Chris Hirata consults with senior NASA scientists, lectures on how to colonize Mars, and probably has the highest IQ at Caltech. At the moment, though, he's concentrating all his brainpower on a distinctly less-than-cosmic goal: trying to convince his mom to let him walk to school.
Chris, 16, faces his skeptical mother across the dining room table at their Pasadena home. He is armed with complicated charts and tables showing how the Earth orbits the sun and how that orbit slowly fluctuates. As a result of these "orbital eccentricities," he says, the days are getting longer. Sunrises are earlier, sunsets later. Thus there's more daylight for a kid -- such as, ahem, Chris -- to safely walk to and from school.
Chris' mom has heard it all before: orbital eccentricities, wave functions, harmonic oscillation. Whenever the kid wants something, he trots out the scientific mumbo jumbo. Terese Hirata watches bemusedly as her off-the-charts-brilliant son diagrams the solar system and scribbles hieroglyphiclike equations -- all in a somewhat desperate bid to convince her to stop dropping him off at Caltech every day.
Terese, a self-described ex-hippie, knows it's got to be a little humiliating. Having your mother drive you to college, for Chrissakes! But she's unmoved by her only son's carefully logical plea.
After all, Chris has galloped so far ahead of her and her husband intellectually that he isn't exactly easy to spend quality time with. His IQ is so high -- somewhere around 225 -- that it can't be measured accurately. In his sophomore year at Caltech, he racked up a 4.2 grade point average -- taking all upper-division classes. His idea of fun is studying the math Einstein used to formulate his theory of relativity. So driving Chris to school is one of the few normal, momlike things Terese can still do with him.
"I treasure that time and am not ready to let go," she says. "Whenever I say no is when we get into the bamboozling with the mathematical/science bullshit. He often comes up with stuff like the whole orbit thing with charts and trapezoids.
"But what it's really about is a teenager and his parents and figuring out who is in charge of what."
The mind of a Nobel laureate in the body of an adolescent -- that's Chris Hirata's cross to bear.
He skipped seventh through 10th grades but still can't vote. He schmoozes with Caltech professors about black holes and gamma rays but can't legally buy beer. He won a gold medal and ranked fifth in the world at the international Physics Olympiad but doesn't have enough hair on his chin to shave.
And his mom won't even let him walk to school.
If you ran into Chris at the local mall, you wouldn't take him for anything but a typical California teenager. He wears baggy sweatshirts over jeans or running pants. His silky brown hair is a little unruly. He has a swimmer's broad shoulders (he's on the Caltech swim team) and good looks inherited from his Japanese-American father and Caucasian mother. His smile reveals an orthodontic retainer.
But start talking to Chris and you'd think you were in the presence of an Oxford don who's more than a little eccentric.
When asked how old he is, Chris sharply responds, "16-point-one-eight" years. He often seems lost in thought. When a reporter reaches out to shake his hand for the first time, he acts as if he has been pulled into the present from some very distant place. "Oh," he says, looking startled as he extends his hand.
He has trouble with small talk but waxes eloquent about perturbation theory. (When you have two problems that are similar, perturbation theory means you figure out the answer to one and use that to approximate a solution to the other.) He's very precise in his speech, often pausing to think before answering a question. And he's direct to the point of brusqueness.
The signs of Chris' awesome intellectual prowess emerged early.
By age two, he was building Roman numeral clocks out of sticks in the living room. At three, he rode in the grocery cart as his mother shopped and calculated how much her bill would be -- with and without tax -- in his head. He was always correct, Terese Hirata says, to the penny. At five, he was building sundials in the backyard.
Chris' parents began to understand the power of their son's brain after his IQ was tested in the second grade, when the family lived in the Chicago suburb of Deerfield, Illinois. The tester called Terese and Richard Hirata in and said, "We couldn't put a ceiling on his IQ. He is off the charts." While Chris' classmates were still learning to add and subtract, he was doing complex mathematical equations and measuring the Earth's gravitational field with homemade pendulums.
Richard Hirata, a statistician for ACNielsen, had tried as delicately as he could to prepare teachers at Chris' elementary school for his son, the prodigy, telling the principal of the child's gifts. But Walden School principal Harry Grover thought Hirata was just boasting. Grover had heard it all before from pushy parents who wanted special attention for their kids.
