David S. Cohen, who explored P-type and NP-type problems while studying for his master’s degree in computer science at the University of California, Berkeley, has a hunch that NP-type problems are indeed much easier than we currently think, which is why P = NP appears behind Homer in his 3-D universe.
However, Cohen holds a minority view. When William Gasarch, a computer scientist at the University of Maryland, polled one hundred researchers in 2002, only 9 percent thought that P = NP, while 61 percent favored P ≠ NP. He repeated the poll in 2010, and this time 81 percent favored P ≠ NP.
Of course, truth in mathematics is not decided by a popularity contest, but if the majority turn out to be right, then Cohen’s positioning of P = NP in the landscape of “Homer3” will look somewhat incongruous. This, however, should not prove to be an issue in the short term, as half of the mathematicians polled did not think that the problem would be resolved during this century.
Finally, there is one more mathematical reference in “Homer3” that deserves a mention. More accurately, the reference does not actually appear in the “Homer 3” segment, but rather in the credit sequence for the whole “Treehouse of Horror VI” episode. By tradition, the credits in the Halloween episodes of The Simpsons have always been quirky. For example, Matt Groening is credited variously as Bat Groening, Rat Groening, Matt “Mr. Spooky” Groening, and Morbid Matt Groening.
This tradition was inspired by a comic book titled Tales from the Crypt, which regularly contained mutant credits for its writers and artists. Its publisher, EC Comics, became notorious after the Senate Subcommittee on Juvenile Delinquency ran comic book hearings in 1954 that concluded that Tales from the Crypt and its other titles were partly responsible for corrupting the nation’s youth. This resulted in the removal of zombies, werewolves, and their ilk from all comics, and in turn these constraints forced the discontinuation of Tales from the Crypt in 1955. Nevertheless, Tales from the Crypt still has many fans, most of whom were not even born when it went to an early grave. Al Jean is one these fans, and it was his suggestion to pay homage to the comic by mimicking the idea of mutant credits in “Treehouse of Horror” episodes.
All of which explains why the credits for “Treehouse of Horror VI” include Brad “the Impaler” Bird, Lycanthropic Lee Harting, and Wotsa Matta U. Groening. And, if you look very carefully, you will spot a charming reference to the Pythagorean theorem and the writer of “Homer3”:
DAVID 2 + S. 2= COHEN 2
EXAMINATION IV
MASTERS DEGREE
Joke 1
Q: What’s a polar bear?
2 points
A: A rectangular bear after a coordinate transformation.
Joke 2
Q: What goes “Pieces of seven! Pieces of seven!”?
2 points
A: A parroty error.
Joke 3
Russell to Whitehead: “My Gödel is killing me!”
3 points
Joke 4
Q: What’s brown, furry, runs to the sea, and is equivalent to the axiom of choice?
2 points
A: Zorn’s lemming.
Joke 5
Q: What’s yellow and equivalent to the axiom of choice?
2 points
A: Zorn’s lemon.
Joke 6
Q: Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?
3 points
A: That’s the law of spline demand.
Joke 7
Two mathematicians, Isaac and Gottfried, are in a pub. Isaac bemoans the lack of mathematical knowledge among the general public, but Gottfried is more optimistic. To prove his point, Gottfried waits until Isaac goes to the bathroom and calls over the barmaid. He explains that he is going to ask her a question when Isaac returns, and the barmaid simply has to reply: “One third x cubed.”
6 points
She replies: “Won thud ex-what?”
Gottfried repeats the statement, but more slowly this time: “One . . . third . . . x . . . cubed.”
The barmaid seems to get it, more or less, and walks away muttering over and over again: “Won thud ex-cubed.”
Isaac returns, he downs another drink with Gottfried, the argument continues and eventually Gottfried asks over the barmaid to prove his point: “Isaac, let’s try an experiment. Miss, do you mind if I ask you a simple calculus question? What is the integral of x2?”
The barmaid stops, scratches her head, and hesitantly regurgitates: “Won . . . thud . . . ex-cubed.” Gottfried smiles smugly, but just before the barmaid walks away she stares at the two mathematicians and says: “. . . plus a constant!”
TOTAL – 20 POINTS
From left to right, the cast of Futurama includes Zapp Brannigan (a twenty-five-star general and captain of the starship Nimbus), Mom (the Machiavellian owner of MomCorp), Professor Hubert J. Farnsworth (the 160-year-old founder of Planet Express), Leela (captain of the Planet Express ship), Bender (a debauched robot), Philip J. Fry (a twentieth- and thirty-first-century delivery boy), Zoidberg (the Planet Express staff doctor, hailing from Decapod 10), Kif Kroker (a member of the Nimbus crew, who is in love with Amy), and Amy Wong (a member of the Planet Express crew, who is in love with Kif).
CHAPTER 14
The Birth of Futurama
While The Simpsons was reaching new mathematical heights with the transmission of “Homer3” in October 1995, Matt Groening was beginning to focus his mind on another project. His first animated TV sitcom had become such a massive global success that the Fox network asked him to pitch a sister series.
