So I re-read it. And then I watched the movie again, for good measure.
It turns out Contact was always supposed to be a movie, in fact it was originally supposed to be a movie, but when none of the studios were that interested Carl Sagan just turned his script into a book. Then when the book sold well, it became a movie. So the story started to be put on paper in 1979, and was predicting events of the world in 1999. By the time they made the movie in 1997 it just had to be set in "present day" which makes it a lot less interesting. Sagan used the story to tell his version of the future, he made all kinds of predictions about nuclear disarmament, improvements in US foreign policy, even the reorganization of television networks. He failed to predict the impact of the internet or the fall of the communism, but I give him lots of credit for taking a stab at what the world would be like in 15-20 years. It takes courage.
Here's the important gist of Contact, the book:
Dr. Arroway is an agnostic. She says that if God wanted us to believe in Him, there'd be a lot more direct contact with our creator and the Bible would make a lot more sense. Or maybe there'd be clues in the Bible... not just vague predictions about the return of the messiah, but facts about how much the earth weighs or the speed of light, things that the early prophets couldn't have known but we could eventually discover.
Then she goes to meet the aliens and they tell her that the universe contains the signature of a creator. The beings who contact earth are incredibly advanced, yet they didn't make the network of wormholes that take the humans on their journey. They also didn't make the universe, or the fabric of it. They didn't make the speed of light or pi or e. But they've found elements in these dependable concepts that reflect an unmistakable proof of an intelligent creator... the example they give is patterns once you calculate pi out to the ~billionth digit. They (the aliens) are still finding messages within the numbers, and struggling to figure out what they say.
Like in the film, the aliens send the scientists back without proof of their existence and people on earth don't believe they've gone anywhere. The aliens are a sort of galactic census-taking organization, and just by having five humans out on their planet they gleen information they need about our race. They prefer to stay out of our affairs as much as possible, and because they didn't create the wormhole transit system there isn't time to answer many questions the humans have.
So in the end our agnostic Dr. Arroway is faced with the idea that not only is there a creator, but an even larger creator than she's ever imagined... one that was around billions of years before these billion-year-old aliens were. There are layers of omnipotence.
In the movie, the aliens seem to have a desire to be involved with humanity but don't send back proof because "this is how it's been done for billions of years". Dr. Arroway goes on the journey alone. She hooks up with a preacher. There's just a lot of things that don't make quite as much sense. And the religious themes never come around full circle... there's no mention of the Creator signature in the numbers. I feel like this is the biggest shortcoming in the movie. Maybe they really wanted to avoid math, or think the average american doesn't know what pi is? But it's sort of the whole point of the ending of the book. Ellie writes her story down and gives it to someone and then goes to work on finding the messages in the scientific concepts the aliens told her about, so she'll have her evidence. She'll prove that there are aliens and a God, all in one discovery... that's what we're left with. Not just a fun story but hope.
So anyway, Contact is staying safely on my "must read" list of books I will encourage the general population to look into, because it has this great idea contained in it. Science is searching for God, God is speaking to us through science because science has a way of only being revealed to us in incremental steps as we make discoveries. This is a good way to understand big things like God and the universe that are really way beyond our comprehension.
Important related point 2 is that God, science, aliens, the universe, our friends, all have one thing in common: they favor us when we love each other.
Important related point 3: the most important contacts we make aren't the ones with the aliens in other galaxies, because even they are searching for something bigger. Contacting your neighbors and friends is just as important, because it's also a struggle for us to reach out, and those neighbors are on the same "level" as the aliens. We all didn't create the universe, if that makes sense.
But that's just my summary, to really get the point you should read the book.