> Science makes me feel stupid too. It's just that I've gotten used to it.
When I started my PhD program, a group of us were given a little talk by the department secretary.
She told the story of how she went to audition for Jeopardy!, a trivia game show. She saw a whole bunch of other people at the audition get really nervous and choke up; her take on it was that they were used to being the most knowledgable in the room -- they were used to sitting in front of the TV screen with their friends or family and knowing every fact, and when they were suddenly confronted with a situation where everyone was as knowledgable as they were, they were suddenly very intimidated.
She, on the other hand, was completely relaxed -- she spent her days working with Nobel prize winners and loads of other people for whom she had no doubt were smarter than her. Being confronted with loads of people smarter than her was a daily experience.
She told this story to us to say, a lot of you will experience the same thing: You were used to being the smartest person in your High School, you were even used to being the smartest person in your classes at the prestigious university you attended. Now you'll encounter a situation where everyone is like you: the best and most driven people in your classes.
You'll feel stupid and inferior for a bit, and that's normal. Don't let it bother you. Eventually you'll notice while that most of these other people have areas where they're better than you, they have areas where you're better. And there will still be the occasional person who seems better than you at everything: that's OK too. You're not the best at everything, and you don't have to be.
For every job I've ever had, I've been the "math and functional programming nerd", where I know lots of tricks in Haskell and F# and even concurrency theory within Java. I felt very smart.
I went to ICFP in 2019, and I can say with a high degree of confidence that I was the dumbest person there [1]. Everyone was speaking on four-syllable mathematical notation that I had never heard of, and talking about intricacies in GHC that I wasn't really familiar with, and different aspects of type theory that were completely foreign to me.
It was very humbling; it didn't depress me or anything, but made me realize that there's a lot to learn and improve on, and the people there were actually extremely nice and gave me some pointers so I can get incrementally closer to being as smart as they are.
I think 2024 Tom would be the second dumbest guy in the room if I went again.
[1] Knowledge-wise, I have no idea about IQ or anything.
That secretary is probably hard funded, makes more money than 75% of the scientists she supported, enjoys vacations, and will have a comfortable retirement.
> She, on the other hand, was completely relaxed -- she spent her days working with Nobel prize winners and loads of other people for whom she had no doubt were smarter than her. Being confronted with loads of people smarter than her was a daily experience.
I'm a college dropout who has managed to work professionally, in software, in RF / embedded development, medical robotics, all over the web, and most recently in AAA games. I've called PhDs colleagues, people with multiple Masters, people with decades of industry experience at the top of their fields...
I always feel like the odd-man out, and, while it used to bother me a bit, I'm pretty content with the fact that I probably always will. I frequently feel like I'm inferior to my colleagues, because of the sheer depth of their knowledge as it relates to whatever the particular domain is.
But I have the sense that I'm doing something right because I get great reviews, I frequently find moments where I can teach my colleagues something they didn't know, and they come to me for help, advice, and say good things about me (and vice versa).
But it is still a very odd feeling and I think it'll be with me for however long I work in this industry.
Athletes deal with it too. You go from being the best football player in your school, maybe even the best football player in your college. Then you go to the NFL and you're middle of the pack. Lots of guys get lost at the transition: a first round draft pick gets to the NFL and immediately loses his mojo.
> if we don’t feel stupid it means we’re not really trying
He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing. But one of the big problems with math education is that we force students to struggle to a far greater degree than other subjects, under a belief that personal struggle, the “trying”, is the only way to truly get it. This is a pervasive cultural belief that extends to work and money too. And we force it from the beginning when kids are very young, without taking the time to develop their curiosity, and without setting up the system to gracefully nudge people who for whatever reason don’t see why they should try so hard.
Personally I suspect there are lots of things that could help motivate many more students than we do using our current system of demanding kids “try” to grok abstract rules using Greek letters. A combination of more visual storytelling, math history, and physical less abstract problems, along with a grading and progression system that ensures kids get it before moving to topics that depend on having got it might help a lot of people; too often kids are pushed to progress without ensuring they’re ready, and once that happens, “trying” is a fairly unreasonable expectation.
