I don't think 20,000 is a reasonable bound; here in the tropics (Puerto Rico in my case) it doesn't get cold at night; you'd have a lot of starvation and the society would be feudal pretty quick, but I'll bet you'd end up with more than 20,000 people on this island alone. Now multiply by the rest of the tropics.

But the likelihood of our returning to a technological civilization after that? No. I'm betting we never would, for two reasons.

First: all the data's gone. It's just skills in people's heads, and most of the people with skills will be dead in a few months. And the ones that don't die right off the bat will be too busy not starving, and making sure their kids don't starve, to write anything down, on non-existent paper with non-existent pencils, until they themselves die of old age at 55. No medicine. No antibiotics. Plenty of privation and overwork, though. (And even if some overachiever does write stuff down -- how long does that survive? And how does it get distributed beyond his own little village of 100 people? Answer: it doesn't. And all the resources he knows how to use are no longer available from Edmund Scientific.)

OK? So there's no skills, really fast. But there are legends of the fast-burning city civilization that let us all down. Humanity will never try it again; I just don't believe it. We're barely trying it now -- how many people really still believe in technological progress these days? I mean, in terms not of making a buck, but of inevitable progress towards a better life? Damned few. And that's before it all goes away and 99% of the people in the world die as a result.

It's a bleak question.