To respond to deep thought's writeup, it should be noted that a lot of the technical details were dumbed down severely in order to adapt Carl Sagan's book to the big screen.  I remember when I saw the scene where they discover the primer in the movie theater, and I had to restrain myself from shouting at the screen, "Oh come ON!  Putting the pages together three-dimensionally would've been one of the first things any scientist worth his salt would have tried!"

I just read the book for the first time last night, and was extremely gratified to find out that, in the book version, spatially organizing the pages in 3D was one of the first things the scientists tried.  The primer in this version was hidden through phase modulation, something the scientists might at least plausibly have not been looking for.

But yes, the scene in the movie was much more dramatic.  :P

The movie was great--I think it really should have won Best Picture in '97--but as with so many other things, the book is even better.