Think about how you learned your first language. Your mom taught it to you by rote repetition. She didn’t expect you to come to any of it on your own, and you weren’t expected to struggle with grammar or understand the rules or judged for getting them wrong, you were just gently corrected when wrong and celebrated when right. I don’t know if first language learning is a good way to learn math, but it is obvious that we have alternatives to today’s system and that today’s system isn’t serving everyone who’s capable of doing math.
I don't know your background, but speaking as someone who has done a PhD in Pure Math, and working with a lot of people who have done PhDs in Pure Math, I disagree with you. It's very much a case of feeling stupid, and being able to embrace that and live with it.
The "being curious" thing is independent of the "feeling stupid" thing. It definitely exists, but it's absolutely not the same thing.
Looking at the rest of your comment, maybe we have a lot in common, but I definitely disagree with a lot of what you've written here, so no doubt our experiences are wildly different. Perhaps over a coffee[0] we could talk constructively about education, math, struggles to understand, and work ethics, but suffice to say here that even if we do have substantial common ground, I think we might have very different points of view.
Well, mathematics at a graduate level really is a subject that can only be self-taught, as are most subjects at the graduate level. Yes, some guidance can be available, but the pedagogical hand-holding that is undergrad is simply not possible. The analogy to language only really applies to mathematics that is well-understood and can be taught this way. In grad school, almost no mathematics you encounter is that well understood, so the teaching methods are absent.
There are two authors here, since the post contains an inset about dealing with your own ignorance by another professor. They aren't saying quite the same thing. The inset is saying that every grad student will confront their "absolute ignorance" and it will be difficult, scary and possibly painful. The author of the post is saying it can be a source of joy. I suppose they can be reconciled. It could also be that so little of our behavior is based on knowledge that the only sane reaction is at least somewhat negative, whether characterized by being overwhelmed, or sad, or detached.
Reframing it as curiosity is a good point, although the essay as written resonated with me because it emphasizes the "productive ignorance" of research.
One of the central problems of our time in research and academics, I think, is an incentive to focus on areas that are well-established because we know they are likely to produce results that we have confidence in (according to whatever inferential criteria we use). The idea of it being ok to not know something a priori, to have lack of confidence in it, seems sort of discouraged in the current climate, because it's too risky.
> But one of the big problems with math education is that we force students to struggle to a far greater degree than other subjects, under a belief that personal struggle, the “trying”, is the only way to truly get it.
I disagree. In fact, I found that often the better and more didactically streamlined the exposition is in a book, the less deeply I end up learning the material. It is precisely the personal struggle, having to make my own sketches and derivations, starting out with a misconception because of bad phrasing in the book and having to explore that misconception until I find what I misunderstood etc. makes the knowledge stick much better because it now feels my own, like an intimate friend.
Spoonfeeding may get people quicker to the point of solving the standardized quiz at the end of the chapter but that's not the same as learning and understanding. Another instance of metric-chasing in action.
It's a bit like how I learned MS Office or Photoshop by trial and error as a kid, or programming by mucking around trying to make a website do what I want. And you bet it was a struggle. Struggle but with reward at the end. Compare that with a handholding tutorial where you do learn how to do whatever the tutorial makers had in mind, but it won't generalize as much. Sounds totally dry. I loved computers, but hated school lessons that tried to teach us MS Office in the handholding spoonfeeding way. It's the death of the subject.
It's a safari in a safe car, looking at the animals through binoculars vs running around in the jungle in your own adventure amongst the beasts.
kids struggle with grammar, pronunciation, pragmatics, vocabulary, etc. they do so naturally, and maybe you've forgotten your own struggles, but they're very real
i think we can do better than we are doing at math education, much better, but there is no way to learn math, or anything else, without diligent effort. it won't happen by passive absorption. you can listen to people speaking spanish all day every day for years without learning more than a few words of spanish if you don't make any effort
curiosity is one possible motivation for making that effort, but the immediate result of the effort is, at first, failure. that's true of language, it's true of playing the guitar, it's true of programming, it's true of throwing clay on a potter's wheel. that failure feels like being clumsy, weak, or stupid, depending on the form it takes
and that's what the article is talking about. trying to do things that are beyond your mental ability makes you aware of, and frustrated with, that mental ability. that's not curiosity, it's feeling stupid. it's also how you increase your mental ability!
