It did get me thinking though... what kind of message would you send? For this thought experiment, suppose we follow the suggestions and sweep out portions of the sky on the regular basic at common frequencies likely to be noticed. Add a "Contact"-like header of bursts of signals representing the prime numbers to get attention, and then follow with the message.
What would its form be? A binary encoding? What would the message be? Intention? Form? What clues could you include to help with the decoding?
I think that makes little sense. How could aliens think that we have the same gestures? Or that we had knowledge of theirs? It is our gesture, that's the point. We are just saying "This is what we do. It's our greeting gesture."
>The scientists say that another problem is in our assumption that aliens can properly perceive pictures or sounds with their own unique sensory organs.
I'm sure they'll figure it out. That's the point. If we got a message from an intelligent extra-solar species, we'd put tremendous energy and time into examining it. We'd probably find more in it than that is there.
As for what I'd put: I think the Voyager and Pioneer missions did well. They started with basic shared information, the excitation of electrons in hydrogen, and build up from there. I think the pulsar position map is a good idea too.
http://en.wikipedia.org/wiki/Voyager_Golden_Record http://en.wikipedia.org/wiki/Pioneer_plaque
I don't think the intent of the message is important. We are just giving them a primer, so the more information they have, the more context they have to build a picture from. Let's given them enough to have fun. I'd send Wikipedia if I could. -In multiple languages. They would decode it in no time, with no help from us. We could do the same, and chances are, they are far more advanced.
For a EM signal that we sent out, I'd send a repeating signal, that was a sequence of primes. Maybe have the primes alternate at two nearby frequencies, creating a binary signal that coded the message.