Aparently dolphins and certain other animals are able to functionally sleep one brain hemisphere at a time. One side goes into a sleep state while the other stays active. This is usefull of course in order to stay somewhat allert at all times. The dolphin can efectivly sleep and watch for predators at the same time.

my question/comment. wouldn't it be great if humans could do this? I could sleep and work on my problem sets at the same time.

very interesting stuff
here are some links on unihemispheric sleep in dolphins

http://www.cco.caltech.edu/~alex/Evolution%20of%20Sleep%20Lecture.htm

http://mb-soft.com/public/brain.html

http://www.madsci.org/posts/archives/dec96/845582164.Zo.r.html

I must say I function quite decently without either hemisphere awake.