But he is not talking about education, about doing a course, where "getting the right answer makes you file smart". He is talking about research where nobody knows the right answer.
> He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing.
I disagree.
How can you be curious without something you don't understand?
The point, as I see it, is that if you find yourself in a position of complete understanding, then you must also have a complete lack of curiosity. If you think you are in that position, then the way to revive your curiosity is to deconstruct your position of expertise, i.e., recognize your position of stupidity.
---
Curiosity is step 2. Stupidity is step 1. Learning moves us from step 2 to step 3. The important thing to recognize is that step 3 is actually a new instance of step 1. Expertise is the base case of this recursive tree traversal: it's how you stop the learning process.
As someone who is currently studing maths I strongly disagree with this
> He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing.
One of the most important characteristics to succeed in maths is the ability to acknowledge things you don't understand, to fail, and to persist in spite of failure. Trying really is the only way to understand some hard things, because there are some things that are conceptually extremely difficult.
He's not talking about relative stupidity where there are other people you feel are smarter, he's talking about stupidity on an absolute basis. You don't know. You don't understand. But somehow you have to find a way to carry on, and then later on, looking back once you do understand, you're baffled by why you didn't know/understand or couldn't see some crucial things. You have climbed up a ladder and pulled it up behind you and it's hard now to imagine what it is like to be on the ground.
It's not about curiousity. Of course you have that - if you didn't you wouldn't be there in the first place.
I think the framing as "stupidity" is to highlight that you don't always chase creative questions. Quite often, you should chase the obvious or understood points.
The problem, I think, comes from the weaponization of "stupid" against people. The XKCD of the lucky 1000 plays a good role here. If you are constantly deriding others for stupid takes, then anyone that derides one of your stupid takes will hit hard. And that seems to be getting worse.
> if we don’t feel stupid it means we’re not really trying
Sounds a bit like Kernighan's lever: "Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it. Yet." [0]
In its impact on teaching, I'll say that based on teaching since 1979, students take feeling stupid as convincing evidence that their instructor is doing a bad job. No amount of assuring them that it is the gateway to enlightenment or however you put it will save you.
I've become convinced that, in the end, no one really teaches you anything, you end up teaching yourself. That phrasing is a bit hyperbolic. It's more accurate to say a good teacher only gets you 50%, 60%, maybe 70% of the way there, and it's up to you to get you to 100%.
To be able to truly learn any given concept means being capable of answering a practically infinite number of different questions about that topic. The process of teaching is essentially trying to uncover which questions the student can't answer. The challenge, of course, is that the student doesn't know what questions they can't answer, because the questions haven't occurred to them. That is, until they start testing themselves, to see if they really do understand the concept.
Problem sets in textbooks are the canonical way of addressing this teaching challenge, but there are only so many pages in a textbook, and there are other concepts that need to be taught, so the scope of the problem sets are necessarily finite.
How many times have you nailed all the problems in a book, only to discover that there was some aspect of the topic you didn't understand, despite getting all the right answers?
I'm a recent graduate, but also worked in colleges for a couple of decades. Students I've interacted with almost universally blame themselves first when they don't get something. Only when they see many fellow students in the same boat do they tend to blame the teacher. From my vantage point it seems you're either assuming their frustration with the subject is frustration with the instructor, or overgeneralizing based on non-representative students, a non-representative subject, or... a non-representative instructor. I'm not trying to be a jerk, but career longevity wasn't a great indicator of pedagogical insight or its prerequisite EQ.
