The Numbers Behind NUMB3RS (29 page)

4.29.05
– “Sacrifice”

A senior computer-science researcher, working on a classified government project, is found murdered in his Hollywood Hills home. The FBI discovers that data had been erased from the dead man's computer around the time of the murder. Don's investigation reveals that the victim was going through a bitter divorce, and was trying to keep his wife from getting his money. Using what he refers to as a predictive equation, Charlie is able to recover enough data from the victim's erased hard drive to learn that the project the man was working on seemed to involve baseball statistics. But when Charlie runs a Google search on some of the number sequences, he discovers that the data came not from baseball but from government statistics on people living in different kinds of neighborhoods.

5.6.05
– “Noisy Edge”

Together with an agent from the National Transportation Security Board, Don investigates eyewitness accounts of a mysterious unidentified object flying dangerously close to downtown Los Angeles, that has raised concern of a terrorist attack. After Charlie is recruited to help with the investigation, they discover that the flying object is part of a new technology that could revolutionize air travel. But the investigation takes a more sinister turn when they discover evidence suggesting sabotage that leads to the crash of the aircraft, killing the lead engineer who was piloting the plane on a test flight. There is considerable discussion of the “squish-squash algorithm,” developed by a mathematician at the University of Alberta to uncover weak signals (such as radar) in a noisy environment.

5.13.05
– “Manhunt”

As Don investigates a prison bus crash, Charlie uses probability analysis to conclude that the bus crash was not an accident, but part of a conspiracy to free a dangerous killer who is bent on revenge. Don and Charlie must find the killer before he is able to carry out his intent. Charlie uses probability theory to try to predict where the killer is likely to go next. This involves the use of Bayesian analysis to determine which of the many reported sightings of the fugitive by the public are more likely to be reliable. He uses the results to plot places and times to furnish a trajectory.

SECOND SEASON

9.23.05
– “Judgment Call”

The wife of a federal judge is shot and killed in her garage. It's unclear whether the intended target was her or her husband, who was hearing a death penalty case involving a gang leader. Don wants to know which of the many criminals the judge has sent to prison are most likely to seek revenge. Charlie's task is to narrow down the list of possible suspects. He initially refers to his approach as using a “Bayesian filter” and later talks about “reverse decision theory,” Presumably what he is doing is using Bayes' theorem “backwards,” to compute for each suspect the probability that he or she committed the murder, so that Don can concentrate on the ones to whom Charlie's calculations assign the highest probabilities.

9.30.05
– “Better or Worse”

A young woman attempts to rob a jewelry store in Beverly Hills by showing the store owner a photograph of his kidnapped wife and child. As the woman is leaving the store with a large quantity of diamonds, she is shot and killed by a security guard. Charlie assists the FBI by cracking the code of the keyless remote from the woman's car, found in her purse, to help identify her through her car purchase, and hence locate and rescue the store owner's kidnapped wife and daughter. Since the security of car remotes depends on sequences of numbers, the “obvious” mathematical approach is to look for numerical patterns that provide a clue to the entire code. Presumably this is what Charlie does, but he never specifies the techniques he is using.

10.7.05
– “Obsession”

The young wife of a high-profile Hollywood movie producer is stalked while alone in her home. The house is fitted with an extensive system of security cameras, but none of them has recorded any image of the intruder. Charlie realizes that the intruder must know the house and the location of the cameras, and is using a laser to temporarily “blind” the cameras as he passes in front of them. This leads him to analyze the video recordings using sophisticated image enhancement algorithms that are able to generate a reliable image of the stalker from relatively little information.

10.14.05
– “Calculated Risk”

Clearly inspired by the Enron case. A whistle-blower is killed, the financial officer of a large energy company who had exposed a major financial fraud. The problem facing Don is the sheer number of people with a motive to kill her: the senior people at the company who want to prevent her from testifying against them in court, the thousands of company employees who will lose their jobs if the company goes under, and the still greater number of people who are likely to lose most of their pension. Charlie uses a technique called “tree pruning” to narrow down a probabilistic suspect relationship tree from all of those affected by the swindle. He then models the flow of money through the company using methods of fluid flow in order to identify the killer.

10.21.05
– “Assassin”

During an arrest of a forger, Don uncovers a notebook containing encoded entries. He asks Charlie if he can decipher the contents. Drawing on his background of consulting for the NSA, Charlie is able to crack the code, and discovers that the notebook contains plans for a skilled and trained assassin to murder a Colombian exile living in Los Angeles. His remaining contribution to the case is to suggest to Don ways to pursue the assassin based on ideas from game theory, speculating on how the killer will behave in different situations.

11.4.05
– “Soft Target”

A Homeland Security exercise in the Los Angeles Metro turns into a real emergency when someone releases phosgene gas in a train. Don is assigned to the case. Using classical percolation theory (based on statistical mechanics, which determines the flow of liquids and gases based on the motion of the individual molecules) to determine the flow of the gas, based on the readings from the people in the car, Charlie figures out the precise location where it was released. After Don identifies a likely suspect, Charlie tries to predict where and how he will strike next, by applying linear percolation theory, a fairly new field which Charlie explains in terms of a ball running through a pinball machine.

11.11.05
– “Convergence”

A chain of robberies at upscale Los Angeles homes takes a more sinister turn when one of the homeowners is murdered. The robbers seem to have a considerable amount of inside information about the valuable items in the houses robbed and the detailed movements of their owners. Yet the target homes seem to have nothing in common, and certainly nothing that could provide a source to the detailed information the crooks are clearly getting. Charlie approaches the task using data-mining techniques, applying data-mining software to look for patterns among all robberies in the area over the six-month period of the home burglaries. Eventually he comes up with a series of car thefts that look as though they could be the work of the same gang, and this leads to their capture. His other contribution to the case is figuring out that the gang keeps track of the homeowners' movements by intercepting signals from the GPS location chip found in all modern cell phones.

