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While we have notable variation in grammar certain patterns can be found in almost all human languages. For example verbs, nouns and adjectives can be found in some form. They are strung together into sentences and paragraphs.

The most famous "alien grammar" is probably Yoda. Speak differently, he does. However even in his case it's a fairly simple switch around and it wouldn't surprise me if many earth languages could be found that follow that pattern.

So my question is - is there such a thing as a truly alien grammar? Is it even possible to come up with a language structure completely different to that used by humans? Ideally something that reflects the alien nature of the speakers in some way.

Note that I've added a follow on question about transmission: How alien can a language be - transmission?

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    $\begingroup$ "For example verbs, nouns and adjectives can be found in some form" - counterexample: modern Mandarin, where the boundary between verbs and adjectives is fuzzy indeed. Re Yoda - he seems to speak strange because he English with different word order speaks. But for German with its clause-final verb and verbal bracket, Yoda speech is quite natural. $\endgroup$ Commented Nov 24, 2015 at 18:28
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    $\begingroup$ Have a look at the differences in procedural and object oriented programming. $\endgroup$ Commented Nov 24, 2015 at 21:55
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    $\begingroup$ @FraserOfSmeg That's almost the same... for a real difference, try declarative languages (e.g prolog) $\endgroup$ Commented Nov 24, 2015 at 22:24
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    $\begingroup$ Darmok and Jalad at Tanagra. $\endgroup$
    – Ajedi32
    Commented Nov 25, 2015 at 14:39
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    $\begingroup$ @Ajedi32 Came here to supply the same comment. You beat me to it :-) $\endgroup$
    – Tonny
    Commented Nov 25, 2015 at 16:09

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One example would be aliens that communicate in a parallel fashion. Take an alien that has multiple mouths, and talks with all of them simultaneously (using pitch or some other factor to differentiate). Or possibly it just has a more complex vocal apparatus.

They might therefore simultaneously communicate nouns, verbs, and adjectives all at once, grouping them appropriately or in some kind of contextually important rule.

So while we say: "The quick brown fox jumps over the lazy dog."

The alien might say:

quick ----> jumps ---> lazy

brown ---> over ----> dog

fox

This isn't an extraordinarily alien language - it would be comprehensible by humans, or at least by humans with basic computer assistance - but we are literally incapable of handling the grammar, so I'd say that makes it fit the question.

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    $\begingroup$ I gather that the various sign languages used by the deaf do make use of parallel channels, e.g. facial expression plus hand position. $\endgroup$ Commented Nov 24, 2015 at 21:32
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    $\begingroup$ @DanSmolinske What qualifies as a "word" is a fuzzy concept, so it's hard to answer that precisely, but using multiple channels to represent different things simultaneously is very common in signed languages. For example, in some sign languages "turn the car left at the gas station" will typically be done by signing "gas station", then placing the left hand in front of you with a building classifier hand shape, then giving the right hand a vehicle classifier hand shape, then turning the right hand left at the left hand. $\endgroup$ Commented Nov 25, 2015 at 2:07
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    $\begingroup$ But even spoken languages use multiple channels to communicate (e.g. with prosody or intonation) what other languages will express with separate words. For example, to disambiguate between a statement and a yes-no question, some languages will use intonation ("You wanna go to the store./You wanna go to the store?") while others will use a question particle ("你想去商店。你想去商店吗?"). The same is true for signed languages, where some languages will use facial cues (e.g. raised eyebrows in ASL) to mark a yes-no question, while others use an extra sign or modify the syntax. $\endgroup$ Commented Nov 25, 2015 at 2:27
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    $\begingroup$ @FedericoPoloni: There are several human languages where word order, or sequence, is free-form (like the spoken alien language in that story). Latin being one of the most studied. Also to a limited extent Hungarian, Turkish and Finnish. No need to delve into fiction for what seem to English speakers as non-sequential grammar. $\endgroup$
    – slebetman
    Commented Nov 25, 2015 at 9:34
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    $\begingroup$ This reminds me of Puppeteer language from Niven's Known Space universe (the most famous series out of which is probably Ringworld). Puppeteers have two mouths and each mouth can reproduce exactly the sound of a piano or violin as well as human speech (in any voice) as well as animal sounds. Puppeteer speech is said to sound like an orchestra playing out of tune combined with the sound of a crashing car. $\endgroup$
    – slebetman
    Commented Nov 25, 2015 at 9:40
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The answer is, we do not know.