A good teacher can offer some tools and methods (as in methods of "learning to learn") to bridge the gap between stupidity and (for lack of a better meaning) "enlightenment" Something especially my math teachers in general lacked..
I disagree. I think good students judge their teachers based on how motivated and passionate the teachers themselves are about a topic.
Though I've had classes where I only realized their importance multiple semesters after having them. (Mostly the non technical, business classes)
I had a junior helpdesk employee that I was training/mentoring years back. He was 20 years old, fresh out of tech school. He was good at what he did, but he only did things he knew how to do. When he didn't know something, he'd ask me. Which is great. I'd say "Well, this sounds like DNS, it's like a phone book..." or "That's an APIPA address, it must not be getting DHCP. The computer shouts out to the network asking for an address..." and so forth. However, he kept asking the same questions.
After a few months in one of our monthly meetings he kind of broke "I don't understand what I'm doing out there, you need to train me! I need to be trained!" Completely perplexed I asked him what he was talking about. "You just answer my questions, but you're not training me!" I realized he was expecting me to learn him the answers to everything. I had to explain to him that the responsibility of learning was actually on him. "This isn't school, there's no study guide. We have documentation and Google. It's your responsibility to read it and make sense of it."
I told him that I can give him all the puzzle pieces but I can't put them together for him. To be fair, helpdesk is kind of about making things work and remembering the quick fixes and tricks for things to close out your tickets.
So I said, "Ok, I think you need a project. What do you do at home for fun?"
"Well I play a lot of video games."
"Perfect, we're setting up a Minecraft server". He laughed.
I said "No, I'm serious. We're using like 5% of this massively overblown server that was sold to us. Maybe this will help you put the pieces together."
I gave him a restricted vSphere account for his DMZ'd VM, sent him a guide and unleashed him.
"Well, I've never done this before..."
"Exactly. That's how you learn my dude."
"But..."
"RTFM"
"This VM doesn't do anything."
"Right, it needs an OS."
"We'll how do I install one?"
"Here's a guide."
"I installed the OS, how do I get into it?"
"SSH"
"No I mean the desktop."
"There isn't one."
And so he learned that a computer isn't the Windows desktop.
"I can't SSH in, it says connection refused."
"Right, that's the firewall."
"Well what do I do?"
"Google UFW"
"I can't SSH in anymore, it says connection timed out."
"Can you ping it?"
"No."
"Check the IP address in vSphere"
"It changed..."
"Why?" I asked.
"DHCP...! That's what a static IP is for!"
From then on he finally understood that learning actually takes a little effort and curiosity AND yes, it's OK to Google things. He had this idea that he had to know everything, memorize everything, and looking things up was "cheating". Not knowing something and feeling dumb is actually where learning happens rather than pure repetition.
About a year later he thanked me and said that he completely misunderstood my motivations initially and that he thought I was brushing him off and being lazy, when in reality I was giving him the opportunity to learn by not feeding him every detail. He felt like he was failing because he didn't know all the answers and said that he looked back at himself a year ago and couldn't believe what he was doing now and how far he'd come. "I had no idea what an IP address was but now I understand how the packets move through the switches, request an address..." etc.
We both ended up quitting and going our separate ways as the IT department there was an absolute shitshow. He's now a sysadmin and we chat now and then and he's mentioned that he's actually glad he learned in such a fucked up environment because you were absolutely forced to understand due to all the ridiculous hacks and workarounds that had been piled on over the years. Nothing could be taken for granted.
I learned in a similar way and I think trial by fire may be one of the best teachers. "Smooth seas never made a skilled sailor."
My current view on this is that it's a symptom of exactly what "expertise" means in academia. It does not mean expert judgement, nor expertise forged in experience.. no it means being an expert at giving accounts of one's knowledge in connection with other explicit accounts of knowledge.
Very little of anything worth knowing, in practice, can be given this account or a reliable one at least (physics sure,.. teaching?). Say, after decades of teaching, an exceptional teacher is not going to be able to (in general) report their methods in terms of the explicit accounts of methods as established in books. These are highly varied anyway, and full of rival theories.
