Why bother to hack one's sleep? The simple answer: "more time" -- but this has all sorts of embedded complexity, so I am going to break it down a bit.
Time is the most important resource we have. We can use time to produce things we want: money (by working a job), friends (by talking to people), well-being (by talking to people or eating), and so on. We also (practically speaking) have a limited amount of time: about a thousand months in a lifetime (though there's some chance that life extension will work and we'll get more months, you can't count on it).
So the number of months seems kinda fixed and it's hard to see how to get more months. But if you drop down to hours, it's easier to see how to optimize things: We rarely feel like we wasted a month, but we often notice wasting hours at a time. If we can waste fewer hours, or do better things with each hour, then we can get more of the things we want out of life. By wasting an hour, I am talking about: procrastination in various forms; sleeping unnecessarily; reading unimportant things; and working on things that aren't important.
OK, so sleep seems like a waste. Sleep less and we waste fewer hours. Win? Maybe, but the obvious problem is that missing sleep might cause us to be less effective with the remaining time. Sleep deprivation leads to all sorts of problems: weird aches and pains, immune system compromise, poor focus when working, and periods of grogginess where I'm completely useless. So we need to strike the right balance, because these effects are definitely bad, and I would pay a lot to not experience them.
It's worth looking at the value of those extra hours. Hours are valued differently for different people, and at different times. The most valuable hours -- the ones I would hurt most losing -- are the ones in the middle of the day, when it's easy to coordinate with people. Evening hours, around 7-11pm, seem the least valuable to me because I don't typically get very much done during that time, and there are a lot of distractions. The early morning would be the next best, followed by the late night. Obviously, this depends on what I'm doing also -- if I'm in a flow state, it doesn't matter what time it is, I want to stay awake another hour to stay in flow.
My Sleep Diet:
Sleep no more than six hours during the night, then take as many naps during the day as I feel like.
I've been doing this sleep diet for two weeks and it seems like a boon. Why does this work for me (so far)? First, it's flexible. I highlight its flexible nature because being able to work straight through flow states is really important, so I can't tolerate a rigorous napping schedule.
Second: I am risk-averse with respect to weeks of my time. I've failed to adapt to Uberman and Everyman 3 (polyphasic schedules), and both adaptation periods were very costly to me. I don't want to pay that cost in the short-term unless it's guaranteed to succeed; I have a lot of work to do in the short term and I can't tolerate long periods of ineffectiveness.
Third: It succeeds in reducing my effective amount of sleep. I used to sleep 7.5 hours or so each night. I've shaved that down to an average of 5.75 per night plus 0.5 of napping, so 6.25 -- that's 1.25 hours per day that I've gained. Mostly this time comes in the morning, so I get up around 7:30 or 8 instead of 9.
Fourth: It succeeds in reducing my midday, post-lunch sleepy periods. I think the main reason is that I usually get a nap before midday, and that revives me during the midday hours. The naps are working; I get at least a couple minutes of REM in most of my naps, though I rarely get a lot of REM.
Just a couple notes on my experience: I've tried polyphasic before so I know what it feels like to be sleep deprived. I don't generally feel sleep deprived at all. There were a couple times in the last week where I felt sleep deprived for ~30 minute-1 hour periods, usually in the morning or right after a nap. I haven't gotten that in about five days, though, so it seems to have gotten somewhat better.
I'm taking melatonin each night right as I get into bed. Gwern suggests that melatonin may help him need less sleep, so I've tried it. It seems helpful but I'm not sure. Overall, it was easy to get on this schedule. My original goal was to do it for two weeks, but now I don't see any reason why I can't keep doing this schedule indefinitely.