Dr. Andrew Nestler's Analysis of NUMB3RS and the We All Use Math Every Day (WAUMED) worksheet program

This page contains analysis of the CBS television program NUMB3RS and the affiliated worksheet program sponsored by Texas Instruments and the National Council of Teachers of Mathematics. Of primary concern are evidence of Charlie's pathological behavior and inappropriate relationships, instances in which Charlie's mathematical work is either useless or unnecessary for solving the crime at hand, and inaccuracies in the worksheets that are often such that they render the worksheets useless as a tie-in to the episode.

According to the NCTM, "Activities are based on the math presented in the episode and take 5–15 minutes to do.... The math used in each episode of NUMB3RS is based on real FBI cases."

Legend for worksheet comments below:

T = worksheet
recommended time is greater than 15 minutes

U = worksheet is
useless as a tie-in to the episode, referring to events or dialogue that do not
appear in the episode

E = worksheet
contains errors in mathematics or describing events or dialogue from the episode

NC = worksheet is
based on math that is not related to solving crimes

"No student should leave high school without thinking they are not good at math." (Melendy Lovett, President of Texas Instruments Education and Productivity Solutions, WAUMED interview)

9/30/05 "Bettor Or Worse" 9/22/06 "Spree"
Season Four episodes

10/7/05 "Obsession" 9/29/06 "Two Daughters"

11/4/05 "Soft Target" 10/6/06 "Provenance"

11/11/05 "Convergence" 10/13/06 "The Mole"

11/18/05 "In Plain Sight" 10/20/06 "Traffic"

11/25/05 "Toxin"
10/30/06 "Longshot" [sic]

12/9/05 "Bones Of Contention"
11/3/06 "Blackout"

12/16/05 "Scorched"
11/10/06 "Hardball"

1/13/06 "Double Down"
11/17/06 "Waste Not"

1/27/06 "Harvest"
11/24/06 "Brutus"

2/3/06 "The Running Man"
12/15/06 "Killer Chat"

3/3/06 "Protest"
1/5/07 "Nine Wives"

3/10/06 "Mind Games"
1/12/07 "Finders Keepers"

3/31/06 "All's Fair"
2/2/07 "Take Out"

4/28/06 "Rampage"
2/9/07 "End Of Watch"

5/5/05 "Backscatter"
2/16/07 "Contenders"

5/12/06 "Undercurrents"
2/23/07 "One Hour"

5/19/06 "Hot Shot"
3/9/07 "Democracy"

3/30/07 "Pandora's Box"

4/6/07 "Burn Rate"

4/27/07 "Art Of Reckoning"

5/4/07 "Under Pressure"

5/11/07 "Money For Nothing"

5/18/07 "The Janus List"

**4/23/05 "Dirty Bomb"**

Charlie attempts to exploit the classic Prisoner's Dilemma model to get a criminal to confess. The suspects are sitting next to each other, and Charlie publicly analyzes how much each suspect has to lose if he is convicted.

"[Charlie] uses math that I made up. I admit this isn't very realistic." (Series math advisor Gary Lorden's comments on this scene, "Do the Math - the Cal Tech Analysis" featurette on the season 1 DVDs)

**9/23/05 "Judgment Day"**

The instructor portion of the "How Tall is the Criminal?" worksheet
says,
"Charlie shows FBI agents a scatterplot [sic] of data from their case files in order
to quickly see which cases are relevant to their current investigation and which
are not. By looking at where and how the data is spread on the graph, Charlie
may find a rule or pattern that describes this cluster of data." In the episode,
Charlie's 3-D scatter plot is shown with *x*-axis labeled "perpetrator," and
*z*-axis
labeled "log likelihood." As Megan observes, "It looks like a random buckshot of
points." "Except," Charlie says, "for a small number of cases that stand out." They discard all but a small fraction of perpetrators (which do not appear to
stand out, or to describe "a rule or pattern") even though according to the
labels on the axes, only the suspects with highest (logarithm of) likelihood
should have been considered. Later Charlie states that "[there were] only two
cases that sparked extremely high values in my analysis." In fact neither of his
final two candidates had a *z*-value anywhere close to the highest ones of other
suspects in the scatter plot. Thus this worksheet is undermined by the content
of the episode.

"There was initial skepticism mostly from the people who were mathematics [sic] ... and I think that feeling hung in there for the pilot and first episode but then it sort of gradually dissolved away as they saw the math was actually accurate." (Series creator Nicolas Falacci, "Crunching Numb3rs - Sea5on One" DVD featurette)

Charlie asks his former graduate student Amita, who assists him with his FBI work, out on a date, and she says yes.

Charlie cracks a code for the dead suspect's car key remote, and says that then the car manufacturer can tell them what model the car is. However the code won't tell the FBI the name of the manufacturer.

Charlie says "I'm applying constructal theory: point-area, and point-volume flows" when all he does is draw a circle on a map based on the fact that the suspect was driving on the 101 Freeway South thirty minutes ago.

"[Mathematicians] are thrilled to have mathematics presented so well." (Nicolas Falacci, "Crunching Numb3rs - Sea5on One" DVD featurette)

[E, U] The "Telling Time with the Sun" worksheet for Act 1 and students in grades 7-10 says that Charlie has a photograph that shows a basketball hoop and its shadow from the sun, and that he applies trigonometry. This does not happen, and hence the tie-in to that act of the show is useless. In fact, in Act 3 they use image enhancement to try to clarify the image and they discuss the fact that there is no Nobel prize:

Larry: They say that Alfred Nobel's mistress had an affair with a very famous
mathematician, so naturally Nobel wouldn't want to share

his prize with his
rival.

Megan: So all you math guys are aced out because one of you is good in bed.

Charlie receives an anonymous love letter, and a question at the CBS website asks students whether his former graduate student Amita wrote the letter.

In Act 5, not Act 1, they discuss using spherical astronomy, not trigonometry as mentioned in the worksheet, to determine the sun's angle of elevation and location, although the differences between these terms are minor. Later on in the worksheet, this is discussed more correctly (in the Extensions section).

The "Art Gallery Problem" worksheet is aimed at grades 8-12 and begins: "In the Numb3rs episode 'Obsession', pop star Skylar Wyatt is being stalked in her home by an intruder." There is no indication of the difficulties in addressing stalking for 8th graders, nor suggestions of how to do so in a way that will lead to successful implementation and positive effects for students. In fact the opening credits state that 1,000,000 women have been stalked, with 4400 murdered, and 170,000 celebrities, and 1 obsession. These numbers seem to contradict a statement occurring later that studies show that 85% of all women will experience some form of stalking in their lifetime. The same worksheet says, "Oddly, none of her home's security cameras pick up an image of the stalker. This leads Charlie to consider the placement of the home's cameras as it relates to Chvatal's Art Gallery Theorem. The theorem proves that a maximum of n/3 cameras are needed to guard a room comprised of n vertices." In fact, while Charlie mentions Chvatal's Art Gallery Theorem early on, he does not mention it again. Larry specifies that the theorem would assume a simple polygon, and they do not appear to utilize the theorem.

[E] The "Guarding the Goods I" worksheet says that Charlie helps Larry figure out where the cameras could see and where they couldn't by applying his knowledge of "the Art Gallery Problem." In addition, it says that Charlie makes a diagram of the floor, marks the corners, and then circles where the cameras are. In fact, Charlie and Larry make a model, but viewers do not see Charlie marking the corners and circles where the cameras are - this is represented in his "Charlie vision" instead. The last worksheet, "Guarding the Goods II," also discusses the "Art Gallery Problem" and says that it relates to Act 3, which it does not. These worksheets worksheet were removed from the site and, months later, are unavailable.

[E] The "Percolation Theory" worksheet says, "Charlie talks about how Percolation Theory can be used to model the random movements of a disoriented criminal trying to escape FBI agents during a terrorist attack drill. He uses an analogy to a porous material in which liquid is poured on top." Both of these statements are incorrect. Charlie claims that he can use percolation theory to "postulate an m.o." rather than to locate the terrorist, and his analogy involves a pachinko game he has in his office.

[E, U, NC] The "When Does 1+1=2?" worksheet supposedly is related to Act 1. It begins, "In 'Convergence', Charlie writes '1+1=2' on the board and gives his students the homework assignment of explaining why he is right and why he is wrong." This never happens. There is no scene with Charlie teaching in the entire episode. Scene 1 opens with a Frisbee game and ends with a home invasion. Thus this worksheet is useless as a tie-in to the program. It is unrelated to solving a crime in the episode.

Charlie mispronounces a common mathematical term when he tries to say, "I ran a Fourier analysis."

"If the series does go down the tubes after a few episodes, it won't be because the math is wrong." (Author Keith Devlin, MAA Online article)

[E, NC] The activity "Air Hockey" related to Act 3, with suggested grade level 8-12, says, "In 'Convergence', random matrices and asymptotics are discussed." These terms are not discussed; rather, the words are spoken 1 or 2 times by mathematicians with no context or meaning supplied. The worksheet activity is an introduction to matrices. It is unrelated to solving a crime in the episode.

"You don't have to be a mathematics major to understand the show." (Worksheet author Terry Souhrada, Montana Kaimin)

What is discussed, however, is Charlie's penis. Charlie says to his nemesis Penfield, "Amita's a sharp mathematician, so no matter how hard you try, you're never gonna get her to believe this [holds fingers one inch apart] is six inches." Penfield replies, "I bet with you, that subject's never ... come up."

"Surely almost anything that can improve the image of mathematics in the population at large deserves the support of the mathematics community." (Keith Devlin, MAA Online article)

[E] The "Where is the Bullet?" worksheet supposedly is related to Act 4, and says, "Charlie uses parametric equations and a TI-84 Plus to simulate the trajectory of the bullet." In fact the related scene takes place in Act 3, in which David uses a calculator which does not have the model number shown. Charlie is not in this scene.

