Which Came First: The Science Or The Fiction?

I was flipping through a Popular Science this weekend and it occurred to me that many of technology's latest innovations have existed in fiction for years if not centuries. I also remember stuff science has done that might inspire a what-if for a speculative author.

So which came first, the science or the fiction?

Jules Verne brought us deep sea and under-the-earth adventures. Now we're designing communities of floating cities and underwater hotels and discovering caves of giant crystals in Mexico.

Star Trek communicators undeniably inspired the need for and look of modern cell phones.

Ray Bradbury took us to Mars long before NASA did.

But at the same time, Einstein's theories make stories/movies like Paycheck plausible.

PopSci had an article about a plane-mounted chemical laser capable of destroying a target 3 feet square. Star Wars is just one of several movies that come to mind with such weapons.

So which is it? Is this another chicken-egg argument? Or does fiction tend to inspire scientists and inventors to think beyond themselves and stretch the limits of possibility? Is it the other way around?