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Generic alien race A has developed advanced spacecraft technology, and through tedious exploration, has found Earth. Astronauts orbiting our planet see the craft as well, and notify our human governments. The most important thing to do here is to first see whether the alien species is hostile or not. However, to communicate, we need some sort of common language. (This happens on present day Earth).

Here are a few givens:

  • The alien species has an extremely advanced understanding of complex mathematics, ranging from basic algebra to differential equations. As such, they are aware of the existence of pi and the Fibonacci sequence.

  • The aliens are humanoid, and do have a spoken language primarily composed of spaces between guttural, throaty noises that they make.

  • The aliens have not invented (or discovered) the concept of something like Morse code, so using that to communicate wouldn't be possible.

Since human linguists and scientists wouldn't be able to figure out the basics of the alien language for a while, and alien scientists couldn't decipher the mysteries of human languages, how could the two different species communicate? I'd prefer if the answer used some sort of mathematical sequence or something similar to that.

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    $\begingroup$ It's a cookbook. $\endgroup$ – userLTK Mar 23 '16 at 2:06
  • $\begingroup$ @userLTK Uhh what? $\endgroup$ – fi12 Mar 23 '16 at 2:07
  • $\begingroup$ @fi12 The context for that is: "The Twilight Zone". Look up the Kanamits. Using math as a basis for communication is very well established. When we sent the Voyager probes out of the solar system, they contained plates which attempted to express who we are using math. In Sagan's book and movie "Contact", the signals that the aliens sent to us were mathematically encoded into our own reflected TV transmissions. They ended up decoding into very complex blueprints. $\endgroup$ – Omniwombat Mar 23 '16 at 2:18
  • $\begingroup$ Why was the craft seen by astronauts and not by others? $\endgroup$ – JDługosz Mar 23 '16 at 3:10
  • $\begingroup$ @userLTK Why didn't they wait? Those poor people. Anyway, what I really wanted to say was that their language pretty much is morse code, it's based on the spaces between the noise. $\endgroup$ – Xandar The Zenon Mar 23 '16 at 20:03
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Communication Basics

By this, I mean the primary sensory channel of communication. For example, we humans communicate through two channels: sound (speaking) and sight (reading). Before deciding how to form a common language, we must decide which sensory channels are available to aliens for communication.

By our knowledge and experience so far, there are four possible channels for this purpose: sight, sound, smell (through pheromones as a lot of animals do) and esp (aka telepathy). We would need to determine which of these channels do the aliens utilize and if hybrid communication systems are possible for faster information exchange.

The Easiest Channel

If the aliens can use multiple channels for communication like us, the easiest channel for us to use would be sight. We can use paper signs for this, hand gestures and computer screens to utilize this channel. This would require the least coding and decoding effort required. It may or may not be the fastest channel, considering that electromagnetic waves can carry a huge amount of information, but almost everyone on Earth prefers using sound for communication instead of sight.

The next easiest channel would be sound. This would probably require some sensitive sound recording and transmitting equipment. Plus it would require more technical coding and decoding which would limit the number of scientists who can work on this type of data (it is easier for most of us, humans, to code and decode visual signs than audio communication which involves infra and ultra sonic ranges).

Smell would be a quite complex channel as we aren't so good with quickly releasing and then absorbing chemical compounds. This would be slow, tedious and complex.

ESP (telepathy) would probably be the hardest of all, considering how many esp hoaxes and wannabes are busted regularly in science documentaries and researches.

After Channel Decision

Once the channel has been decided and it has been known what frequency ranges the aliens operate at, the next step would be the communication of some primary realities which would function as breaking the ice and informing each other of the extent of knowledge we have.

Here again, it would be much easier to use sight channel than sound. For example, we would start with counting from 0 to 99. This would inform them about the signs we use for our number system. Place one bead on the table and write 1. Place two beads next to it and write 2 and so on.

Once the number system has been established, we would show them number tables (sequences). As in:
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8

and so on. At this point, we would leave some blanks in our tables and expect the aliens to fill them. If they do it successfully, it would mean that they have successfully understood our number system and we can progress.

We would not continue towards complex mathematical equations, factorials, differentials, integrals and that sort of thing.

Non Mathematical Communication

This would involve teaching them abc from the very start and then progressing with images. If we succeed in teaching them our written language form, we can communication to them as we communicate with each other in text. If not, we would have to restrict ourselves to images and signs which would be a slower method, but still functional.

If the aliens only use audio channel, it would require us to learn their audio communication basics instead of teaching them ours. This would go by understanding what reactions do they show against which audio messages.