[E] In the "Follow the Flock" worksheet, the only connection to NUMB3RS is the line, "Much of Charlie's role in this episode is dedicated to his trying to figure out how an unknown, unforeseen variable fits into the 'flock'." This is false; much of his role is spent decrypting a computer code to locate a pedophile and his victim. The instructor portion of the worksheet says, "In the episode 'In Plain Sight', Charlie tries to figure out how new variables fit into a 'flock'. The structure of a criminal network changes shape with a new boss, much like a flock of birds reorganizing behind a new leader. In much of the episode Charlie is trying to figure out how an unknown, unforeseen variable fits into the 'flock'. By understanding individual behavior as it relates to the 'flock,' he hopes to understand the operations of a criminal network." In fact, there is no new boss in the episode's criminal network; Charlie surmises that the man who escaped the explosion using the underground tunnel is the ringleader of the meth operation. While Charlie says the words "flock theory" in the opening of the episode, he spends the bulk of his time in this episode searching through computer hardware and software for a pedophile. This worksheet is in error, and only barely related to the episode, in the sense that Charlie says the words "flock theory."

[E, U] The "Error Correction" worksheet begins, "In the episode 'In Plain Sight', Larry scratches a music CD but says it will still play perfectly because of the error correction code on the CD." This is false; he does not mention error correction. The instructor portion of the worksheet says, "Charlie explains, '[With] Reed-Solomon Error Correcting Codes, the software fills in the gaps, making an educated guess about what it should be - resulting in complete images from partial data'." In fact Charlie does not say the words "Reed-Solomon Correcting Codes" - no mention of error correcting codes is made, and thus the worksheet on this topic is not useful as a tie-in to the episode.

Charlie says, "Information theory ... it's about getting a message from point A to point B." His work is useless as obviously the FBI would investigate the origin of the toxic substance, which was pulled from the market 4 years ago.

Charlie had exams to grade, but gets wrapped up in Don's case, so says he'll have his TAs grade the exams instead.

Charlie mispronounces the common mathematical word "tori." His version rhymes with "hoary."

"They get the mathematician and the math right." (Keith Devlin, MAA Online article)

Charlie's use of Voronoi diagrams is useless in finding the location of the archeologist suspect. The FBI decides, obviously, to return to the site where the skull was found. The crime is solved when the FBI questions for a second time the museum security guard who reveals that he had allowed the chief into the museum on the night of the murder. Math is not used to solve the crime.

"NUMB3RS uses math to combat criminal activity." (Worksheet author Johnny Lott, letter to Notices of the AMS)

Charlie's work with the fire print is unnecessary. Watching news footage of two fires, agents observe one young man with a college cap on. Using a student ID photo match, they find him and interview his roommate. After they arrest their suspect, the roommate confesses to impress the eco-movement people. Later he reveals that he'd given explosives information to someone online, who turned out to be the main arsonist/murderer (the arson investigator).

"The result is a crime show in which math generally plays a fundamental role in solving the crime." (Writer Ivars Peterson, MAA Online)

[T] The "Making 'Fireprints'" [sic] worksheet was removed from the site for several months. The recommended work time is 30-45 minutes.

Charlie berates Amita for having left one of his classes early.

Charlie encourages Larry, his colleague who is a recovering gambling addict, to gamble in a casino.

The "Meltdown" worksheet says, "In 'Harvest', Don and David discover a secret operating room in the basement of an old motel, which is being used to perform illegal kidney transplants. They find blood-soaked sheets and a pile of ice melting on a sheet of plastic in a corner. When Charlie sees the FBI's pictures he notices the size of the puddle formed by the melting ice depends on the time the picture was taken. He and Amita discuss how this information can be used to determine when the ice first started to melt. This will tell them when their suspects last used the operating room." "Discuss" is quite generous here. Charlie does almost all the math talking and talks to others including Megan and Don, and doesn't really even look at Amita. Amita only says, "That will help us determine the rate of flow," and later, "It's why certain bugs can run over the top of a pond, and why raindrops are round." In fact, Megan thanks Charlie, not Charlie and Amita, just after this "discussion."

[E] The worksheet says, "In the episode, Charlie also refers to surface tension." This is true. The worksheet also says, "Part of Charlie and Amita's discussion is about properties of water on different surfaces. Their discussion involves adhesion ... and cohesion." In fact they don't specifically mention adhesion.

[T, U] The "Waxing Elliptical" worksheet introduction says, "In 'Harvest', Charlie is helping Don investigate illegal kidney transplants in Los Angeles. After analyzing the trip log of the ambulance suspected of transporting the kidneys, Charlie is able to determine that the ambulance went out of its way to go to an unknown location, traveling 26 miles when the straight distance was 20 miles... Assuming the ambulance traveled in straight lines, the unknown location must lie on an ellipse with the start and end points as the foci. Using this information, Charlie and Larry find the likely locations where the transplants occurred." The worksheet recommended time is 35 minutes.

The "Getting In Focus" worksheet says, "In 'Harvest', Charlie is helping Don investigate illegal kidney transplants in Los Angeles. After analyzing the trip log of the ambulance suspected of transporting the kidneys, Charlie is able to determine that the ambulance went out of its way to go to an unknown location, traveling 26 miles when the straight distance was 20 miles.... Charlie believes that the foci of the ellipse may give the location of the start and stop points of the ambulance.... Using his map of LA, Charlie sets up a coordinate system (in units measuring one mile) that overlays the map. Charlie plots the focal points."

In the episode, Charlie mentions the words "Hidden Markov model as well as an elliptical analysis to narrow the possibilities of the most likely hidden destinations and unrecorded routes," and the treasure map does not show anything resembling an ellipse or focal points, but instead a bunch of points and interweaving paths.

Charlie reads off log entries to Larry, who has a map: "Point C36 2km north/south, 3 east/west" and Charlie writes something on the board, while Larry seems to be plotting on the map. Charlie: "Centering on point Y12, n is not unknown." In fact, Larry and Charlie determine that the ambulance made unofficial and unrecorded stops to the hospital; there are no mention of miles at all, or ellipses, or foci.

Charlie uses an unrelated analysis involving blood and other match compatibility to determine the likely transplant patient, and then they find the location by getting it from the patient's daughter. Hence almost all of these quoted statements from these two worksheets are false.

The "Markov Chain Links" worksheet was removed from the site and, months later, is unavailable.

In the episode, Charlie presents his former graduate student Amita with the 2006 Milton Prize for her dissertation. Charlie calls Amita "much more than a colleague" and kisses her on the cheek. It is only at this ceremony that Charlie's father learns that Charlie had won the prize previously.

[E, U] The "The Eyes Have It" worksheet says, "In the episode, a security camera has taken a photograph showing a partial front view of the face of one of the criminals. Don wants to create a sketch of the criminal's face to help identify the suspect. Charlie suggests that iris recognition using the partial photograph might be a better choice. He uses probabilities to persuade Don that iris recognition greatly reduces the chance of misidentifying the suspect." In fact none of this happens. There is mention of "passive informed motion detectors" but no mention of a security camera. There are further errors in the first page of the student's portion of the worksheet, such as, "The FBI is investigating a robbery at the research facility of a large company." The robbery is at the university Cal Sci. The following paragraphs state that Charlie quoted much research and statistics regarding mug shots and iris recognition, none of which occurred in this episode as aired. Thus this worksheet is useless as a tie-in to the episode.

"If kids do see this, and they actually see the activities we are doing, they are getting an honest slice of how math is applied." (Johnny Lott, Montana Kaimin)

[E, U, NC] The "An Irrational Approach To Music" worksheet begins, "In 'The Running Man', Charlie talks about a willow flute that he built. A willow flute is typically a flute without finger holes...." In fact Larry picks up and plays the so-called "Norwegian willow flute" by using the flute's finger holes. The worksheet continues, "He discusses how a simple continued fraction can be used to approximate the irrational number needed to ensure that the flute will have an equal temperament." Charlie does not do this. All he says is, "The pentatonic scale - it's fascinating how a simple set of fractions can come alive." This worksheet on continued fractions is useless as a tie-in to the episode. It is unrelated to solving a crime in the episode.

"Producing timely activities gives an example of mathematical power." (Johnny Lott, letter to Notices of the AMS)

[U, NC] The "A Recursion Excursion" worksheet begins, "Written on one of Charlie's boards in a scene from "Protest" is the Collatz Conjecture, a problem Charlie is working on in his spare time." Perhaps this is written on the board shown at the 48 min. mark, but if so then it is out of focus and illegible. No character mentions this or any other conjecture, or any problem being worked on in spare time. Thus this worksheet is useless as a tie-in to the episode. It is unrelated to solving a crime in the episode.

"Each activity has been derived from the math used in the TV show." (WAUMED worksheet program)

Charlie's off-screen social network analysis is unnecessary and does not contribute to solving the case, since the big break is the doctor's giving up the name "Sisko." Charlie's only contribution in this case is to suggest that the construction worker's son forged his father's name on the check for explosive materials.

Charlie says, "It's just like blindly throwing darts. You throw enough darts, you're gonna eventually hit a bull's eye." This is untrue, although as the (finite) number of darts thrown increases, the probability that one hits a bull's eye certainly increases.

"NUMB3RS gets the math right" (Keith Devlin, MAA Online article)

The instructor portion of the "Right Or Wrong" worksheet begins, "In 'Mind Games', a psychic shocks Charlie by incorrectly guessing the color (black or red) of 25 cards in a row. As Larry says, "the probability of getting them all wrong is the same as getting them all right." In fact, in the episode what Larry says is, "The odds of getting them all wrong are the same as getting them all right."

