Natural question follows: can humans train ourselves to do the same as animals in water? Live a bi-phasic life where creative / analytical sides of brain each get to "sleep"?
If you want to have a peek, you can read about the Wada Test https://en.wikipedia.org/wiki/Wada_test . (And somehow related https://en.wikipedia.org/wiki/Split-brain )
If it does appear in humans, it'd probably be best to study those with extreme insomnia or people who claim to have very short sleep patterns (<2 hours a night) or maybe those who are narcoleptic (the other end of that scale).