"Mr. Hirata told me Chris was very bright, and I said, 'He'll fit right in. We have a lot of bright children,' " recalls Grover, now retired. "Mr. Hirata said, 'Chris could read when he entered kindergarten,' and I said, 'We have a lot of kids who could read when they started kindergarten.' Then Mr. Hirata said, 'Chris could calculate square roots in the first grade, and he figured out how to do it himself.' I thought the guy was exaggerating."
Before long, Grover realized that Mr. Hirata was not a typical stage parent bragging about his kid. In fact, Hirata had dramatically understated his seven-year-old son's brilliance.
Two weeks after Chris started at Walden, his teacher, Debbie Bowers, rushed into Grover's office and demanded, "What am Isupposed to do with this kid?"
Bowers related how she had shown Chris and her other second-graders a detailed map of the Middle East. The other kids were mildly interested, but Chris was transfixed. A few minutes later, Bowers recalls, Chris called her over to his desk. He had drawn the map from memory with all the details from the original, including national boundaries, cities, mountain ranges, and rivers.
"He did it so fast -- he was like a computer," Bowers says. "Everything was spelled right. He had the topography and where all the countries were -- all right. It was fantastic."
Grover wanted to see for himself just how smart the kid was. He called Chris into his office for a chat. The former principal remembers that talk as the most extraordinary he ever had with a student.
Okay, so the kid knew his planets. The principal was impressed but decided to amp things up a bit and really put Chris to the test. He began talking about Kepler's laws of planetary motion -- complex mathematical formulas that explain how planets orbit in space. Grover explained how Kepler's laws worked and then wrote down the equation for the third law, which involves cubes and cube roots.
The boy listened intently.
"Chris started doing the math in his head and began explaining it to me," says Grover. "I couldn't believe it. It had taken me months to understand Kepler, and Chris understood it in a matter of minutes. For a seven-year-old, this was utterly amazing....Pretty quickly, we realized we had quite a find here."
From that day on, the teachers at Walden took a whole new approach to educating Chris. They drew up advanced math and science courses and began bringing in outstanding high school students to tutor him daily. But their jury-rigged curriculum didn't last long. "As he progressed, he outstripped us of everything,' Grover remembers. "By the time Chris was nine, he started taking advanced placement classes at the high school."
Chris began spending his mornings taking AP physics, calculus, and chemistry classes at nearby Deerfield High and his afternoons back at the elementary school.
"You'd see this little pip-squeak in the halls, and he came up to everybody's knees," recalls Mary Beth Kravets, Chris' counselor at Deerfield. "He was like the high school mascot."
Chris, who often seemed lost in a vapor of deep thoughts, stuck out at the elementary school, too. "The other kids didn't relate to him," Grover says. "They wanted to talk about cartoons, and his mind was working at a whole different level, thinking about gravity and things far beyond."
Although he was several years younger than most other Deerfield High students, Chris quickly became the school's top scholar, earning straight As in his AP science and math courses. "When he was 11, he used to teach my AP physics and honors physics classes when I was at a conference or absent," says David Thiessen, a retired Deerfield teacher. "The students thought he was a better teacher than I was."
While most kids spent their summer vacations having splash fights in the neighborhood pool, Chris took math and science classes at Northwestern University's Center for Talent Development, an institute for academically gifted children. The center's director, Paula Olszewksi-Kubilius, says she had never seen anything like Chris.
"Chris is the only kid I've known at that level of intelligence," she says. "His needs could not be met by any school program....His talent is extremely rare. Statistically, very few people exist in that [IQ] range."
At 12, Chris began attending Deerfield High full-time. But he tore through the curriculum like an alcoholic at a wine tasting, quickly mastering course after course.
"I told the school board that to call Chris Hirata one in a million would be doing him a disservice," says Vince Malek, chairman of Deerfield's science department. "It was obvious to me when he was in fourth grade that he could win a Nobel Prize if he wanted. He's probably brighter than most Nobel Prize-winners."
David Thiessen, who has a master's degree in physics, was so amazed by Chris that he began videotaping the boy as he worked out complex problems. "He would come up to the board after class and start expanding on what we had done, taking it to a higher level," Thiessen says. "It just blew me away....It was so fantastic."