[U, NC] The student portion of the "Right Or Wrong" worksheet begins, "In 'Mind Games', Charlie is surprised when a psychic attempts to predict the color of 25 cards and gets every card wrong. Because it is equally likely that each card is red or black, the probability of correctly (or incorrectly) guessing the color of each card is 1/2." Since the cards are not replaced after they are drawn and the deck is not reshuffled, the mathematics of the worksheet is completely wrong, and thus this worksheet is useless as a tie-in to the episode. For the same reason, the "Thumbs Up!" worksheet does not relate to the situation in the episode, as it includes questions such as, "If the probability of incorrectly guessing the color of a single card is 0.5, what is the probability of guessing all 25 incorrectly?" It is unrelated to solving a crime in the episode.

[E, NC] The "Sudoku Puzzles" worksheet says, "Charlie remarks that there are 6.67 sextillion solutions to the 9x9 sudoku puzzle." This is incorrect. In fact, Charlie says that there are "six and a half sextillion possible completed grids and five and a half billion essentially different grids." Sudoku puzzles, while mentioned by name, are neither explained nor described in this episode, and they obviously are not related to crime-solving. Thus the value of the worksheet to as a tie-in to the episode is minimal at best. It is unrelated to solving a crime in the episode.

[U] The "Guess My Type Or Lose" worksheet says, "Charlie helps Don find a mathematical model with which Don can choose proper suspects with some degree of confidence based on the suspects' actions. Charlie talks about using game theory to analyze how this might be done.... Charlie considers the needed model to be similar to a game in which incomplete or missing information about the suspects can be turned into one with imperfect or imprecise information." None of this happens. While Charlie says the words "social image typology" as stated in in the instructor portion of the worksheet, Charlie does not mention game theory at all, and thus the worksheet is at best a weak tie-in to the episode.

Charlie's contribution to solving the crime is that, off-screen, he "applied social image typology" to further narrow down a list of possible murderers.

The "Circling Around" worksheet says, "Charlie and Don Eppes discuss Inequality Bounding as a method of trying to locate a suspect." As usual, the word "discuss" is very generous. Charlie talks about how a leash constrains a dog's movement, which is obvious. Also obvious is his conclusion that given possible ranges of movement for a suspect and a victim, and time constraints, they could determine whether it was possible that the two individuals came into contact. The worksheet uses intersections of two circles in two totally different types of activities. The first is a Venn diagram, which is used not for geometry but for combinatorics, and thus has no meaningful tie-in to the episode, except for the fact that Charlie had two intersecting circles on his blackboard. Strangely, the Venn diagram activity in the worksheet is said to be "based on one found in Billstein, et al. (1984)." It is unclear why the included exercise was not original to the author.

The "Tesseract" worksheet says, "[Charlie] and Amita end up discussing the idea of dimensions and refer to a tesseract, a four dimensional cube. Amita helps Charlie look at things from a different point of view or perspective. Seeing the tesseract model reminds Charlie that he needs to look at the big picture and not be so narrowly focused." This is false, although the writers appear confused as to what Charlie is supposed to be realizing. In the episode, Charlie says, "Three-dimensional objects exist in a fourth dimension, in time." Thus he appears to realize that time is an important factor in the path of the person who shot up the FBI office (which is obvious). He continues, "So if we add a fourth dimension to the cube just like we added a third dimension to the square, we get a tesseract." So here he mentions the very different idea of a fourth spatial dimension. However, when he presents the results of his work at the FBI office, he points out, "This is Shane's journey through the office - and when we render it over time, a flaw becomes apparent." So he is back to the idea of the fourth dimension in his analysis being time. Of course none of this work nor any mathematics whatsoever was necessary, as the path of the shooter, including the doubling-back (the "flaw"), is detailed by video surveillance and eyewitness testimony. Strangely, the worksheet's introduction for the instructor cites a website when it needs to give a definition: "More formally, dimension is defined by www.Mathworld.com as '...a topological measure of the size of its covering properties'."

"Math consultants work with NUMB3RS throughout the production to ensure the accuracy of the mathematics used to analyze and solve crimes." (NCTM)

[NC] The "What Are You Implying?" worksheet says, "In 'Backscatter', the topic of explicit and implicit functions is discussed as Charlie is lecturing to a class." As usual, the word "discussed" is very generous, as all Charlie said was, "There are two ways to define functions: implicitly and explicitly." There was no context, and he gave no definition or additional information. This worksheet is based on a throwaway line that has nothing to do with crime solving.

The "Chains And Pyramids" worksheet is barely related to the episode, a worthwhile activity but quite independent of the show. The worksheet says, "In 'Backscatter,' Charlie uses the mathematics of "Backscatter Analysis" to trace an Internet attack back to its source. One of the techniques used in such attacks is called "message flooding," which clogs the system along targeted paths, slowing down all transmissions in order to make the bad ones easier to trace." The worksheet goes on to explore chain letters and to a lesser extent pyramid schemes, even though the idea of message flooding does not arise in the episode.

The "Creating Codes" worksheet says, "The code in the show used numbers generated by a 'modular polynomial'." Unfortunately the code cracked by Charlie's student is the simplest alphabet code of them all, with each letter represented by numerical place within the alphabet, even though the student had to cite "Sloane's Encyclopedia of Integer Sequences."

[U] The "The Graph Tells The Story" worksheet has nothing at all to do with the episode. It says, "Charlie uses a technique called backscatter analysis to help track the flow of distribution on an Internet attack. Charlie uses the analysis to figure out the prevalence of denial-of-service attacks in the Internet. He gathers data to assess the number, duration, and focus of attacks, and to characterize their behavior." The events described in those last two sentences do not occur in the episode. All Charlie does is, after he hears David say the phrase "fake out," he proposes that the mob attacks were designed to divert Don's attention from the bank and phishing attacks: "Logically, whatever Koverchenko was trying to distract you from seeing was right in front of you." Thus the key to solving the mystery this week was, as usual, logical thinking and supposition. The worksheet introduction says, "The focus of this activity is to interpret some graphs that Charlie might have used in his analysis." One could create a fake graph to model just about anything that fails to appear in a television episode.

In the episode, Amita and Charlie's work tracing internet activity leads to a violent ambush by the Russian mob, not a break in the FBI's case. Charlie's contribution to the case is to say, "Logically, whatever Koverchenko was trying to distract you from seeing was right in front of you."

Amita: So, besides the hacker, how many players are on either side?

Charlie: That's an unknown variable.

A mathematician would say "That's unknown" or "That is a variable."

"For the mathematicians out there, we want to be as engaging and accurate as possible." (Nicolas Falacci, MAA Online)

Charlie asks his former graduate student Amita out on a non-math date, with no mention made of their previous non-math date. Amita tells Charlie that she has been offered a 3-year assistant professor of math position at Harvard. Somehow Charlie, her thesis advisor, had not known about this, had not written her a letter of recommendation, etc. His response is "That's really amazing." Later Charlie suggests that she stay at Cal Sci in a new 3-year temporary position. He tries to kiss her as she talks about Harvard, and she walks away.

"Amita Ramanujan: She has indeed become more of a collaborator and received a prestigious thesis award and a tenure-track offer from the Harvard math department!" (Gary Lorden, letter to Notices of the AMS)

After working for six hours at the board, Charlie can't tell that a 10-digit number starting with 310 (a Los Angeles area code) is a telephone number.

Charlie says, "I don't even dream normal."

"One is in the real world; the other one seemed to be lost or distracted in his own world in the creative process of mathematics." (Executive Producer Ridley Scott on the main characters of FBI Agent Don Eppes and his brother Charlie, "Crunching Numb3rs - Sea5on One" DVD featurette)

Charlie says, "There's something called a direct network flow problem." Later he calls this a "directed" flow problem and that word is written on his board. The case moves forward not due to Charlie's math but because the FBI follows up on the voicemail on the victim's office phone; the Pilates instructor leads the agents directly to the killer.

The "Sinks & Sources" worksheet explores directed graphs. Again, Charlie's work on this topic was not needed to solve the crimes.

[E] The "A Stab in the Dark" worksheet begins, "In 'Hot Shot', the FBI is investigating a possible serial crime involving the deaths of two victims injected with a combination of drugs." This much is true. The worksheet continues, "The FBI attempts to determine at what time the victims were injected, to see if they could place the suspect at the scene at that time. Don thinks the victims were injected at least 13 hours before they were found. Charlie suggests that the amount of the drugs left in the victims' systems could indicate when they were injected." This is not in the episode. The timing is not an issue and Charlie says no such thing. The worksheet makes up data related to amounts of morphine and diazepam found in a body. The instructor portion of the worksheet says, "This activity will focus on creating and interpreting histograms and their relationships to probability." Thus this worksheet is not based on math from the episode and is not effective as a tie-in to the show.

[NC] The "Parabolic Food Fight" worksheet begins, "In 'Hot Shot', Larry is in his office catapulting grapes with a spoon to practice for the Physics Department food fight.... These parabolic paths can be modeled with quadratic functions." There is no math in the episode drawn from Larry's littering. The worksheet could be said to be related to any object that travels in a parabolic path. It is unrelated to solving a crime in the episode.

"I cringed, so what. The real point of the show is it gives the real spirit of working on math or any of these endeavors that we do at Cal Tech." (Gary Lorden, on the show's use of the phrase "Riemann's Hypothesis" instead of "the Riemann Hypothesis," "Do the Math - the Cal Tech Analysis" featurette on the season 1 DVDs)

Amita has accepted Cal Sci's professorship offer, presumably in mathematics. There is no mention of whether this position is permanent or temporary. She says she is giving a seminar on the adaptive enumeration of implicit surfaces. There has been no mention of whether she completed the second graduate degree she was pursuing last year.