Indeed, a person who could give such a count is most likely to be a poor teacher by comparison: since all their labour has been in the creation of these accounts, not in teaching (or far less).
You cannot do both. You cannot both acquire a vast depth of expertise that grounds good judgement (risk/reward, problems that arise in practice, context-sensitive question, intuitions for failure/sucess, etc.) -- and develop baroque accounts of that knowledge (its origins, remembering which papers you read, remembering all your projects, all the theories developed by academics, their history, and so on).
If knowledge is only, as academics say, just their own sort of accounting -- then one would feel stupid all the time. Since almost nothing can be thus accounted for.. and yet the world is replete with highly practiced experts in a very large number of domains.
Was anyone else very unimpressed with the video of the kid, water, and playdoh, until the very end? The whole time I was thinking that it's clearly a miscommunication, they are just assessing the kid's understanding of the word "more". If he thought it meant the tallest one, then all his answers would be correct.
But at the end, there is a question about sharing a graham cracker, which I am 100% sure a child of that age understands. They want at least the same amount of graham cracker as the other person. The kid also gets that one wrong, at the cost of his own bottom line. That really sold it.
This seems analogous to productive laziness in engineering. A good engineer is a bit lazy in a certain kind of way: they think about how to simplify or if that fails isolate or manage complexity. An insufficiently lazy engineer will create mountains of hideous complexity full of opportunities to show off but horrible to maintain and brittle.
The analogy there isn't as direct as I'd like, because both engineers found a path between A and B[0], and I'd thought TFA was saying (because my experience has been) the initial feeling of stupidity comes from not seeing any path at all between them[1].
The way I currently think about it is that a learning space is a sort of skill tree (poset), and the easy concepts/skills are the ones where we can learn all the prereqs, and then just combine them (join reducible elements), whereas the tricky concepts/skills (the ones which make us feel stupid) are the ones that only have a single prerequisite, so we can't just combine things we already know, but have to do something novel[2] in order to acquire them (join irreducible elements).
[0] and both of them were probably confident all along that they'd make it, the former because they had already sketched out a few likely paths in their mind, the latter because they've always managed to muddle through before
[1] furthermore, having travelled from A to B multiple times, it's difficult for a teacher to empathise with those who are not following
[2] to https://news.ycombinator.com/item?id=41566945 I'd say maybe that's why traditionally we've waited until people are in their late teens/early twenties, significantly ego-invested in research as a career path, and have an experienced mentor, before we throw them overboard into the lake of obligate stupidity[3]?
(there are exceptions: Feynman habitually tested himself by attempting to self-derive [practising research mode] before allowing himself to read expository texts [entering spectator mode]. Somewhere he[?] claims something along the lines of him not being that smart, just that people were impressed after they asked him questions for which he could give answers he'd already spent hundreds of hours thinking about)
[3] everybody genius until it time to do genius shit, yo
The best feeling of my PhD was whenever two intuitions (or what I thought were facts) were predicting different outcomes. While maddening and nothing seemed to make sense, it was also the feeling of some big revelation waiting nearby to be found.
I imagine that an issue for many isn't so much that feeling stupid is uncomfortable so much as it's a good heuristic for when you're in over your head in a way that could be dangerous to your life or livelihood. So then, it's actually a matter of trust: "I trust that wrestling with this problem for a few hours/days/weeks isn't going to disrupt my ability to get food/pay rent/be physically-safe." It's super easy to plow through feelings of insecurity when you can convince yourself that you're actually going to be secure, in the long run. If there are, however, negative and material consequences for getting things wrong...
The lawyer friend who dropped out went into a field where her "bag was secured", to use a contemporary phrase. The author acknowledges that she was capable; perhaps the root issue wasn't "feeling stupid", so much as "feeling like I'm going to be broke even if I crack this nut."
