Holy canoodles, how is this for weird?
Monophasic sleep, which is how most people sleep, is divided into five stages. Polyphasic sleep causes the brain to bypass the first 4 – 4 1/2 stages and instead slip almost immediately into a short stage of NREM, followed by a lengthened stage of REM.
The thing is, one only sleeps about two to three hours every 24 hours (six 20 – 30 minute naps a day, which is a nap every four hours.) Even with this reduced total amount of sleep, total REM increases.
Read the Wikipedia entry for more information and this Everything2 article for a few firsthand accounts from people who have converted. This blog is solely dedicated to polyphasic sleep.
I think I like sleeping too much to try it, but it is definitely intriguing.