[E] The introduction to the "Missing City" worksheet begins, "In 'Spree, Part I', Don and Edgerton (another agent) have plotted a precise map of a crime spree carried out by two lovers. The map ranges from Austin, TX, to San Bernardino, CA, through the cities given below. Charlie thinks the criminals visited another city along the way but did not commit a crime there. In this activity, students are asked to compute the mileage between the pairs of cities along the route and make a conjecture about the location of the 'missing city' that Charlie thinks the criminals visited." In the answers on the second page of the "Missing City" worksheet, it says "Reasonable choices for the missing city are Rock Springs, WY, Green River, WY and possibly Rawlins, WY. Charlie chose Green River." This is false. Charlie does not mention a city by name. Moreover, his finger points to Rock Springs, not Green River. In fact, in the episode David says "That dot that Charlie saw in Wyoming? A robbery on the 15th of this month - a bar outside of Red Desert, Wyoming." This worksheet activity involves no mathematics whatsoever. The introduction says, "Unlike usual NUMB3RS activities, there are no sophisticated mathematical tools needed - only basic arithmetic is required." However, even arithmetic is not required, as the worksheet encourages students to use randmcnally.com or mapquest.com to obtain the driving distances between the cities.

Strangely, even though Charlie predicts the existence of a missing city very early in the episode (as any intelligent person would, judging from the distances between the established sightings and crimes along interstate highways), he and Amita and Larry give a presentation on their crime spree pursuit analysis halfway through the episode, only to confirm that Charlie's hunch of a Wyoming town had merit. This is not at all helpful at that point. As usual, Charlie's work results in a suggestion that FBI agents would have come to on their own, namely that the agents should visit the home of the cousin of Crystal's target Billy Rivers.

During Charlie's vision when he first looks at the map, one of the Frenet frame equations is shown: n(s) = 1/K d/ds t(s). This equation from differential geometry is out of place here.

[U] The "Traveling on Good Circles" worksheet says, "Charlie thinks the criminals visited another city along the way but did not commit a crime there." In the episode Charlie believes that there is a missing city, but he says nothing about whether or not a crime may have been committed there. The worksheet continues, "He identified his 'missing city' by finding the distances between other pairs of cities on the spree using a formula involving the latitude and longitude of each city." Charlie says nothing of the kind. There is no mention of latitude or longitude and thus this worksheet on distances along great circles on spheres is useless as a tie-in to the episode. The activity website says that the topic for this worksheet is an introduction to pursuit curves, which is false. [This was corrected later.]

The activity website says that the topic for the "Chase" worksheet is geodesics on a sphere, which is false. The topic for this worksheet is pursuit curves. [This was corrected later.]

The "pursuit curve" entry at MathWorld, written by NUMB3RS consultant Eric
Weisstein, includes the following. "Under the name "path minimization,"
pursuit curves are alluded to by math genius Charlie Eppes in the Season 2
episode "Dark
Matter" of the television crime drama *NUMB3RS* when considering the
actions of the mysterious third shooter." Charlie Eppes is not identified
in this encyclopedia entry as a fictional character. The word "NUMB3RS" is
linked to the Amazon.com page selling the Season 1 DVDs of the series.

In the episode, Cal Sci professor Larry Fleinhardt, who sold his house last season and never mentioned why or where he was moving, now is homeless and has been sleeping in his car and in his office.

Charlie's ignorance of the disinterest and limited capabilities of his audience again is on display when he rambles on about how the agents might look for Megan, was abducted. Agent Edgerton asks, "Is anyone else following this?" and Colby replies, "Just nod your head and wait for the punch line."

There appear to be only two moments in this episode in which Charlie's math supposedly assists the agents. First, he says, regarding the criminal they want to find, "Crystal Hoyle - really, she wants more than one thing," and David replies, "Rivers has been pretty good at hiding from her and from us though." Charlie responds, "However, we can apply some forward induction to that problem as well." Charlie's "forward induction" is, as usual, a practical consideration that the FBI would have realized in time, namely that Rivers has used a particular lawyer in the vast majority of cases in his arrest record, and so they probably can locate the suspect through his attorney. Charlie declares, "Even a lawyer can't argue with math," which is an odd thing to say since no one did any math at that moment. Moreover, later on when the lawyer is found murdered, David says, "[She] had the same idea Charlie did: if you can't find Rivers, talk to his lawyer." David probably isn't calling Crystal a mathematician, but rather restating that the lawyer was an obvious connection to Rivers.

The "Trawling for an Intersection" and "Spiraling Out" worksheets say, "Don believes the criminal is within a certain bounded area in Los Angeles. Charlie compares the situation to a famous problem known as the Trawler Problem." A Google search for the phrase "trawler problem" results in only nine results, none of which are about a math problem. The Trawler Problem entry at Wolfram's MathWorld site was written two months ago by MathWorld creator and NUMB3RS consultant Eric Weisstein.

[E] The worksheets continue, "The surprising solution to the Trawler Problem is for the fast boat to proceed to the point where the boats would have met if the slow boat had made a 180 degree turn and headed back towards the fast boat.... From that point the fast boat should spiral out logarithmically." However the spiral that Charlie drew on the map is not logarithmic, as the spacing between loops is neither constant, strictly increasing or strictly decreasing. According to the MathWorld site, the spiral supposedly would be logarithmic under the conditions that the slow boat be traveling in a straight line and at a constant speed, neither of which would be part of a mathematical model for the path of criminal Crystal Hoyle.

[E] The "Spiraling Out" worksheet asks students to answer questions about spirals based on graphing calculator observations, with no indication of whether the questions could be answered using mathematics. This worksheet ignores negative values of r when it says, "Remember that in polar notation, a point (r, theta) is defined in terms of its distance from the center r and the counterclockwise angle theta (in radians), measured from the positive x-axis." The same worksheet allows negative values of r in its formulas for the spirals.

[NC] The "Tic-Tac-Toe" worksheet says, "Charlie tells David that negotiating with a suspect is similar to playing a game. 'It's like two people playing tic-tac-toe. If both play rationally, and neither one makes a mistake, the game will always end in a draw'." In fact, Charlie says, "Imagine two people playing tic-tac-toe. If both play rationally, and neither make a mistake, the game will always end in a draw." Charlie suggests new rules such as allowing X to make two consecutive moves or prohibiting O from choosing a crucial square. Rather than explore these options that Charlie does mention, the worksheet explores completely different variations on the game. Though this worksheet contains no mathematics and concerns a game that young children play, and even though the episode is rated TV-PG rather than TV-14, its suggested grade level is 9-12. The topic of tic-tac-toe is unrelated to solving a crime in the episode.

"What the activities try to do is try to take the math that’s discussed in the show, which is sometimes very high-level mathematics, and bring it down to middle school to high school-age mathematics." (Terry Souhrada, Montana Kaimin)

"It's FBI level, so it's really, really hard stuff." (Worksheet author Chuck Biehl, Delaware Online)

[U, NC] The "Galton Board" worksheet says, "In 'Spree, Part II', the FBI is trying to rescue a kidnapping victim. Charlie discusses how this problem is similar to balls falling through a Galton board." This is false. At the end of the episode, the FBI is tracking criminal Crystal Hoyle, not searching for a kidnapping victim, via her cell phone signal. There is an unrelated scene in which Charlie and Larry leisurely play with a Galton Board. The entire scene is comprised of the following conversation. Larry says, "Galton board, huh? Drop enough balls ... you get a bell-curve distribution," and Charlie replies, "I could do this all day long, observing what happens when we begin to block the paths. The distribution changes, the pattern alters, and the ball no longer has a choice where to fall." Thus this worksheet is only as worthwhile a tie-in to the episode as any worksheet exploring one of the many manipulatives observed in Charlie's office would be. It is unrelated to solving a crime in the episode.

The Extensions portion of the "Social Security Numbers" worksheet, added for the 1/26/07 repeat, asks, "What is the probability of having a Social Security number comprising of only two different digits?" The reader is referred to a web page for "more detail on the question and the answer." However the answer does not take into account the "no block of zeros" rule that is used throughout this worksheet.

In the episode, Charlie continues to give Amita very mixed signals as to whether he wants to date her, even though she turned down a 3-year position at Harvard in part to be with him. After he apologized for blowing her off when she was hoping to share a meal with him, he touched her intimately in his (their?) office.

Each episode begins with four examples of counting written on the screen. In this episode they are, "1 Fatherland," "1000 Years," "800,000 Works of Art" and "6 Million." Here the appropriate number for the final phrase would be "6,000,000," as in for example "6,000,000 people."

Charlie muses about his "supposed commitment-phobia" and "failure to settle down" in the workplace in front of Larry and Amita, further creating an uncomfortable environment for Amita, his on-again, off-again romantic partner.

Charlie is so absent-minded that he has overdrawn from his bank account, even though in the past he has said that he has earned a lot of money due to prizes and grants, and he was able to purchase his father's house with cash. After the fact, he attempts to balance his checkbook by performing arithmetic on a blackboard.

Larry, a physics professor at a supposedly renowned university, says, "Now you see why I sold my house: I renounced all worldly cares for the more sublime pursuits," and he "sleeps on couches" according to Charlie's father.

[U] Charlie claims that he will use a network diffusion probability model to predict the stolen painting's destination. After he tries this off-screen, he later announces, "My network analysis came up empty." Despite this, the "Set the Trap" worksheet says, "Charlie creates a 'Network Diffusion Probability Model' to keep track of the possible routes the paining could travel. On the show Charlie creates an 18 x 18 probability matrix to determine the most likely hiding places for the painting." Charlie does no such thing and there is no mention of probability matrices. Since that is the topic of this worksheet, it is useless as a tie-in to the episode.

Charlie's contribution in this episode was to use a computer to closely examine photographs of paintings, and as a result determining that the stolen painting was a fake and identifying the forger.