One day, Chris began analyzing harmonic motion, or the way objects vibrate around a point of equilibrium. For example, if a taut piano string is pulled up an inch and released, how long does it take to return to its original position? If the string is pulled two inches, does it take longer to snap back to its normal position or not?
Overnight, Chris came up with an elegant formula that provided the answer. He found that the further the string is pulled, the quicker it returns to its equilibrium position. His equation also made it possible to calculate exactly how much the snapback time decreases as the object is pulled further away from its starting point. His formula worked not only with piano strings, but with atoms, electrons, and sound waves.
Chris' physics teacher, Thiessen, couldn't believe what his star student had come up with. It was brilliant. So Thiessen wrote a paper about it and sent it off to be published. Chris' formula was published in the December 1995 edition of The Physics Teacher, a national publication widely read by high school and college physics instructors. The magazine subsequently received letters and e-mails from physicists around the world praising the work.
"One physicist told me that if this was done by a 12-year-old, I had a Mozart on my hands," Thiessen recalls.
Meanwhile, Thiessen took Chris to physics colloquiums where the boy discussed harmonic motion and other knotty physics problems with professors from throughout Illinois. Chris once made an hour-long presentation to 300 teachers and professors at the University of Illinois on three-dimensional equilibrium balance, or how different forces affect an object's rotation. He had come up with a breathtakingly simple equation for solving the problem.
At 13, Chris' brains gained worldwide attention.
After passing a battery of difficult tests at a weeklong physics training camp, he was picked to represent the United States in the 1996 Physics Olympiad in Oslo, Norway. He was one of five students from the U.S. in the competition, which drew top math and science students from around the world. Chris was the youngest of the 259 contestants, who ranged in age up to 19. His selection got him a standing ovation from the entire Deerfield High student body at an assembly.
The Olympiad is a weeklong competition that involves two five-hour-long exams. One test has theoretical problems, and the other is a lab exam. Competitors' work is then graded by a team of physicists, and winners are selected. Patrick Knox, assistant director of the American Association of Physics Teachers, which assembles the U.S. team, describes the tests as comparable to "exams for Ph.D-level students."
Chris won a gold medal in the competition, ranking fifth in the world.
In addition to his medal, Chris received a special award for "being the youngest medalist ever in the Physics Olympiad," says Knox. In 1997, Chris qualified again for the Olympiad. That year, he won a silver medal.
Meanwhile, Deerfield High was losing its battle to keep Chris stimulated intellectually. In two years he had gone through every advanced placement and honors class the school had to offer. He was taking math classes at a nearby community college, but high school officials knew it was time for him to move on.
"Considering his brain, it would have been cruel and unusual punishment to keep him in our high school," says Kravets, the Deerfield High counselor. "There were no classes for him to take."
So Kravets helped Chris look for a college.
Caltech, one of his top choices, admitted him quickly, despite reservations about letting in a student so young, Kravets said. The college sent him a bunch of tests to determine what level classes he should be taking; he aced them all. He entered the Pasadena school at 14, taking junior- and senior-level courses, with titles like "Waves, Quantum Physics, and Statistical Mechanics" and "Computational Physics."
Chris' dad got a job transfer, and the family moved to Pasadena in late 1997 so Chris could live with his parents while attending college. On his first day, his mother dropped him off at campus for a high-level math class called "Classical Analysis."
The boy, uncharacteristically, was nervous, wondering if he'd be able to keep up with his fellow students at the legendary college for science and math whizzes. "I wasn't quite sure what to expect," he says.
He quickly relaxed. After the professor introduced himself, he began writing labyrinthine equations on the blackboard. "I was looking at the stuff and thinking this is odd," Chris recalls. "This is stuff that I've already seen before."
It's Monday night, and the weekly meeting of the Caltech chapter of the Mars Society is under way in a bare-walled classroom.
At the blackboard, Chris Hirata has his fellow society members mesmerized as he describes the ideal launch vehicle to deliver humans to the red planet. His listeners are a multiracial group of serious-faced young men with short hair, unpressed shirts, and acne eruptions -- plus one young woman with pink hair.
"We have, right now, a three-stage core vehicle, so liftoff mass here is 2,200 metric tons....The capacity is 53 metric tons to trans-Mars injection," says Chris, diagramming a rocket on the board as the others munch cookies and sip orange juice. "The ratio of the thrust to the mass is not that much greater than G."
