I don't know how much context you need for the more personal examples, so I figure I'll give them without context and then if you need more you can ask:
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Having both the motivation and the mental stamina to work 60-hour weeks reliably.
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Gaining 15+ points of IQ or the thing that IQ is measuring.
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Becoming good enough at a field (abstract mathematics, mechanistic interpretability) that I've previously tried and found myself to be not that good at or interested in, such that it would then be worth my pursuing it as part of a research direction. (Another way you could write this is "Taking something that isn't my comparative advantage and making it that way")
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Convincing an arbitrary person my values are good and worth adopting within a sixty-minute conversation. (I don't actually WANT to do this in full generality! But it sure does seem impossible and it sure would be nice to do things that are closer to that area, sometimes)
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Becoming a professional tennis player at the age of 33 with little tennis experience. (Again not something I actually want, but it sure does seem impossible. I figure if this is a bad example, you can just not include it.)
1For a couple of those (whichever ones you most actually want), what exactly is impossible about it? Say you just were going to set this as your goal and get started, where do you run into the thing that is "impossible" rather than merely "hard."
On thinking about them:
"Having both the motivation and the mental stamina to work 60-hour weeks reliably." Actually this probably would be "hard" rather than "impossible". There are things I can try here that I haven't tried that might work, so I have not yet tried enough things to declare it impossible. It's more like I anticipate the possibility of this being impossible, as opposed to actually considering it impossible. Not a good example.
"Gaining 15+ points of IQ or the thing that IQ is measuring." - So it seems like there are two ways this problem could go. In World A, there exists some stack of exercises and nootropics that can already let me do this without sacrificing something I'm not willing to sacrifice. In this case the problem is that of finding it - people can bullshit or lie, supplements are not a field where I expect complete honesty, and it wouldn't surprise me if there's a high amount of individualism such that someone could truthfully say they gained 15+ IQ points on X, but I need Y instead to achieve the same outcome. If I had to try each combination myself I'd run out of time very quickly. It's impossible in the sense of winning the lottery is impossible - not something I can reliably make happen, as opposed to literally can't be done. This is close enough that I consider it to be equivalent.
Alternatively, maybe this stack just doesn't exist at all. Nootropics and exercises will not get you there. In which case, solving the problem means making advances in cognitive science that our culture hasn't yet figured out how to do. And it's not clear to me how I would succeed where lots of others have failed, here - leading onto my third point, I don't see how I have a comparative advantage in this area, and if I have to work full-time for years to get to this point it is no longer worth it, when the point is to make me more effective at solving my current chosen problem.
"Taking something that isn't my comparative advantage and making it that way" - I can think of a bunch of actions I can take here that would let me do better than I currently am. Getting tutoring, improving my ability to learn, talking it over with more experienced practitioners, etc. The key impossibility here is that people who are better than me at this can just do this stuff too and probably already are.
Like, imagine I want to be a top mathematician since I'm convinced that's the only skill worth knowing for alignment. I can hire a tutor (and have done so), but better mathematicians can also do this and probably have. How do you get good enough to meaningfully contribute when people exist in this field who did the IMO at 17 and can do any of the same improvements I can come up with? So, I would have to find some method that was A) Incredibly effective, enough to bring me up to par with more talented people and B) Other people are unable or unwilling to do this thing, even really talented people in the field.
"Having both the motivation and the mental stamina to work 60-hour weeks reliably." Actually this probably would be "hard" rather than "impossible". There are things I can try here that I haven't tried that might work, so I have not yet tried enough things to declare it impossible. It's more like I anticipate the possibility of this being impossible, as opposed to actually considering it impossible. Not a good example
Well since the point of this is that sometimes you can do impossible things, and the point is to notice the anticipation of impossibility and dig more into it, I'm still interested: what goes wrong if you tried to do this? What's impossible and/or hard about it?