[T, NC, E] The "Checkbook (Mis)Calculations" worksheet says, "A running gag in 'Provenance' concerns Charlie's inability to balance his checkbook." Charlie's inability to monitor his finances is presented not as something humorous but rather as a consequence of his inability to function as a mature adult; this also results in his total neglect of the maintenance of his house, despite the repeated complaints and advice from his father, who lives in the house with him. The third part of the answer to exercise 2 on the instructor's portion of this worksheet contains an error: it should read 1000a+100c+10b+d, not 1000a+100c+10b+a. The grade level on this worksheet is given as 9-11, even though there is no reason why a 12th grade student could not punch numbers into a calculator as younger students are asked to do. This worksheet asks students to use a calculator to identify an integer solution to a linear Diophantine equation related to a "classic problem." There is no mention of the mathematics behind this topic, such as existence or uniqueness of a solution, even though linear Diophantine equations can be completely solved using a division algorithm; such a process is outlined at mathworld.wolfram.com/DiophantineEquation.html. This topic is unrelated to the solving of a crime in the episode. The suggested time required for this worksheet is 30 minutes.

[T, NC] The "Magnetism" worksheet, which was unavailable until three days after the episode aired, is based on the brief conversation between Larry, Amita and Charlie regarding circular motion. The suggested time required for this worksheet is 45 minutes, and this is unrelated to the solving of a crime in the episode.

[T, E] In the "Matrix Operations" worksheet, added for the 12/1/06 repeat, the matrix and activity are based on a city graph that is labeled differently from how it appears. C2 should be C3, C3 should be C5, and C5 should be C2.

[E] Both the "Cycloid I" and the "Cycloid II" worksheets say, "Charlie states that 'when you walk, it's really a series of little circles rotating inside a larger circle. The heel orbiting backwards, then forward past the knee is a small circle within the larger circle of walking'." In fact in the episode Charlie says, "Think of someone's stride like the Moon orbiting around the Earth. As the Moon moves around the Earth and the Earth moves around the Sun, the Moon traces out a curtate cycloid curve in space; in essence, a smaller circle moving within a larger circle. Now when you walk, the heel orbiting backward then forward past the knee creates the same pattern of circles." This is an extremely confusing, if not inaccurate, description. The Earth travels in an elliptical orbit around the Sun, not a circular orbit. When one walks, one's heels move forward, not backward.

Regardless, Charlie's description of a curtate cycloid curve supposedly was related to his analysis of how the hit-and-run victim was struck by the car. His conclusion that she was deliberately run down is based on the fact that the marks on her legs made by the car lights were high. This would have been revealed by a standard forensics exam, and moreover, the fact that she was deliberately killed did not assist the agents in their investigation, which progressed because Agent Granger noticed his buddy's name in her file, and he pursued that agent. Thus these worksheets are barely related to the episode.

[U] The Extensions page of the "Cycloid II" worksheet says, "Charlie tells us that cycloids are 'rectifiable curves' because they have a finite length." This is not true, Charlie says nothing of the kind, and thus this portion of the worksheet is useless as a tie-in to the episode.

The Extensions page of the "Cycloid I" worksheet says, "The cycloid is sometimes called the Helen of Geometers because [sic] the number of arguments that have centered on it among mathematicians. This Web site gives an account of many of these disputes." There is no mention of whether or how an instructor might handle the issue of the sexist nature of the alternative name for the curve. The Web site given has no author or contact information listed.

[E] The "Branch and Bound" worksheet says, "Charlie proposes that 'by running an algorithm that analyzes the features of the existing meeting places to find key variables, then applying a branching and bounding algorithm, I can hopefully give you a location for the mole's next probable destination'." In fact Charlie says, "... then by applying a branching and bounding algorithm, we can hopefully identify where Carter's next meeting place will be." The result of Charlie and Amita's work is a location at which Carter does in fact conduct a meeting, however he eludes capture and is only brought to justice when Granger visits him at his boat and secretly records his revealing admissions on tape.

In addition to the previously mentioned two times when Charlie supposedly uses math to help, there are two other such moments in this episode. In one, Charlie glances at digital photographs on the victim's laptop computer and declares that there are hidden messages in the pixels, because he found them before in a completely unrelated case. The data he finds (names of two agents and what may be a bank account number) do not assist in the investigation, which is basically completely solved by Agent Granger who pursues his former colleague Carter. Finally, Charlie supposedly uses an "asymmetry model" based on video footage from the victim's lobby to piece together an image of one of her frequent visitors. This face matches Carter's, but of course Colby had already suspected and confronted Carter after seeing him wearing his sunglasses on his neck in the video footage.

[E] The "Coded Messages" worksheet appeared days after the episode aired. The worksheet contains multiple mathematical errors in the matrix multiplication example. A revised version which appeared online weeks later still contains a mathematical error in the matrix multiplication. The worksheet says, "In 'The Mole', the FBI discovers that a suspect downloaded a number of images off the Internet." This is untrue, the laptop belonged to the victim. The worksheet continues, "Charlie points out that the NSA has discovered groups like al-Qaeda and Hezbollah hide messages in photographs through a process called steganography." This is false, Charlie says no such thing.

Each episode begins with four examples of counting written on the screen. In this episode they are, "12 Million Motor Vehicles," "9,096 Miles of Freeway," "5,339 Accidents," and "7 Freeway Attacks." Here the appropriate number for the first phrase would be "12,000,000."

Larry has written the Law of Cosines, a fundamental result of trigonometry,
incorrectly on the blackboard as C^{2 }= a^{2 }+ b^{2 }=
2abcosC. The correct statement would be c^{2 }= a^{2 }+ b^{2
}- 2abcosC.

"The producers have gone to great lengths to get the math right." (Keith Devlin, MAA Online article)

"Most of it is going through and being written by Gary Lorden, who is the chairman of the math department at CalTech [sic] .... Wolfram Research helps us a lot." (Cheryl Heuton, The MIT Tech)

[U, NC] The "Birthday Surprise" worksheet says, "As Charlie teaches his class about randomness and probability, he refers to the famous 'birthday problem'." Charlie does not do this, and thus the worksheet is useless as a tie-in to the episode. Moreover the topic is unrelated to solving a crime in the episode.

"The activities will be based on the mathematics presented in each episode." (WAUMED worksheet program)

[T, NC] The "Pythagorean Triples" and "To Pythagoras and Beyond" worksheets are based on the fact that Charlie says the words "Pythagorean theorem" while looking at Larry's writing on the board. These activities are basic explorations of the theorem, and are not related to solving crimes or any plot point in the episode. The "Pythagorean Triples" worksheet has a suggested work time of 30-40 minutes and lists a calculator as a required material, though this is not necessary. The other Pythagoras worksheet lists a calculator among the required materials, and not only is it not necessary, there is no mention of the use of a calculator in the activity.

**10/27/06 "Longshot"** [sic]

In this episode, no math from Charlie or anyone else was used to solve a crime. Several winners of a Pick 6 (a set of six consecutive horse races) are determined to be dead, with their bank accounts cleared. At the 46-minute mark of the episode, Don says to Colby, "Why don't you just start checking into their backgrounds?" Colby looks at the phone records of the unemployment agency used by the dead winners, and this leads him to the initial victim's girlfriend who had steered the victims to the racetrack for interviews. Don brings in the track owner, who without much pressure confesses his relationship with the mobster Tabakian.

[E, U, NC] The "Harmonizing Means" worksheet says, "Charlie determines that the equations were designed to pick the second place horse, but not the first place horse. Charlie observes that some of these equations involve the harmonic mean." Charlie does not mention anything about a mean, and thus this worksheet is useless as a tie-in to the episode.

Homeless physics professor Larry Fleinhardt says, "I just think I may have lost touch with certain important aspects of life in the real world."

Each episode begins with four examples of counting written on the screen. In this episode the first one is "22,000,000 Megawatts," unlike in at least two previous episodes in which numbers of millions were counted using one- or two-digit numbers.

In this episode Charlie says, "Coincidence is, after all, an absolutely valid mathematical occurrence," which is utter nonsense.

On the dead utility commissioner's notepad, the mathematical symbol meaning "is an element of" is denoted by the capital letter E instead of the correct symbol.

[E] The "Maintaining Balance" worksheet says that Charlie says, "There's enough redundancy that many of the [JENGA] blocks can be removed or knocked out, without a great affect [sic] to the system as a whole ... but if the wrong block, or in this case substation, is taken out, especially after the network's been weakened ... then the entire system could come crashing down." In fact the quote from the episode is, "Many of the blocks can be removed without having a great effect on the entire system as a whole. However if the wrong block, or in this case substation, is knocked out, then, yeah, the whole system could come crashing down."

[T] The "Navigating Networks" worksheet has a suggested work time of 30 minutes.

[E, U, T, NC] The "Implicit Orbits" worksheet says, "Charlie hypothesizes that people who disappear and are alive are like satellites that have lost their planet. Charlie explains that if the planet vanishes, the satellites would not have a focus to their orbit, and would travel in another direction, likely to another source of gravity." Charlie says no such thing, and thus this activity on the topic of orbits is useless as a tie-in to the episode. Though the worksheet requires the use of implicit differentiation, the suggested grade level is 10-12. Moreover the topic is unrelated to solving a crime in the episode. The suggested work time is 20-30 minutes.

[E] The "Pythagorean Expectation" worksheet states that Charlie says that Sabermetrics is "a powerful form of analysis in baseball - because the physical nature of the game involves chance. The difference between a hit and an out can be millimeters or milliseconds. At the same time, there's a tremendous amount of data recorded throughout the season. Literally thousands of at bats." In the episode Charlie does not say those last two sentences.

[NC] The "Less Is More" worksheet says, "In this activity, students will analyze a scatter plot of strikeouts versus home runs." This application of least squares regression to baseball statistics is not related to math used to solve a crime in this episode.

In the episode, Charlie's only contribution to the case was nonmathematical: while talking to Charlie, Oswald recalled that he had told his friend Chris that according to his research the baseball player was using steroids. The case proceeds via an investigation of Chris's emails. Earlier, Charlie's examination of Oswald's work and determination that it reveals steroid use were not necessary or helpful toward solving the case.