Chris' ideas about getting to Mars have attracted attention far beyond this little band of adolescent space-flight buffs. Earlier this year, he e-mailed NASA with some of his ideas, and the space-agency nabobs were keenly interested in what he had to say. They have been corresponding ever since.
John Connolly, the man in charge of NASA's Mars mission at the Johnson Space Center in Houston, was astonished to learn, during a New Times interview, how young his Internet pen pal actually is. "I didn't know he was 16," Connolly exclaimed. "I assumed he was a Caltech graduate student working on this.
"His ideas are incredibly sophisticated. When you talk about sending humans to Mars, it's an incredibly complex mission, and Chris understands the many variables and is able to juggle them in his mind. That is a very, very advanced thing for a student. Most people at NASA haven't mastered that....To do what he is doing usually requires years of experience. Anyone who is a good systems thinker, like Chris, is very valuable to the space program."
So taken is Chris with the romance of exploring and possibly colonizing Mars that he created an intricate computer program to help NASA determine the best launch date and trajectory for a Mars mission. He outlined his program last summer at the Mars Society's annual conference in Boulder, Colorado, which drew top-drawer space scientists and engineers from around the country.
"Chris presented alongside people from NASA," recalls Robert Zubrin, the society's president. "Chris' Mars mission strategy allows a free return to Earth without extra propellant. The beauty of that is that if your engine conks out, you can return to Earth."
As Chris elaborates on his let's-fly-to-Mars scheme at the chalkboard, a faint smile crosses the face of his friend Derek Shannon, a soft-spoken freshman who's bright enough himself to have won a full scholarship. Shannon cofounded the campus Mars Society chapter with Chris, and the two teens have bonded thoroughly over the idea of sending rockets to Mars.
"Chris could be doing this entire mission architecture by himself, but he wants it to be an effort on the part of the whole group," says Shannon, who is studying aeroengineering and geobiology. "Chris keeps telling us we need to design something that NASA and the Mars Society will like, so there is a unified voice talking to the president and Congress about getting humans to Mars."
With his years as an intellectual sideshow freak finally behind him, Chris is clearly enjoying life at Caltech. Watching him interact with the other brains on campus is almost like seeing a Cheyenne chief embrace his fellow warriors after being released from captivity. Caltech is filled with young men and women who, like Chris, spend far more time thinking about wave functions and particle balls than about the opposite sex.
After all, where else but here could a 16-year-old boy have his own small office, filled with books with titles such as Molecular Spectroscopy and the Differential Geometry of Curves and Surfaces? Where else would he be the sole student working on a professor-led project exploring the use of gamma rays to track gases being sucked into black holes and other invisible high-energy processes in deep space?
"You see, you've probably seen the map of the sky at longer wavelengths. The soft gamma-ray sky has never really been adequately mapped," he says, happily covering a blackboard with impenetrable wavelength diagrams. "What I am doing is constructing a computer model of the instrument we are going to use to map the universe. Then we're going to write a paper about all this."
Taped to the wall of Chris' office is an elaborate, odd-looking chart labeled "FSL versus Time." At first he refuses to explain what it means but, several interviews later, he slowly gives in.
"This is a graph of a certain parameter that is not exactly the quality of my life but is related to it," he says cryptically. "FSL stands for fraction of social life versus time."
In other words, the kid's measuring how much he hangs out with friends.
"I have a new plot every month of FSL versus time," he says. "I always take it to the dorms and let it drift around and see how much [other students] enjoy looking at the various features." Then he sternly warns me not to tell his parents about his charts.
"I don't want them to know I care enough to plot it out," he says. "I'm not sure what their reaction would be."
Charts, graphs, computer spreadsheets -- such are the tools that this child genius uses to navigate adolescence. While other boys his age might seek clues from their dad's old copies of Playboy or during bull sessions at the local diner, Chris tries to reduce the complexities of kidhood to mathematical models.
He never really explains why he's so interested in keeping track of how much time he invests in social activities. But his mother has her own interpretation.
"He was in high school so briefly and there was the age difference, which made [friendships] difficult," she says. "He didn't fit it for many, many years....Coming to Caltech is the first time he's had an opportunity to spend time with friends."
Later, Chris reluctantly admits he needs to involve himself more with friends. But he says he has put together a special computer program to handle this dilemma. He doesn't want to talk much about it, though.
