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First-Contact Math
- 207 statements
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- 30 referencing feature instances
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First Contact situations with Starfish Aliens have an inherent problem — since the aliens are so incomprehensible, how will you even realize that they're intelligent? For that matter, how can you convince them that you are? The generally accepted universal signal of intelligence in this situation is the ability to produce a sequence of prime numbers: numbers that are only divisible by the number one and themselves. Why? Because it doesn't matter what number base you are using or what you call the numbers, 7 rocks cannot be divided up into any whole number of equal groups of rocks without breaking them. If the aliens have math, they'll get this — resource allocation is one of the first tricks any group has to figure out. The idea is that they're too irregular to arise from any natural processnote Although reproduction cycle periods of some insects tend to be a prime number of years to prevent matching another kind and then predators synchronising on them (i.e., no mathematical equation is known that will exhaustively produce them in reasonable timenote There are equations that can produce an unlimited amount of prime numbers, but not all of them, and methods that will get them all, but the computation time is by brute force and thus enormous.), but mathematically simple enough that it's assumed any intelligent being can recognize them as non-random. More generally, anything obviously recognizable as simple math (such as digits of pi, or a proof of the Pythagorean theorem) can serve the same function. Of course, the digits of pi will change if the aliens don't have a base-10 system (odds are that they don't), while the prime numbers will not change if you represent them properly. Often this can look like an instance of Only Smart People May Pass (just like plenty of humans do not know about prime numbers or basic math, plenty of otherwise intelligent aliens won't know what to do with the puzzle). However, while Only Smart People May Pass happens in the context of a pre-created puzzle or situation, the entire point of First Contact Math is that it provides the best hope we might have of communicating without having any context at all. See also First Contact Team, for when First Contact Math might fail and you need to plan for any contingency. |
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Contact: The alien transmission begins with a sequence of prime numbers, before continuing on to more useful mathematics and science. The novel by Carl Sagan (who also championed the use of primes in this context in Real Life SETI) makes considerably more of this, also using prime numbers in the encoding of the more complex layers of the transmission. | |
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The basic story of Arrow 18 Mission Logs is of first contact between humans and ponies. After Twilight Sparkle leaves Randy (the human astronaut who just landed in Equestria) a basket with some food, he leaves a sheet of paper with basic math problems on them (including a chart indicating that "1" means one, "2" means two, etc.) Twilight's reaction when she figures out that the "stridetaur" is trying to communicate with math is one of unbridled glee. | |
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In Fine Structure, "Eka", AKA "The Script", starts out from prime numbers and works its way up to describe the entire physics of the universe. | |
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The Mission Stays the Same: When they leave Illium, the Normany crew picks up a Gyrinx, a large alien feline that communicates through Telepathy with other psykers. In order to prove its sapience to the Citadel Council and get First Contact rolling, Mordin has the Gyrinx (named M'tarr) answer some basic math questions in a recording while Maeteris translates more complex language. Not only does M'tarr answer the questions correctly, she also displays several other signs of sapience that Mordin was watching for: emotions (flattening her ears in annoyance and asking through Maeteris if Mordin thinks she's stupid when he gives M'tarr a very basic question), creative thinking (answering his second question with a riddle), and understanding of astronomy (said riddle being an accurate calculation of the lunar cycle of M'tarr's homeworld Moarheff). | |
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Tom Swift Jr. and his father communicate with some aliens by sending mathematical symbols at them (and vice versa) throughout his entire series. Exactly what is meant by "mathematical symbols" is never made particularly explicit. | |
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In "Cold Snap" by Kim Newman, the villain has revived a dormant non-human intelligence that existed before all other life on Earth. While the hero is trying to figure out how the villain communicates with it, he goes through several of the standard options including numbers, but concludes that the creature is too alien even for those to be common ground. "A being on her scale has no use for any number other than 'one'." | |
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In The Long Utopia, human scientists use this when trying to communicate with the silver beetle creatures. They are summarily ignored, and Lobsang admits that he'd probably just laugh if he saw some strange creature counting out basic numbers with rocks. | |
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Contact has aliens contact Earth by sending a sequence of prime numbers. Later, they send instructions for building a machine to reach them by embedding basic universal math principles into the instructions so any race with knowledge of mathematics can decode it and build the machine. | |
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Giants Series: In a related "First Contact Chemistry", in James P. Hogan's Inherit the Stars, the key to deciphering an alien language comes when someone recognizes a Periodic Table of the Elements in an alien book. | |