Each episode begins with four examples of counting written on the screen. This week the opening counting numbers are back to 2-digit numbers, including the phrases "13 million tons of hazardous waste" and "9.6 billion dollars in fines."

In this episode, Dr. Mildred Finch, who asks her colleagues to call her Millie, is appointed the chair of the Physics, Mathematics and Astronomy division at Cal Sci. Throughout the episode Charlie refers to Millie as Mildred.

Charlie, to Amita: "We can protect you. I just want you to know I'm willing
to go to bat for you with Dr. Finch."

Larry: "If she has any sense, she'll make you tenure-track."

Amita: "She already has."

Larry: "Already?"

Charlie: "Tenure...?"

Amita: "With a higher salary."

Neither Charlie nor Larry congratulates Amita on her switch to tenure-track status. Charlie, at the chair's induction ceremony, says to her, "Congratulations! Honestly, do you know how wonderful it is to have a chair conversant in math, physics *and* cosmology?" Then he expresses astonishment when he hears Amita accept Millie's offer to work on research together.

"Some people don't realize that female mathematicians are really acceptable." (Worksheet author Brother Pat Carney, WAUMED interview)

Millie determines that homeless professor Larry, who sold his house and therefore presumably is wealthy, has been living in the steam tunnels under the university. Charlie, supposedly a friend of Larry's, says that he thought Larry had been living with Megan for the last few weeks. With dental floss in his front jacket pocket, Larry says that he will move into a hotel.

When Amita tells Charlie, "I'm not sure if it's such a good idea for us to go out," he shuts her up by kissing her for at least the second time in the series.

Series consultant Eric Weisstein gets his book *CBC Concise Encyclopedia of
Mathematics* prominently showcased in Charlie's office.

[NC] The "Group Of Symmetries" worksheet is not related to math used to solve a crime in the episode. It is based on Millie's reading aloud the term "Kac-Moody algebras" and the brief illustration of related equations on the blackboard as Charlie prepares for a seminar in his office. No description or explanation of the term is given. In a show of lack of continuity in the episode's filming process, the minus sign that Charlie draws on the board disappears and reappears several times.

The "Different Or Not?" worksheet says, "The FBI may have used a statistical technique called a two-proportion test to decide whether the rate of cancer seems to be unusually high in this location.... This activity contains an introduction to this test." As the worksheet admits, the math in the activity does not come from the episode.

[E] The "Hide and Seep" worksheet says, "In 'Waste Not', an elementary school playground collapses into a sinkhole. Charlie and Larry work to figure out what caused the sinkhole - they suspect underground water flow and work to verify their hypothesis. Though the actual mathematics is not discussed, the maps around the office, as well as the equations displayed, come from the mathematical modeling of the seepage (percolation) of water through the ground. This activity employs one way to create a visual model of this process, namely a cellular automata model." In the episode the sinkhole was determined to have been caused not by water flow but by escaping toxic waste which had been buried below the playground.

[E] The "Risky Business" worksheet says, Millie enters the room and asks for an explanation of Charlie and Amita's use of the school's computer time. Amita replies, 'We're working with odds ratios to conduct an analysis of childhood cancers, birth defects, and neurological deficits related to a potentially toxic material.'" In fact, after Amita replies, "We're working with odds ratios," Charlie continues, "We're analyzing childhood cancers, birth defects, and neurological deficits related to a potentially toxic material."

In this episode, Charlie's mathematical work is unnecessary. Standard geologic tests at the sinkhole reveal benzene residue, believed to have killed the woman repeatedly referred to as "the old lady" and to have given the injured children a rash. Seismic imagery reveals the presence of several drums of toxic waste buried under the playground. The superintendent admits to having allowed Kentwell to bury drums of an unknown substance under the playground in exchange for their bankrolling her school board campaign. When she is murdered via her peanut allergy, the FBI solves the case simply by sending in an agent who impersonates a new EPA investigator and who surreptitiously records an incriminating conversation.

[T, E, U] The "Orchard Problem" worksheet says, "When Charlie's facial recognition program fails to find any matches when searching for a renegade CIA agent, he remembers Euclid's Orchard problem." A Google search reveals only six hits for the phrase "Euclid's Orchard," four of which are related to the page at MathWorld, created by series advisor Eric Weisstein. The worksheet continues with the following quotation attributed to Charlie: "I kept coming up with zero matches. Then I remembered the classic example of Euclid's Orchard. When we look at an orchard from the sky, we can see all of the trees that comprise it. If we stand on the ground, however, our view is considerably different. Some of the trees block your view of others. This means we were looking for someone who had access to all of the CIA program files - instead, we should be looking at people who only had access to some of them. At first, this seems like it would increase our suspect list - but, in fact, it dramatically decreases it."

The vast majority of these words are spoken by no one in the episode. Charlie says something related to only one of these seven sentences, when he says, "We realized that what we have is a classic example of Euclid's Orchard. Because each perspective on the orchard is unique, not only giving us information about the trees, but [sic] about the position of the observer." The worksheet instructions state, "Just as Charlie restricted his search to agents who had access to only some of the files, restrict your search to a smaller orchard where the trees are planted at lattice points...." Thus this worksheet contains gross errors and is useless as a tie-in to the episode. The suggested time requirement is 30 minutes.

[E, U] The "Dial the Phone" worksheet says that when Charlie uses a network analysis to locate the remaining three straw guns sold by a black market dealer, "he explains that this network of people is similar to a network of telephones.... In this activity you will create a network of telephones and calculate the value of the network...." In fact, in the episode, Charlie says, "I applied networking theory to a directed graph, using the graph and the known nodes to determine the sink ... kind of like a telephone, which is actually the classic example of networking. What I did was study the call pattern, the straw purchases, and I listened for the ringing telephone." The worksheet says, "Charlie states that a network with only one telephone is fundamentally useless. Explain why this is true." Since Charlie says nothing about a network with only one telephone, this worksheet's value as a tie-in to the episode is minimal at best.

[E, T] The "Crowded Ballroom" worksheet says, "Charlie and Amita help the FBI model real-time crowd dynamics in a crowded ballroom. In this activity you will develop a method for determining the size of a crowd in a ballroom (or any other setting)." In the episode, the FBI and Charlie are trying to determine which individual could be the person who phoned in a report of a gun in the ballroom. They are not determining the size of a crowd. Charlie's work is unnecessary, since Megan observes a suspicious individual using her monitor: "I have a male ... the body language is right, he has slumped shoulders and a slack expression, he's holding his jacket with his right hand."

Exercise 5 on this worksheet is, "Suppose that a crowd has gathered in a rectangular ballroom with an area of 5,000 square feet and that that [sic] the room is filled to capacity. If each side of the ballroom were enlarged by 25%, determine if it is true that 25% more people could stand inside this larger ballroom." The worksheet answer is, "It is not true; the area does not increase by 25%, it increases by 56.25%." This answer is incorrect; if the area increases by 56.25%, then 25% more people certainly can stand inside the larger ballroom. The suggested time requirement is 45 minutes.

As with the previous episode, there is more product placement for series
advisor Eric Weisstein's book and *Wolfram: A New Kind Of Science* in
Charlie's office.

Again, Charlie ends a conversation with Amita by kissing her and leaving the room.

Homeless physics professor Larry claims that he is going to live on the international space station. Charlie, supposedly Larry's friend, does not congratulate Larry, say good-bye to him, or even believe his claim.

The four counting phrases at the beginning are "491,000 Registered sex offenders," "3.2 Million uploads" (?), "34 Million teenagers," and "24,452,615 Chatroom sites."

Charlie suspects that his division chair may have called Larry's competence into question: "Mildred - and just when I was beginning to think she was a living, breathing human being...!"

Later:

Amita: I think by now I can distinguish between Professor Eppes
puzzling over a math problem and Charlie Eppes, worrying about a friend.

Charlie: It's not Larry -- it's me.... I think I was glad that my
best friend's dream had been destroyed.

[E] The "Perfect House" worksheet says, "The FBI found three bodies in three different unoccupied houses, all for sale. Because the victims are completely unrelated, Charlie decides that profiling the houses might reveal a discernable pattern. 'By profiling the house, we can profile the killer. Using a Multi-Attribute Compositional Model, I can analyze houses by looking at the individual parts that make up the whole. I can analyze our killer's past choices to assign probabilities to his future ones, and I can composite his 'dream house,' which I can compare to databases of other houses for sale, generating a list of likely locations where he'll strike again.' In fact, in the episode what Charlie says is, "By using a multi-attribute compositional model, I can analyze houses by looking at the individual parts that make up the whole. And given what we know about the killer's preferences, I can composite his 'dream house'." Charlie admits that his work (off-screen with no explanation) yielded nothing: "We hit a wall trying to composite our killer's dream house, because we realized he's not choosing houses." Amita: "He's choosing by neighborhoods." In fact their analysis of Jessica's Law hot zones in Los Angeles turns out to be useless as it reveals dozens of hot zones with homes on the market.

[E, T] The "Stylometry" worksheet says, "Charlie proposes he use Statistical Linguistic Analysis to identify the author.... Charlie's [sic] says to 'think of it like a jeweler beading a necklace. The jeweler chooses certain beads, decides what pattern to string them in, depending on his personal style. Other jewelers will have different styles, exhibiting different patterns." In fact, what Charlie says is "'Think of it like a jeweler beading a necklace. The jeweler chooses certain types of beads, then strings them in a particular pattern, according to his own unique personal style." The recommended work time is 30 minutes.

[T] The "Onion Peeler" worksheet has a recommended work time of 20-30 minutes.

The crimes are solved after Charlie's linguistic analysis reveals a near match between the "cheerchik15" Internet handle and Brendan McCreary of the Parents Stop Predators group. Though he had an alibi for two of the murders, his son Matt admits that he downloaded predator names from his dad's laptop and gave them to someone else. Megan notes that one sentence spoken by Matt reminds her of her interview with the wife of the first victim, the wife who turns out to be the murderer. Charlie's contribution to the case appears to be that he either created or just performed a computerized linguistic analysis of chatroom transcripts, and that at the end he somehow found 5 possible locations for the next murder, by matching strong Wi-Fi connections to Jessica's Law hot zones.

