The biggest problem with that movie was its lame ending. It would have been much more satisfying if she'd told the skeptics at the end, "It doesn't matter what you believe. _They_ know that we're here. It's their move now."
_________________________
Paula said,
> It is far from elementary to even send a signal containing numbers.
And yet, we humans send signals containing numbers and much more. Somebody told me a long time ago that Mossad had once stolen the complete blueprints for a French fighter jet, and it was considered to be an amazing feat because it supposedly took five trucks to carry it all. I have no idea whether that story is true, but with today's technology, I can carry that much information in my pocket, and I could transmit it half way around the world in less than an hour.
> The aliens may or may not use a 10 base number system. We do, and we can't
> imagine another system.
Paula, You just imagined one. You could not have written that sentence without imagining one.
> At some point it would be necessary to learn the entire alien language. That's gonna
> be a nightmare without a tutor.
Hard, yes. Impossible, no. And that's the whole point of the story. The message was an intelligence test. The aliens broadcast their message out to the galaxy, and they hope to get a reply, but they don't want to talk to just anybody; They want to talk to somebody who has the intelligence, and the technological capability to decode the message and, to build the machine.
___________________
@L.E. Gant,
I'm pretty sure Dr. Sagan wanted to transmit sequences of prime numbers. He thought it would be much less likely that the recipients of the message would think there could be any natural phenomenon that could transmit the primes.