History Main / FirstContactMath

* The Twilight Zone episode [[Recap/TheTwilightZoneS3E93TheLittlePeople The Little People]] has one of a pair of stranded astronauts contact the titular group. When his partner arrives, the first explorer explains that he used math to establish communication with the alien society. He soon uses his ability to communicate with them for a much darker purpose...

* ''Literature/ChildrenOfTime2015'': The human project to fill the galaxy with life involves terraforming planets, introducing monkeys infected with a virus that will [[UpliftedAnimal uplift]] them over generations, then putting a satellite in orbit to broadcast a radio message containing a simple mathematical sequence at the planet over and over again. The expectation is that, as the monkeys attain human-like intelligence, they will develop the means to detect the message and reply to it with the next steps of the sequence, signaling that they’re ready to meet their makers. However, circumstances cause all but one world to suffer ecological collapse, and on that world, the monkeys never arrived. What arises instead is a sentient species of jumping spider, and [[AgainstMyReligion cultural]] and [[BizarreAlienPsychology psychological factors]] prevent them from responding to the message until centuries after they first detect it, and the interstellar human empire imploded thousands of years before that.

* ''Literature/ChildrenOfTime'': The human project to fill the galaxy with life involves terraforming planets, introducing monkeys infected with a virus that will [[UpliftedAnimal uplift]] them over generations, then putting a satellite in orbit to broadcast a radio message containing a simple mathematical sequence at the planet over and over again. The expectation is that, as the monkeys attain human-like intelligence, they will develop the means to detect the message and reply to it with the next steps of the sequence, signaling that they’re ready to meet their makers. However, circumstances cause all but one world to suffer ecological collapse, and on that world, the monkeys never arrived. What arises instead is a sentient species of jumping spider, and [[AgainstMyReligion cultural]] and [[BizarreAlienPsychology psychological factors]] prevent them from responding to the message until centuries after they first detect it, and the interstellar human empire imploded thousands of years before that.

* In Creator/CJCherryh's ''Literature/ThePrideOfChanur'', when the human Tully is cornered by the [[CatFolk 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 [[http://en.wikipedia.org/wiki/Positional_notation positional notation system]].

See also FirstContactTeam, for when First Contact Math might fail and you need to plan for ''any'' contigency.

* In Creator/HGWells' ''The First Men in the Moon'', Cavor discusses using math to communicate with his alien captors, but he doesn't really have any idea how to do so.

** In the ''Series/StarTrekTheNextGeneration'' episode "Allegiance", Picard is kidnapped by unknown aliens; he attempts to convince them that he's intelligent by repeatedly tapping out the first six prime numbers.

* In ''Literature/{{Dreamcatcher}}'' by Creator/StephenKing, a population of infected send pleading messages interspersed with a recitation of prime numbers. One of the characters speculates it is to prove they've an intelligent species. They must not be that intelligent though, since they include 27 and 117 in their list. (Also 1, but that's actually reasonable.) 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.

* In ''Cauldron'', Literature/PriscillaHutchins realises that SpaceClouds they are observing have formed a GiantEyeOfDoom looking back at them. While everyone else freaks out, she tries flashing her navigation lights at them, 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.

* The Twilight Zone episode [[Recap/TheTwilightZoneS3E93TheLittlePeople The Little People]] has one of a pair of stranded astronauts contact the titular group. When his partner arrives, the first explorer explains that he used math to establish communication with the alien society. He soon uses his ability to communicate with for a much darker purpose...

* In ''Series/DoctorWho'', this problem is usually absent due to the presence of the TARDIS's [[TranslatorMicrobes Universal Translator]], However, it arises in the episode "[[Recap/DoctorWhoS34E9Flatline Flatline]]" when the Doctor encounters 2-dimensional entities who have been abducting and killing people. Hoping that the creatures are a NonMaliciousMonster 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 [[EvilGloating the number of the one they're about to]].

Elaborations would have to wait.* In Creator/CJCherryh's ''Literature/ThePrideOfChanur'', when the human Tully is cornered by the [[CatFolk 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 [[http://en.wikipedia.org/wiki/Positional_notation positional notation system]].

* ''Literature/ChildrenOfTime'': The human project to fill the galaxy with life involves terraforming planets, introducing monkeys infected with a virus that will [[UpliftedAnimal uplift]] them over generations, then putting a satellite in orbit to broadcast a radio message containing a simple mathematical sequence at the planet over and over again. The expectation is that, as the monkeys attain human-like intelligence, they will develop the means to detect the message and reply to it with the next steps of the sequence, signaling that they’re ready to meet their makers. However, circumstances cause all but one world to suffer ecological collapse, and on that world, the monkeys never arrived. What arises instead is a sentient species of jumping spider, and [[FantasticReligiousWeirdness cultural]] and [[BizarreAlienPsychology psychological factors]] prevent them from responding to the message until centuries after they first detect it, and the interstellar human empire imploded thousands of years before that.

