How did humans learn that faster than light, instant communication was possible?

During the three-month flight to Eros, Graff and Ender talk about everything from Command School to Earth, to astronomy, physics, and most importantly the buggers, although Graff does not know much about them. They speak mind to mind, instantaneously. This ability taught the humans that it was possible, and they thus built a machine called an ansible which, according to Graff, means that "ships could talk to each other even when they're across the galaxy."