There are indeed some universal grammar features, Chomsky hypothesised that those are inborn to human brains. Even if that is true, alien brains can differ.

On the other hand, we have no idea of knowing if there could be a human language that differs markedly in some aspects from every known language, or indeed if there has been one. If the history went differently and the subsaharan languages died out, would we ever think that clicks can be incorporated into a language as normal phonemes? Without east Asian languages, would we consider normal to have a language without obligatory grammatical number or gender? Without Vietnamese, would it seem possible that language can function without personal pronouns? Without ergative languages, would it ever occur to us that the subject might not be in the nominative? Limiting the focus to Europe, without Polish and Russian, would we realize that the colour "blue" can be analyzed as two different colours? Likewise, with Hungarian, the same goes for "red". Without English, would we consider normal that every noun can be verbed? Whatever you consider normal in your language, some other language on the Earth breaks it.

For really alien concepts: consider sign languages. Not the medium of expression, but the grammar. It is still highly linear, but there are some parallelisms. And some sign languages can create pronouns "on the fly" (in other words, they have infinite number of them). Yet, these are normal, widely used human languages.

For constructed languages created by humans, but deliberately breaking some of those language universals (and thus being extremely hard to learn), see loglan/lojban for languages based on predicates, or the stack based language Fith.

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  • $\begingroup$ I'm sorry, are you saying that Hungarian doesn't have a separate word for pink, or that Hungarian does have one for dark red as opposed to red? $\endgroup$
    – No Name
    Commented May 18, 2023 at 4:59
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    $\begingroup$ @NoName "pink" does exist as a separate (although compound) word. The difference between piros and vörös may be a bit about the exact hue, but it is more about literal vs. figurative use or emotional attitudes $\endgroup$ Commented May 18, 2023 at 14:23
  • $\begingroup$ Ah, okay. So it's the difference between "being red" and "seeing red" in English (as an imperfect analogy) $\endgroup$
    – No Name
    Commented May 18, 2023 at 17:14
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I think the answer is actually "clearly, yes, you can have a truly alien grammar".

The reason I think this is that to be truly alien the language must have none of the elements we think of. These are (simplistically) nouns, verbs, adjective and adverbs.

So - candidate alien grammar: every word means a sentence.

foo: how are you today
bar: I'm well, how are you
frob: not so well
frobs: not so well, how are you
eckythump: I'm well
ni!: I hate Mondays

etc.

This grammar is alien. It has only words, and each word is a sentence.

It's so alien it's hard to see how it would "work", but it might. And since I could think of this one in a few minutes, there are likely other grammars that don't have the elements that we have, but are more convincing in their complexity and workability.

Another such grammar is the foundation-language-phrase-grammar of the language of the aliens in the Star Trek episode where Picard is forced to fight their leader in single combat on the planet while the ships are helpless above.

This is a language that is built on another langauge using metaphor. So for example. "Grr-un-gecky" was translated by the universal translator as "With sails unfurled". But that's just the translation of the underlying foundation language - it's like saying what the letters of our language are.

What the person was actually communicating in their language was "let's go". Instead of using words as the building blocks of their language, these aliens have come to use phrases of a different language. Another example was something like "Damok and Jalad at Tanagra". This was a reference to a myth, but it was a sentence that meant something like "We need to negotiate".

That's an alien grammar.

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    $\begingroup$ Google has the same problem with Mandarin. "Fruit tired" came up the other day, summarizing that the band had a variety of performances. $\endgroup$
    – JDługosz
    Commented Nov 25, 2015 at 8:33
  • $\begingroup$ You just invented functional programming :) $\endgroup$
    – slebetman
    Commented Nov 25, 2015 at 9:37
  • $\begingroup$ Sorry, but the Star Trek episode was just writers not able to come up with truly alien languages. Everything about our language is metaphor. You can't teach a child what "red" is. "Red" just means "like an apple and a sunset and Ferrari". The difference is just that we've condensed all these metaphors into thousands of short sounds and the people in Star Trek combine longer sounds and gestures. And, of course, speaking in more deliberate metaphors isn't exactly an alien concept. $\endgroup$
    – MichaelS
    Commented Nov 26, 2015 at 5:53
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    $\begingroup$ My answer had two distinct examples. The first one is the "I hate Mondays" one. I agree it's hard to see how it evolves, but I was envisaging grog going "Hnghr" every time he goes out hunting tigers, and "Hrak" every time he goes hunting squirrels, so those words come to have those complete meanings, and it never occurs to them to break things down. $\endgroup$ Commented Nov 30, 2015 at 0:38
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    $\begingroup$ BTW, here is an interesting analysis of the Tamarian language. $\endgroup$
    – celtschk
    Commented Dec 12, 2015 at 19:25
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Syntactic components of spoken languages (which most of the times are not context-free but context-aware) are defined by human interaction. There are a lot of problems:

