The Numbers Behind NUMB3RS (30 page)

3.31.06
– “All's Fair”

An Iraqi woman, a human rights activist in Los Angeles to make a documentary promoting the rights of Muslim women, is murdered. Charlie examines the statistical records of many possible suspects to try to find the ones most likely to have committed the crime. To do this, he has to weigh all the factors that might indicate a willingness to murder. This enables him to give each suspect a “score” or probability, with the ones having the highest scores the primary suspects. Creating a weighting in this fashion, based on statistics, is called statistical regression, and the particular type that Charlie uses is called “logistic” regression.

4.7.06
– “Dark Matter”

Don and his team investigate a high school shooting in which eight students were killed, along with one of the shooters. The school has a radio frequency identification system to track the movements of each pupil throughout the day, and Charlie uses the recorded data from the system to track the movements of the shooters and their victims through the school's hallways, using “predator-prey” equations. When his analysis uncovers an abnormal pattern, Charlie is sure there was a third shooter that no one had suspected earlier.

4.21.06
– “Guns and Roses”

A government law enforcement agent is found dead in her home. At first it looks like suicide, but when details of the woman's recent investigation and private life start to emerge, Don grows suspicious. Charlie uses acoustic fingerprinting, based on recordings of the gunshot picked up by police radios in the area, and concludes that there must have been another person in the room at the time the agent died. Acoustic fingerprinting has been used on several occasions in actual shootings, including the 1963 Kennedy assassination, where the mathematical analysis indicated the high probability of a second shooter firing from the famous “grassy knoll.”

4.28.06
– “Rampage”

A man steals a gun from an agent in the FBI office and starts shooting people at random. After agent David Sinclair overpowers him, it is discovered that he is a respectable husband and father, seemingly without motive. After considerable investigation, Don learns that the man was a pawn in an elaborate scheme to derail an upcoming trial of a dangerous arms dealer. Charlie provides a key step in the investigation by determining how closely the shooter's path resembled Brownian (random) motion. He also uses an analogy with a four-dimensional hypercube to motivate an examination of the shooting as a spacetime event.

5.5.06
– “Backscatter”

Don investigates a computer hacking scam that breaks into a bank's system to gain access to the identities and financial assets of its customers, including Don. It turns out that the Russian mafia is behind the activity. Interestingly, although the security of bank computer and data systems depends on masses of advanced mathematics, some of which Charlie mentions, the solution to this case does not make much use of math—it's all “beneath the hood,” buried in the tracking systems that Charlie and Amita use to help Don.

5.12.06
– “Undercurrents”

The bodies of several young Asian girls are washed up on the beach, possibly having been thrown overboard. The situation becomes more critical when it is discovered that one girl has avian flu. Charlie carries out some calculations focused on ocean currents to determine the most likely location where the victims entered the water. As the investigation continues, Don and his team discover a connection between the girls and the sex trade industry.

5.19.06
– “Hot Shot”

Don investigates the murders of two young women, found in their cars outside their homes. Their deaths were made to look like drug overdoses, but Don soon concludes that a serial killer is responsible. Charlie tries to help by analyzing the daily routines of the two women, looking for patterns that might provide leads to the killer, but Don solves the case largely by standard investigative techniques.

THIRD SEASON

9.22.06
– “Spree”

The first installment of a two-part season-opener. A young couple embark on a cross-country spree of robberies and murders. When it becomes clear that their movements are influenced by the pursuit of an FBI agent, who joins forces with Don and his team, Charlie uses “pursuit curves” to help the agents track them down. The effectiveness of the mathematics becomes critical after one of the fugitives is caught and the remaining one kidnaps Agent Reeves to trade her for her partner.

9.29.06
– “Two Daughters”

This is the completion of the previous week's episode, “Spree.”

10.6.06
– “Provenance”

A thief steals a valuable painting from a small local art gallery. The case turns more sinister when one of the key suspects is murdered. Charlie analyzes a high-resolution photograph of the missing painting through the use of mathematical techniques and, by comparing his results with a similar analysis of other paintings by the same artist, he concludes that the stolen painting is a fake, leading Don to revise his suspect list. His analysis uses a method developed by a (real) mathematician at Dartmouth College, which reduces the fine details of the painting (relative areas of light and dark, choice of colors, perspective and shapes used, width, thickness and direction of brush strokes, shapes and ridges within brushstrokes, etc.) to a series of numbers—a numerical “fingerprint” of the painter's technique.

10.13.06
– “The Mole”

An interpreter at the Chinese consulate is killed in a hit-and-run traffic accident. When Charlie carries out a mathematical analysis on how she must have been hit, it is clear she was murdered. When Don investigates the dead girl, he discovers that she was probably working as a spy. Though Charlie also provides assistance by using the facial recognition algorithm he has been developing, as well as using steganography extraction algorithms to reveal messages hidden in computer images, Don and his team solve the case largely without Charlie's involvement, using more traditional, nonmathematical techniques.

10.20.06
– “Traffic”

Don investigates a series of attacks on L.A. highways. Are they coincidence or the work of a single attacker? Are some of them copycat attacks? Charlie and Amita first help by analyzing traffic flow using the mathematics of fluid flow, a technique frequently used in real-life traffic-flow studies. But Charlie's main contribution comes when it is suggested that the characteristics of the attacks and the choices of victims seem too random. He examines the pattern of the crimes and convinces Don that they must be the work of a single perpetrator. The challenge then is to find the hidden common factor that connects the victims.