Amita and Charlie begin a 5-hour drive from Los Angeles to a math conference at Stanford. It is unknown whether Charlie has a valid California driver's license. She begins to play a music CD that she made for the drive including some of her mother's favorite music. Charlie's reaction: "Can we just put on something else? Or maybe let's drive quietly." Amita: "Quiet? For five hours?" Charlie: "Yes."

Charlie calls his division chair Mildred "Millie" twice more, despite her repeatedly asking him not to.

[T] The recommended work time for the "Lost And Found" and "A Breed Apart" worksheets is 20-25 minutes.

As in many episodes, Charlie's mathematical contributions are (1) identifying a search grid, and (2) quickly writing a computer algorithm, in this case so that photographic information from the NSA's five satellites can be scanned for a yellow truck.

[E] The "Barging In" worksheet says, "The body is traced to a salvage barge that has a bloody handprint on it. After further investigation, it is discovered that the blood is not from the dead diver, but someone else who was murdered on the barge." In fact the blood contained three samples, from the dead diver and the brothers who owned the salvage operation. The worksheet continues, "Charlie learns that the barge consumed 68 gallons of fuel on its last voyage, and the engine log shows that the barge was out for 16 hours. From this, Charlie calculates that the barge could not have traveled more than 20 miles." Charlie makes no mention of how he comes to this conclusion.

[T] The recommended work time for the "Barging In" worksheet is 30 minutes and that for the "The Leaf Drops" worksheet is 20-25 minutes.

Charlie sees spider webs in his house, and somehow concludes that there are not one but two teams of restaurant attackers.

Charlie mispronounces the common mathematical term "Laplacians" like "La-playsh-ee-uns," this despite numerous paid mathematical advisors and consultants behind the scenes of the series.

[E, T] The "No Fly Zone" worksheet says that Charlie says, "Think of it like looking for a spider or its prey by studying a web. We can use tension values of the silk web, vibrations - mixed with weather conditions, surrounding terrain, other variables - to reliably predict both where the spider's location is and where the next insect will get tangled." In fact he says, "It's like searching for a spider or its prey by studying its web. We use tension values of the silk web, like vibrations, weather conditions and other variables - to reliably predict where the spider is and where the insect's gonna get tangled." The recommended work time is 20-30 minutes.

[E] The "Restaurant Ranking" worksheet says that Charlie says that he applies "a mixture of multi-dimensional graph Laplacians and page-rank matrices," and that he goes on to say, "It's a way of investigating a group of things - in this case, restaurants - and identifying their shared properties. Think of a refrigerator filled with groceries. Steaks, apples, wine and a pie. Each item is unique, and you can buy them separately at any number of places. But more likely, the family made a single shopping trip. Basically, I figured out where the robbers went shopping for their targets. They're using the L.A. Restaurant Guide for their list of targets. They're looking for diners with the fattest credit cards." In fact, he says, "That's a way to investigate a group of things and identify their shared properties. Think about a refrigerator stacked with groceries. Steaks, wine, apples and a pie. Each of those items is unique, and can be purchased at several different stores, but more likely, the family makes a single shopping trip." David responds, "You figured out where the robbers are shopping for their targets.... They're after the fattest credit cards." Charlie's use of the word "unique" here is strange.

The instructions of this worksheet say, in exercise 3, "Notice that restaurant B splits its referrals between restaurants D and C. Consequently it only passes 1/2 of its probability of referring patrons on to each restaurant for their rankings." First of all, the notion of splitting referrals is very unclear. As stated in the exercises before the exercises, referrals are of the form "If you like this restaurant [B], you will like these others [C and D] as well." That is, the referral is to a plurality of restaurants, not one at a time. There is nothing to split. Moreover, there is no explanation for what appears to be an even splitting of referrals, in the event that the intention was that a referral would be for either one restaurant or the other.

The Extensions section of this worksheet says, "When a number is squared it either becomes very large or close to zero." This is not true. When the number 1 is squared, it becomes neither very large or close to zero.

[E, T] The "Outliers" worksheet says that Charlie explains that tracking financial transfers is "a matter of using a target-specific optimization model. Something called Outlier Detection. We have been doing a brute-force search in which you throw a net across a river and catch everything. Outlier Detection, though, is target-specific. It's like fly-fishing the data stream, choosing your spot by the spawning behavior, selecting the right bait, a method by which we are able to cast our rod exactly where we wanted, and catch exactly the type of fish we needed." In fact he says that tracking financial transfers is "a matter of using an optimization model, something called Outlier Detection. At first we were doing a brute-force search in which you cast a net over a river of information and you try to catch everything. Outlier Detection, however, is target-specific. It's like fly-fishing the data stream, choosing a spot by spawning behavior, selecting the right bait, a method in which we are able to cast our rod in the spot we wanted, and catch the exact type of fish we needed." The recommended work time is 30 minutes.

In this episode, Amita resigned as chair of the curriculum committee because some faculty are discussing her relationship with Charlie. Charlie and Larry had not been invited to chair that committee. Later Amita changes her mind with no reason given.

In this episode, Charlie did not make a necessary mathematical contribution to solving the crime. His initial mapping of the construction site did not locate the body of the policeman, excavation equipment did. Charlie identified two possible destinations that the cop had planned to visit, but this was not necessary as the case progressed following the re-interrogation of suspect Calvin Bradley by the FBI and police. Finally, Charlie matched the fatal drug combination to that of a particular drug dealer simply by searching the coroner's database.

[NC] The "Angling For Distance" worksheet is based on Charlie's shooting of a projectile at a model, which he did apparently for fun in his spare time.

[E, T] The "Critical Maths" worksheet says that Charlie says, "You need to prepare and cook each part of the meal in a specific order and monitor them simultaneously, so that you can serve everything at the same time. Otherwise, your food will be cold, or even worse, burnt. So you choose the most efficient order to cook your meal." In fact he says, "If you're cooking a holiday dinner, and you cook it all at the same time, well, some of your food's gonna end up burnt, some of your food's gonna end up cold. What you need to do is prepare and cook each part of the meal in an effective order, and monitor them simultaneously, so that you serve all hot food at the same time." The recommended work time is 25-30 minutes.

[T] The "Candy Land" worksheet recommended work time is 20-30 minutes and the "Ants Go Marching" worksheet recommended work time is 20-25 minutes.

Again, in this episode, Charlie did not make a necessary mathematical contribution to solving a crime. He had two supposed contributions. First, he supposedly derived an algorithm to look at 50 cell phone records to see which one contains calls like fugitive Ben would be making. The suspect turned out to be Ben's cousin who was living in Los Angeles. Second, Charlie and Amita analyzed idealized fight trajectories and determined that fighter Ken Bainsworth had had his schedule manipulated so that he wouldn't lose. This was unnecessary since Megan and Claudia, the medical examiner, determined that the poison was being planted on the fighters' mouthpieces, and this led to the arrest of the fight promoter.

[NC, T] The "Choosing Contenders" worksheet has a recommended work time of 20-30 minutes, and is related to the study of sports rankings using weighted averages, which was not used to solve the crime in this episode.

[E, T] The "Dialing Ben" worksheet introduction says, "Charlie explains that he will be using a "change-point detector" algorithm.... Due to the large number of calculations involved in carrying out change-point detection algorithms, this activity will instead search for change points in data using a variety of statistical plots that can be done on a graphing calculator." In fact Charlie does not refer to a change-point detector algorithm. The student instructions say, "Charlie uses a change-point detection algorithm to find Ben's calling patterns in his friends' cell phone records." The worksheet continues, "Charlie uses sophisticated techniques to look for change points, but his methods do use some of the same statistical ideas you will use in the following problems." In fact Charlie does not describe his techniques even using buzzwords as he normally does; instead all he does is claim that he devised an algorithm. Charlie says that he is looking for a particular call pattern among the cell phone records of 50 of Ben's frequent contacts. In fact the purpose of this activity as stated is more appropriate: look for a change in the call patterns of Ben's contacts. The recommended work time is 20-25 minutes.

Charlie's only contribution toward finding the kidnapper is that he somehow, off-screen, determines that that the kidnappers want Colby to take the cash back inside Disney Hall, and thus FBI agents can arrive there in advance for an ambush. Charlie and Amita's earlier work in tracing a phone call led to a quick confession by the wounded bodyguard/accomplice which would help build a case but was not needed for locating the remaining kidnappers.

[NC, T] The "Turing Origami" worksheet is based on a throwaway couple of lines by Charlie and Amita that was unrelated to the storylines and had no context. Charlie says, "I haven't seen an inductive Turing machine used [quite] like that before." Amita replies that she is "trying to figure out the finite state machines." The recommended work time is 20-30 minutes.

In this episode Charlie declares, "It's mathematically improbable that these deaths are coincidence." The phrase "mathematically improbable" is nonsense.

[U, NC, T] The "Shaken, Not Stirred" and "All Shook Up" worksheets are based upon a scene that is not in the episode as aired, and thus are useless as tie-ins to the show. According to the worksheets, in one scene Charlie is to pose a combinatorics problem to Oswald as a way to convince him to apply to CalSci. This problem, in addition to being absent from the episode, is unrelated to solving a crime in this episode. The recommended work time for the first of the two worksheets is 20-30 minutes.

[T] The "No Desk Left Behind" worksheet says, "In this activity students estimate, using simulation, the likelihood that more than four students in a class of 30 are left-handed when it is assumed that only 10% of students are left-handed." There is no mention of whether this probability can be calculated, as opposed to merely estimated." The recommended work time is 20-30 minutes.

