http://yudkowsky.net/sing/shocklevels.html
Oh, thanks for posting that, Dave. That paper was actually the thing that solidified the name in my mind while I was working on the game. I'm gonna sticky this thread so others can see it.
Heh. And here I just thought it was coincidence. *chuckle*
That was interesting. Actually I have read something with SL5, called Sister Alice. The society in the book didn't utilize the Singularity, but in many ways it was because they had advanced so far in technology that there was literally no way for them to raise up without transcending reality (which is actually part of the story). In it humanity is the most powerful species in the universe, ruled by a class of 1,000,000 aristocrats (maybe less, but I know 1,000 houses) that utilize a technology made out of dark-matter (and he gets dark-matter much more correct than most sci-fi) that literally modifies their transcendental consciousnesses, rendering them as individuals the size of suns, though their physical bodies are still human. They can compute at a faster speed than any computers, so most computers are obsolete, they can exist as energy and travel as near-light speeds, and can forms whole suns, planets, and ecosystems with their minds from the dust of supernovas, sometimes as quickly as a few hundred years. (Don't worry, I'm not giving away anything that you don't learn pretty quickly in the book's beginning.)
Hrm, now that I look at the article again, I guess Sister Alice is just SL4, though really really high up in SL4. I guess he's right. Anything above SL4 would require the transcendence of 3D space/time, so we would never be able to truly comprehend what it would be. *sigh*