FirstContact situations with StarfishAliens 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?

* ''ComicBook/UltimateFantasticFour'' - 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.
* ''ComicBook/SupermanUnchained'': 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.

* The basic story of ''FanFic/Arrow18MissionLogs'' 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 [[{{Squee}} unbridled glee]].

[[folder:Film]]
* ''Film/ColossusTheForbinProject''. How Colossus establishes a common language with the Soviet MasterComputer 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. [[NukeEm The computers do not react well]].
* ''Film/{{Contact}}'' has aliens contact Earth by sending a sequence of prime numbers. Later, they send instructions for building a machine to reach them by imbedding basic universal math principles into the instructions so any race with knowledge of mathematics can decode it and build the machine.
* Attempted by Lob in the Soviet cult classic ''Film/MoscowCassiopeia'', when he encounters a pair of HumanAliens (actually, they're RidiculouslyHumanRobots, but he doesn't know that yet) on a planet seemingly devoid of intelligent life. Despite possessing a UniversalTranslator, he tries this trope by writing out the "(a + b)[[superscript:2]]" formula and turning it into "a[[superscript:2]] + 2ab + b". One of the aliens grabs his marker and adds the "[[superscript:2]]" to the last symbol.
* ''Film/{{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.

* ''Film/{{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 RealLife SETI) makes considerably more of this, also using prime numbers in the encoding of the more complex layers of the transmission.
* In ''Literature/SchildsLadder'' by Creator/GregEgan, 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.

* ''Literature/TomSwift 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.
* The Creator/BarbaraHambly novel ''Literature/TheSiliconMage'' shows Antryg and Joanna communicating with an extra-dimensional via Pi and Planck's Constant.

* This fails in ''Calculating God'' by Creator/RobertJSawyer; transmissions to Delta Pavonis go unnoticed by the native Wreed, because the Wreed have a brain structure that makes them incapable of doing math. (They can automatically recognize numbers of up to 46, and that's it.) They are very good at ethical problems and analog simulations, though. The Forhilnor also admit that they were astonished to find a civilization on the Wreed homeworld, but stoutly defend their intelligence, noting that the Wreed build beautiful cities out of the sparse available materials there.
* In Creator/CJCherryh's ''Literature/ThePrideOfChanur'', when the human Tully is cornered by the [[CatFolk 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 [[http://en.wikipedia.org/wiki/Positional_notation positional notation system]].
* Used, then subverted in the series beginning with ''Emprise''. An alien transmission is recognized and eventually translated into a simple depiction of the aliens and their system. However, one mathematician claims to have found many more levels of meaning embedded in the message, a la ''The Bible Code''. Ultimately, it turns out that these new levels are the product of his overactive imagination.
** Double subverted in that the message turns out to be from [[spoiler:the remnants of a human colony from humanity's ''first'' attempt at interstellar colonization '''during the last ice age''', which came to an abrupt end when the ''real'' StarfishAliens wiped out (almost) all of the colonies and bombed Earth back into the stone age.]]

* Creator/LarryNiven and Jerry Pournelle's ''Literature/TheMoteInGodsEye'' has the human exploration party and the Moties use this method for initiating communications.
-->Cargill and Horvath's team worked together to answer the pulses. ''One, two, three, four'' blinked the light, and Cargill used the forward batteries to send ''five, six, seven''. Twenty minutes later the light sent ''three one eight four eleven'', repeated, and the ship's brain ground out: ''Pi, base twelve''. Cargill used the computer to find ''e'' to the same base and replied with that.\\
\\
But the true message was, ''We want to talk to you''. And ''[=MacArthur=]'''s answer was, ''Fine''.\\
\\
Elaborations would have to wait.

* In Creator/HGWells' ''The First Men in the Moon'', Cavor discusses using math to communicate with his alien captors, but he doesn't really have any idea how to do so.
* In a related "First Contact Chemistry", in James P. Hogan's ''[[Literature/GiantsSeries Inherit the Stars]]'' the key to deciphering an alien language comes when someone recognizes a Periodic Table of the Elements in an alien book.
* Creator/HBeamPiper's "{{Literature/Omnilingual}}": This {{novelette}} uses the Periodic Table as [[CommonTongue a universal key]]. It helps that the Martian language tends to make new words by combining existing ones, so that (for example) the word for "metal" is part of the names of various metallic elements.

