I want to thanks Jeff Herman for his discussion on ET's existence in the supernatural forum for sparking this.

If alien life forms do exist, how would we communicate with them if they are light years from us? How would we communicate if they came to earth? Is mathematics truly a universal system of communication? 

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The larger question is, why would we communicate with each other? I don't think I'd have anything to say. I'd be polite by asking nothing. I'd show them my kitchen in case they're hungry or thirsty, and perhaps show them some articles on the computer about how toxic human bodies are, in case they get any unfortunate ideas. 

Why? Human curiosity. If no other reason but the constant quest we have as a species to know. 

Maybe I'm underestimating myself, but I think the first thing I'd want to know is where to run. 

If ETs were even close to humanoid then I am sure we would find a way. Maths will certainly be universal across the Universe

First, while math would be universal, the symbology that we use to express it would not. As such, any communication involving mathematics would have to be independent of such things as a plus or minus sign.

The other matter is this. For an alien civilization several light years removed, if they are primitive enough to still use radio then they would probably not bother to communicate that way as the lag time would be incredible impractical. On the other hand, if they are advanced enough to know such things as how to break the light barrier, then they would not be using radio or any light-based communication, but something which we do not yet have the science to receive and interpret.
The best hope would be to assume that such advanced cultures would just have journeyed here in person to observe our primitive and immature little civilization. Communication then amounts to sending up a red flag of some sorts asking them to come on over for a BBQ or something.

Here's a wild theory: They simply don't communicate with others, for the simple reason that they are suspended in a nano second of Earth time but an infinity in their time. They are programmed to do everything that they do, and communication outside their reality has no purpose. Can we communicate with ants? Interference doesn't count as communication.

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