The Military Drinking-Water Crisis the White House Tried to Hide

The Trump administration feared it would be a “public relations nightmare”: a major federal study that concluded that contaminated groundwater across the country, especially near military bases, was more toxic than the government realized. So political aides to President Donald Trump and Environmental Protection Agency head Scott Pruitt pressured the Agency for Toxic Substances and Disease Registry against releasing the results.

“The public, media, and Congressional reaction to these numbers is going to be huge,” an unidentified White House aide wrote, according to Politico. “The impact to EPA and [the Defense Department] is going to be extremely painful. We cannot seem to get ATSDR to realize the potential public relations nightmare this is going to be.” The study was not released.

That is, until Wednesday. Amid a media firestorm about the administration’s immigration policy, the ATSDR—a division of the Department of Health and Human Services—quietly published its 852-page review of perfluoroalkyls, or PFAS, which are “used in everything from carpets and frying pan coatings to military firefighting foams,” according to ProPublica. “All told, the report offers the most comprehensive gathering of information on the effects of these chemicals today, and suggests they’re far more dangerous than previously thought.”

These chemical compounds pose health risks to millions of Americans. They’re in roughly 1 percent of the nation’s public water supply, according to the EPA; in roughly 1,500 drinking water systems across the country, according to the Environmental Working Group. People who drink from these systems, even if their exposure to PFAS is low, now have a potentially increased risk of cancer; of disruptions in hormones and the immune system; and of complications with fetal development during pregnancy.

But military personnel and veterans are particularly at risk, because PFAS compounds are in firefighting foams, which have been used in training exercises at military bases across America since the 1970s. Those foams have leached into the groundwater at the bases, and often the drinking water supply. Nearly three million Americans get their drinking water from Department of Defense systems.

The DOD has reported widespread contamination at its bases, as well as the surrounding area. In a March report to the House Armed Services Committee, the department provided a list of 126 military facilities where nearby water supplies contained PFAS levels above the EPA’s standard, and 36 bases with drinking water contamination on site. “In all, 25 Army bases; 50 Air Force bases, 49 Navy or Marine Corps bases and two Defense Logistics Agency sites have tested at higher than acceptable levels for the compounds in either their drinking water or groundwater sources,” the Military Times reported.

The EPA had been assuring people who lived on these bases that they were safe from the potentially harmful effects of PFAS—which range in severity from weight gain to liver disease to cancer—at levels of 70 parts per trillion. But the new ATSDR study says safe levels were actually much lower, from 7 to 11 parts per trillion.

“It’s pretty pervasive problem,” Melanie Benesch, a legislative attorney at the Environmental Working Group, told me. “It’s getting into the groundwater and tap water on bases, so people living on base are of course affected.” Military personnel often live on bases with their families, so those drinking contaminated water can include pregnant women and children—two populations especially vulnerable to PFAS. And these compounds can remain in the body for six to ten years. “Veterans who have since moved off likely continue to have it in their bodies,” Benesch said.

In 2016, the Grand Rapids Press spoke to several veterans who blamed various health problems—spinal defects, thyroid problems, and hypertension—on PFAS-contaminated water at Wurtsmith Air Force Base. They began connecting the dots when, that February, Michigan officials warned against consuming well water near the facility due to the presence of the compounds. “We thought that if anything was wrong, of course someone would tell us,” one veteran said. “It feels like we’ve been betrayed.”

Since becoming aware of PFAS contamination, the DOD has “shut down wells, provided alternate water sources, or installed water treatment systems” at 11 military installations, according to a 2017 report from the Government Accountability Office. But despite that progress, “the pace of actual cleanup has been quite slow,” the Berkeley School of Law said in a report cited by the Center for Public Integrity. “Most of the time and money has been spent studying the problem,” the report added.

That time and money is wasted when those studies are delayed unnecessarily, Benesch said. “It was ready six months ago,” she said. “Six months that the government agency responsible for setting these levels, for doing the toxicology, was not able to provide us with their findings.” Providing the study earlier would have forced the EPA to consider changing its regulations sooner, Benesch said. Had parents and pregnant women on military bases known about the study, perhaps more of them would have avoided the tap water.

What, then, did the study’s temporary suppression achieve for Trump and Pruitt? It bought some time for the chemical manufacturers that support them, so they can prepare for the inevitable onslaught of personal injury lawsuits related to PFAS contamination. It also delayed public pressure to increase government spending on environmental cleanups at military bases and on updating rural water infrastructure. But the study’s delay may not have achieved what Trump and Pruitt most wanted it to. Let the public relations nightmare begin.

“The New Republic is frankly an experiment.” First issue, first sentence, November 1914.

Over the years as a The New Republic reader, I’ve seen TNR invoke this line in different contexts with different inflections. (I quoted the whole paragraph it’s taken from last month, myself.) It always seemed bold. Of course, it is. The idea at the time of writing was that “national audience for a journal of interpretation and opinion” was a super-uncertain prospect: “Many people believe that such a journal is out of place in America; that if a periodical is to be popular, it must first of all be entertaining, or that if it is to be serious, it must be detached and select.” It would take a more refined historical understanding than I’ve so far developed to know what precisely Herbert Croly, our first editor, and the gang would have meant 103-plus years ago by entertaining. I expect it’s something like diversionary or lite. (Actually, are you a historian of early-twentieth-century American life or otherwise someone who’d know better than me? Please hit us up: hello@newrepublic.com.) Detached and select seems straightforward enough: maybe, of and for abstract intellectual reflection—vs. keyed to the urgency and relevancy TNR has gone for from the outset. Whatever, haters, we seem to have been saying, we’re an experiment!

Now over the months as a The New Republic editor, I’ve noticed this one word, frankly, standing out more. It’s come to feel slightly confessional—like a sort of poised admission: We know there’s not an especially overwhelming immediate consumer demand for our thing, what with the weird course it plots for itself, as a popular yet serious magazine, between entertainment and detached selection. But we believe in it. And we believe in it not just as an idea but as an institution—as something that can be meaningful and generative to people in their day-to-day lives. In 2018, the main experimental ambiguity for the The New Republic we have in mind—the central frankly—turns on whether there’s an audience for a liberal magazine that cares about more than shoring up liberal resistance to the regressive monstrosity that’s trying to pass itself off by way of manipulative nostalgia as conservatism. It turns too, and more broadly, on whether there’s an audience for a liberal magazine that wants to rethink American liberalism with us—on the premise that democracy can’t thrive merely on victory.

If that compound vision speaks to you, whoever you are, you’re our kind of person. In which case, we’d love for you to be a part of TNR’s future. You might want to connect with us at the email address above. Or you might even want to subscribe: newrepublic.com/subscribe. Thanks either way—and excelsior.

