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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross


Contact (1997)

This movie is based on the novel by Carl Sagan with the same title. It deals with a first contact between people on Earth and an alien civilization in the form of a “pulsating” radio signal from outer space. Jodie Foster plays the astronomer Ellie Arroway who discovers the signal using the VLA (Very Large Array of radio telescopes) in New Mexico.

The official mathematics consultant for this movie was the Dr. Linda Wald and the radio astronomy consultant was Dr. Tom Kuiper. In fact, both scientists really cooperated closely to ensure that the mathematics in this movie is correct.

Just when Ellie and her colleagues have pinpointed the signal it stops, only to reappear after a few moments. We hear two pulses.
ELLIE: Come on.
We hear three pulses.
ELLIE: All right. It is restarting. Wait a minute, those are numbers. That was three, the one before it was two. Um, base 10 numbers, just start counting now and see how far we can get.
Five Pulses.
Seven Pulses.
ELLIE: Seven
Those are primes 2, 3, 5, 7. Those are all prime numbers, there is no way this is a natural phenomenon.

Jodie Foster’s comment on this scene on the DVD: “It is really once again Michael Goldenberg’s and Bob Zemeckis’ genius to figure out how to make this idea that these signals are delivered in prime numbers, to make people understand what that is, by really spelling out the process of getting the message. I mean normally it would take you many, many years of scientific study to really understand this stuff.”
According to the science consultants, the film makers were very disappointed to find out that 1 is not counted as a prime number. In the next scene, the press, national security, military etc. arrive at the scene.

DAVID DRUMLIN (scientist turned evil science manager): Let’s get the decryption people in here. Lunacharsky is visiting at Cal Tech.
KITZ (national security advisor): Explain this to me. If the source of the signal is so sophisticated, why the remedial math?
SENATOR: Exactly, why don’t they just speak English?
ELLIE: Well, maybe because seventy percent of the planet speaks other languages. Mathematics is the only truly universal language, Senator. It is no coincidence that they’re using primes.
SENATOR: I don’t get it.
ELLIE: Prime numbers. That would be integers that are only divisible by themselves and 1. Well, we think that this may be a beacon. Some kind of announcement to get our attention.
KITZ (to Ellie): I'm saying you might have consulted us; obviously, the contents of this message could be extremely sensitive.
ELLIE: You want to classify prime numbers, now?On closer inspection the signal contains pictures of many thousand square pages full of drawings and writings in an alien language. Decrypting this information turns out to be a problem until S.R. Hadden, the mysterious genius engineer and superrich entrepreneur who supports Ellie’s research meets with Ellie and reveals that he knows the key to solving the puzzle. But first we get to know a little bit more about Ellie.

HADDEN: I’ve had my eye on you a long time. I consider you one of my most valuable long-term investments, and when it comes to my investments, I always do my homework.
He starts up a video sequence on a wall monitor.
HADDEN: Eleanor Ann Arroway, born 25th August 1964 in DePere, Wisconsin. Mother, Joanna, died from complications during childbirth. Early testing indicated high pre-disposition towards science and mathematics. Father, Theodore, advised to provide enrichment activities along these lines, did so conscientiously until his death from myocardial infarction November 10, 1974. You graduated from high school in 1979, almost two full years early. Rewarded full scholarship, MIT, graduated magna cum laude. Doctoral work, Cal Tech, where you did breakthrough work on the lanthanide-doped ruby maser, dramatically increasing the sensitivity of radio telescopes. Subsequently, offered a teaching position at Harvard University, which you turned down, to pursue SETI work at the Arecibo observatory in Puerto Rico. Changes in NSF policy gave rise to certain funding problems, at which point you came to my attention.
ELLIE: You found the primer.
HADDEN: Clever girl! Lights.
Another video appears on the wall monitor.
HADDEN: Pages and pages of data. Over 63 thousand in all, and on the perimeter of each...
ELLIE: ...alignment symbols, registration marks, but they don’t line up.
HADDEN: They do, if you think like a Vegan. An alien intelligence is going to be more advanced. That means efficiency functioning on multiple levels and in multiple dimensions.
ELLIE: Yes! Of course. Where is the primer?
HADDEN: You’ll see. Every three-dimensional page contains a piece of the primer; there it was all the time, staring you in the face. Buried within the message itself, is the key...
Here by three-dimensional page he means six of the square pages combined into a cube. In the simulations the six faces become transparent except for the writing. When two opposite faces are superimposed a hidden message becomes visible.