Outside of the office, I generally find it difficult to get appreciable amounts of work done. It feels like it takes a significant exertion of willpower to go from not doing a work-related task to doing one, at which point it generally becomes easier to continue with that task for a while. Performing this mental motion a few times per workday is enough for me to get close to full time hours in, but doesn't feel enough for sixty hours. If I don't perform this mental motion successfully, I wind up in a state of internal tension where I'm not actually putting in consistent mental effort towards solving the next problem in front of me. I do have a fix for this already - I work better in an office, where everyone around is also working.
So, the natural solution here would be "Find yourself an office type environment doing valuable work where it is entirely normal and expected for people to work these kind of hours." This runs into the second issue, which is that on the rare occasions I have worked 10+ hours in a day, or generally pushed myself harder to try and stretch the edge of my conscientiousness, I tend to get headaches. Which are both unpleasant and also reduce my productivity, which ruins the entire point of the exercise. (The headaches are a known problem - I'm on a headache preventer that minimizes them. I could try upping the dosage, but I've already been told by one doctor that I should probably try not to be on this medication indefinitely.)
This also means that it wouldn't be a good idea to go to an environment where everyone's expected to work 60 hours, if I then don't end up being able to do that even with the social and logistical environment set up in my favor. So it'd have to be an environment where it was both normal and expected to work 60 hours AND to work 40, AND the work was object-level valuable in my opinion, to be worth trying this experiment. This could be possible - I haven't actually tried to seek out such an environment. But I do notice that I still do anticipate failing the original 60-hour goal due to the problem in the second paragraph.
I drowned and in the process lost a lot of brain function, including significant IQ loss. Would be great to get that memory, executive functioning, and problem solving capacity back. But it appears that brain implants are more focused on physical control over mental capabilities; and the longevity field has more progress in prevention of loss over restoration. Adult brains are not totally locked down, but major improvement doesn't appear to be on the field of possibilities. I would be happy to learn I am wrong.
I have to be careful what I say on this one, so these are only the examples that are in the news. Know that it is worse behind the scenes. I work in Hawaii State Government. Technology implementations are grossly incompetent. See the Hawaii Health Connector news articles for a great example (https://www.hawaiifreepress.com/Articles-Main/ID/11216/Hawaii-Health-Connector-director-steps-down-after-health-exchangersquos-failure). Our rail project resulted in 9 federal investigations for corruption, and two separate Governors requesting the whole management board resign over their incompetence (https://www.hawaiinewsnow.com/2025/06/24/governor-calls-hta-board-resignations-while-lawmakers-grill-its-leaders/). When our first state chief technology officer tried to get agencies to modernize their accounting software (which included asking some entities to use software instead of paper ledgers) he was fired for the audacity. My agency still uses typewriters. After 20 years of trying to implement digital, we still use paper records and ink signatures. It should fall into the very hard category, but actual proven performance appears to be in the impossible side due to the perversity of incentives.
I have variable levels of cognitive function that I can't predict. How can I learn/study, maintain routine, and make plans?
How do I improve my cognitive work capacity?
Think of problems as Lean does: A problem state consists of some hypotheses/assumptions, a goal, and tactics we can apply to hypotheses to infer new statements. We seek to infer a statement with the type of the goal.
Some problems only require making the right local step at each successive problem state. That's what makes them easy in some sense. Hard problems require determining (something about) the path before useful progress can be made. I think this is intuitive, if not I can give examples.
Complication: I have variable mental clarity and energy levels.
Completing a task well first requires understanding how a task breaks down into specific actions. Then the follow through only requires executing the local steps on path. The first part is "solve a hard problem". Requires good mental clarity. The second requires cognitive work.
Any concrete action I take ends up being just local step in the immediate context's problem state that doesn't have any persistent effect on my ability to assess and resolve problem states, and diminishes my reserves of energy. Feel the difference between completing a task vs practising a technique: I want persistent effects that help me respond to challenges, and the work capacity to benefit from this ability.