- J.J Gould

On a spring morning last year, in the Keith Creek neighborhood of Rockford, Illinois, Eric Thurmond stopped his patrol car on a street shrouded by trees and veined with cracks. The homes on the block were modest and weathered, many of them low-end rentals that had been chopped up into multiple units. The surrounding streets were cratered with foreclosures and vacant properties. Thurmond, a rookie on the Rockford police force, had been shown the statistics documenting the neighborhood’s decline—burglaries, shootings, home invasions. It was not a desirable place to live. But he would be moving there in less than two weeks. He was part of Rockford’s newest experiment in policing—a program designed to help cops put down roots in high-crime sections of the city. The police department had procured a house for him. He would be living there rent-free for a minimum of three years, with his only mission to serve the community—to be a good neighbor.

Thurmond got out of his cruiser to inspect his new home, a brick and wood-paneled bungalow with peeling paint above the brim of a beveled awning. As he stood on the front steps, he noticed a neighbor peeking at him from behind makeshift curtains. The neighbor—a scruffy-bearded white man in jeans and a T-shirt—came outside to meet him. He looked concerned. Thurmond is 25 years old, built squat and burly like a washing machine, with a laid-back manner and a round, cherubic face. Realizing how the arrival of a uniformed officer must look, he assured the man that there was nothing to worry about. No crime had been committed. He wasn’t responding to a call for service, just checking out the house prior to his move. He described the police residency program, extending a hand as he introduced himself.

“You going to have cameras up?” the man asked, his eyes scanning the front of Thurmond’s bungalow.

“Yeah, if anything happens in the neighborhood, I’m going to be able to see what’s going on.” To Thurmond, it sounded assuring. The man nodded and turned away.

A few days later, when Thurmond returned to measure the inside of the bungalow for furniture, his neighbor was gone. The rental was trashed, the family leaving behind chairs and garbage bags stuffed with clothes. Other people on the block told Thurmond that the guy had been selling drugs. Cars used to pull up at the house at all hours of the night, they said, and after an exchange, they sped off. The landlord knew about the drug deals, but he said he’d been unable to carry out an eviction. One woman mentioned her repeated calls to 911, saying the police had done nothing. When Thurmond related all of this to his superiors, they were thrilled. He hadn’t even moved in his belongings and he had already made the neighborhood safer.

Rockford is a Rust Belt city that straddles the Rock River 90 miles northwest of Chicago. Until the mid–twentieth century, it was among the nation’s manufacturing contenders, a builder of tools and fasteners, the self-proclaimed “Screw Capital of the World.” In 1949, an article in Life magazine portrayed Rockford as the embodiment of the country’s promise of upward mobility for all. But today, with the bulk of its factory jobs gone, the city of 150,000 is better known for ignominy. Rockford has the highest percentage of underwater mortgages of any city in the nation: Nearly a third of its homes are worth less than the money owed on them. Rates of violent crime are higher than in Chicago. Homicides are up. A quarter of the population lives in poverty. Rockford is now typical of many small and midsize cities across America that are suffering from what we tend to think of as big-city problems—guns, drugs, and gangs. A sense of purposelessness and despair has settled in the areas outside the economic activity of downtown and the prosperity of the outer-ring suburbs. Although businesses and new development have sprawled toward Interstate 90 on the eastern edge of the city, the black neighborhoods west of the river, in particular, have been ground down by disinvestment, crime, and, many residents contend, over-policing. After I visited last fall, a local poet and activist named Christopher Sims sent me a bit of verse he wrote about his hometown:

Sheriffs, judges, they’d rather see us

locked in jail cells. Welcome to Rockford:

a black man’s hell if you’re not living

financially well.

Only a very small percentage of Rockford police officers reside within city limits, and there are fewer than 60 officers of color on the force of 300, in a city that is little more than half white. That discrepancy—between those policing and being policed—is a common one. While departments have slowly diversified, three-fourths of the nation’s police remain white. Many departments across the country have scrapped residency restrictions to retain officers and attract new recruits. Yet even in cities that still require police to live in the municipalities where they work, officers usually settle in neighborhoods among themselves. At the same time, decades of tough-on-crime policies have rewarded the warrior cop who racks up stops and arrests. Too many officers have come to know the communities they patrol primarily for their dangers, seeing everyone who lives there as a potential threat. And too many residents now view the police as an invading force, defined by their worst instances of abuse and impunity. Trust in law enforcement has hit historic lows in recent years, causing clearance rates for major crimes to stagnate. The high-profile killings of unarmed black people by the police over the past several years have demonstrated how dire the divide between cops and citizens really is—and how urgently it needs to be repaired.

In this climate of mistrust, Rockford was betting that its version of extreme community policing would be a model for how to undo entrenched practices and antagonisms. Thurmond and his partner, who would be known as resident officer community keepers, or ROCK cops, would be tasked not with arresting criminals but with treating the underlying conditions that breed crime. Unlike regular beat officers, they would have no fixed schedule or responsibilities. Available 24 hours a day, with their cell phone numbers widely distributed, they would go where the community needed them. The hope was that this small pilot program would not only shape the mind-set of individual officers but also grow to transform the culture of the department as a whole, in the process helping to reconstitute the fundamental way civilians and police interact with one another. If the job of policing could be redefined in this way, then maybe the city would be made safer.

Last year, when Rockford announced the program, Thurmond was one of only two officers to sign up, both of them African American. Thurmond lived on Chicago’s West Side until he was nine, and kids used to tease him for declaring that he would grow up to become a soldier/fireman/cop, an imagined trifecta of uniformed public service. His mother, who’d served in the Navy, moved the two of them to the western suburb of Bolingbrook. In high school, Thurmond readied himself, joining the military drill team and the Reserve Officers’ Training Corps. He abstained from drugs, knowing, he said, that one day he’d be peeing in a cup for the police exam. At Western Illinois University, he paid his way by signing up for the National Guard. He tattooed the archangel Michael, the patron saint of police officers, on his left biceps, and he joined the Rockford Police Department in 2016, one year after graduating.

When he announced the news, Thurmond estimates that 50 of his friends and family members dropped him on Facebook. “Fuck the police,” he read in their posts. Their cynicism amid reports of police violence and eruptions of protest didn’t surprise him. But Thurmond held to a conviction, at times even quixotically, that he could show the haters that the police were no different from those they served. He didn’t begin the job seeing himself as a reformer. He’d actually chosen Rockford in part because it was, as police say, “busy” with robberies, opioids, prostitution, and theft. Making a difference, he believed, meant getting guns and drugs off the streets. But the residency program appealed to his desire to reach out to those who feared or despised the police, as well as to his own evolving sense of doing good. “As a cop, you don’t have to talk to people tough and mean-mugging,” he said. “You can talk to them as you would a friend.”

The other officer who volunteered for the program was Patrice Turner, a 41-year-old veteran of the force. Short and unassuming, with a wide, toothy smile, Turner manages effortlessly to be both calming and commanding at the same time. She’d been stationed inside Rockford public schools for several years. “Positive contacts with students,” she said. “Not buddy, homey, friend. I don’t play games. But if you want to talk, if you’re hungry, if you need something, I’m there.” She grew up in Rockford public housing, and although she moonlighted several nights a week doing security for a bank—to help pay for what she called her “one vice” of overseas vacations—she was die-hard in her commitment to the city. So last July, she and her teenage daughter moved into a little house on the west side of the river, in a neighborhood with rows of ranch houses and neat patches of yards. Her car was broken into, other cars in the area were vandalized, and crowds sometimes parked in the middle of the streets talking, smoking, playing music. Turner didn’t pretend to know why crime in Rockford went up or down. She saw lots of heroin and knew that guns were easy to acquire. But she felt that the ROCK program matched the way that she had always thought about the job. “People are going to eat no matter what,” she told me. “They are going to rob or steal if they need to meet their basic needs. We can arrest them after the crime or help them beforehand.”