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  • $\begingroup$ I'm more than a little confused by the inclusion of ESP as a possible channel when the asker hasn't listed that as being a thing in their world. $\endgroup$ – Saidoro Mar 23 '16 at 16:07
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Draw pictures.

You indicate that the alien craft was discovered by astronauts in orbit. So presumably they looked out the window and saw the alien craft pull up near by. So, we can see them and interact up close.

I always figured a way to start would be with numbers: show how to write digits for different quantities, illustrate the full positional notation, then on to simple arithmetic symbols.

The fact that the aliens made contact with an isolated group of humans is a sign that they peaceful and want to communicate. Otherwise they would attack by surprise, and would not have uncloaked like that.

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With near-by contact and open communication (presumably pictures, videos & sounds) and back and forth. Clear teaching methods could be transmitted and all that's needed for communication would be for one to learn the other's language, not for each side to learn the others. I think it would happen pretty quickly.

It's a different ball game when you have reciprocity and you can work out Yes/No and build from there. (2+2=4) is yes (2+2=3) is no. A couple months max, I think, with top minds working on it. It can take years to work out ancient languages, but that's just a handful of tablets and ruins. Back and Forth with graphics and being interactive, much faster I would think, unless the languages are just light-years apart, then it might take longer, but I think a relatively short period of a couple months would likely be sufficient. I can't prove that, but that's my guess.

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This is actually an answer by way of an anti-answer. One problem that we face is that we've never encountered life (aside from micro-organisms, ostensibly) that originated from outside of our planet. Because of that, everything would make assumptions about alien lifeforms being very similar to humans. Even discounting the things that are common - like assuming that aliens would be bipedal, or would have limbs at all, or would even roughly resemble life as we know it - there are more uncommon things as well. Consider creatures that are not carbon-based or that do not utilize DNA/RNA constructs. It's difficult, but only because we know of no other form of life.

Aside from that, language and even math are human constructs. We've molded mathematics over many many centuries to allow us to explain the universe. But even universal concepts of mathematics are human constructs and are really only universal to humans (more than likely). Even sight, the way we perceive it, isn't something that would necessarily be an alien trait. We have sightless creatures here on Earth already - do we really believe that all intelligent alien life would perceive lightwaves the way that we do? Or maybe they have "sight", but sight which is attuned to a different section of the EM spectrum. Maybe they "see" pictures in the microwave spectrum.

At any rate, maybe it's bold of me to count this as an "answer", but I like to challenge these notions. I think that coming at the idea of aliens from a truly new and fresh perspective will take some serious creativity and a hard look at assumptions we make about life.

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  • $\begingroup$ Taken out of context your 'anti-answer' is very valid. That said, the ability to construct and navigate an advanced spacecraft outright demands a certain level of understanding of mathematics, physics, language, certain existing social structures, etc. Also being advanced enough to traverse interstellar distances also guarantees that not only will they be able to see, they'll be able to perceive the entire EM spectrum (albeit mostly through technological means - like our false colour pics of the sun in X-Rays, etc) $\endgroup$ – Scott Downey Mar 23 '16 at 14:58
  • $\begingroup$ I don't think that's accurate - at best it's an appeal to probability fallacy. Why would they need language, at least in any manner that we understand language? Conceptual telepathy would forego the need for language - think hive mind ideas or the like. Sure they would need something akin to mathematics and physics, but math and physics as we know them are human constructs - things that we have created to understand the universe. Really, the same is true of language. Just because we can't easily comprehend science without them doesn't mean they are inherently required for other species. $\endgroup$ – Jesse Williams Mar 23 '16 at 15:33
  • $\begingroup$ I'm not going to explain why all those things are required in the scope of a comment but if you think it through logically, (e.g. any advanced civilization needs long term data storage (which by nature must be non-telepathic) therefore some form of language however you want to express it) Regardless of what you call it, Maths and Physics are required. Yes you can have anything you like if they're wandering their homeworld with nothing more advanced than a wheel but the question specifically refers to a species capable of building a spacecraft and that has requirements. $\endgroup$ – Scott Downey Mar 23 '16 at 15:49
  • $\begingroup$ Points 2 and 3 from this article will explain better than I have in 600 characters, huffingtonpost.com/derek-abbott/… The Non-Platonist view of mathematics suits my explanation. The truth is, nobody can say for sure that it's one or the other. That's an assumption we can make, in either direction, based solely on the sum of human experience; and existential experience that is not as wise as we like to believe. $\endgroup$ – Jesse Williams Mar 23 '16 at 16:17
  • $\begingroup$ Or, alternatively, read 'Where Mathematics Comes From' by George Lakoff. $\endgroup$ – Jesse Williams Mar 23 '16 at 16:20

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