That is...THE SINGULARITY (spoken in a loud, booming voice coming from a cloud near you.).
Now, I've written on this topic. One of my novel ideas, Strategic Withdrawal, has a Singularity in it. And I've designed Starsong Systems for the 4th Book of Worlds, which has superhuman intelligences in it.
And I'm working on Tech Surge: Apocalypse or Ascension which is about a Singularity occurring.
Let me add, I loved reading Vinge.
But there is a distinct element of religiosity in supposedly skeptical materialists in this stuff. Ken McCleod is supposed to have come up with the term The Rapture of the Geeks. A lot of its supporters are older middle aged, white, male, technogeeks who really don't want to end the fun by dying, and finding out for sure if there skepticism about God was well grounded.
Understandable, really. I'd be happy to live to be two or three hundred years old in good health. There is a lot of neat things I'd like to do. You could study dozens of topics, meet people (including my own great-great grand kids), and so on. Life is fun.
Because God made it that way.
Now I'm not so sure I'd like to be a superhuman intelligence a trillion times smarter than I am. I'm real sure, I don't want to be reporting to one, except for God.
But eventually, even a superhuman brain will die. Even if it requires a supernova.
Eventually. So maybe spend some of that time you speculate with for getting ready for that Last Door, hmmh?