Dan O’Shea, Rockford’s police chief, said that the traditional way officers understood policing wasn’t going to move the needle on high rates of violent crime. “We have to change the old-school, cuff-and-stuff mentality of policing,” he told me. “It doesn’t work.” He wanted his officers to immerse themselves in the city’s neighborhoods; they needed to know residents personally, understanding that just a tiny percentage of the population were serious offenders. The police had to convince the public that they were legitimate and sincere. Only by joining with the community could his officers solve crimes and address their root causes. “Instead of 300 cops, I need 147,000 people working on this,” he said.

Thurmond and Turner began by walking their new neighborhoods, introducing themselves door to door, explaining their presence in the community. They were goodwill ambassadors, frontline resource providers, and they were there to learn what the city’s neighborhoods required. They attended church services and community meetings. They rode their police bicycles, visiting local businesses and classrooms. “Why do you guys shoot everybody?” a little girl asked Thurmond. A high schooler met Turner with his arms lifted above his head, the “Hands Up, Don’t Shoot” pose of protest adopted after Michael Brown was killed by an officer in Ferguson, Missouri. “I’m just sayin’,” he told her.

The two of them weren’t required to respond to calls coming over dispatch, but they did when they weren’t otherwise engaged. During the days, they cruised the residential streets and alleyways in their districts. At the shopping complex near Turner’s new home, a couple of the storefronts were vacant—there was an empty Payless, an abandoned Curves, and a dry cleaner with ghost lettering above its entrance. I followed her as she checked in with a guard at a bank that had recently been robbed and chatted with a hardware store manager. The anchor store was a Schnucks supermarket, and Turner drove a few minutes away to a boxy, one-story house to speak with an elderly woman who’d been banned from the store for putting cheaper price tags on groceries. Turner told the woman about the food pantries in the area and made her promise to see a doctor after she complained of vomiting and fainting. On another day, I was with Thurmond when he stopped to talk to one of his neighbors, a young African American woman who had moved to Rockford from Kentucky not long ago. She was working three jobs, she said, and she asked for Thurmond’s help dealing with whoever was dumping old electronics behind her garage. “They wouldn’t do that if they knew my heart,” she told him. He pulled up alongside a school where fourth graders were out on recess, and one of the boys on the wood-chip playground shouted, “We didn’t do anything bad.”

“I know,” Thurmond said. “I’m just sayin’ whatsup.” By the swings, he matched dance moves with a couple of the pigtailed girls.

Many officers in Rockford seemed to distinguish between what Thurmond and Turner did and what “real police” work entailed. “It’s a cushy job; he kisses babies for us,” a veteran cop ribbed Thurmond in front of me. I heard a training officer bark at him as greeting, “You watch Sally Jessy Raphael yet today?” I never saw Thurmond lose his cheerful buoyancy. “Not yet,” he said.

But what Turner and Thurmond were doing was arguably the brunt of police work. Nationally, only an estimated 25 percent of 911 calls have anything to do with crime, and just 5 percent of arrests are for violent offenses. In Rockford, a third of the calls were the result of a domestic dispute, and engaging people properly could be the difference in whether a situation ended violently. The police are the boots-on-the-ground government workers who first encounter the mentally ill, the drug-addicted, the homeless, and the unemployed. As cities try to reduce the steep social and economic costs of mass incarceration, police departments are increasingly prioritizing communication skills, patience, and a better understanding of the support services that offer an alternative to lockup.

Research has supported this social-minded approach. In his new book, Uneasy Peace, Patrick Sharkey, a sociologist at New York University, documents how the dramatic drop in crime starting in the 1990s, which took place nationwide, corresponded with an increase in the number of nonprofits serving high-crime areas. That drop had previously been attributed, by politicians such as Bill and Hillary Clinton, and many others, to aggressive policing tactics that emerged from the “broken windows” theory of law enforcement. “Broken windows”—the idea that small infractions left unchecked lead to a collapse in social order—was first introduced by criminologists George Kelling and James Wilson in The Atlantic in 1982. “If a window in a building is broken and is left unrepaired, all the rest of the windows will soon be broken,” Kelling and Wilson wrote. “One unrepaired broken window is a signal that no one cares.” In the 1990s, the widespread adoption of “broken windows” policing resulted in the criminalization of panhandlers, loitering teens, and pot smokers; it contributed to the War on Drugs, the 1994 Clinton crime bill, the Los Angeles Police Department’s rampaging CRASH unit, the horrors of “Giuliani time” in New York, and a police department in Chicago that demonstrated “no regard for the sanctity of life when it comes to people of color,” according to an independent review in 2016.

But there is another way to interpret Kelling and Wilson’s findings. If a window is broken, police can arrest the person who broke it, but they can also help repair it. Sharkey believed that what makes areas safer is police who partner with the kind of nonprofits that do the “broken windows” work of maintaining social order—cleaning up trash, creating youth programs, helping people find jobs. Many departments are slowly beginning to understand “broken windows” in this way. In Los Angeles, a new policing program credits officers not for arrests but for walking their beats, often teaming up with former gang members to stop violence, and working with civic groups to start soccer leagues and develop health initiatives. The areas patrolled by these “guardian” officers have seen the steepest declines in crime of any Los Angeles districts. Rockford is hoping for similar results.

On a sunny day last October, Thurmond and Turner were preparing to host a Halloween event at one of the precincts. They had been living in the community for five months at that point, and “Pumpkins with the Police” was the third large function they had organized. They traded anxious calls throughout the day to figure out whether they had enough pumpkins and how to pay for additional ones. The ROCK program didn’t have a budget, and the two officers regularly spent time soliciting donations from local businesses. When Thurmond arrived at the station house to set up, the contents of his trunk spoke to the wide-ranging job he was now undertaking: Next to a tumbleweed of police tape, collected from a recent homicide scene, were three plastic bags from Walmart filled with cookies, plastic cups, and napkins.

Pumpkins with the Police was being held in a gymnasium at a station that had previously been an abortion clinic, and before that a school. At one end of the gym, pumpkins the size of basketballs awaited their fate. Bales of hay were stacked against the opposite wall, in front of a “Rockford Police Department” backdrop. A young white woman with five children, the youngest of them a baby she carried on her hip, showed up 30 minutes before the event’s start time, announcing that she had nowhere else to wait after picking up her kids from school. Thurmond greeted her with a smile, leading two of her boys to a beanbag toss in the center of the basketball court. The woman said she appreciated the station house being opened for them. Over the next hour, 30 other families arrived. The children sat at folding tables with their pumpkins, scooping out the goopy innards. One of the kids recognized Thurmond from his school and waved. Other police officers were there as volunteers, most of them in uniform, though one of the women from the precinct had on a sweatshirt that said: I STAND BEHIND THE THIN BLUE LINE. Turner’s teenage daughter passed out cider and cookies. A pregnant African American woman shooed away her five-year-old son, deflecting his pleas for her help with his pumpkin: “You need to ask one of the police to carve it.”