11.18.05
– “In Plain Sight”

A raid on a methamphetamine lab goes wrong and an FBI agent is killed when the booby-trapped house blows up. The lab was identified in part by Charlie's analysis of social networks using flocking algorithms. Attempts to enhance a photographic image from a computer found at the house reveal a child pornography image encoded using steganography. Further analysis of the computer hard drive yields a hidden partition, the contents of which provide a clue to the leader of the meth lab.

11.25.05
– “Toxin”

An unknown person is spiking certain over-the-counter medications with poisons. This soon leads Don and his team to a hunt for a fugitive who has disappeared into the California mountains. Charlie takes inspiration from information theory and from combinatorics (Steiner trees) to help Don solve the case. The mathematics is not so much applied as used to provide an illustration of what actions Don should take.

12.9.05
– “Bones of Contention”

The discovery of an ancient skull leads to the murder of a museum antiquarian. Charlie uses his knowledge of carbon dating and Voronoi diagrams (a concept in combinatorics related to the efficient distribution of goods) to help solve the crime. The carbon-dating part is a now standard application of mathematics to determine the age of death associated with skeletons and bone fragments. The Voronoi diagram part is not unlike Charlie's mention of Steiner trees in the previous episode, “Toxin”: it is more a way of focusing attention on a key aspect of the investigation.

12.16.05
– “Scorched”

An arsonist sets a fire at an SUV dealership that kills a sales person. The name of an extremist environmental group is spray-painted on the scene, but the group denies involvement. Don has to determine whether the group is responsible or someone else set the fire. Charlie is called in to help figure out whether there is a pattern to the fires that would help provide a profile of the arsonist. He says he is using “principal components analysis” to produce arson “prints” that will be sufficiently precise to identify the criminal.

1.6.06
– “The O.G.”

An FBI agent working undercover as a gang member is killed. When it appears that his cover had not been blown, it begins to look like yet another round in an ongoing battle between rival gangs. Charlie thinks that with so many gang killings, 8,000 over four years, there is enough data to use social network analysis to look for tit-for-tat chains of killings. His analysis uncovers several chains much longer than the average chains, and he thinks they are likely to be the work of the same killer or killers. His detection of unusual features of some of the chains eventually enables Don to solve the case. The episode title stands for the term “old gangster.”

1.13.06
– “Double Down”

When a young man who is killed just after leaving a casino with considerable winnings turns out to be a brilliant mathematics student at a local university, Don suspects that the victim was part of a group of players using “card counting” to improve their chances of winning. Charlie's analysis takes into account the latest developments in the fifty-year history of using mathematical analyses to win at blackjack.

1.27.06
– “Harvest”

A report of suspicious activity in the basement of a hotel leads Don to uncover a black market scheme trading in body parts. Young girls from a poor area of rural India are persuaded to sell, say, a kidney, to be transplanted to a wealthy patient in Los Angeles. The girls are brought over, the operation performed, and then they are sent back. But after one of the girls dies, Don worries that the gang will feel they have nothing more to lose if others die, too. Charlie's contribution is to determine the most likely time of the girl's death based on photographs of a pile of partially melted ice taken by the police when they arrived on the scene. The ice would have been brought in to preserve the kidney in transit, and would have been fresh at the time of the operation on the girl.

2.3.06
– “The Running Man”

A gang steals a DNA synthesizer from CalSci, and Don suspects that the thieves intend to sell it to a terrorist group that would use it to manufacture biological weapons. Charlie provides assistance (in a very minor way) by suggesting a possible analogy with Benford's Law, which describes a surprising distribution of leading digits in tables of real-world data (1 thirty percent of the time, 2 eighteen percent of the time, 3 twelve percent, down to 9 a mere four percent). Naïve intuition would suggest that with randomly distributed figures, each digit would occur one-ninth of the time, but this is not so for data from a real-world source. In the case Don is working on, the equivalent of the prevalent leading digit turns out to be CalSci's LIGO lab, which Larry directs. LIGO stands for “Laser Interferometer Gravitational-Wave Observatory”. (Caltech—the real-world “CalSci”—actually does operate a LIGO lab, though the facility itself is not located on their campus, or even in California.)

3.3.06
– “Protest”

Don and his team investigate an antiwar bombing outside an Army recruiting center that resembles the work of a 1970s antiwar activist who, thirty-five years earlier to the day, had planted a bomb that killed two people. That bomber was never caught and the FBI's principal suspect at the time had disappeared soon after the explosion. Charlie uses social network analysis to help Don figure out who might have carried out the 1971 bombing, leading to an unexpected discovery about the undercover activities of the FBI in the anti–Vietnam War movement.

3.10.06
– “Mind Games”

Following leads provided by a self-proclaimed psychic, a search team finds three dead girls in the wilderness. The victims, all illegal immigrants, were apparently murdered under bizarre, ritualistic circumstances, but it is later revealed that they were killed to recover illegal drugs they had smuggled across the Mexican border inside their stomachs. Much of Charlie's activity in the episode is devoted to trying to persuade Don and the others that there is no such thing as ESP and that people who claim they are psychics are frauds. He does however contribute to the solution of the case by using the Fokker-Planck equation (which describes the chaotic motion of a body subject to certain forces and constraints) to determine where the next group of smugglers may be hiding out.