WHITE HOUSE - CABINET ROOM (Ellie finishes the sentence that she started in the previous scene)
ELLIE: decoding it. Within the layering of the matrix, we have these basic equations. So with this very elementary foundation, they have given us a kind of general scientific vocabulary. We now have the symbols for true and false...
Every three-dimensional page contains three messages corresponding to the three pairs of opposite faces of a cube.
DAVID DRUMLIN: (Cutting Ellie off) ...This was the key, to put it simply, that allowed us to decipher their language for physics, geometry, chemistry, next frame Ellie.

ELLIE: Occam's Razor, you ever heard of it?
PALMER: Hackem is Razor, sounds like some slasher movie.
ELLIE: No, Occam's Razor, it is a basic scientific principle. And it says, all things being equal, the simplest explanation tends to be the right one.
PALMER: Makes sense to me.
ELLIE: All right. So what is more likely (Palmer puts his jacket around Ellie), thank you...
PALMER: You’re welcome.
ELLIE: all powerful and mysterious God created the Universe, and then decided not to give any proof of his existence, or that he simply doesn’t exist at all, and that we created him so that we didn’t have to feel so small and alone?
PALMER: I don’t know. I couldn’t imagine living in a world where God didn’t exist. I wouldn’t want to.
ELLIE: How do you know you’re not deluding yourself? As for me, I’d need proof.
PALMER: Proof. Did you love your father?
PALMER: Your Dad, did you love him?
ELLIE: Yes, very much.
PALMER: Prove it.

NEWS READER: The decryption team here at the VLA has been working around the clock, and all the hard work has finally paid off. This key section uncovered tonight, and obtained exclusively by CNN, shows an illustration of what is unmistakably a human figure inside a geometric structure of some kind. This and other contextual clues, now lead scientists to believe that the message is in fact device designed to take a single human occupant into space. Presumably to the star named Vega...
The geometric structure is a spherical capsule inscribed in a dodecahedral frame. It is not entirely clear how this last piece of the puzzle is buried inside the message. The video sequence on TV seems to suggest that, just like the pieces of the primer, this image emerges when one looks at one of the three-dimensional pages from the right direction.

PALMER: Can we talk about Einstein?
ELLIE: Yea, sure, ok.
PALMER: Special relativity. This machine, now if it works and you travel to Vega at even close to the speed of light when you come back...
ELLIE: ...if you come back.
PALMER: If you come back, you will only be 4 years older, but over 50 years will have passed here on Earth, and everybody that you care about will be gone, dead and buried.
ELLIE: If you came back, if you survived it all, which is... look Palmer, no one is saying that this isn’t dangerous, all right. I - The rest of the candidates and myself we fully understand the implications, the risks that we’re taking.
ELLIE: Because it is a historic opportunity, because the world needs...
PALMER: You, Ellie, you. You personally. I mean by doing this you’re willing to give your life to it, you’re willing to die for it... why?
ELLIE: For as long as I can remember, I've been searching for something, some reason why we're here -- what are we doing here, who are we? If this is a chance to find out even just a little part of that answer, I don’t know, I think it's worth a human life, don't you?
The machine described in the transmission from outer space gets built. We get a first good look at the dodecahedral capsule. It is worth pointing out that opposite edges of a dodecahedron are parallel and that the capsule is suspended along two such opposite edges.