My trouble is that they may have a totally different theory & understanding of numbers, language, symbols, names, etc.
For instance, what if they don't have the concept of symbolic representation of objects/concepts in visual/auditory ways? That seems incredibly fundamental from an anthropocentric perspective, but their neurology would be totally different - maybe they evolved a different way to store concepts.
Or say they do, but we get to math - and their understanding of math is similar to ours and they represent it symbolically, but beyond that their perception of time, self vs other distinction (theory of names type stuff), senses are so radically different that we can't ever reach enough common ground to communicate.
Maybe they communicate with like, pulses of IR light that we can detect & reproduce, and they represent numbers basically like morse code and they have words for standard mathematical and logical operators. And maybe they have hearing and can see the visible light spectrum - just to make things easy.
But
- their neurology is such that they can't comprehend the link between sounds and meaning
- same with visible light. It'd be like us seeing magnetic fields and making the leap to thinking planets were talking to us.
- they don't have an understanding of names. Individuality for them is not a concept they understand - there are individuals, but they are not referred to. Maybe they speak in generalities & objectives. Not "you, go farm the field" but "satiate hunger" - perhaps who does and where/how this is done is not particularly important or it is marked with pheromones or context or something.
- they do not have phonetic components of speech.
So, how do we communicate?
We can broadcast numbers at them maybe. We place 2 apples in front of them and broadcast "two" on repeat in distinct, discrete sequence: Two. Two. Two.(..--- ..--- ..---) Maybe we start throwing the word for apple in there in morse code. ( ..--- . - .--. .--. .-.. .)
To get the message, they'd need to understand that:
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sequences of IR pulses generated by things other than them can have meaning. Granted, seems simple enough.
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the length and cadence of the pulses matter. We could presumably figure that out by observation & tailor our communication to them, granted.
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intention is to name the two objects in front of them. Hmmmm that is suddenly a bit harder since they don't typically view names the same as we do. But maybe.
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phonemes can be represented with IR flashes. Oops, they don't have a concept of those... they'd have to make a massive leap to understand that. But maybe they'd view the word as an ideogram.
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the 2 we were broadcasting referred to the quantity of the apples and not some other feature. Not a given at all, they could take it to mean any number of things, in theory.
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the specific type of thing that an apple is can have a name. Not a given.
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that we are referring to the apples and not to something else. Maybe the act of presenting objects, the act of flashing IR light, the concept of presence vs non-presence, etc.
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that we were labelling the thing as apple and not instead talking about what you use it for, where it comes from, how old it is, it's scent, who knows - could be anything.
It is not a given that they get past apple. The likelihood, I think, goes up when you contrast it with something else, but what if they don't understand comparison and contrast similarly to us?
Okay. Say they understand apple. We go through thousands of things to build up their vocabulary of objects. Maybe we show them someone eating an apple next and they know the word for human and the word for apple.
They have to understand what verbs are, have some concept of grammar, the relation of things in the sentence, the conveyance of cause/effect - the specific human is causing the action of the apple being eaten.
"Human eat apple" could really mean anything in this context. Perhaps they don't know that words like these presented in a different context have the same meaning. Or they don't understand eating in this case - like it is an unimportant concept, the concept they understand is what is achieved by eating.
Anyway. It all gets very abstract. But, what I'm trying to say is: thinking we can communicate with creatures that evolved in a totally different context assumes their neurology is strikingly similar to ours in ways I think are honestly far-fetched. Some of the above could be solved, with difficulty, given enough time and motivation, but it takes a lot more assumptions than I think people typically realize regarding how anthropic the aliens would be. And the challenges go beyond mere logistics & extend to fundamental linguistic/psychological/philosophical/neurological barriers.
That's just what has happened on Earth, though. Also I didn't specify they'd be coming to us - if they landed here in something we'd recognize as a rocket, then I'd suspect we'd have a lot more in common with them.
But what if they evolved in gas clouds? Or hell what if they perceive higher dimensions? What if it's a 4D being, capable of instantaneous long distance travel through spacetime - they don't need math for that. Or even language. Those are far-out scenarios, but I'm just saying that it takes a very earth-centric, anthropocentric view of intelligent life to assume the sorts of things that'd make communication possible.