Challenges like "Learn to use a new mode of public transport in an unfamiliar city", "Prove Cauchy's theorem for finite groups", "how to pass this exam" are all difficult for the same reasons.
How to solve problems (read: do anything substantial) when clarity and capacity are variable/limited?
A nontrivial, complete, consistent, and morally acceptable solution to population ethics. Deep down, I suspect there's a meta-ethical incompleteness theorem similar to Gödel's first incompleteness theorem, which is an example of a truly impossible problem.
Losing weight slowly and sustainably without serious drugs (e.g. BMI 30 => 25).
The main problem is that for many people this thing works like a ratchet, it’s easy to get +0.5 BMI very quickly, and if one lets a few days after that slip, then one is often stuck at that new level.
As a result, both going down and staying there often require consistent discipline, and the whole thing is rather unforgiving in terms of slip-ups, social occasions, and such.
One thing that almost nobody tells you about exercise, which I think needs to be said more often, is that if you stick with it long enough it becomes enjoyable and no longer requires discipline.
Eventually you'll wake up just wanting to go to the gym/on a hike/play tennis, to the degree you're looking forward to it and will be kind of mad when you can't.
It's just that it takes a few months or maybe even a year to get there.
Yes, I have found that this is true.
But I have also found that it’s really easy to lose, an illness or injury forcing a long break is enough.
If the activity is one I really like intrinsically, like walking, it’s one thing, but when it’s the one I value more for results than for the process, then yes, it’s not too difficult to start enjoying it, but this does not always survive long breaks.
EDIT: This is actually a good exercise for me: to try to enjoy that other part of my exercise routine more, so that the natural pressure is towards doing it.
People say that often enough that I believe it is true for them. Yet the relapse rate within groups after experiments suggests that you and those like you are in the minority.
Very few people keep exercising, meditating, etc after year long interventions. They keep it up for a while, but it definitely doesn't stay a permanent part of their life. And the desistance rates during experiments are not small either.
There is something internal that remains to be identified about who falls on which side of the line.
This is why the drugs for weight loss have been so transformative. If people could actually come to enjoy exercise in a reliable way, there would never have been a market for the drugs.
I'd be interested in seeing what kind of exercise were used for those experiments.
I do think there's a certain minimum level of intensity involved to get to the dopamine/seratonin release phase.
Most of the studies I am familiar with are from cardiology and describe "moderate" and "light" categories. Where light is walking, and moderate is 30+ minutes three to five times a week, of gym or calisthenics.
From personal experience as a competitive track runner in youth, and trying to lose weight as an adult, I have never experienced anything but loathing for exercise at any level of intensity. I do it anyway. Daily, for my whole life.
I hear the same thing about cold immersion, which a lot of people swear by, but also doesn't induce any dopamine reaction in me.
What I want to see is someone do the research but break out groups by body type (endomorph, ectomorph, mesomorph) and see if that's part of it.
Have you tried different types of exercise? Sports, heavy vs light lifting, running vs swimming, etc?
I'm wondering if the effect is just universal for physical exertion or if there's just something that's a good "fit" for you.
Yes, even team vs solo. Fencing, weight lifting, soccer, baseball, calisthenics, yoga, hiking, rock climbing, swimming, primal movement, and more.
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As a result, both going down and staying there often require consistent discipline, and the whole thing is rather unforgiving in terms of slip-ups, social occasions, and such.
I personally found it very helpful to use a "budget"-style calorie counter - ie. instead of just having a 2100kcal goal every day, you can eat more on some day and then your next day goal will be lower to keep the average at 2100 (and vice versa - if you eat less on a given day, you'll be able to eat more later). This gave me a lot of freedom to not worry about eating too much at social occasions or just on bad days, while still keeping the weight loss results consistent.
Of course though, as with any weight loss method, this will really vary from person to person. I understand that for some people this might not be helpful or maybe may even be detrimental.
Yes, immediate compensation is useful, even if one has no idea how many calories have been involved (I would not usually know).
