons—including dangerous rogue states like Mao’s China, the Iran of its day—have consistently found them militarily and diplomatically useless, except as ego boosters and perhaps as defensive weapons to forestall attack. The odds of terrorists’ obtaining and deploying nuclear weapons are much lower than most people appreciate, for a host of technical and political reasons. ISIS, meanwhile, is an unusually vicious and destabilizing actor in a region that is full of them, but its menace has been almost entirely local. (In this issue’s cover story, Graeme Wood examines this threat, and the appropriate response, in detail.)

Pinker, a psychologist at Harvard, mused in a recent speech about Americans’ odd refusal to appreciate their security. The bad news for Obama, if Pinker is correct, is that presidential palaver will have no effect, because people are hardwired to overreact to threats, real or perceived. In today’s world, where intricate social systems keep us safer than our forebears could ever have imagined, overreaction is maladaptive: it is often more disruptive and damaging than whatever provoked it. In the world we evolved for, however, humans needed to be hyperalert. Something rustling in the bush was more likely to be a predator or an enemy than a friend with glad tidings. Moreover, Pinker says, people are biased to overestimate the likelihood of the sorts of events that stand out in our memory, as violence and mayhem do, and as peace and quiet do not. Add alarmism’s usefulness to politicians and pressure groups, and you have a standing order for overreaction—always, not just now.

Still, now is special. Given how safe we are, and how frightened people nonetheless feel, it seems unlikely that Americans’ threat perception has ever before been quite as distorted as it is today. Never have so many feared so little, so much. In an era of overreaction, a president who lectures the public about its insecurities, instead of pandering to its fears, necessarily seems impolitic, out of touch, tone-deaf, pedantic, negligent, complacent—choose your adjective. For precisely that reason, we can be grateful his instinct is to underreact. Historians will thank him, even if we don’t, for his steadfastness in the face of unprecedented safety.