The original idea for the Rockford program can be traced to a 71-year-old retired police chief named Charles Gruber. In the 1990s, Gruber became the top cop in Elgin, a city near Rockford. As one of his first directives, he announced that he would refurbish a number of houses in Elgin’s most troubled neighborhoods and assign cops to live in them rent-free. Gruber said his officers needed to demonstrate that they did not show up only to make arrests; they had to intervene and participate in the community. At first, no one signed up for the new officer residential unit. Police found their jobs hard enough and wanted to leave work at the end of the day; they did not like the idea of becoming downwardly mobile by relocating to an area of high crime. “People in Elgin thought I was nuts,” Gruber told me.

Early in his career, Gruber had studied with Herman Goldstein, a pioneer of community policing who preached that the “community must police itself, and the police, at best, only assist in that task.” Goldstein was at the forefront of what is called, anachronistically, the “community era” of American policing. The notion that the police function might be other than enforcement had its beginning after the racial unrest of the 1960s, when police departments in northern cities felt pressure to improve their strained relationships with the black neighborhoods they patrolled. Some departments added special walk-and-talk units, and many made attempts to diversify their ranks, often after African American officers demanded change. The efforts were moderate and peripheral, but the results were generally positive—public trust in law enforcement increased, and officers reported greater job satisfaction—and the idea spread. By the start of the ’90s, the Justice Department had formed its Community Oriented Policing Services, or COPS, and was funding cities nationwide to create special community policing units. But officers were still promoted for making busts, not for creative problem solving or neighborhood accountability, and the prevailing belief remained that crime be met with swift and severe punishment. Community policing units of this era were increasingly isolated and drained of resources.

Eventually, Gruber was able to persuade seven cadets just out of the training academy to move into the renovated homes. Many residents welcomed the permanent presence of these cops; some did not. A couple of officers had their cars vandalized. Bullets were fired into one of the homes. A bowling ball dropped from an apartment window barely missed another officer, and three teenagers tossed a homemade bomb through the window of a third. But serious crimes in the targeted areas declined, and community members said their problems with gangs and drugs diminished. They were able to seek out the cop on their block for nagging quality of life concerns, like broken street lights and speeding cars or help with tutoring. A neighbor at the time said he liked having the officer nearby: “He’ll actually put some law and order back into this neighborhood.” By the end of the decade, Elgin had expanded the program to nine officers, and similar initiatives had been adopted by a handful of other cities in Illinois.

In Rockford, however, police-community relations would have to get a lot worse before they could get better. In August 2009, two Rockford cops, both of them white, spotted a 23-year-old African American man named Mark Barmore outside the Kingdom Authority church on the city’s west side. Barmore, who was wanted for questioning after threatening his girlfriend the night before, was talking amicably to the pastor’s wife. When he saw the police, he ran. The officers chased him inside the church, drawing their guns as they followed him downstairs where a child daycare was in session. Barmore shut himself inside a boiler-room closet. The officers did not call for backup. They did not pause to clear out the dozen children in the daycare cowering beside their teachers. And they did not try to reason with the barricaded suspect. They pushed their way into the cramped closet. The cops said Barmore grabbed one of their pistols before they shot him four times at close range; three of the bullets entered his back. Barmore died at the scene.

Hostilities erupted in Rockford after the shooting. Marchers waving I AM HUMAN placards demanded that the two officers be brought to justice. Pro-police demonstrators took to the streets in response. Jesse Jackson and Louis Farrakhan drove up from Chicago to call for accountability and peace. A grand jury ruled the officers’ use of deadly force justified, and no criminal charges were filed. In a separate federal civil rights lawsuit, the city of Rockford settled the case without admitting fault, agreeing to pay Barmore’s family $1.1 million. Melvin Brown, the pastor of Kingdom Authority, said Barmore’s killing was not an isolated incident. “There were two dozen homicides by the police at that time, all ruled justified,” he told me. “The people here do not trust the Rockford Police Department.”

After the Barmore incident, the police in Rockford did begin to institute reforms. Two civil rights attorneys were invited to conduct an independent review of the department, and the force followed most of their 27 recommendations. The department changed its rules on engagement. It added training on nonlethal force and removed obstacles to citizens filing complaints against officers. And the department ended the practice of investigating deadly force incidents internally, creating an oversight body made up of police officers from municipalities in the surrounding counties. Then, in 2016, Dan O’Shea, who had been on the force in Elgin for 17 years, was hired to lead the Rockford department. Although he had not been a resident officer in Elgin, he decided to replicate the program. He had seen the difference when cops lived where they worked. “When one of these officers shows up at the scene of a fight, he’s known the kid for five years,” O’Shea told me. “The personal level leads to de-escalation. There’s no success with us and them.”

In Elgin, budgetary concerns led the city to cut the number of resident officer homes back to four. Gruber now investigates police departments for the civil rights division at the Justice Department. He said the resident officer initiative should be the basis for policing standards around the country. “Every community, and especially what are thought of as the ‘bad’ ones, wants protection and help,” he said. “But community policing can’t be just a program. It has to be a philosophy. It has to be embedded in everything a department does.”

Turner started most days at a police precinct just west of the river, across from a low-rise public housing complex that was in the process of being shuttered. She liked to keep in touch with patrol officers and check in with her district commander before grabbing a squad car. One morning last November, I waited for her on the benches beside the precinct’s front desk. A man in his early twenties with a faded neck tattoo sat across from me, making faces at a baby in his arms. “I’m sorry I’m not the best dad,” he said to the rawboned blond woman next to him.

“You just have to care, or whatever the fuck you said,” the woman told him. At least one of them was required to report regularly at the police station for a felonious reason I didn’t make out. She groaned loudly. “I’m tired of Rockford.”

Moments later, a homeless man, immense and treading gingerly, rolled a suitcase through the electric doors into the precinct. He took a seat alongside me. His name was Jeremy, he broadcast to the room, and he had been banned from most of the shelters in the city for making threats and also, he added sheepishly, for carrying them out. Now he had nowhere to sleep, and the temperature had dipped into the forties, with a chilling rain. “It’s OK, I’m used to it,” he said. But he was trying to puzzle out how he might retrieve a pair of his boots from a halfway house, because he could not legally come within 300 feet of the building.

The next person to enter was a man in his fifties with thick glasses, one of the holdouts from the neighboring housing project. It was his second visit that morning, and the administrator behind a glass partition greeted him by name. He had come by earlier to report that his television had been stolen. He knew the thief. She wasn’t in Rockford at the moment, but the man had returned after sleuthing her real name. The clerk checked it against a database and announced excitedly that there was an existing warrant for the woman’s arrest.