Although, in my experience, one needs to be very careful at least for the next two days (if not three) in order to avoid a partial bump.
The most difficult situation is when there are few "wrong days" in a row (e.g. guests are staying, and so on).
But, generally speaking, it seems that there is (often) a very strong asymmetry between the directions of "up" and "down", the system has a bias to go "up", that's what one is fighting against.
Very drastic changes (like serious drugs, or like making one much stronger (and more consistently) committed to some set of goals, not necessarily directly related to one's body) might sufficiently shift the equilibrium, that's true...
What a fruitful question. There are already things I deemed impossible that I managed to make happen :)
So two examples of what feel impossible now (but still in the realm of reality, not like wanting to eat the concept of a color x) ) :
Preventing the general European move towards fascism (even achieving that in my country, France, would be amazing). Feels impossible because :
Many competent and intelligent people already attempted that, without success.
I don't think these kind of mass movements are controllable by one person. It feels like they behave following laws we don't necessarily know but can hardly break.
I tried a little my hand at politics, it seems like a domain where deontology loses against consequentialism and it felt rotten + was really bad for my happiness. That's the most obvious way to fight fascism and it's extremely difficult and too exhausting for me to make the kind of effort necessary to have a chance
Approaches like debate or education are great on paper but more long-term approaches.
I am one person, it already requires a ton of effort to change minds at the level of my family or my company, the effort to change the minds of several countries i.e millions / billions of people feel inhuman
I want to (non-negotiable) be happy and I get exhausted quickly, this has to be taken into account to assess the feasibility of any solution
Finding an extremely satisfying place to live, which satisfy all the important criterion I care about : close enough to my family and friends in Paris and Rennes (several hours maximum), where people speak french, a great non-remote job with less than 30" commute by bike, both calm, clean and safe and full of life, where people are kind to each other, where there is a feeling of community and welcoming of newcomers but no harsh judgment of difference, where I can find easily like-minded people to learn with, dance with and sing with, very close to beautiful nature, cheap enough to live well with a 80% part time salary. Feels impossible because :
A lot of people look for that, if it existed, I would likely know about it
I am looking for a combination of the best qualities I found in places I visited. Typically, I want the pros of big cities and of the countryside without accepting the cons. I want to have my cake and eat it, which is impossible :D
The location limitation reduces tremendously the chances. The number of candidate places is finite and not so big, I've visited dozens of cities within the location bounds and they all fall short in one way or another. My current city is great in many ways, but the center is dirty, not so safe and smells like piss, which sucks.
Start with a finite and not so big number of candidates, add more and more constraints which are very hard to satisfy and go in opposite directions ... That's the recipe for building a problem with no solution
>> It is likely really impossible when the problem is presented like that. I see it as a hint that I should look for a better description of a place that would feel like a fully satisfying home. No cause for despair yet here.
I've found this a very provocative question. And it really depends on how specific the conditions are. In my case, I think it is impossible to make a full-time career from directing feature films. On the other hand I think it's very hard but not impossible for me to make a full-time career from making video content (i.e. I currently get commissioned to make music videos, but not enough to make it full-time - the business model is totally different).
It is also possible, very very very hard, but not impossible to subsidize an expensive filmmaking hobby with the income from a day-job.
Do you really have a license to sell hair tonic... to bald eagles... in Omaha Nebraska? Impossible! To sell hair tonic, maybe, but the joke works because impossibility = specificity.
Can I find a Ming vase tomorrow? No. In the next Month? Maybe. In 10 years? Probably.
Specificity is the expressway to impossibility.[1]
Often, things that seem impossible, are not, actually. If you list out exactly why they are impossible, you might notice ways in which it instead it is merely Very Hard, and sometimes not even that.
