I find the recommendation in favour of discrete categories over numeric probability for confidence level intriguing, because it goes against the grain of all advice I've read for humans interested in forecasting.
The easiest argument in favour of numeric probability is that it's simple to evaluate. Someone claiming to be 90 % certain better be right about nine out of ten times -- no fewer, but also not too often! This is useful when you're learning to judge your own confidence, which most people are bad at. (Almost everyone can train themselves to be better at i but some people seem to be good at it with no training.)
The typical argument against categories is that people can mean very different things with the same word: https://i.ibb.co/kQT4Ymz/q.png
It seems like TFA gets around these problems by creating a translation table between a fixed set of categories and the probabilities implied by the model for those categories. That's an interesting approach!
> On one particular Friday afternoon, he stated a conjecture that he hoped was true, and invited us to try to help him prove or disprove it.
This kind of professor/researcher/teacher needs more praise. One of the first engineering courses I took when I started out in higher education was taught by such a person.
Maybe it's just me, but I never felt so welcomed and included during my time in higher education as when that lecturer told a bunch of first-year students "here are some things we haven't figured out which you can help with, let me know if you come up with something". It was inspiring and a great introduction to what's otherwise a rather dull first couple of years of academia.
> During his study in 1939, Dantzig solved two unsolved problems in statistics due to a misunderstanding. Near the beginning of a class, Professor Neyman wrote two problems on the blackboard. Dantzig arrived late and assumed that they were a homework assignment. According to Dantzig, they "seemed to be a little harder than usual", but a few days later he handed in completed solutions for both problems, still believing that they were an assignment that was overdue.[4][6] Six weeks later, an excited Neyman eagerly told him that the problems he had solved were two of the most famous unsolved problems in statistics.[2][4] He had prepared one of Dantzig's solutions for publication in a mathematical journal.[7] This story spread and was used as a motivational lesson demonstrating the power of positive thinking. Over time, some facts were altered, but the basic story persisted in the form of an urban legend and as an introductory scene in the 1997 film Good Will Hunting.[6]
The article doesn't really state why one would do this, so here's my reason: I'm the sort of person who likes to challenge myself to geometrical problems, but I'm not good enough at it to do any higher maths.
Flight simulation, or, more specifically, finding my way around the sky by radio navigation aids scratches that itch. The procedures involved are precisely solving simple 3D geometrical problems on the fly.
I agree. I didn't mean to imply the article should have stated that. I just wanted to add to the article with additional context that's hopefully helpful to some HN readers.
It's not exactly rocket surgery, is it? Because they are fighting on the other side of the world. I feel like the article glosses over this way too quickly.
It's not surprising the US aren't winning. It's surprising they are at all able to do something that resembles waging war at that distance. Wars are incredibly hard to fight away from home. On the other side of the world? There is basically only one country in the history of ever that has been able to do that.
The article does go on to discuss the Kuwait case and that's a meaningful discussion to have, because actually winning a war so far away is surprising. It's interesting to dig into why that might have been, and the article briefly does. But why they aren't winning is less interesting.
For more meat on how important a factor distance is, Bueno de Mesquita's The War Trap presents one of the most accurate models for predicting wars[1] I know of. That model measures the fighting ability of a country by two factors:
1. It's at-home military power as a sum of population size, metal production, fuel consumption, military expenditure, etc.
2. It's power projection as the distance between its capital and the closest point of enemy land.
Note that the second number is weighted equally to the sum of all other factors, because wars are a logistical nightmare.
I was thinking of the British Empire. Their naval technology was superior enough to overpower the distance term.
I was under the impression the Dutch didn't really wage interstate war in the same sense, but rather that a bunch of paramilitary private organisations happened to fly Dutch flags. I have to admit I know very little about the Spanish case, but again I thought they mainly fought proxy wars with other European colonial powers, i.e. both were equally disadvantaged by distance.
Well Spain had most of south America, some of the carribean and the Philippines. The Dutch had the Spice Islands, half a world away. Portugal had Brazil, Azores, a bit of India and a base in China.
France had most of continental Europe, with distances that were much greater comparitively, considering they only had horses and sail boats. They also had big interests in the Indian ocean, Madagascar for instance, and the Caribbean.
Wiping out the natives isn’t the same thing as waging a war. Even from the beginning the European empires had very tenuous control over their New World colonies* and once they had to actually fight wars against well equipped European colonists to defend their control, it was a disaster for them (Bolivar, American Revolution, French and Indian war, etc).