10.27.06
– “Longshot”

This was one of the rare
NUMB3RS
episodes where they got the math badly wrong. A young horse-race gambler is murdered at the racetrack. It turns out that the bettor had made thirty bets on thirty races over the past five days and won them all. This is such an unlikely occurrence mathematically that all the races must have been rigged, yet Charlie, who is usually right on the mathematical ball, never makes that observation. If he had, Don, always on the real-life-knowledge-of-the-world ball, would doubtless have gone on to say that there is no way even organized crime could rig so many races. All in all, from a mathematical perspective and in terms of believability, this episode misfired. 'Nuff said.

11.3.06
– “Blackout”

A series of failures at electricity substations cause localized blackouts in areas of Los Angeles. Don worries that a terrorist group is running trials prior to launching an attack intended to cause a cascading failure that will plunge the entire city into darkness. But when Charlie analyzes the flow network, he discovers that none of the targets would have such an effect, and suspects that the attacks have a different purpose. By analyzing the target substations and the ones left alone using elementary set theory (Venn diagrams and Boolean combinations), he is able to identify the real target—a prison housing a man waiting for trial, whom various other criminals would prefer to see dead.

11.10.06
– “Hardball”

The sudden death of an aging baseball player during practice turns sinister when steroids found in his locker turn out to be in a lethal dosage that can only be deliberate. The player was murdered. The discovery of what seem to be ransom-threat e-mails to the murdered player brings Charlie into the picture because the unknown e-mailer based his accusations on a mathematical analysis of the player's performance that indicated exactly when he started using steroids. Initial suspicion falls on a young baseball fan who uses sabermetrics (the mathematical analysis of baseball performance statistics) to play fantasy baseball. The key mathematical idea that led the young fan to spot the steroid use is called changepoint detection.

11.17.06
– “Waste Not”

When a sinkhole opens in a school playground, killing one adult and injuring several children, Don is called in because the company that constructed the playground had been under investigation for suspected negligence. Charlie's analysis of health issues in the Los Angeles region turns up unusually high incidences of childhood cancers and other illnesses concentrated in areas where the company had constructed a playground using an asphalt substitute made from recycled toxic waste. The material seems harmless, but when Charlie spots a discrepancy between the waste material sent to the company and the surfacing material produced, he suspects that drums of untreated waste had been buried beneath the playgrounds. Charlie uses reflection seismology to locate some of the buried drums. This is a method for obtaining an image of the terrain beneath the surface by mathematically analyzing the reflections of shock waves from a small underground explosion.

11.24.06
– “Brutus”

A California state senator and a psychiatrist are murdered. The two cases appear very different, but Don thinks the two murders are related. Charlie helps by using network theory to unearth possible connections between the two victims. The trail leads to a long-kept government secret. The episode opens with Charlie testing a crowd-monitoring surveillance system he has developed, based on the mathematics of fluid flow.

12.15.06
– “Killer Chat”

Charlie helps Don track a killer who has murdered several sexual predators. The predators had all taken advantage of teenage girls they met in online chat rooms, and the killer lured them to their deaths by posing online as a teenage girl. Charlie's principal contribution is to analyze the linguistic patterns of the various participants in the chat, captured by the chat-room logs, a technique often used in real-life law enforcement.

1.5.07
– “Nine Wives”

Don, Charlie, and the team search for a polygamist who is on the run. The man is on the FBI's “Ten Most Wanted” list for rape and murder. The events of this episode closely mirror those of the real-life case of Warren Steed Jeffs, and the fictitious cult “Nine Wives” was based upon the Fundamentalist Church of Jesus Christ of Latter Day Saints (FLDS), of which Warren Steed Jeffs was the leader. Charlie's principal contribution comes when he analyzes a network diagram found at one of the cult's hideouts, which his department chair, Millie, recognizes as a genetic descendant graph.

1.12.07
– “finders Keepers”

When an expensive, high-performance racing yacht sinks during the middle of a race, Don is not the only one who gets involved. Agents from the NSA show up on the scene as well. Charlie helps by using fluid dynamics equations to calculate the most likely location where the vessel can be found. When it eventually turns up somewhere else, it becomes clear that there is far more to the story than first appeared. Charlie carries out a further analysis of the yacht's journey and concludes that it must have been carrying a heavy cargo hidden in the keel. The NSA agents are forced to disclose what brought them into the picture.

2.2.07
– “Take Out”

A gang has been robbing patrons of upscale restaurants, killing diners in the process. Charlie analyzes the pattern of locations of the restaurants to try to figure out where they are most likely to strike next. When the gang strikes at another restaurant, not on Charlie's list, he has to reexamine his assumptions. It soon becomes clear that there is more to the robberies than simply the acquisition of money. To track them down, Charlie has to find a way to trace the flow of funds through off-shore banks that serve as money-laundering operations.

2.9.07
– “End of Watch”

Don and his team reopen a cold case when an LAPD badge turns up at a construction site. Charlie uses a highly sophisticated (and math heavy) technique called “laser swath mapping” to locate the buried remains of the owner of the badge, an officer who has been missing seventeen years. LSM uses a highly focused laser beam from low-flying aircraft to identify undulations in the ground. Later in the episode, Charlie uses critical path analysis to try to reconstruct the dead officer's activities on the day he died. The episode title, “End of Watch,” is a police idiom for the death of a cop. At police funerals, “end of watch” is used to indicate the date that an officer passed away.