  1. Semantic elements like pronouns are defined in a per-language basis. We could say that in English we have a pronoun "nosotros" which can be translated as "we" in english. It is the same in each aspect. However in Quichua they have a distinction between "we (but not you; I'm describing a situation involving my people)" translated to noqayku (exclusive-we), and "we (you and me, or you and exclusive-we)" translated to noqanchis or noqanchik (it depends on the region), but people talking mapudzungu (lit. language of the Earth from Mapuche tribe in Argentina/Chile) has a strange form of dual we (you and me, just 2 people).
  2. Entire words or particles? It is also a matter of language! In English you can say "my dog" where "my" is a possessive for 1st-singular and "dog" is the man's best friend. In quichua you say just a word: allkuy (or allqoy or ashqoy in other regions) where allku is dog, and an aggregate ·y particle is the possessive (not a separate word).
  3. Communicating with words or world-alike sounds is just too mammalic. Perhaps you can even imagine a world without words (ej. bees, ants). Perhaps lights, lower-frequency waves, farts. Spoken languages are spoken sequentially and depending on the sequence they will also define the involved culture (Quichua and German speaking people will not tend to interrupt a lot as people from Argentina does, because the verb comes at the end!). Sequence becomes important in spoken languages, but not necessarily in other type of communications (e.g. if I insult you saying Gordo Puto I'm remarking the 2nd insult which could be translated as "gay", whereas if I'm insulting you as "Puto Gordo", I'm assuming you're gay but remarking the "fat" part: even when they are two distinct elements in the same syntactical category, the order matters). If you are bound to use a word-system (i.e. language) and need words with different structure you will need a different conception about surrounding phenomena (alikes, objects, stuff moving, attributes, time, senses), and you will have to even redesign (shallowly) the most important matters about their brain and interaction. Before you define the language, ensure you define the brain somehow. If you conceive aliens from a human perspective, you will get human-like aliens.
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  • $\begingroup$ JFTR re 3.: In German, the finite verb always is in second position (i.e. SVO or OVS, not SOV or OSV), but if (and only if) that one is an auxiliary verb another infinitive verb will follow at the end of the clause. $\endgroup$
    – Crissov
    Commented Nov 25, 2015 at 20:53
  • $\begingroup$ +1 for reference to context-free and context-aware languages. $\endgroup$
    – Green
    Commented Nov 30, 2015 at 15:28
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Their communication could be more rudimentary: They say they are sad, angry, happy, etc... But with no information why. That's quite different than our communication, where we would often give the information (why) but not the emotion. The aliens could, for example, say what they see in a way that transmits their emotion, but to understand what they mean - is a matter of context and logical deduction.

Or, they could be more developed than us: they read the situation much better, know all the data, so their communication is not understandable to us because it is a few steps ahead. Like, when you ask someone if they have a watch, and they tell you the time. Now, take this further! You ask an alien if they come for peace, they see our horrible political system and understand peace is not an option with us barbarians so they want to say no, then they see this will mean you open fire on them so they say they come in peace and eradicate us nonetheless.

Or a hive mind: Each part only knows and communicates a little bit. So, if you talk to one element, you intercept something like: "left eye move left" and that's totally not understandable to you. You need to speak with a certain % of the hive mind to understand what they mean. "left eye move left" "right eye move left" "mouth make consonants" "throat make vowels" - the verbs/nouns here are not part of speech, they are an instruction set

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  • $\begingroup$ Expanding on your third paragraph, I think the one way you could have a truly alien grammar is with minds that have very different capacities to ours. Things like communication by different means don't necessarily demand a very different grammar, e.g. speech and writing in the same language are different means but the same grammar. $\endgroup$ Commented Nov 24, 2015 at 18:34
  • $\begingroup$ The problem is that to understand their communication you will have to find equivalents to your communication method and that would involve grammar. So, they won't be using grammar but you'd be experiencing grammar as a layer of interpretation because that is what you know. $\endgroup$
    – DraxDomax
    Commented Nov 24, 2015 at 18:49
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Kind of. Natural languages and most practical computer languages tend to fall between context free and context sensitive languages. Thus an alien language that would have fully context sensitive grammar (no structures not expressible as context free) would be almost certainly too complex for humans to use and entirely different from any human language. Truly alien. But still probably comprehensible for most practical sentences.