“You can call it in to Crime Stoppers,” she told him. If the police ended up making an arrest, he’d get a reward. “It could at least pay for the television.” The half-listening waiting room snapped to attention.

“Lure her back to Rockford, bro,” the guy holding the baby shouted.

“What you need to do is tell her you got a new TV,” another man plotted.

“Nah, I’ll tell her I got some drugs,” the TV-less man said, warming to the plan. “She’s a heroin addict.”

There was general agreement that this was the right tack.

“Get her in jail, bro!”

A few minutes passed, and Turner emerged to collect me. The baby-swaddling man said he recognized her. He’d been a student in a high school where she sometimes worked. “Were you good, or did you get on my nerves?” Turner asked. He’d been good for two years, he confessed, but then was kicked out.

Turner looked him over. “You working?” she asked. She had a knack for extending conversations, drawing people out to discover their needs. She told him about a bus that shuttled people from Rockford to a cluster of factories 45 minutes away. She learned about the opportunity not from her department or a team of social service providers or a list of vetted programs provided to the ROCK officers. She’d seen one of those suspect posters on the side of the road displaying only the word JOBS and a phone number. Turner had phoned—the transportation was free, the staffing company didn’t ask about a criminal record or do a background check, and the pay was $12 an hour. All the young man would need was an ID and a social security number.

“No background check at all?” he asked eagerly. He turned to the mother of the baby. “I’d do 16 hours a day if they let me.”

Turner now walked over to Jeremy, who was missing his boots. He said he had no family in Rockford and wouldn’t return to the Illinois town where he was from. Turner told him she would drive over to the halfway house and try to fetch his shoes.

Community policing is often dismissed by rank and file officers as “women’s work.” Connie Rice, the civil rights attorney who helped the LAPD devise and implement its new community policing strategy, said that officers there disparaged the effort as “pussy policing.” But it may be that departments could learn from a less masculine approach. Women make up about 12 percent of the nation’s police officers. While women have been found to use routine force at about the same rate as men, data collected by the National Center for Women & Policing showed that they accounted for only 5 percent of citizens’ complaints of excessive force. Recent studies by Phillip Goff, a social psychologist at John Jay College of Criminal Justice, have determined that a sense that his manhood is being challenged—more than racism—predicts whether an officer will use excessive force against an African American suspect. Departments encourage and reinforce macho behavior in countless ways, and Goff pointed to community policing as an antidote. “By devaluing hypermasculinity, community policing can reduce the masculinity threat that results in hegemonic racial violence,” he wrote in a 2015 paper with L. Song Richardson. “Although male police officers would still ‘do’ gender, their performance of masculinity would not be tied to physical aggression but rather to their ability to solve problems through creativity and innovation.”

As I rode with Turner, she took me through an affluent neighborhood nestled against the banks of the Rock River, drawing my attention to the aging mansions with handmade wood shingles and copper gutters gleaming in the sun. She said she wasn’t the type to tell her colleagues how to do their jobs. “I am not a teacher of officers by any means,” she insisted. “I’m definitely not the one to say, ‘Hey listen to me.’ ” But she explained that she was one of only five black women on the force, and she did believe that her department would be more effective if officers were better connected to the neighborhoods they patrolled. “If you grew up in Byron, Illinois, and never saw a black person, you might be fearful of your life,” she explained. “Where I might say, ‘Derrick, sit your punk-ass down. Every time you get mad, you talk shit.’ That’s the difference. I call it bringing gasoline or water to a fire. You don’t bring gasoline. If I can talk my way into or out of a situation without putting my hands on anyone, that’s a beautiful thing.”

Later in November, less than a week after I left Rockford, a young officer named Jaimie Cox pulled over a pickup truck on a commercial stretch of State Street, four miles east of downtown. It was 1 a.m. on a Sunday. No dashboard footage captured what happened next—Chief O’Shea would later say that the department couldn’t afford the $5,500 cost to equip each car with a camera. But Cox apparently scuffled with the driver, a 49-year-old African American man named Eddie Patterson Jr., a supervisor at the Rockford sports arena who was driving with a revoked license. Patterson sped off, with Cox somehow tangled in the truck. Cox fired his service revolver and the truck crashed two blocks away. Patterson died from multiple gunshot wounds. Cox died of blunt force trauma.

I had met Cox while out on patrol with Thurmond. He was a baby-faced 30-year-old, who, like Thurmond, had served in the military and was relatively new to the force. He lived with his wife in South Beloit, an Illinois city of 8,000 along the Wisconsin border that is 83 percent white. Thurmond described Cox as a friend and a good officer. “He would tease me about the size of my big head,” he said. Cox was the seventh police officer to be killed in the line of duty in the city’s history. After a funeral at the First Free Rockford church, his body was driven to the cemetery in a procession of police cruisers that extended for miles. It was a frigid day, but hundreds of people lined the streets, lofting blue flags. Chief O’Shea said the displays of support were proof that their community efforts were already bringing the police and the people there closer together.

But the incident also exposed some of the same fault lines that have long divided the city. There were those in the community who saw Eddie Patterson as another Mark Barmore—an unarmed black man in a deadly encounter with a cop. One of Patterson’s daughters filed a wrongful death lawsuit against the city. Pastor Melvin Brown of Kingdom Authority led a small march from his church, where Barmore had been shot, to City Hall. “They already put Cox out there as a hero,” he told me. “What if Cox didn’t use police policy correctly and caused Eddie Patterson’s death and his own death?”

Police officers wield an awesome power to determine what we know and believe to be true. On Rockford’s streets, in any search or interrogation, the police author the factual reports and corroborate a version of reality that’s hard to dispute. “It’s not what happened, it’s what the police said happened,” was a common refrain among those who trusted the police the least. Brown, whose family has been locked in ongoing legal disputes with the city over the Barmore case, demanded a federal investigation into Patterson’s death. He had no faith in the police review board, created amid the Barmore fallout, that ruled on officer-involved shootings. Of the eight shootings by Rockford police since 2010, the oversight body made up of police officers had found each one justified. “Blue and blue ain’t going to tell on each other,” Brown said. “All of them are buddies. Who’s going to trust that?”

After Cox’s death, Thurmond took a few days off work, visiting family members and getting together with fellow officers, but then he picked up extra shifts, wanting to stay busy. “I’m just trying to learn from it,” he said. “Slow down and assess every situation.” Turner told me that she felt the double tragedy of the traffic stop: “Two human beings lost their lives that night; two families were left behind to mourn.” She wasn’t any leerier of her city or her job, and she repeated that there was a need for more police to reside in the areas they patrol. At one point, she exclaimed, as if seeing a prophecy of a better future, “Can you imagine what crime would do if all our officers lived in this city?”