I'm not sure about this, I think Very Hard and Impossible do mean very different things even if "impossible" is technically not applicable. It seems like when I label something "impossible" what I really mean is it's so specific that "it's a total crapshoot"[2] or to be more specific what I mean is "I do not have any faith that persistence is a reliable predictor of success with this task" and implicitly it is not worth pursuing, since the risk return ratio is both lousy and fixed. (Compare this to something which is "very hard" but for which persistence [3]has a demonstrable effect on the odds - the harder/longer you work at it, the vastly better your chances of success gets, but the return is still attractive even if you work for a very long time at it).
For example, I'm sure learning the Mandolin is very hard - not impossible - if I took lessons and stuck with it practicing every-day, I'm sure even a four-thumbed tone-deaf person like me could learn it. (it just doesn't interest me enough)
However, generating a full-time income from successive feature films? There is no "just stick with this every day" that will make that a near-certainty. You can make a feature film, you can bootstrap, self fund it - but you can't be sure that it will translate into enough commercial success that you can quit your day job to work on the next.
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The irony is, you must, absolutely must have "success metrics" and clearly defined goals to increase your chances of success. But beyond a certain threshold it renders it impossible.
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Precision versus Accuracy?
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Since I'm speaking in generalities I'm choosing to gloss over the notion of "work smarter not harder", which personally I'm all for. But obviously something for which working 'smarter' increases the odds of success is very different to something which is a "total crapshoot".
I think it's been surprisingly like 50/50 when I specifically flinch away from an idea because it felt impossible, and it turned out to be "actually pretty impossible" vs "okay actually sort of straightforward if I were trying all the obvious things".
Obviously, if I systematically list out impossible things, there will be way more actually-pretty-impossible things. But somehow when it actually comes up (sampled from "things I actively wanted to do"). Maybe if I got better at dreaming impossible thoughts more of them would turn out to actually be impossible.
and it turned out to be "actually pretty impossible" vs "okay actually sort of straightforward if I were trying all the obvious things".
Interesting, because looking at this question, things not appearing "straightforward" appears to be why I flinch away from them - I know that 'straightforward' doesn't imply "easy" or "effortless" but I assume it does imply something like predictability? As in, digging a big hole can be very straightforward in that you you grab a shovel and dig, and then keep digging until it's big enough. But the act of digging is also very hard and effortful. Does "straightforward but effortful" seem to characterize, in flavor, how a task appears once you've forced yourself to question if it is impossible?
Maybe it's not you're not deficient in dreaming impossible things so much as you're very good at seeing "obvious" means and ways of accomplishing something and mapping how the dominoes land.
My followup to "What's hard about this? What can I do about that?" is going to be called "What (exactly) is impossible about this?".
It's a somewhat similar move to asking "what's hard about this and what can I do about it?". But, in practice, the things people label in their brain as "impossible" are noticeably different from things they label as "hard".
Often, things that seem impossible, are not, actually. If you list out exactly why they are impossible, you might notice ways in which it instead it is merely Very Hard, and sometimes not even that.
Unfortunately, this is difficult to write a post about because, for pedagogical purposes, I need examples that are a) real-feeling, and b) simple enough that I can demonstrate diagnosing them in ~3 steps, and c) cover a variety of "types of impossibility", to demonstrate the versatility of the technique.
It would be nice to have more Real Impossible Examples.
Some existing examples on my mind
I started asking around for Impossibilities. One person brought up "dealing with depression", another was The impossible problem of due process.
The former is a bit of an edge case because depression distorts your thinking which makes things meta-level-hard. In some sense dealing with depression is harder than solving peace in the Middle East, because I can at least think clearly about the latter. I do think I will probably include the depression example, but it kinda needs to be a special case.
The latter is a fine example but it has like 8 different impossible subcomponents. I could make pick a subset of them, but, I'd prefer a cleaner example where you can see the whole thing working.
The motivating example is "deal with AI takeoff before AI takes off", but that's going to be more like the payoff at the end of the post, rather than one of the intro examples.
So, with that in mind, what are some impossible-feeling problems you have? (For now, don't worry about whether they're a good fit for the blogpost, just seeing the array of what people feel is impossible is pretty useful).