Additionally a language could be recursive, the next step up in the hierarchy, and still be usable by aliens. To humans such language would be incomprehensible.

So it is possible. It is however extremely unlikely. Computer languages manage to be Turing-complete with mostly context-free grammars and mostly context-free grammars are much simpler to parse and thus languages based on them with few extensions would be more efficient in practice and preferred by the evolution of languages. There isn't really, as far as we know anything to gain by using more complex recursive grammars for communication.

But that could of course be just a human limitation. Maybe a recursive grammar would enable compression of communication and thought or something if our brains just could support it natively. Or maybe the aliens just think that communicating in a needlessly complex language is sexy. Or maybe it helps comprehend some problems in mathematical logic that help them deal with some issues our evolution did not have to deal with.

And yes, I know this answer is not very useful in practice as it gives no real idea what such languages would be like.

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Reverse Polish Notation Linguistics

Consider that every word is either a noun, a verb or a modifier on another word. Grammatically would then become possible to create a completely unambiguous (but very irritating) language based on reverse polish notation.

Consider:

The dog (definite article) (noun)

Here, the modifies the noun dog to inform us that dog is a In RPNL:

Dog the

We can extend this further:

The brown dog -> Dog brown the

In The quick brown fox jumps over the lazy dog, jumps over is a single verb related to two other objects, so this become:

(The quick brown fox) (jumps over) (the lazy dog) -> (Fox brown quick the) (dog lazy the) (jumps over)

Here, we can precisely parse this, as the verb jumps over works on two nouns, or noun structures.

Why is this irritating and how would it cause conflict... well, consider a person who interupts mid-sentence after 5 words:

A: How did this mess happen? B: The quick brown fox jumped... A: Get to the point man!

Versus:

A: How did this mess happen? Alien: (Fox brown quick the) (dog... A: Get to the point man!

Whenever an alien talks, it needs to finish a sentence in its entirety, otherwise you only get fragments of thought, with no relation until right at the end.

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    $\begingroup$ Only part in jest, I think you have just described formal German, in which language the main verb comes last in a sentence, after the subject and object (which may both be lengthy clauses). $\endgroup$
    – nigel222
    Commented Nov 25, 2015 at 12:33
  • $\begingroup$ @nigel222: Actually the verb comes only last in subordinate clauses; in (non-question) main clauses it comes second (note that this doesn't mean it always follows the subject for main clauses). However if there is a helper verb, it's that one that goes to second position, while the main one moves to the end even for main clauses. Maybe the alien part of that conlang is that it is far simpler than real languages. ;-) $\endgroup$
    – celtschk
    Commented Dec 12, 2015 at 22:39
  • $\begingroup$ Not alien at all. This is just SOV. $\endgroup$ Commented Nov 15, 2017 at 15:43
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Try Star Trek: "Darmok and Jalad at Tanagra".

For another alien grammar, Sheri Tepper's "The Companions" features scent as a major communication method, and how this forms messages is definitely interesting.

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  • $\begingroup$ Thanks for the correct name - I fixed my answer's ref accordingly! $\endgroup$ Commented Nov 28, 2015 at 22:49
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Languages can be as different as the experience of the alien species is.

Imagine something as alien as possible: Sentient crystal formations (a favorite of mine). They perceive the world only through vibrations and electromagnetic waves of some frequencies, using radio to communicate with each other. They recognize each other by shared resonance frequencies that are unique to each pair and change over time as the crystals grow.

What is their grammar like?

  • The crystals have no verbs as they have no concept of action. Even outside forces acting on them are only described in terms of the end results, since the how does not matter if they cannot change or prevent it.
  • The crystals address each other by the shared resonances, mixing in more frequencies if they are talking to or about more crystals. They have no subject-object distinction. Something is either present in the harmony or not.
  • The environment is described by reproducing vibrations and light/radiation frequencies.
  • Time is expressed by using older resonances after the initial hail and flow of time by a progression through the past frequencies. The future is only roughly defined by continuing a progression past the current resonances.
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    $\begingroup$ If they are not predicting the future and trying to maximize success in an environment where they hqve choices to make, why are they intelligent and what do they need to talk about? $\endgroup$
    – JDługosz
    Commented Nov 25, 2015 at 8:36
  • $\begingroup$ It's an obscure joke and Douglas Adams reference. $\endgroup$
    – Cyrus
    Commented Nov 25, 2015 at 10:02
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I think a common property of all human languages is their ambiguity. E.g. english is full of these, on very different levels including homonymes, grammar and syntax, often all munched together ("Time flies like an arrow, fruit flies like a banana").