So, in 1996, Groening teamed up with David S. Cohen to develop an animated sci-fi series. Cohen was Groening’s natural ally, because he had a lifelong fascination and love for science fiction which dated back to watching repeats of the original Star Trek series. Cohen had also developed a great respect for the eminent figures in science-fiction literature, such as Arthur C. Clarke and Stanislaw Lem. Hence, for Cohen, taking science fiction seriously was an important starting point for the sitcom: “The decision Matt Groening and I made early on was not to go too silly. We didn’t necessarily want to make fun of science fiction, so much as to make funny science fiction.”
Cohen also had the necessary nerdy knowledge required to deal with the inevitable technological issues that arise in sci-fi adventures, such as how to travel intergalactic distances in a reasonable time. This is a perennial problem in science fiction, because neither spaceships nor indeed anything can travel faster than the speed of light, and light takes more than two million years to travel to the nearest spiral galaxy. Cohen came up with two solutions that would enable characters to travel intergalactic distances in a reasonable amount of time. One of his solutions was to introduce a plot point stating that scientists had succeeded in increasing the speed of light in 2208. His other, even cheekier, solution was to propose an engine that achieved superluminal velocities by accelerating the universe around it, not the spaceship to which it was attached.
Together, Groening and Cohen began working on a series of storylines based around the adventures of a character named Philip J. Fry, a New York City pizza delivery boy who was cryogenically frozen in the first few hours of 2000. Revived one thousand years later in New New York, Fry eagerly looks forward to embarking on a new life in the thirty-first century, optimistic that his new career will be more rewarding than his old one. Alas, he is frustrated to learn that he is to receive a career implant chip that will condemn him to his same old job as a delivery boy. The only difference is that, instead of delivering pizzas around New York, he will be an interplanetary delivery boy with a company called Planet Express.
Groening and Cohen then began to invent the other members of the Planet Express team. Most notably, Fry’s colleagues would include Leela, a one-eyed mutant who would repeatedly break Fry’s heart, and Bender, a robot whose hobbies included stealing, gambling, cheating, drinking, and worse. Other characters on the drawing
board were Professor Hubert J. Farnsworth (the 160-year-old founder of Planet Express Inc.), Dr. John A. Zoidberg (the company’s lobster-like alien doctor), Hermes Conrad (ex-Olympic limbo champion and the company’s accountant), and Amy Wong (intern).
In many ways, the plan was for this animated series to be just like any classic workplace-based sitcom, such as the American series Taxi or the British series The IT Crowd. The only difference was that almost any storyline was possible, because the Planet Express crew could encounter all manner of strange aliens on weird planets with peculiar problems while gallivanting around the universe delivering packages.
Despite initial interest from Fox, Groening soon realized that network executives were not impressed with his quirky cast of misfit characters and their cosmic adventures. When Fox then tried to interfere, Groening resisted. The pressure increased, and Groening dug in his heels even further. Eventually, after what Groening described as “by far the worst experience of my grown-up life,” he prevailed and the new series was commissioned on the same terms as The Simpsons, with the writers in control.
After being officially green-lit, the series was given the title Futurama, after the name of an exhibition at the 1939 New York World’s Fair that took visitors on a journey into “the world of tomorrow.” Next, Groening and Cohen began recruiting a new team of writers, because it had been tacitly agreed that Futurama would not poach staff from The Simpsons. Not surprisingly, several of the Futurama recruits had backgrounds in subjects such as computing, mathematics, and science. One of the new writers, Bill Odenkirk, had completed a PhD in organic chemistry at the University of Chicago. Indeed, he was a co-inventor of 2,2'-Bis(2-indenyl) biphenyl, which can be used as a catalyst to make plastics.
During this recruitment phase, writers of animated shows became eligible to join a union. Since there was already a union member named David S. Cohen, and unionized writers are not allowed to share the same name, the Futurama writer changed his name to David X. Cohen. The X is not an abbreviation, but instead it neatly encapsulates some of Cohen’s main interests, such as science fiction and mathematics—Cohen is both an X-Phile (lover of The X-Files) and an x-phile (lover of algebra).
The first episode of Futurama was broadcast on March 28, 1999. Although everyone expected that this new science fiction series would contain plenty of science fact, the more erudite viewers were soon impressed by the sheer quantity and a quality of nerdy references.
For example, the third episode, “I, Roommate” (1999), reveals how Fry decides to move in with Bender, the foul-mouthed, bad-tempered robot. Hanging on the wall of their new apartment is a framed cross-stitch message:
This is a reference to a computer programming language known as BASIC (Beginner’s All-purpose Symbolic Instruction Code), in which each instruction is given a number, and the instructions are followed in numerical order. The GOTO instruction is commonplace in BASIC, and in this case the instruction 30 GOTO 10 means go back to line 10. Hence, the cross-stitch conveys the idiom “Home sweet home.” If we take the cross-stitch to its logical extreme, then it actually reads, “Home sweet home sweet home sweet home . . .”
