One of the most interesting things to think about in this regards is the past and the crazy things they thought, and why they probably didn't seem especially crazy at the time. In the earlier ages of exploration of our world people have been able to discover ever more amazing things from springs mysteriously heated even in the coldest of times and places, to a tree producing bark that chewing on can make ones pain completely disappear (more contemporarily known as willow/aspirin), and endless other ever more miraculous discoveries.

Why would it thus be so difficult to imagine there being some spring or treatment that could effectively end illness or even aging? A fountain of youth just awaiting its discovery. It was little more than a normal continuation outward from a process of exponential progress. But of course the exponential progress came to an unexpected end, and consequently the predictions made now look simply naive or superstitious.

We're now currently in our own period of exponential discovery and the fabulous tales of achievements to come are anything but scarce. Of course, this time it'll be different.