* In ''The Andromeda Affair'' the aliens are transmitting a sequence of bits whose length is the product of two primes. The hero assumes correctly that this implies the bits should be arranged in a two-dimensional grid to be understood.
* Creator/IsaacAsimov:
** ''Literature/TheLeftHandOfTheElectron'': This NonFiction book describes the concept of "parity" in physics, and creates a FramingDevice where you are sending an interstellar radio message to an alien culture. How do you describe the concepts of "right" and "left"? Start with math.
** "Literature/NotFinal": 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 {{UsefulNotes/Jupiter}}.
* In ''Literature/{{Dreamcatcher}}'' by Creator/StephenKing, a population of infected send pleading messages interspersed with a recitation of prime numbers. One of the characters speculates it is to prove they've an intelligent species. They must not be that intelligent though, since they include 27 and 117 in their list. (Also 1, but that's actually reasonable.) 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.
* The RealLife attempts by SETI are described in ''Literature/EarthTheBook'' or, as Jon Stewart calls it, "drunk-dialing the universe".
* In ''[[Literature/TheLongEarth 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.
* Referenced in ''Literature/NoughtsAndCrosses''. 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.
* In James Cambias' ''A Darkling Sea'', when one of the Ilmataran tried to properly establish communication with a human on their planet (after the FirstContactFauxPas that cause conflicts between humans and Sholens over AlienNonInterferenceClause issue on contacting Ilmatarans), Rob, the main character, tried to tap 1+1=2 and 2+2=4 to see if the Ilmataran can realize that he's an intelligent being and try to start learning to communicate. It works. This is probably helped by the fact that non-echolocation-based component of Ilmataran language is based on math and mapping words to numbers.
* In "Literature/ColdSnap" by Creator/KimNewman, 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'."

* In the ''{{Series/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.
* In the ''Series/StarTrekTheNextGeneration'' episode "Allegiance", Picard is kidnapped by unknown aliens; he attempts to convince them that he's intelligent by repeatedly tapping out the first six prime numbers.
* ''Series/StarTrekVoyager'':
** 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."

%%* On ''StargateSG-1'', one of several tests set by the Asgard to see whether a colony of humans under their protection was sufficiently advanced to meet the Asgard in person was whether they knew the meaning of pi. This is not an example of this trope, since the Asgard already know that the humans in question are sentient. It actually belongs and is listed under OnlySmartPeopleMayPass, but it's staying here in a comment because people keep trying to add it.
* In the ''Film/CloseEncountersOfTheThirdKind'' 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.

[[folder:Webcomics]]

* In ''Band'' by Creator/{{Tailsteak}}, [[http://tailsteak.com/archive.php?num=126 intelligence is established]] with square numbers (1, 4, 9, 16)

[[folder:Other]]
* Parodied in ''Website/TheOnion'': [[https://www.theonion.com/earth-contacted-by-extraterrestrial-nerds-1819563984 Earth Contacted By Extraterrestrial Nerds]].
[[/folder]]

* Space probes we sent out of the Solar System (like Pioneer 10) usually contain this in some form. [[note]]Pioneer 10 included a star map telling them [[WeComeInPeaceShootToKill where we are]], even if the probabilities of the probe being found by aliens is ''[[SciFiWritersHaveNoSenseOfScale very low]]''. [[NakedPeopleAreFunny And naked people]]. (That last one to show what humans actually look like. ItMakesSenseInContext -- otherwise the aliens might assume that the probe itself is the intelligent life![[/note]]

* In ''Series/DoctorWho'', this problem is usually absent due to the presence of the TARDIS's [[TranslatorMicrobes Universal Translator]], however it arises in the episode "[[Recap/DoctorWhoS34E9Flatline Flatline]]" when the Doctor encounters 2-dimensional entities who have been abducting and killing people. Hoping that the creatures are a NonMaliciousMonster 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 [[EvilGloating the number of the one they're about to]].

* Parodied in ''Website/TheOnion'': [[http://www.theonion.com/content/node/30246 Earth Contacted By Extraterrestrial Nerds]].

* Queen Watevra Wan'abi in ''WesternAnimation/TheLegoMovie2TheSecondPart'' tells the gang she's going to talk to them in the universal language. Princess Uni-Kitty guesses it's math but it turns out to be song to Lucy's horror.

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 process[[note]]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[[/note]] (i.e., no mathematical equation is known that will ''exhaustively'' produce them in reasonable time[[note]]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.[[/note]]), 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 ([[AlternativeNumberSystem odds are that they don't]]), while the prime numbers will not change if you represent them properly.