Because it is merely part of the background to the scene, this joke about BASIC obeys the first rule of the Futurama writing room: Obscure references are fine as long as they do not get in the way of the plot. A similarly obscure joke appears in “Mars University” (1999), when we briefly see a blackboard covered in esoteric equations relating to a branch of particle physics known as supersymmetric string theory, except in Futurama it is called superdupersymmetric string theory. The main joke involves a diagram labeled Witten’s Dog, which is a sly reference to both Ed Witten and Schrödinger’s cat.
Ed Witten, one of the fathers of superstring theory, is generally considered the world’s greatest living theoretical physicist and arguably the smartest scientist never to have won a Nobel Prize. By way of compensation, Witten can at least claim the accolade of being immortalized in Futurama. Schrödinger’s cat is a famous thought experiment, one that is conducted in our imaginations rather than in the laboratory. Erwin Schrödinger, who won the Nobel Prize in Physics in 1933, asked what would happen inside a wooden box containing a cat, some radioactive material, and a poisoning mechanism that can be triggered by an unpredictable radioactive decay. After one minute, is the cat dead or alive? Has there been a radioactive decay that has triggered the poisoning mechanism? Back in the nineteenth century, physicists would have said that the cat is either dead or alive, but we do not know which. However, in the early decades of the twentieth century, the newly developed quantum view of the universe offered different interpretations. In particular, the Copenhagen interpretation suggested the bizarre notion that the cat was in a so-called superposition of states, which means it is both dead and alive . . . until the box is opened, at which point the situation is resolved.
Schrödinger and his cat make a guest appearance in another episode, which is titled “Law and Oracle” (2011). Traffic cops chase after a speeding Schrödinger, who eventually crashes. When he emerges from the wreckage, he is questioned about the box in his car. The cops are URL (pronounced Earl) and Fry, who has temporarily left his job at Planet Express.
URL:
What’s in the box, Schrödinger?
SCHRÖDINGER:
Um . . . A cat, some poison, und a cesium atom.
FRY:
The cat! Is it alive or dead? Alive or dead?!
URL:
Answer him, fool.
SCHRÖDINGER:
It’s a superposition of both states until you open it and collapse the wave function.
FRY:
Says you.
[Fry opens the box and a cat jumps out of it, attacking him. URL takes a close look at the box.]
URL:
There’s also a lotta drugs in there.
Of course, this is a book about mathematics, not physics, so it is time to focus on the dozens of scenes in Futurama involving everything from convoluted geometry to incredible infinities. One such scene appears in “The Honking” (2000), which tells the story of Bender returning to his late uncle Vladimir’s haunted castle in order to attend the reading of Vladimir’s will. As the robot sits with his friends in the library, the digits 0101100101 appear on the wall, written in blood. Bender is more confused than spooked, but when he sees the digits reflected in the mirror—1010011010—he is immediately terrified.
Although no explanation is given in the dialogue, binary-savvy viewers would have appreciated the horrific significance of this scene. The number that appears on the wall, 0101100101, when translated from binary into decimal is equivalent to 357. This number has no unpleasant connotations, but its reflection is spine-chilling. We can convert the reflection, 1010011010, from binary to decimal as follows:
Binary number
1
0
1
0
0
1
1
0
1
0
x
x
x
x
x
x
x
x
x
x
Place value
29
28
27
26
25
24
23
22
21
20
Total
= 512
+ 0
+ 128
+ 0
+ 0
+ 16
+ 8
+ 0
+ 2
+ 0
= 666
666, of course, will forever be associated with the Devil, because it is the Number of the Beast. Therefore, perhaps 1010011010 should be considered the Number of the Binary Beast.
Mathematicians, who generally do not have a reputation for diabolical numerology and demonic worship, have a surprising fondness for 666. They have e
ven singled out a particular prime number that includes this series of digits: 1,000,000,000,000,066,600,000,000, 000,001. It is labeled Belphegor’s prime, in honor of one of the seven princes of hell. As well as containing 666 at its heart, this infamous prime also has thirteen unlucky zeroes on either side of the Number of the Beast.
The reversed hidden message in “The Honking” is a nod to The Shining, a classic horror film from 1980. In one of the film’s most famous scenes, a child named Danny enters his mother’s bedroom and scrawls on the door in lipstick. She awakes to find him standing next to her bed with a knife in his hand, and then glimpses the writing reflected in her dressing table mirror, which now reads .
666 written in reversed binary is a neat mathematical code, one of many coded messages that appear in Futurama. All these messages demonstrate various principles of cryptography, the formal name for the branch of applied mathematics that deals with code making and code breaking.
For example, several episodes contain billboards, notes, or graffiti that display messages written in alien scripts. The simplest alien script appears in “Lethal Inspection” (2010), when we see a note that reads:
Cryptographers call this a substitution cipher, because every letter of the English alphabet has been replaced by a different character, in this case an alien symbol. This type of cipher was first cracked by the ninth-century Arab mathematician Abu al-Kindi, who realized that every letter has a personality. Moreover, the personality of a particular letter is adopted by whichever symbol replaces that letter in the coded message. By spotting these traits, it is possible to decipher the message.