Any thoughts on polyphasic sleeping? My gut reaction was that it's pseudo-science, but I had similar reactions to meditation, and advanced mnemonics. It turns out the former allows well trained individuals to self-immolate in complete stillness, and the latter to memorize a deck of cards as fast as you can flip through them.
Some individuals have mutations which allow them to sleep for very limited amounts of time while remaining fully alert. A family friend is included among these, needing only four hours of sleep or so to be a successful dean at a large state school.
Polyphasic sleeping with a reduction in overall hours to potentially as low as four hours (and rarely lower) is known to be possible in the medium-term, seemingly without severe negative consequences for cognition even for those without adapted genetics. It's not clear what the long-term effects would be, and if it's overall beneficial if you're attempting to maximize aggregate thinking ability.