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In Schild's Ladder by Greg Egan, the protagonists realize that there's intelligent life inside a pseudovacuum when they notice that a series of pulses coming from it represent consecutive prime numbers. | |
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Queen Watevra Wa'Nabi in The LEGO Movie 2: The Second Part tells the gang she's going to talk to them in the universal language. Princess Unikitty guesses it's math, but it turns out to be song, to Lucy's horror. | |
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The Action Hero's Handbook has a chapter on communicating with extraterrestrials, and suggests starting with basic concepts like numbers and shapes because the authors of the book believe that no matter how alien the culture is, they would still be able to have dialogue about that, especially if they're able to go into space. | |
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Schlock Mercenary: When investigating the ancient, planet-sized artifact Oisri, it doesn't take long for people to start noticing that there are too many mathematical coincidences to be anything but intentional. To start with, there's a large effect that is exactly 2063 times the planetoid's radius. This is the first step to deciphering the tools to reading the data Oisri contains. | |
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Discussed but ultimately averted in The Next Frontier. The odds of anything remotely recognisable as prime numbers or similar at interstellar distances are pretty much nil, but a single repeating tone or a noise like this could carry much further. And by the time first contact actually happens, the aliens have Learnt English from Watching Television anyway. | |
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In the Farscape episode "Through The Looking-Glass", Crichton realizes an extradimensional being is trying to communicate with the crew rather than hunt them when he recognises that the talon slashes that it makes in reality are the first few successive prime numbers. | |
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In A Martian Odyssey by Stanley Weinbaum, the human explorer communicates with the Martian first with the words "one" and "two" demonstrated with rocks. The bird creature learns a few English words, at one point saying "No One One Two" to describe a creature that is unintelligent, and "One One Two Yes, Two Two Four No" for a creature of very rudimentary intelligence. | |
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In the Close Encounters of the Third Kind parody short "Closet Cases of the Nerd Kind", which features aliens coming down to Earth and hitting people in the face with pies for no apparent reason, some researchers keeps receiving the number 3.14159 and don't understand why. Finally, one character speaks up. | |
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Star Trek: Star Trek: The Next Generation In "Allegiance", Captain Picard is kidnapped by unknown aliens; he attempts to convince them that he's intelligent by repeatedly tapping out the first six prime numbers. Downplayed in "Darmok" where the Children of Tama make known their intent to make first contact by sending a Subspace Ansible transmission that Data describes as a "standard mathematical progression" that doesn't carry any message. Turns out the Tamarians are Strange Syntax Speakers and so the rest of the episode involves Picard and the Tamarian captain trying to establish a dialogue. Star Trek: Voyager: In "Blink of an Eye", an alien species living on a planet where time moves extremely fast attempt to communicate with Voyager (or, as they call it, the Sky Ship) via radio by using prime numbers and universal constants. Since, by the time they receive and recognize the signals, the scientist who sent them is long dead, the Voyager crew don't bother responding. Amusingly played with in "Future's End", where after being sent back in time to Earth in the year 1996, they're picked up by an astronomer who attempts to communicate with the "aliens" in orbit by sending the SETI message. A crewman asks Harry if they should respond, to which Harry says, "Absolutely not." |
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Parodied in The Onion: Earth Contacted By Extraterrestrial Nerds. | |
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Attempted by Lob in the Soviet cult classic Moscow — Cassiopeia, when he encounters a pair of Human Aliens (actually, they're Ridiculously Human Robots, but he doesn't know that yet) on a planet seemingly devoid of intelligent life. Despite possessing a Universal Translator, he tries this trope by writing out the "(a + b)2" formula and turning it into "a2 + 2ab + b". One of the aliens grabs his marker and adds the "2" to the last symbol. | |
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Averted in a Mickey Mouse comic: Mickey was kidnapped by aliens and treated as a pet. When he wrote complex mathematics on the walls of the spaceship, it was dismissed as random scribbling. How he got the aliens to recognize him as an intelligent being? Cooking. | |
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Ultimate Fantastic Four: When Reed makes contact with some residents of the Negative Zone, their first few exchanges are conducted in binary. After Reed sends them Pi and the human symbol for "hydrogen", their computer takes over and downloads the first contact package he prepared. | |
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In Dreamcatcher by Stephen King, a population of infected send pleading messages interspersed with a recitation of prime numbers. One of the characters speculates it is to prove they're an intelligent species. They must not be that intelligent though, since they include 27 and 117 in their list. (Also 1, but that's somewhat reasonable, depending on how you define primes.) This deviation from the primes isn't noted in the novel though, and was probably either unintentional or done because the numbers have significance to Derry, the novel's setting. | |