The closest counterexample is probably the partitioning of China but that’s got its own mitigating factors
* they couldn’t even enforce the most basic sovereignty like when Spain introduced the New Laws and the encomenderos were like “lol no”
On a similar note, people are way too precious about their dead-tree books. Feel free to chuck them in bags, make notes in the margins, fold pages, underline, and strike through text in them. It's yours. Make it yours! Your scribblings don't detract from what's in there – they elevate it to something unique.
(This is particularly true if it's a book that's still in print, or was in large enough print runs it's easy to buy another second-hand copy when the one you have falls apart. It's still somewhat true even when that's not the case.)
I was riding my motorcycle in heavy rains and had a book in my work bag which, as I later found out, doesn't resist water at all, and the book got soaked. Half the pages puffed up, and I hated myself for it at first, but after a while I realized I like it even better since it feels like the book has been through something with me and I will always remember that incident whenever I think about the book.
Though admittedly, caring about this is even more vapid than caring about my books being pristine.
I'm like this for everything _except_ paper books. I grew up sharing books a lot, books I finished would go to younger kids in my extended family or my mom's students, and I got a bunch of books like that as well. So we took a lot of care keeping books in good condition. I don't buy many paper books anymore, and ones I do buy tend to be new and stay with me, but folding pages or breaking the spines still feels wrong to me
i'm someone who takes a lot of care about their books, i especially don't like when the back is wrinkly/broken on paperbacks because of opening them all the way. after all that makes them break down faster in general, over time. and it looks worse in a shelf.
anyways, everyone handles their items differently, which is fine - a friend once borrowed a book from me which was in pristine condition after multiple years of me owning and reading it. when he returned it, the back was completely wrinkled, pages had dog-ears, he had bent the cover all the way around to be able to hold it better etc.
that kind of made me sad because it felt like something i took a lot of care to keep it in good condition was "destroyed" in a matter of weeks. of course i wasn't mad towards my friend because i realized that people handle books differently.
that being said. if someone borrows you something, try to keep it in more or less the same state as when it was given to you. accidents happen, of course. i on the other hand have learned to either not borrow books i care about, or make a point about me taking care of them when reading.
sometimes it's also not as easy as "just buy another copy". some books i care about because i bought them on a vacation, or someone gifted them to me. so the exact item has a sentimental value an additional copy will not be able to replicate. but again, i just learned to create two categories of books in my mind, those i borrow, and those i don't.
after all it's 2026, just download an eBook from Anna's Archive (if they borrow the physical copy from me there's no monetary transaction towards the author as well, so i really don't feel bad about it in these specific situations).
My parents (both teachers) always told me to respect books, and it means keeping them in good shape, among other things. It is almost a religious idea: books represent knowledge, something that is important and must be preserved.
To be honest, it is not like we were maniacs about that, books are meant to be read, and accidents happen, but damaging a book if you could avoid it just felt wrong.
And I am also thinking about libraries that have books that are hundreds of years old or more. The reason we still have them is that people cared.
It is not entirely rational, but it is one of these things, like playing with food, a moral consideration more than a practical one.
Because for it to be effective it must have reasonable cost compared to the benefit. The cost for such a sweeping lifestyle adjustment seems quite high, and the authors have not showed any benefit to interventions.
The article never says anything about causation. It says sleep regularity is a predictor of mortality. That means if you find someone who already has poor sleep regularity they're more likely to die sooner, not that if you force someone into a bad sleep schedule they will become more likely to die sooner.
Self-stopping is called autonomation (or jidoka) in lean/Toyota terms. It's born out of the realisation that automation is capable of producing mistakes at a very high rate, so anything automated needs a way to detect when it's operating outside of the narrow envelope for which it is designed, and shut itself down.
The easiest argument in favour of numeric probability is that it's simple to evaluate. Someone claiming to be 90 % certain better be right about nine out of ten times -- no fewer, but also not too often! This is useful when you're learning to judge your own confidence, which most people are bad at. (Almost everyone can train themselves to be better at i but some people seem to be good at it with no training.)
The typical argument against categories is that people can mean very different things with the same word: https://i.ibb.co/kQT4Ymz/q.png
It seems like TFA gets around these problems by creating a translation table between a fixed set of categories and the probabilities implied by the model for those categories. That's an interesting approach!
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