But many activists dismiss community policing as a distraction from the greater problem of a racist criminal legal system. “We don’t just need friendly officers,” Antar Baker, a youth program coordinator from Rockford’s west side, told me. “We need laws in place that protect against abuses. We need rogue behavior prosecuted.” That sentiment is echoed by communities elsewhere that are calling not only for the defunding and disarming of police departments but also for them to be disbanded entirely. They have determined that it is fruitless to seek solutions from the very entities whose misdeeds they’re protesting, and they are looking for alternatives to policing in community action and restorative justice. In Chicago, groups of organizers have opposed the building of a new training facility for police officers. The #NoCopAcademy movement said that the $95 million cost of the facility could be better used bolstering neighborhoods that were already heavily policed: “Real community safety comes from fully funded schools and mental health centers, robust after-school and job-training programs, and social and economic justice. We want investment in our communities, not expanded resources for police.” When I reached out to a group called Rockford Youth Activism to ask about police-community relations in the city, I received a short note that began: “Abolish the police.”

Community-minded police strategies have also come under attack from those on the other side of the political divide. Donald Trump has denounced criminal justice reforms as a “war on police,” and his administration has so far launched only one investigation of a police department anywhere in the country. During the Obama administration, a dozen police departments entered court-ordered reform agreements with the DOJ. Trump’s attorney general, Jeff Sessions, has tried to roll back these consent decrees. Last December, the DOJ announced that its COPS division would no longer fund police forces nationwide looking to correct patterns or practices of misconduct that had tainted their reputations; instead, the office created to advance community-centered programs would focus on combating violent crime through hawkish policing strategies.

This retrenchment has resonated with officers in Rockford and around the country. The Fraternal Order of Police has requested that President Trump allow departments to ignore the recommendations of the Task Force on 21st Century Policing, which was established by the Obama administration to mend the public’s rift with law enforcement. Blue Lives Matter groups, bristling at the idea that cops are racist or abusive, have gained large followings. Last fall, while riding along with Thurmond, I met Aurelio DeLaRosa, a Rockford police officer who had recently retired after 26 years on the force. He said the police chief who implemented reforms after the Barmore incident had stoked anti-police views and empowered the wrong people. “He kept us from going out and being pro-police,” DeLaRosa told me. “Wins gained previously went away and crime became rampant.”

In order for community policing experiments like Rockford’s to become more than an idealistic sideshow—for them to become a model for a more democratic form of policing—they will have to survive these charges both of irrelevance and criminal abetment. The research shows that the war on drugs failed, that broken windows decimated neighborhoods, that community policing methods, even in the limited forms in which they’ve existed, increase trust in legal systems and make cities safer. Big-city police chiefs say they’re on board, but neither the funding nor the social and political will necessary to change police culture has followed. Despite edicts from above and earnest efforts from within police forces, uniting cops and communities in a deep and lasting way remains a theory rather than a practice.

After decades of economic decline, there are signs of revival in Rockford. A hotel and a few new businesses and residential high-rises have sprouted downtown. The city’s former industrial prominence means there’s still a symphony orchestra, an impressive art museum, ample parkland, and blocks of stately Victorians that are good candidates for restoration. Several manufacturing holdovers endure as well. “You can’t find an airplane that doesn’t have a Rockford product on it,” Tom McNamara, the city’s young mayor told me in his City Hall office. In 2013, local business leaders formed Transform Rockford, a nonprofit committed to turning the city into “a top 25 community by the year 2025.” The group was focusing on 14 different action areas, but crime reduction was key. “It all centers around safety,” said Jacob Wilson, the program director of Transform Rockford.

This emphasis on crime meant Chief O’Shea was testing a number of different policing strategies to contend with violent offenders and the prevalence of domestic abuse. He said he would also like to expand the ROCK program, placing a resident officer in nine of the city’s ten patrol areas. But in the financially strapped city, a fuller investment in this form of preventive policing has yet to emerge. “Cops are very, very hesitant with change,” O’Shea said. Nevertheless, he believed he had found the right people in Turner and Thurmond: “She’s super community-minded, and he’s outgoing and wants to solve problems.” More importantly, O’Shea added, all of his officers were supposed to be doing the work of building up trust and legitimacy. “The day-shifters and old-timers who have pushed back, either you come around or find another job,” he said. “That’s my number-one directive. It’s a nonnegotiable. Every officer is to be out engaging with the community. Positive contacts, sitting around, chewing the fat, being a regular person. They need to see you for what you are.”

On one of the days I rode with Thurmond in his patrol car, he drove past the Stockholm Inn, a breakfast spot where he posted up one morning a week to talk with residents. He turned into a nearby Walgreens and went inside to view security footage of a retail theft. At Nelson Elementary, the school where he read to second graders, no kids were on the recess yard. He’d run out of ways to engage the community for the moment, and as he headed back to his east side bungalow he stopped to offer an older African American man a lift. The man, who was carrying several bags of groceries, declined Thurmond’s offer, smiling but not breaking stride. “You sure?” Thurmond pressed. A ride, he insisted, was no problem. The man looked at the empty back seat of the squad car being presented to him. It represented far too much history. He repeated that he was good walking, and Thurmond left him reluctantly.

Thurmond pulled up outside his house moments later. He spotted a 14-year-old who lived on the block with his grandmother. The teen was wandering the streets with a friend. It was the middle of a school day. “I don’t go to school,” the boy told Thurmond, without further explanation. He wore slippers, despite the cold, and he backed away incrementally as he gave clipped-sentence replies to Thurmond’s inquiries. Whatever he and his buddy were up to, they were eager to get back to it.

“If you need anything, let me know,” Thurmond volunteered. “Just ’cause I’m police doesn’t mean you can’t talk to me.”

Commentators are once more worrying over America’s waning preeminence. A New Yorker headline in January suggested Donald Trump was “Making China Great Again.” When the president withdrew from the Iran deal in May, Washington Post columnist Anne Applebaum lamented that “the era of American hegemony” had been “remarkably brief.” And just last week, reflecting on the G7 summit, the New York Times exhorted Americans “to recognize that this president has transformed ‘America First’ into ‘America Alone,’ and that this is the last place that a great and powerful nation wants to be.”

While the United States has defied many declinist predictions in the postwar era, there is good reason for recent anxiety. Withdrawing from the Trans-Pacific Partnership has reduced America’s leverage in the Asia-Pacific and enabled China to gain further traction for its own economic initiatives in the region. Trade tensions with longstanding allies including the European Union, Japan, Canada, and Mexico have compounded U.S. isolation. And unlike his postwar predecessors, President Trump harbors a deep skepticism toward U.S. support of and participation in what is loosely called “the postwar order.”

But shifts in the world’s strategic balance are more complicated than they seem: While the rise of other countries and the growing heft of nonstate actors mean that America’s relative decline will likely continue, there is more to a country’s standing than headline-grabbing metrics. A “superpower” is bolstered not merely by the force it wields, but by the vision it embodies: a conception of world affairs that holds widespread appeal, enabling it to advance its objectives and amplify its values far more than it could do with military and/or economic coercion alone. Washington has a significant edge over Beijing in this regard—one reason why we are less likely to witness a clean, discrete power transition between the two countries than an uncertain, fluid bilateral balance—if the United States can rebuild, rather than dismantle, the structures that work to its advantage.

