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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross


Sphere (1998)

To investigate the crash site of a space craft of unknown origin somewhere at the bottom of the Pacific a "Contact team" consisting of a biochemist Beth (Sharon Stone), Harry a mathematician (Samuel L Jackson), Ted an astrophysicist and Norman a psychologist (Dustin Hoffman) is sent to investigate.
The following dialogue identifies Harry as somebody who is good with numbers.

BARNES: You tell me. That's the fuselage. Ultrahigh-res S.L.S. bottom scan, came in a week ago. There it is...buried under about eight yards of coral.
BETH: There's something wrong with that measurement. Pacific coral grows at a rate of an inch a year. You can set your watch by it.
BARNES: That's right.
BETH: So, you're saying this spacecraft crashed in the year...
HARRY: 1709.
BETH: You're saying this spacecraft crashed three hundred years ago?
HARRY: Two hundred and eighty-eight.

The reason for having a mathematician as part of the group is spelled out by Barnes the leader of the expedition.
BARNES: A mathematician, because that'll probably be our common language.

We find out that the mathematician has three PhDs from M.I.T. and got his first one at the age of 18.
It turns out that the space ship is an American space ship from the future and crashlanded because of an unknown entry event. Later on this event turns out to be caused a huge golden sphere which is the only living thing left on board the space ship.

TED: I'll bet if you put a laser micrometer on this, it'd be a perfect sphere.
Perfect to a thousandth of an inch. That's a message in and of itself.
HARRY: Really?
BARNES: What do you mean?
TED: When Pope Benedict asked Giotto to prove his worth as an artist Giotto drew a perfect circle, freehand. Perfection. It's a powerful message.

HARRY: We're all going to die down here, you know.
NORMAN: What? What?
HARRY: You see, it's curious. Ted did figure it out. Time travel. And when we get back, we're going to tell everyone how it's possible, how it's done, what the dangers are. But why fifty years in the future, when the spacecraft encounters a black hole does the computer call it an ''Unknown Entry Event''? Why don't they know? If they don't know it means we never told anyone. And if we never told anyone it means we never made it back. Hence we die down here. Just as a matter of deductive logic, Norman. Damn, l wish l could get inside that Sphere.

Harry: This has a pattern. See? It's like a code.
BARNES: A code from where?
TED: How'd you do that?
BARNES: How'd you see that?
HARRY: Try binary.
The numbers change to a string of "0"s and "1"s
HARRY: See? Letter breaks.
Later on this whole binary business turns out to be irrelevant since they are only
Arguing with decimals anyway and the letter breaks are already apparent in the string of decimal numbers anyway. Why use decimal numbers anyway?
TED: You think this is coming from the Sphere?
HARRY: Don't know.
BARNES: This mission is ultra top-secret. What you translate is for my eyes only.
HARRY: If you were it, how would you know our alphabet?
TED: Same way it's configured on a keyboard. But reflected in an orb, spherically. A keyboard, but spherical. Take a keyboard...wrap it around a sphere...then starting at the center key, G, number the letters...spiraling out.
Why? If we think of the keyboard touching the sphere in the G key and then project the keyboard onto the sphere by moving perpendicular to the keyboard, then the V,B,F, and H keys are projected to points in a circle contained in the sphere that is parallel to the keyboard. This makes them equally "close" to G. So why start the spiral at B and not anywhere else? A keyboard is asymmetrical, but somehow it is not clear why you start the spiral where they start it, nor why it winds in the anticlockwise direction and not in the clockwise direction.
Shouldn't that 20 be the 13? Also some of the other choices to generate the spiral seem to be fairly random.
HARRY: All we got to do now is plug in the numbers.

Using the above key we can now actually decode the message: 00322125262632 (heloo. this one is messed up. The first 26 should be a 25) 032629 (How) 30|13|21 (are) 04261037 (youq, here the q is probably supposed to be the question mark. Strange because they do have a special key allotted to this key. Also the red markers seem to be slightly out of sync) 18 (I) 3016 (am) 0618082132 (fine. actually on their keyboard there is a > instead of a period.) 2903305 (What) 1822 (is) 04261013 (ypur), here they got one letter wrong) 0830162137 (nameq the q again should be the question mark) 1604 (my) 08301621 (name) 1822 (is) 0330313130432 (This one seems messed up again. It is supposed to read Harry. Going from back to front you translate 13130432 in arry. However, continuing this way yields nonsense. From the front 0330 is Ha, so there is one 3 too many.)
Message decodes on the computer
So the computer actually does get it wrong and translates Harry as Jerry. Very strange mistake, though. Also does not have any problems with the other inconsistencies.
HARRY: Friends in the ,OOO years of recorded history, this is a first. You're now on-line with an alien intelligence.

Later on Norman the psychologist tries to figure out what is wrong with Harry.
NORMAN: He's got G equals one. That's right. He's got B equals two. He's got H equals three. That's not right. Harry's got the code wrong, H doesn't equal three.
So he figures out that Jerry should read Harry and this gives a clue that Harry is really the source of the messages.

And what I can't understand is that ever since he went in the Sphere the Sphere has a power that projects every subconscious thought Harry has onto the computer.
It prints it out and we interact with it.
We thought it was Jerry. It's not Jerry. It's Harry.