An alien race communicating completely "logical", exact and unambigous would be very hard to understand. There are attempts to create such languages, e.g. the Loglan language family.

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"Alien nature of the speakers" contains an assumption that may be completely unwarranted: that your aliens communicate by means of sound waves. Even here on earth, we have creatures that communicate visually, and creatures that can create complex patterns on their skins and vary those patterns at high speed (using chromatophores).

So how about aliens who evolved with (an) extra eye(s) dedicated to communication, and patches of skin-like tissue on which they can form fast-moving patterns of considerable complexity? I'd hazard a guess that such communication would be far more impenetrable than a mere succession of glyphs mapping onto human words.

Or even if they use sound: an ultrasonic carrier may have sufficient bandwidth to be modulated in several of the ways used by humans for radio communications. Multiple sidebands, for example. Human speech breaks down into words, with (in European languages) a non-verbal but emotional side-channel conveyed by pitch. Imagine several channels, each conveying a stream of information of similar density to speech, with meaning conveyed via their inter-relationships rather than each as a unit. Being able to appreciate every note and harmony in a Bach fugue might get you as far as one of their babies.

back on Earth: we're still unable to talk to dolphins. Are they just not that intelligent (ie less intelligent than great apes, African Grey parrots, and domesticated dogs)? Many observations suggest otherwise. What other wild animals not only have sufficient empathy to realize that another species (humans) are in trouble in the water and need help, but also enough intelligence to know that to help them these "aliens" have to be assisted back to land, a place where dolphins cannot go and the margins of which are perilous to the rescuers. My own guess is that they do have language, and it is sufficiently alien that we can't map their language onto ours.

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One thing that I think is universal throughout human languages is that they are a sequence of words. So how if this principle doesn't hold for alien languages? While the aliens would still have syntactic units, those units would not fulfil the role that words fulfil in human languages. A single concept, like "dog" or "bite" would be distributed over several syntactic units, while each syntactic unit would express some relationship that would be encoded by things like the word order in our languages.

For example, consider the sentence "Yesterday I saw a dog biting a man." There are several relationships here:

  • A relationship between "yesterday" and "saw" that gives the time of the act of seeing.
  • A relationship between "I" and "saw" that gives the subject of the seeing.
  • A relationship between "saw" and "biting" giving the object of the seeing.
  • A relationship between "a dog" and "biting" giving the subject of the biting.
  • A relationship between "biting" and "a man" giving the object of the biting.

So in this sentence we have three types of relationships: time, subject and object. Let's say these types of relationships are associated with the following sounds:

  • "s" for the subject relationship
  • "b" for the object relationship
  • "tr" for the time relationship (I chose a more complex one because it's less basic)

Now the concepts described by our words may be related to vowel combinations which then are distributed over the syntactic components they are associated with. Say the vowel combinations are

  • "aio" for "yesterday"
  • "eua" for "I"
  • "iauau" for "to see"
  • "ouia" for "dog"
  • "eaieu" for "to bite"
  • "oiau" for "man"

Those vowel combinations are then distributed over the syntactic units of the relationships they are in. So for example the sentence above may translate into

aiotria euasua ubeai ouiasie uboiau

Of course to make that into a complete and viable language, obviously much more consideration (and probably also some tweaking of the above concepts) would be needed. But the above should be enough to give an idea what the language might look like.

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In terms of grammar, there isn't much of a variation in what you can change.

In it's simplest form, a language needs to have words that refer to things, (such as objects, people etc.), and also words to describe what that object is currently doing. Extrapolate this to all other variations of 'things to refer to' (emotions for example), and the most variation you can have is what already varies in most languages on earth.

However, alien life may communicate in many different ways. They may whistle at different pitches, shake their bodies in specific movements as a form of sign language, or have a bio-luminescent antenna that brightens and dims in order to communicate. They could even be telepathic.

In this case, what would one recognize as grammar? Being able to project a picture into another being's head of exactly what you mean would avoid the need for 'language' altogether.

Although, in order to communicate coherently, any language would need at least some form of consistent structure in order for the aliens to understand each other. So grammar would always be needed in some form or other.