Somehow Charlie has transported to his office the chalkboard from his home where he taught an analysis seminar in a previous episode. This is the board with the Calderon-Zygmund material.

Charlie and Oswald are trying to guess what Rachel's table of data means. For some strange reason, in order to try to analyze the numbers, Oswald prints them out without the column headings. He inexplicably suggests that the numbers might be lottery numbers, even though some of the numbers in the file have 1 or 2 places digits past the decimal point. Out of nowhere, Charlie suggests that they are "maybe votes. Let's see what happens when we compare Rachel's numbers to election returns." Later he says, "So I ran Rachel's data against election results and this "brute force" data search found a match." There is no explanation for what is meant by a brute force data search. The match is to a LA County Supervisors election. He continues, "Those vote totals should be random, and they aren't." There is no explanation for what he means when he says that vote totals should be random.

Again, without explanation for his methods, Charlie claims to have identified two occupations necessary to have pulled off election fraud in that district. Megan somehow locates two workers who meet those profiles. Rachel's cell phone records showed that she called both of these individuals before she died, and thus Charlie and Megan's work was a huge waste of time.

Charlie's last supposed contribution in this episode comes when he looks at a print-out of computer code, and says, "All I have to do, then, is write an algorithm to isolate her code from the rest."

As usual, Charlie's work is not necessary to solve a crime, presuming FBI agents and other law enforcement personnel are thorough in their work. Charlie finds the flight management computer just steps away from the cockpit of the downed plane, supposedly using math to find it. The case progresses when the FBI does a standard background check on the Aeronomics plane's mechanic, John Wellner, who showed up at the site of the crash and announced, "My God, if this is my fault...." When the background check reveals that Wellner probably had worked as a drug smuggler, a warrant is issued, and the agents then dig through his garbage where they find a storage facility receipt that leads to the stolen scram jet and the mechanic's body inside the storage locker. Mike, the Aeronomics engineer who says that Wellner had him install a software update in the airplane, picks the criminal mastermind Morales out of mug shots that David shows him on a hunch.

The "Fresh Air and Parabolas" worksheet says, "Charlie states that there is 'nothing like fresh air and the geometry of predictive trajectories.'" In fact he says, "Thank God for the geometry of predictive trajectories."

[T] The recommended work time for the "Thinking Backward" worksheet is 30 minutes.

Each episode begins with four examples of counting written on the screen. In this episode they are, "680 million pieces of mail," "240,000 postal delivery routes," "15.9 ounces" and "1 manifesto." Here the appropriate number for the first phrase would be "680,000,000."

The "Regular Polygon Centroids" and "Irregular Polygon Centroids" worksheets say, "When mail bombs kill a series of seemingly unrelated people, Don asks Charlie to help uncover the source and the link that connects the people." In fact the connection between the bombing victims is clear: the science and technology journalist had reported about the DNA bomber and the Department of Defense worker had pointed out Glazer as a suspect in the DNA bomber case.

In the episode, Glazer says, "I refer you to the axiom of coherent states." There is no axiom of coherent states. Charlie responds, "Coherent states, redundancy, over-completeness...." There is no explanation of what is meant by overcompleteness.

College student Jason Arenau has been in prison after pleading guilty to the DNA bomber cases. After he creates an explosion that blows himself up in prison, the prison visitors log is inspected, and it shows that Arenau had only one visitor the day he died, agent Jessica Molloy. A background check on a prison guard in Arenau's cell block reveals that he is a former San Francisco bomb squad member, in the unit with Reagan who had been killed by the DNA bomber. He's shown on tape to be passing bomb materials to Arenau. He confesses. Charlie's work is not needed to solve the crime in this episode.

[E] The "Random Thoughts" worksheet says, "The FBI develops a likely suspect when Charlie analyzes the patterns involved. However he later realizes that the data is too perfect. Lines from the suspect's house to each data point create equal angles - a result he thinks is too exact to be a coincidence. He calls it 'a perfect storm of data, an improbable event.' Charlie explains the concept to Don by laying out four bolts, forming a square. 'If you want to create a square, you only need four points, right?' Laying out two more bolts on each edge of the square, he continues 'you don't need eight more, but yet that's exactly what I have." There are multiple errors here: 1. Jessica had Glazer as a suspect from the start, before Charlie did anything at all. 2. There was no mention of equal angles. 3. Charlie says "laying out one more bolt" and "you don't need four more." The Extensions page of the worksheet says, "Charlie arranges twelve dots to form a square." He uses eight dots. "Improbable" has no mathematical meaning.

This worksheet says, "Consider the task of flipping a fair coin 25 times.... A sequence with exactly alternating flips or exclusively heads are [sic] not very likely." This appears to be a major mathematical error. If the coin is fair then all sequences are equally likely.

At the end of the episode, Charlie's method of stopping the time bomb is to trick the bomb's clock into thinking that the detonation has occurred, and thus the bomb should be defused. This would be a remarkable achievement that presumably would render all time bombs harmless in the future.

[E, NC] The "Spies Like Us" worksheet says, "Charlie discusses the security of a prison. 'It's a hyper-secure system, but prisoners have nothing to do except think about how to crack it.' " In fact he says, "It's a hyper-secure system, but prisoners have nothing to do but sit around and think about how to break it." The worksheet continues, "As he talks, a fort is shown under siege with a spy trying to break in, using ladders, underground tunnels, and catapults." In fact underground tunnels are not shown in Charlie's hallucination. Charlie claims that his analysis shows that the prisoner, Pony, is not communicating with the world outside. This is not useful.

[E, NC] The "No Place Left To Hide" worksheet says, "Charlie uses the example of a spy trying to get through enemy lines." It continues, "He says that he can 'calculate a ratio of vulnerable points versus the resources required to defend each point, to determine probabilities of penetration.' In fact he does not say this; instead he says, "Now calculating a ratio of points of vulnerability versus resources required to defend those points determines probabilities of penetration." Again, Charlie's determination that the prisoner is not attempting to escape is not necessary for the crime fighting in this story.

Around the 24-minute mark, Charlie says, "It's the water supply. The probability of an attack there is four times greater than at any other target." He states this just after he and his father look at some maps. There is no explanation or method stated. Around the 35-minute mark, Charlie names the terrorist cell leader, Maliki, again with no explanation or method named. When Don tells Charlie that Maliki actually is dead, Charlie immediately infers that the suspect's plan must have been hijacked by someone else.

[E] The "Close Encounters" worksheet says, "Charlie explains that the structure of a terrorist cell is like a complex network." In fact he describes a cell as a "distributed autonomous network." The Extensions page says, "When Charlie further explains his network analysis, he mentions 'weighted connections between vertices.' " In fact Charlie refers to "connections between weighted vertices."

Each episode begins with four examples of counting written on the screen. In this episode they are, "710,000 Zambian orphans," "50 million US dollars," "4 teams" and "1 truck." Here the appropriate number for the second phrase would be "50,000,000."

[T] The recommended work time for the "Truth Or Dare" worksheet is 20-45 minutes.

[E] The "Velocity of Circulation" worksheet says that Charlie says, "The efficiency of microcredit is something like the capillary action of a paper towel absorbing liquid. The economic structure of a community is like a paper cloth - people connected by commerce. The difference is, as money enters the fabric of economy, it actually creates more money. Say a woman has money to buy material and sells clothing at a market. The woman then brings back cash to her village, buys food and other essentials for her family. Money gets absorbed, spreads around, and soon more people have cash to spend and invest." In fact, in addition to many small errors, Sari is the one who says the fourth and fifth sentences.

Each episode begins with four examples of counting written on the screen. In this episode they are, "6 bugs," "7 bombs," "8 questions" and "2 days to live." Taylor Ashby, a psychopathic discharged spy, has rigged explosives to a bridge, and throws away a remote control corresponding to a bomb for each question that Charlie and Don get correct. It is not clear what "8 questions" refers to. Ashby asks 9 questions and throws away 7 remote controls before he is gravely injured in an explosion.

The third question was related to how many bombs they could afford to have go off, and the answer was 6. This would mean that 7 bombs would bring the bridge down. However later in the episode Charlie says, "He asked us how many bombs it would take to take down the bridge and that was six."

The last question Ashby asks Charlie, related to the classic "wheat and chessboard" problem, requires the answer which equals one less than two raised to the 64th power. Charlie reads his answer aloud as 18,446,744,073,799,551,615. Charlie's answer is incorrect, as the first 9 should be a 0. In the episode, however, Charlie's answer is treated as though it is correct, because he is frustrated by Ashby's response, "No, I've given you everything you need," which is followed by Charlie's assertion, "I was right about the wheat and chessboard problem." Charlie discovers that his confusion over why his supposedly correct answer was regarded as incorrect was designed as a hint for him to invoke a code breaking scheme called a straddling checkerboard cypher. Later in the episode he vandalizes a transparent hospital wall in an intensive care unit, writing the 20-digit number correctly on it.

The "Pile It On" worksheet, designed for students in grades 9 and 10, has stated objective "generalization of patterns involving exponents." The problem at hand is to add the sum of the 64 numbers obtained by starting with 1 and doubling the result 63 times. Students are encouraged to evaluate initial powers of 2, and they are asked to "use the answers ... to solve the original problem." Here "solve the original problem" really means "predict an answer to the original problem." There is no mention of the precalculus argument of using a sum of a finite geometric series to solve the original problem.

In a scene requiring some of the most serious suspensions of disbelief on the part of the audience, a severely burned Ashby taps his fingers in his hospital bed and somehow makes the oxygen saturation reading on his electronic monitor cycle through a pattern of certain two-digit numbers.

In what is probably supposed to be an establishing shot at the prison holding Carter, there is a close-up shot of a U.S. flag with only 48 stars on it. There is no visual context or explanation for this.

Season four episodes are analyzed on a separate page.

This page was created and is maintained by Dr. Andrew Nestler at Santa Monica College.