... at least, not for me. The bottleneck is something like mental energy. I can only make progress on a (subjectively) difficult topic for a handful of hours (at best) each day before hitting severe diminishing returns, and being forced to "relax" for the rest of the day. 

In light of the above, the obvious thing to optimize for the sake of "making progress on difficult things" is the amount of "mental energy available per day", not "waking hours available per day". Sleep seems to serve the function of "restoring mental energy"; but I get diminishing returns on sleeping longer (in a single block) as well; for me, there doesn't seem to be a big difference in "available mental energy" during a day whether I'd slept 6 hours or 9 hours.

So, since I'm getting diminishing returns on both my waking and sleeping hours, the obvious thing to try is to split the day up into multiple "sub days", i.e. some form of polyphasic sleep. Ideally, I'd like to spend a larger total fraction of the day asleep; this contrasts things like "the Uberman's sleep schedule", where the goal is to have as much waking time as possible (which, through this lens, is pure folly).

Have any of you (or anyone you know) had any success with something like this?

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There is a book "Daily Rituals" by Mason Currey which looks at the practices of various high achievers. Few were able to achieve much more than 4 hours a day of sustained high calibre intellectual work*. This suggests to me that going much past this is difficult as you would think others who could work harder would do so and win. 

A typical day would look like this

1. Hard work in the morning for 4-5 hours with coffee or breakfast. 
2. Lunch then take care of business. 
3. Relax in the evening.

A nap at lunchtime can help you to eke out another hour or so (as in thar study of violinists who made it to become concert solists - which I can't find right now). Personally I now see sleep not as wasted time but as a useful practice that helps me to learn and to exercise hard or to deal with emotionally challenging situations from the present or the past.

I think people should focus on getting in the 4 hours a day, which is hard enough. If you do that in a goal directed fashion you are likely to be awesome. And the good news is that you can also manage your life and enjoy yourself.

* Note we are not talking about busy work or repetitive work. If there is not a feeling of effort you are probably not working very hard. One example of hard work is deliberate practice. 

Your question resonates strongly with me.  About ten years ago, I decided to try Uberman to solve exactly this problem.  While it didn't solve the problem, it taught me a lot about sleep, and it was worth three weeks of hell for that alone.

In the time since then, I've come to the conclusion that it's probably not that sleep recharges our available mental energy.  Recharging is part of it, but I think a bigger factor is probably the fact that sleep provides memory consolidation, and most importantly, sleep makes us forget things.  We are able to make progress in the morning at least in part because after a good nights rest, things feel new and interesting.  We have insights, see things in a different light, because we're partially relearning things we knew previously, and adding another layer of paint onto the picture.  In the morning, we've probably forgotten why we got bored the previous day.

With this in mind, I've tried things like working on one project in the morning, then switching to a completely orthogonal project in the afternoon, then another completely orthogonal project in the evening.  It's easier to be excited about things when the things you learned in the morning don't interfere with the things you're trying to learn later on.  This worked great for me during the Covid lockdowns, when I learned a lot of biochemistry in the evenings, after spending my mornings doing computer related work.

That said, while switching to completely different projects helps, it's still not great.  There's still an energy loss, an inability to care, an apathy to overcome.  If I didn't have work constraints, I would probably try to switch to a polyphasic schedule again to test or verify some of the above;  based on what I've learned over the years, my next attempt would be a balanced triphasic schedule.  This would put me at 6-6.5 hours awake and 1.5-2 hours asleep, with each six hour 'awake' block being a separate topic/category.

Since I currently have the slack to do so, I'm going to try getting into a balanced biphasic schedule to start with. If I actually manage to pull it off I'll make another post about it.

You talk about the length of your sleep but have you considered variability of your sleep? For me sleeping always 7h30 seems to greatly increase my productivity in the long run. I sometimes add a few sleep cycle every few week ends but try to stick to a regular sleep schedule instead of thinking in terms of duration.

You might want to try by first waking up always at the same time, regardless of when you fell asleep.

I think this is pretty well known among people interested in optimizing for higher productivity. I can't think of any specific examples to link you to now, but people keep rediscovering this point that time != energy/willpower/etc. and that not all hours of the day, week, month, or year are fungible.

I think the real shame is we don't tell kids about this fact when they become teenagers and have to start thinking about this stuff (or maybe we do and I was just too thick to get it!).

Adderall.

A one word answer here is not very useful I think but I somewhat agree.

Adderall and other ADHD medication can, in a context of abuse, lead to somewhat "more productive time" or something like that. This if well known.

But too few people know that having a reduced "attention store" throughout the day can be a symptom of ADHD.

I can recall a patient that was not overly hyperactive but was daydreaming a lot and starting the medication actually helped him go "slower" in his mind but for way longer, hence increasing output.

Meanwhile, Adderall works for people whether they “have” “ADHD” or not. It may work better for people with ADHD – a lot of them report an almost “magical” effect – but it works at least a little for most people. There is a vast literature trying to disprove this. Its main strategy is to show Adderall doesn’t enhance cognition in healthy people. Fine. But mostly it doesn’t enhance cognition in people with ADHD either. People aren’t using Adderall to get smart, they’re using it to focus. From Prescription stimulants in individuals with and without attention deficit hyperactivity disorder:

It has never been established that the cognitive effects of stimulant drugs are central to their therapeutic utility. In fact, although ADHD medications are effective for the behavioral components of the disorder, little information exists concerning their effects on cognition…stimulant drugs do improve the ability (even without ADHD) to focus and pay attention.

I cannot tell you how much literature there is trying to convince you that Adderall will not help healthy people, nor how consistently college students disprove every word of it every finals season.

Adderall Risks: Much More Than You Wanted To Know