Consider a typical indicator of national prowess: military strength. According to a projection by the International Institute for Strategic Studies, Beijing’s military expenditure could overtake America’s by the mid-2030s; but the composition and use of those military outlays matter at least as much as the level. China will not be a military peer until and unless it can apply armed force as quickly, lethally, and globally as the United States. “Most of the military modernization underway in China corresponds to achieving the types of capabilities the United States has already attained,” Cortez Cooper of the RAND Corporation testified in February. Washington is fighting terrorist organizations in at least 14 countries and, as of last year, had special operations forces deployed in 149 countries—roughly three-quarters of the world’s total. No other country can project military power into any corner of the world.

Economic indicators, too, are more ambiguous than they are sometimes made out to be. A recent forecast calculated that China’s gross domestic product will overtake America’s in dollar terms by 2032. But size is not everything; to be considered an economic peer, China would need to have a per capita GDP roughly four times its current level, a comparably robust system of innovation, and a currency that figures as centrally in global financial markets as the greenback. It is undoubtedly making progress on all these fronts. China’s per capita GDP has roughly quadrupled over the past decade. Its ambitious “Made in China 2025” plan, moreover, lays out concrete targets in ten priority areas to help the country become a world leader in advanced manufacturing. And the German Bundesbank’s recent announcement that it would begin to include yuan in its reserves is another small step forward in the renminbi’s internationalization. Still, true economic parity between Washington and Beijing is far away.

A more abstract factor is the ability to regenerate fundamentals of national power such as population size, economic growth, and innovative capacity. In large measure due to immigration, the United States has the most favorable demographic outlook among major powers: The Pew Research Center projected in 2015 that future immigrants and their U.S.-born children would account for 88 percent of the country’s population growth through 2065 (though the Trump administration’s desire to reduce immigration could dampen that trajectory). Thanks to the shale revolution, the United States is on track to become a net exporter of energy products by 2022, a feat it last accomplished in 1953. And, despite a worrisome dip in international students in 2017, it retains an unmatched ability to attract and harness global talent (though it might begin ceding that advantage if the administration tightens student visa requirements as it is reportedly considering).

However one measures overall national power, China will likely continue to catch up to the United States. But history suggests that secular trends alone are insufficient for predicting preeminence. While the U.S. economy overtook Britain’s in absolute size in the last quarter of the 19th century, Washington did not emerge as the world’s central power until the end of World War II. The devastation that Europe and Asia had suffered during the war meant that only the United States had the capacity to fashion a new order. Critically, though, the Truman administration used the moment strategically, building a framework around the United States—grounded in multilateral institutions such as the United Nations, the International Monetary Fund, and the World Bank—that elevated collective interests over narrow ones and gave Washington an unrivaled ability to convene problem-solving coalitions. Subsequent administrations expanded this system, appreciating that the United States could strengthen its perch by enabling the progress of former antagonists and longstanding friends alike.

The Trump administration is the first of the postwar era to challenge this framework, regarding the world as “an arena of continuous competition” and reverting to a largely transactional style of foreign policy. Abandoning the Trans-Pacific Partnership, declaring its intention to withdraw from the Paris climate accord, decertifying the nuclear deal with Iran, and asserting a “national security” rationale for imposing tariffs on longstanding European and Asian allies all steer the United States away from the course of statecraft from which it benefited in the twentieth century. They also reflect the administration’s embrace, as Financial Times columnist Gideon Rachman has argued, of “a power-based order—in which the U.S. lays down the law and others are compelled to follow.” While America’s current margin of preeminence might sustain this sort of approach for now, the strategy could also hasten the country’s relative decline—not only by encouraging competitors to intensify revisionist efforts, but also by accelerating allies’ efforts to reduce dependence on U.S. actions.

Beijing’s resurgence over the past four decades may be one of the most extraordinary trajectories of any country in history. Consolidating its control over the South China Sea, undertaking large-scale projects such as the Belt and Road Initiative, and growing increasingly vocal in its rejection of Western ideology, China is an increasingly formidable long-term competitor. To surpass the United States as the globe’s preeminent power, though, it will likely have to tether its ambition to a coherent, compelling conception of world affairs. “A superpower,” Samuel Huntington observed three decades ago, “has to stand for an idea with appeal beyond its borders.” China has yet to identify the idea for which it stands, not only because it has benefited immensely from the postwar order, but also because taking on the responsibilities of a superpower would detract from its pursuit of a national renaissance. While its foreign policy has enabled it to generate an impressive base of national power, Beijing has been unable to inculcate a distinct vision within a network of alliances.

The United States might consider, instead of trying to match each of China’s initiatives, renewing its own core strengths. The framework it helped establish in the post-World War II period faces a number of tests. A growing number of emerging powers regard the postwar order less as a self-evident gift than as an illegitimate imposition. Borderless problems, including cyberthreats and climate change, are challenging its problem-solving capabilities. Finally, as the 2016 presidential election clarified, Americans experiencing economic hardship and demographic anxiety understandably feel little commitment to abstractions about “order,” “engagement,” and “leadership.”

Washington would have to do an enormous amount of work abroad and at home to modernize the system it constructed after World War II. For now, though, as recent statements by longstanding allies affirm, it is actively undercutting that framework and, in the process, a key source of competitive advantage. “Can countries including China and the U.S., especially China and the U.S., agree on one rule-based order, which President Xi Jinping said he supports?” Singaporean Defense Minister Ng Eng Hen asked after this month’s Shangri-La Dialogue, implicitly questioning America’s commitment to a rule-based order. Ahead of the more recent G7 Summit, French President Emmanuel Macron issued an even more striking rebuke: “The American president may not mind being isolated, but neither do we mind signing a six-country agreement if need be.”

Proponents of an “America First” approach to foreign policy may not worry much about such statements or believe that U.S. influence has benefitted much from a strategic vision. They would do well, though, to heed French political theorist Raymond Aron, who argued that “the strength of a great power is diminished if it ceases to serve an idea.” While geopolitical commentary increasingly abounds with discussion of a power transition between Washington and Beijing, the world may actually find itself suspended between two giants whose behavior defies expectations: a reigning power that attacks a longstanding source of its own influence on one side and a putative replacement that struggles to define itself as an idea on the other.

By now it is commonplace to point out how much of our lives are subject to algorithms. The imperative to provide “analytics” for everything from financial portfolios to security risk, to work and shopping habits seems always on the verge of converting all of experience into some tidy table of figures. Arguments about where or whether we reach something human and unquantifiable typically end up invoking, more or less indignantly, aesthetic experience. Art, it is argued, is the place where analytics hit a wall.

The idea that works of art can be explained quantitatively (aside from quoting some dollar amount), might be caricatured in the description of, say, a Vermeer, by noting that it is a 17 7/8 inch high by 16 1/8 inch wide canvas, on which are arranged a certain combination of color-coded patches and flecks, followed by an account of the chemical processes at work when the pigments change as the picture suffers the ravages of time. Even if all of this turns out to be factually true, such a description leaves a lot out: the way (to take one of a potentially limitless set of examples) a milkmaid tilts a jug so that falling rivulets of milk are caught in a ray of late afternoon sunlight. What is left out, in short, is the experience of the painting. Measurement misses the point.