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Superman Unchained: On the brink of World War II in 1938, US scientists sent a mathematical equation into space, but the mathematical equation was incorrect, and added up to more than the sum of its parts, to signify the message "let us add up to more, together." Eleven seconds later, The Wraith's ship crash landed on Earth, with a similar, more complex equation. | |
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The alien ship in Anathem has a proof of the Pythagorean Theorem on its hull for this reason. | |
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Referenced in Noughts & Crosses. Callum and Sephy are discussing their favourite school subjects, and Sephy can't believe that Callum likes maths. Callum references the countless ways maths is essential, including this trope, in response. | |
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Chanur Novels: In The Pride of Chanur, when the human Tully is cornered by the felinoid Hani, he writes out (in his own blood) numbers from zero on up. When he gets to 10, they realize that he might be using a positional notation system. | |
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"Not Final!": Birnam describes how first contact with Jovians involved a lot of back-and-forth on math, such as adding, square roots, and factorials. This went on for over five years, as human scientists on Ganymede communicated by radio clicks to the surface of Jupiter. | |
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In Cauldron, Priscilla Hutchins realises that Space Clouds they are observing have formed a Giant Eye of Doom looking back at them. While everyone else freaks out, she tries flashing her navigation lights at the 'eye', and gets flashes of 'lightning' inside the cloud as a response. Eventually by using the lights to perform basic math, they're able to start rudimentary communication. | |
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In Doctor Who, this problem is usually absent due to the presence of the TARDIS's Universal Translator, However, it arises in the episode "Flatline" when the Doctor encounters strange 2-dimensional beings, who are so alien that even the TARDIS cannot translate them. The creatures had been abducting and killing people, with the Doctor having hoped they were Non Malicious Monsters, who are simply so alien and confused by a 3-D world they don't realise they're harming sentient beings. He attempts to communicate with them using the digits of pi. They respond with the number on the jacket of the man they killed, and then the number of the one they're about to. | |
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Notably averted in Mass Effect: Clash of Civilizations. Both the UNSC and Citadel have their own method of deciphering language, neither of which involve mathematics. | |
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Colossus: The Forbin Project: How Colossus establishes a common language with the Soviet Master Computer Guardian. It starts with 1+1=2 and in a few hours has developed an entire new language for them to communicate. Unfortunately this alarms both governments as they can't be sure strategic secrets aren't being leaked, so the President and Premier decide to break the link. The computers do not react well. | |
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Arrival: One of the first things attempted for meaningful communication with the aliens. It doesn't work until they try sending extremely advanced mathematics rather than simple ones. Turns out the aliens' minds are structured very differently, so what is simple and easily understandable for humans is not so for them. | |
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In Rama (based on the novel Rendezvous with Rama), the Ramans put many math-based obstacles in your path, presumably for this reason. | |
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Star Trek: Voyager: In "Blink of an Eye", an alien species living on a planet where time moves extremely fast attempt to communicate with Voyager (or, as they call it, the Sky Ship) via radio by using prime numbers and universal constants. Since, by the time they receive and recognize the signals, the scientist who sent them is long dead, the Voyager crew don't bother responding. Amusingly played with in "Future's End", where after being sent back in time to Earth in the year 1996, they're picked up by an astronomer who attempts to communicate with the "aliens" in orbit by sending the SETI message. A crewman asks Harry if they should respond, to which Harry says, "Absolutely not." |
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Subverted in an episode of Babylon 5. A probe sent out by an advanced species containing mathematical riddles appears to be this at first... until it's found out the thing's actually a way for the isolationist species to figure out which other races are a threat and destroy them. Fortunately, the probe's fairly stupid. | |
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In Star's Reach by John Michael Greer, both humanity and the Cetans tried this to find out whether there was other life in the universe. However, it took a while for both sides to realize they were receiving messages, because their math systems are fundamentally different — Cetans, being amorphous and shifting, think in terms of "flows" from one value to another, and their basic math has more in common with calculus, while they can only conceive of our regular math with difficulty. | |
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Star Trek: The Next Generation In "Allegiance", Captain Picard is kidnapped by unknown aliens; he attempts to convince them that he's intelligent by repeatedly tapping out the first six prime numbers. Downplayed in "Darmok" where the Children of Tama make known their intent to make first contact by sending a Subspace Ansible transmission that Data describes as a "standard mathematical progression" that doesn't carry any message. Turns out the Tamarians are Strange Syntax Speakers and so the rest of the episode involves Picard and the Tamarian captain trying to establish a dialogue. |
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