The eschaton is the end of the world as we know it. while the word itself is very old [according to the OED, eschatology is the the department of theological science concerned with the four last things: death, judgement, heaven, and hell] it has acquired a recent connotation: the end of the world brought on by increasing technology, communication, and connectedness: a singularity or omega point.

Terence McKenna has this to say (original here)

he uses Alfred North Whitehead's definition of novelty (original here):

Did you understand that? I'm still thinking about it. It sounds like he's talking about emergence more than anything else. Maybe I should read the book...

Though I think McKenna is crazy in many ways I think the basic idea of increasingly increasing novelty/life/complexity is correct. The fundamental question: what is the topology of the curve? Some predict it becomes infinite in finite time (in 2012 in McKenna's case), this is a singularity. But this injection of the infinite is a religious assertion, just like Tipler's Omega point.

Feigenbaum and Jumping Jesus.

I see no reason for this. To me, the curve appears exponential. This has the important property of scale-neutrality: no matter where you are on the curve (ie no matter what age you live in) it looks the same. Everyone always thinks they live on the verge of great change, because relative to their past, they are! Until we approach the physical limits of computation and energy (if there are any) I see no reason for this to change.

Hans Moravec has some cogent words about the future, see Pigs in Cyberspace and these excerpts from The Age of Mind: Transcending the Human Condition through Robots: one and two.