Logic Mazes on Numb3rs
On February 23, 2007, Numb3rs had a lengthy discussion of logic mazes. It was great to see this concept given a wide audience. In addition, there is a web site connected with the show, called www.WeAllUseMathEveryDay.com. This site gives teachers suggestions about how to use ideas from Numb3rs in the classroom. One of their suggestions for this episode is based on my Theseus and the Minotaur mazes.
In case youve never seen Numb3rs, I should explain that it is an exciting crime drama (and the reason it is exciting is probably because it is produced by Ridley Scott). It also involves mathematics, which everyone thought would be the kiss of death, but the show has been surprisingly popular. The hero is Charlie Eppes, a university math professor who consults with the FBI. Numb3rs is often praised for making math cool, and it really has done that. The best part of the show is the way it can suggest the quirkiness of university professors yet still make them likeable. And the professors are contrasted with the more straight-arrow FBI agents (also likeable). Charlie Eppes is pretty strange looking and has a difficult personal life (I read that the character is loosely based on the mathematician Richard Feynman). Charlies former mentor at the university, Larry Fleinhardt, is even stranger. At one point he was living in the university steam tunnels. A tender moment was the unlikely romance between Fleinhardt and Megan Reeves, a good-looking agent at the FBI.
The weak point of the show is actually the math. They use many mathematical concepts, but none is given a clear explanation (well, a clear explanation would, of necessity, take half of the show). If you understand the concept, you may not see how it applies to the story, and if you see how it applies, then you may not understand how it actually helps them catch the crook. All this is true of their use of logic mazes. I relate part of the episode below to show what they get right and what they get wrong about logic mazes. I wouldnt want anyone to think that understanding logic mazes will help you fight crime (though it will definitely help the next time youre attacked by a Minotaur).
I looked at some of the blogs about Numb3rs (I quote from them below), and they convinced me that my criticism of the math doesnt really matter. Anyway, trying to fix any of these problems would make the show unwatchable.
Sohere are some details about the logic mazes episode. Ill put my comments in red.
Agent Colby Granger is carrying a bag with ransom money to a kidnapper (named Nacio Duque). Duque had told him to go to a certain public phone, and at that phone he told him to go to a different phone. Back at the FBI office, his progress is being followed by agent Megan Reeves, by Charlie Eppes, and by his co-worker at the university, Amita Ramajuan.
Megan Reeves: Were you able to get a fix on it?
Amita Ramajuan: It came from a public WiFi connection at Hill and Temple.
Reeves: Thats right near Keyerleber Plaza. Hes leading us.
Eppes: No theres a deeper process at work. A logical system. Hes methodical. Hes thorough. This guyd make an excellent mathematician.
Colby continues to be sent from phone to phone. At various points the kidnapper orders him to get rid of his gun, to disable a tracking device, and to stop another agent from following him.
Eppes has made a diagram of the points where Colby has been sent.
Eppes: So far, hes moved Colby from here to here to here to here with what objective?
Reeves: Spotting surveillance.
Eppes: Well then its safe to assume that he has more points plotted out. Right? More phone numbers selected.
Reeves: So hes just going to keep moving Colby again and again until he feels safe to take that money.
At this point we see Eppes studying the diagram. Then there is a surreal scene of a giant ball rolling down a street. Why is that ball there? At this point we dont know.
Eppes: Its a maze. Hes building a maze.
Then, after the commercial break:
Eppes: Its a logic maze, one with its own set of rules except in this case the rules change every time Colby arrives at a check point. You know the game Labyrinth?
Reeves: The toy?
Here we have a view of the Labyrinth game. So, thats why that ball was rolling down the street.
Eppes: Huh, toy to you; a classic example of a state diagram to us. See in Labyrinth you use two knobs to move a steel ball through a maze. Those knobs constitute x and y axes, and the ball follows a simple curving path. Now the speed of the ball adds a condition. You eliminate that conditionand fall through the hole.
Reeves: And what, the holes represent being captured?
Eppes: Exactly. Every time this kidnapper gets rid of surveillance or eliminates an electronic tracer, hes navigating an obstacle.
Amita Ramajuan: You know, if we use a state diagram . . .
Eppes: using unified modeling language. Exactly.
Reeves: Exactly what?
Eppes: We may be able to solve this maze. And tell you where it ends.
Well, dammit, no! Besides the fact that nothing Eppes says he will do here would solve the maze, the game Labyrinth is in no way a logic maze. And it certainly isnt a state diagram.
By the way, many years ago I spent a lot of time playing Labyrinth. I was told that if you opened the game up and switched some strings around, you could reverse the actions of the knobs; for example, if you turn the front knob to the right, the board will tilt to the left. I tried this. It was amusing, but I never got the hang of solving the maze under those circumstances.
The next scene is in Union Station where Duque tells Colby to get rid of an ear piece and to stop another agent from following him. Reeves wants to have the agent continue following but Eppes says he should not.
Eppes: Dont follow him.
Reeves: Charlie, I cannot leave Colby uncovered.
Eppes: Duque isnt down there, hes telling Colby to take the train and go back to Disney Hall.
Reeves: How do you know that?
Eppes: Because I know where the maze ends.
Reeves: Yeah, but how can you be sure?
Eppes: Megan, I would never gamble with Colbys life.
Several FBI agents take positions in Disney Hall without letting Duque know they are there. Colby is about to hand the ransom to Duques partner when Duque, from his own hiding place, shoots his partner. Reeves now wants to order all her agents out of there, but Eppes tells her not to.
Amita Ramajuan: Duque has exhibited a highly sophisticated strategy thus far.
Reeves: Yeah, a maze, with rules, and this is the end.
Eppes: No. Its the final obstacle. You see, by shooting his partner, Duque has not only increased his share of the ransom, but hes devised a strategy that assures himself that his previous strategy worked, that Colby is now alone.
After another commercial break:
Eppes: When you build a maze, theres always math there, whether its intentional or unintentional. The level sequence always starts with a zero and ends with an n.
Yeah, and what doesnt?
I wont say what happens next except, well, they do catch the kidnapper. The title of this episode is One Hour, is case you see it listed as a repeat.
So, theres really nothing here that is like a logic maze, except maybe its like a maze and the kidnapper made the rules about where to go through the maze. A better analogy would be a scavenger hunt, or a reverse scavenger hunt since Colby had to get rid of objects instead of acquiring them.
So, thats the end of my critique. Sorry I got so negative towards the end. For a discussion of the good points of the show, please see this article by Paul Devlin. The article also has an interesting history about how the series was developed.
I was looking at some of the blogs on IMDb.com. Someone had written complaining about the show and there were many replies. Here are some excerpts:
By the way, Ed Pegg Jr consults on Numb3rs and he was the one who suggested the logic mazes topic to the producers. Ed told me that he makes many suggestions but doesnt know which they will use. He also has no control over what they do with the suggestion. Ed also wrote an article about logic mazes and how state diagrams can be used to solve them.