If the language is translated (from shiny lights to English, for example), the grammar would need to be translated too, so I don't think there is much wiggle room to adapt an entirely new system of grammar for a current language.

However, you can always use an incorrect grammar system that is still coherent, as Yoda does. In Terry Prachett's Discworld novels, I remember in at least one that the merchants could not speak with the correct punctuation, but it was still coherently readable. So as long as the grammar is understandable, it could be changed to simply be incorrect.

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  • $\begingroup$ As I said in my comment to DraxDomax's answer, I agree that differences in mode of communication would not necessarily involve a radically different grammar. Speech, writing and sign language can all involve verbs and nouns for instance. But telepathy definitely would make a real difference. Direct mind to mind communication might remove the need to make abstract categories, which is the basis of all human language. $\endgroup$ Commented Nov 24, 2015 at 18:42
  • $\begingroup$ I think it is a mistaken premise to say that a language has to have words that refer to things and what they are doing, as separate words. In fact, if you do have words that refer to things (nouns) and what they are doing (verbs) separately, then you do not have an alien grammar. If you give me any sentence, I can give you an alien sentence that means that sentence, and does not have a word for the noun and a word for the verb. Since this is so clearly demonstrably possible, so too is the possible existence of an alien grammar. $\endgroup$ Commented Nov 25, 2015 at 3:26
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I think that the answer is around us. Just listen to the animals. Birds, mammals, reptiles, insects all speak differently and we can't understand its grammar. We even think that they don't speak. We assume they just make simple anger, threat, alarm, invitation sounds without intelligence.

Also a word can be pronounced in infinitely different ways. It means a whole language can be consist of only one word's different pronounciations.

Furthermore, there are no need of sounds to form a language. Colors, light, pressure, scent can also be ways to communicate.

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Grammar is not only order of words in sentence. I would say many things depends on aliens society and culture.

Imagine if your alien race is swarm type society with one collective mind who controls drones. That type of alien will more likely will use different grammatical person than us. Maybe wont have singular form, or maybe if each entity has own independent will, it will have another from, ie singular form to describe single entity, plural form to describe multiple entities influence by different minds/queens and hive form to describe multiple entities control by same queen.

Different alien race might develop different tenses, earthlings use from two to nine different tenses. Aliens might have similar range, or if they master time travel, they might have more.

If your alien race will have different than two genders, this might affect grammatical conjugation.

This is only small snow snow flake, on the top of iceberg, there are so many possibilities within grammatical features which we known and defined. There are some possibilities aliens might have their own, unknown to us.

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I would recommend that you read the short story "Story of your Life" by Ted Chiang that is precisely about this topic. In it, he describes a language that is so different from humans' that learning it changes your perception of time (i.e. you have to "perceive" the future and the past in order to use it).

The core of Chiang's work is on languages, you can also read the other stories in his collection, which I find excellent.

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The answer is, sadly, no.

In many ways it's like computing: once you've got the fundamental parts down, you can translate anything.

If you do want something that seems totally alien though you can have the rules of grammatical construction, suffixing, prefixing, tenses etc change mid conversation. If the rules are clear to the aliens (past participals use the oi suffix if they're even numbered words but the eo prefix if they're odd), they the effect will be baffling to anyone who doesn't have the full immersion.

Even then though the grammar can be worked out, but it might take a long, long time.

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    $\begingroup$ "In many ways it's like computing: once you've got the fundamental parts down, you can translate anything." - very definitely not true. Consider Turing complete programming languages: those are indeed "translatable", within practical limits. Now consider programming languages that are not Turing complete. A different class, not able to express all the algorithms of TC languages. Now Turing machines with halting oracle - these allow for much different algorithms, not implementable in TC languages. Then infinite Turing machines, able to reach limit ordinals. $\endgroup$ Commented Nov 24, 2015 at 18:56
  • $\begingroup$ @RadovanGarabík: I'm not sure how you could build a language that wouldn't be an analogue of 'Turing complete' (IE able to express, through some combination of linguistic features, any concept represent able by language) $\endgroup$
    – Joe Bloggs
    Commented Nov 24, 2015 at 22:03
  • $\begingroup$ Turing machines with halting oracle not only they cannot be translated: they cannot be even made! I don't think that was a good example. You can build a parser for any context-free formal language and produce the contents for its equivalent in another language (context-free defined). $\endgroup$ Commented Nov 24, 2015 at 22:55
  • $\begingroup$ You can quite easily use Yacc and export the new content as part of the semantic rule $\endgroup$ Commented Nov 24, 2015 at 22:55

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