There one theory not yet covered in our discussion. It possible to imaging sleep as a garbage collection process. After N hours of being awake the body needs N/2 hours of sleep to get sort through all the information stored while being awake. It's also possible that it needs (N^2)/32 hours of sleep to sort through all the information.
Based on my experience the couple times I stayed awake for more than 24 hours in a row, I think it's very unlikely to be quadratic, at least for large N.
BTW, does anybody know of anyone who's tried http://xkcd.com/320/ for more than a few weeks in a row?
does anybody know of anyone who's tried http://xkcd.com/320/ for more than a few weeks in a row?

:-D
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