"I've almost solved that problem, but no details on the solution process," he says. "I have two copies of the solution process and only one computer program that can decode it. The wrong password makes the computer crash."
Chris' obsessive use of charts and graphs to analyze human behavior goes way back. When he was nine years old, he began charting how weird his mother became one week out of every month. He didn't know what was going on with her, but he clearly understood that once a month she went nuts a little, and he kept close track of her changing moods.
"He kept the charts on the refrigerator, and I didn't know what it was," Terese Hirata recalls. "Finally, he talked to his father about it and realized it was my menstrual cycle. The two of them finally told me about it, laughing. I felt like a bug under a magnifying glass!"
Chris' Caltech buddies think his charts are pretty strange. But they accept his fixation without question. He's a genius, and geniuses aren't like you and me.
"He keeps track of everything, and that's really weird," says Melissa Todd, a freshman geology major who is on the college swim team with Chris. "He isn't normal, and you can't assume he's working under the same laws of logic as everyone else....But I figure I'll never meet another Chris Hirata in my lifetime, so it would be a shame not to appreciate whatever he is while I have the chance."
At the moment, Chris is working on yet another elaborate spreadsheet, detailing his scheme for moving out of the house and into the dorms. Predictably, he doesn't want to say much about this one either.
"I don't want to hurt my mother," he says. "She is really going to miss me."
But later, in an unusual outburst of normal teen angst, he says he can't wait to move out because his mother is driving him crazy.
"It's the little things that annoy me about by mother," he huffs. "She asks me, 'Chris, do you want the radio on?' I'm like, 'No, Terese, I can turn the radio on and off.' You see, she has this feeling I can't do anything like that. Those little things start to drive me insane."
His irritation with his mom, though, is one of the few manifestations of typical teenage behavior in Chris. He spends much of his free time working on various science projects. His life is so cerebral, says his dad, that he was surprised to find out that "Chris knew who the Spice Girls were."
Another of Chris' friends, Ben Newman, whom he knows from the Physics Olympiad camp, says kids like him and Chris are completely different from other teenagers. But most people don't understand this, he says.
Newman, now a Swarthmore College sophomore majoring in cognitive science, remembers one morning when he and Chris and a group of friends from the physics camp went to McDonald's. At the restaurant, other teens threw french fries at each other and gossiped about schoolmates. But the physics camp bunch were on their own unique trajectory.
"We sat around writing general relativity equations out on the napkins," recalls Newman, 20. "And there was a bullet hole in the window, and we talked about why the hole was a certain shape."
But even by the standards of kids with that level of intelligence, Newman says, Chris stands out.
"You spend five minutes with Chris, and you get the impression he is absolutely brilliant," says Newman. "You can't be a totally normal kid underneath a shell of genius."
For his part, Chris insists -- unconvincingly -- that he isn't all that different from other kids his age. He hangs out with classmates in the Caltech dorms every Saturday night, he says, for all of one hour. He doesn't have a girlfriend and never has, and admits he thinks a lot more about harmonic oscillation than chicks. The subject of sex seems to embarrass him. "Did you read the Starr report?" he says, laughing self-consciously. "Well, I don't want to do that thing they did with the cigar."
But at least one of his friends thinks Chris should act his age more.
"He has little time for fun, and I feel bad for him. He works all the time," says Melissa Todd, his fellow swim team member. "He needs to have fun....I want to get him drunk one day."
Chris overhears this and is not happy.
"Correction!" he snaps, loudly. "I have the time for fun. The question is whether I can use it that way or whether the time is already dedicated."
Shannon, his Mars Society pal, doesn't worry about his social life. He's concerned about something else entirely.
"The only thing I worry about," says Shannon, "is whether he's going to solve all the mysteries of the universe before anyone else has a chance."
If your image of the kind of people who spawn prodigies is of a mercilessly demanding couple who hover over their kid at chess tournaments and violin recitals, Chris' parents will surprise you.
Terese and Richard Hirata are just the opposite: laid-back and low-key and, if anything, eager to downplay their son's brilliance. They don't even use the word "genius" in connection with Chris; the furthest they will go is to describe him as "very bright."
Terese, 47, is funny and self-deprecating. She grew up in the '60s in Ann Arbor, Michigan, and attended a small state university nearby. Petite with dark brown shoulder-length hair, she has long been a homemaker. For the mother of a child who is so astonishingly brilliant, her interests are curiously unintellectual: She loves to train dogs and hike.