Music is more complicated, though, because it is fundamentally bound up with numbers. Even the most gushily emotive piece of music is animated by an explicable numerical substructure: The scales used to make melodies are subdivided into discrete intervals; these intervals may be stacked vertically in thirds and fifths and sevenths and ninths to create chords; and all of it unfolds over a sequence of metrical pulses. This isn’t just some high-flown abstraction. Composers derive structural and expressive ideas from this numerical DNA, allowing for the invention of new kinds of music. All this leads to puzzling questions about where the measure of music ends and where our experience of it begins.

The deep connection between music and math was already in place by about the sixth century BC when Pythagoras of Samos found that audible pitches could be expressed as numerical ratios. Go to a piano, hit a middle C and put your ear to the wood: You’ll hear an overtone resonating an octave above. It’s the same note twice as high—which means the ratio between tone and overtone is 2:1. For Pythagoras such overtones were the royal road to the truth that the world was made of numbers, and that “harmony” described not just relations between pitches, but the rational order of the cosmos itself.

In the nineteenth century, Pythagorean ratios were used to establish the basics of acoustics, the physics of sound. Hermann Ludwig Ferdinand von Helmholtz used graduated glass spheres to isolate overtones and show beyond a shadow of a doubt that they existed (until Helmholtz’s experiments there was some skepticism about the reality of overtones). As Eli Maor tells it in his limpid, lively history Music by the Numbers, Helmholtz invented and built an electrical contraption that could “combine several pure tones, each generated by a tuning fork driven by carefully timed electromagnetic pulses, to imitate the sounds of various musical instruments and spoken vowels—a precursor of the modern electronic synthesizer.” Indeed, when analogue synthesis came into vogue in the 1960s, it brought with it not just a new set of timbral colors but, for many, a crash course in acoustic science, as a glance at the control surface of any synthesizer will show, with its oscillators, filters, wave shapers and resonators. 

The problem of measuring music may shed light on the question of where to draw the line between music and noise. If a tone, as Maor explains, “is generated by periodic vibrations that repeat themselves again and again with precise regularity, producing a sound with a definite recognizable pitch” then everything else is noise, characterized by “nonperiodic, random vibrations.” Hearing the tonal warp of a passing siren may be explained by the Doppler effect (change in the perception of a sound whose source is in motion). Yet it would be wrong to think that the siren sound in Erik Satie’s 1917 ballet Parade could be explained in the same way, since it’s part of the experience of a larger work. Something new has entered with Satie’s siren. It is hard to quantify just what exactly it is. 

Pitch isn’t the only area where the difference between music and noise is hard to pin down: marking time—tempo—is also an essential part of music. But when does the marking of time turn into art? Is a ticking clock a piece of music? How about a series in which every third tick is accented? Maor offers a brief account of the invention of the metronome, a piece of technology for fixing and marking tempo and some of the ways in which this form of measurement has proved inspiring. While the prototype for the metronome was invented in 1814 by Dietrich Nikolaus Winkel, it is usually associated with Johann Maelzel (known for his amusing automata, among them a mechanical chess-player). His metronome was a hit with composers, among them his friend Ludwig von Beethoven who, caught in a rare whimsical mood, improvised a tune in honor of Maelzel’s machine. Later Elliott Carter would take the idea of variable tempo in his technique of “metric modulation” in which metronome markings are as fluid and variable as harmonies and pitches, making for a music of warping, Möbius Strip-like contortions. 

The line between music and apparent noise has in fact been one of the central aesthetic controversies of twentieth century music. John Cage’s 4’33” comes to mind, in which any chance occurrence during a performance of the piece—a passing car heard through the walls, someone sneezing in the auditorium, the slamming shut of the piano—counts as part of the work. A more programmatic—and, depending on your point of view, aesthetically convincing—attempt to challenge ideas of what could be music was Arnold Schoenberg’s dodecaphonic system of serial composition. Schoenberg began as an expressionist composer, extending Wagner and Mahler’s innovations in extreme chromaticism, but later found a way to bypass tonality altogether. In serial composition one moves through all 12 tones in the “row” before beginning a new phrase, building up themes and motifs from that numerical constraint.  

The controversy of Schoenberg’s serialist works—the overwhelming reaction to them as ugly, nightmarish, simply unmusical—shows how firmly tonality had come to condition habits of listening. It also points to a widespread dislike for composition that pushes music too close to its roots in mathematics. 

All sorts of kooky ramifications and bits of weird trivia start popping up the more you look into the connections between music and math. The wiry undulations of the Slinky toy, for example, turn out to be good way of modeling sine waves. And what about the “lowest known musical note in the universe”? It turns out to be a tone emitted by the galaxy cluster Abell 426, 250 million light years away. Maor explains: “the cluster is surrounded by a hot gas at a temperature of about 25,000,000 degrees Celsius, and it shows concentric ripples spreading outward—acoustic waves. From the speed of sound at that temperature—about 1,155 kilometers per second—and the observed spacing between the ripples—some 36,000 light years—it is easy to find the frequency of the sound: about 3x10-15 Hz, which corresponds to the note Bb nearly 57 octaves below middle C.” (You’ll need to tack on 635 keys to the left side of a piano keyboard to find out what this sounds like).

In looking into the links between music and math, one can’t help feeling excited affection for the freewheeling curiosity of previous centuries, when savants played over broad arrays of disciplines like virtuoso keyboardists. The unfettered polymathic openness of a Helmholtz or a Schoenberg seems comparatively rare in our age of narrow expertise and stiflingly corporate “research programs.” This is not to mention the persistence of what C.P. Snow once called the Two Cultures, which still keeps the arts and the natural sciences at a tense, suspicious distance.

While the intimate link between music and math upsets the presumed schism between creative expression and disciplines like physics or engineering, it also dispels the idea that artworks (musical or otherwise) are in any true sense measurable. Musical works may be not “explained” numerically; there is a category mistake in the idea. For all the precision of descriptions of tones as formed from composites of overtones, or how the human ear is a natural acoustic prism, no amount of measure will capture just what it is about Bach’s Goldberg Variations that makes them drop dead gorgeous. (This is not to mention the difference between the piece as performed by one human being, say Karl Richter, and another, say Glenn Gould).   

None of this is to suggest that we should not be interested in the connections between music and numbers. Those connections give one a peculiar and exhilarating taste in the head. It’s one you find in Martin Gardiner’s Scientific American columns on mathematical puzzles and in his annotations to Alice in Wonderland; in the French Oulipo collective who seek in numerical constraints ways of deriving novels and poems; in the “quasi-musical … poetico-mathematical” high Vladimir Nabokov got from composing chess problems; in the twisty, psychedelic speculations of Douglas Hofstadter’s Gödel, Escher, Bach. To spend time in this place is as good an antidote as any to the ubiquity of algorithms.