Richard, 45, resembles his son physically, and the two have similar personalities. Richard has scholarly-looking round glasses and a trim athlete's body. Like his son, he is serious, thoughtful, and likes to work with numbers, though he admits Chris surpassed his own math abilities when the boy was in elementary school. (Richard has a master's in math from the University of Michigan.)
Although he's uncomfortable opening up -- another trait he shares with his son -- Richard admits he worried about Chris through the years and wanted to make sure his childhood was as normal as possible.
"We were concerned about whether he would find friends with common interests," Richard says. "I also worried a little bit about setting expectations that were ours and not his. While I think it's good to set high standards, I don't want him to try and live up to my standards. Chris is already driven himself."
To encourage Chris not to live entirely in his mind, Richard and Terese nudged him toward sports at a young age. Richard, a softball player and runner, was particularly adamant about it.
"Chris didn't have the physical play that other kids had because what he was interested in was very cerebral," Richard says. "But he liked to swim. He enjoyed it, and he worked hard at it." Chris has swum competitively on various teams for years.
Academic research shows that geniuses run in families. But because Richard was adopted at birth and doesn't know his biological parents, he's uncertain if there were any prodigies in his family. Terese says she knows of none in her own lineage.
"I think it was random," Richard says. "At the level Chris is at, I have no explanation for it."
Terese remembers her and her husband getting the astonishing results of Chris' IQ test when he was in second grade and wondering what to do next.
"It was hard to know how to nurture that kind of thing," she says. "There has always been this feeling, raising Chris, that we don't know where to go, and we don't know what to do so he can grow and be happy. It's sort of been like this low-key hysteria all these years."
Almost as soon as they learned of their son's giftedness, the Hiratas also discovered that it often provoked jealousy and anger in others.
Some parents complained that Chris was getting unfair attention or that their child was just as bright and deserved the same treatment. Even some teachers were jealous of Chris' brainpower, which generally dwarfed their own. One high school instructor tried to keep him out of the Physics Olympiad, saying he was worried about Chris missing a week of school. And there were envious classmates who were thrilled whenever he stumbled.
Chris remembers an incident when he and some other high school students were asked to design a protective paper container for an egg. The point of the exercise was to see how far the egg could be dropped before it broke.
The glue on Chris' container still wasn't dry when another student abruptly dropped it. When the egg splattered, students teased him and yelled, "Your equations can't make anything work!"
Prodigy researcher David Henry Feldman says what Chris encountered is typical. Resentment of brilliant kids, he says, is deep and widespread.
"Most people don't like the idea of prodigies because they are confronted with the idea of superior talent," says Feldman, a psychology professor at Tufts University and the author of Nature's Gambit: Child Prodigies and the Development of Human Potential. "There isn't anybody else in the world but me who studies prodigies [exclusively], and that's because nobody really wants to hear about them. My book is the only one on the topic published in this country in the last 50 years."
Ellen Winner, a Boston University psychology professor who also studies gifted children, has found that overly involved, pushy parents can be very dangerous for bright youngsters.
"For these kids, there is great pressure to succeed and to continue to be very special," says Winner. "If parents push too hard and put them onstage, it's not a good thing....Sometimes in the teen years, these kids just quit because they feel they've been pushed terribly."
Chris seems in no such danger from his parents. The Hiratas haven't tried to push him in any specific direction and seem content to simply encourage his interests and abilities. They say they'd be just as happy if he grew up to be a gardener as they would if he became a world-renowned physicist. They even have a sense of humor about raising a boy genius.
"We do often say, 'We know you're smarter than us but...,' " says Terese.
But then again, you probably need a sense of humor to deal with a kid who starts blabbing about planetary orbits when you're trying to figure out the best time for him to take driver's ed.
"For one thing, the latest sunset of the year is out here in this region around [mid-June]. So I drew out a trapezoid," Chris says, explaining how he told his father he should take the course earlier in the year because sunsets are later, and it's better to learn to drive when it's light out. "I use the eccentricity of the Earth's orbit as an excuse for a whole lot of stuff. But there is a real argument here."
Negotiations between the prodigy and his parents continue. In the meantime, says Chris, "I'm preparing some charts."