Indeed, and I find that my humanities/law-inclined smart friends don't reading math texts is supposed to make you feel this way. They read through a 100 pages of law textbooks and at no part do they feel dumbfounded by a paragraph or get stuck on a page for an hour. It's hard to learn it for sure, but you can read and read and read it. Reading math, on the other hand, is a staccato, a constant stop and go (and flip the pages back). One evening I might only progress 5 pages in the math textbooks because I stop after half a page to draw some sketches, some diagrams. Then I stand up and walk up and down the corridor for 10 minutes thinking things through and whether my current understanding makes sense and adds up to explain what I just read.
But they aren't familiar with this mode of reading and working though a text, they think they are stupid or "non-math" people for not getting the meaning instantly, like they would in a book about law or marketing.
I think it’s mostly just that math education is largely suboptimal. It’s really an area where students hugely benefit from individual teaching. It’s cool that AI is making that accessible.
To an extent the techniques are still woefully primitive too. The standout for me personally is the calculational proof. It’s arguably the biggest advance in how math is done since the equals sign, but despite that it’s still rather uncommon. I suspect it will be another generation or two before it really catches on. Thankfully mechanical checking will drive adoption.
I had a very similar observation about engineering early in my career. The first project I worked on professionally felt vast compared to anything I'd seen in school. At first I was embarrassed to be new, to have to ask questions, to have to deal with solving problems in areas I didn't fully understand. It took months and months to "come up to speed", and I felt that I was drowning in complexity and unqualified for the work I was doing. Ultimately I came to understand that this is the normal state of engineering, especially when innovation is happening. The bulk of the work in engineering (not all of it, but the vast majority, especially in software) is fully understanding the problem space, the tradeoffs between alternative paths, understanding how your solution holds up and fixing bugs. In short, once you've gotten all your questions answered and finally feel fully qualified and no longer ignorant, you've also solved the problem you were working on. Time to move on to the next thing.
When I realized that, I realized that feeling dumb was actually normal, and that I should embrace it and expect to spend the majority of my career in that state. Not only did this dissolve my embarrassment, but it made me seek out ways to thrive in uncertainty and chaos -- which skills have been to my advantage for many years.
It is uncomfortable to admit you don't know things, or you don't know the best way to proceed, or you don't understand something. The temptation is to downplay that, to pretend you understand, to retreat toward the things you understand well. But poking at the unknown is how you get smarter, and ultimately how you solve problems. It takes courage, especially in a crowd, but it is also what solving problems normally feels like.
I only feel dumb if I don’t know how to start looking at a problem, in some cases because I don’t understand the description of the problem either.
But as long as I understand to some degree what we want to achieve, and have some vague idea of what corner I might start in, I usually don’t “feel” dumb even if I know very little about the final solution…
I want to distinguish two sources of "feeling of stupidity". One come from the challenge of grasping a difficult concept. The other is the smack on the head when you fail to see a simple but brilliant insight. In my view, you should not feel stupid in either situations, and the teacher should try to ward you against this feeling.
For the first type, I argue it's simply the resistance to a new mental model. The article's example of epsilon-delta language is a perfect example. It's a new way of thinking that takes time (and it did historically) to sink in. Competing on how fast you grasp this new concept is stupid. When the new mode of thinking becomes natural, it won't care how long you took to adapt to it.
For the second type, it's simply an impossible standard to reliably have eureka moments. Clearly, smarter people will have more of these than the average people, but no one can do this reliably. On the other hand, while it takes more work for us mortals to have these insights than a genius, there are plenty of ways to get there that don't require a super high IQ. Teachers should try to foster these moments because they are huge confidence builders, but try to minimise the impact of someone showing off their brilliance.
I understand where the author is coming from, but these are just useless statements. Stupidity and knowing that you don't know stuff are not the same thing. The former involves an inability to understand or learn, whereas the latter involves an acknowledgment of our current state of ignorance and that we can do better.
I don't believe one can be successful in science by constantly feeling stupid and getting used to it. You have to be comfortable with not knowing stuff, but with the drive and self-confidence that you can discover new things and expand your knowledge, which is of course not easy either.
But when people quit STEM degrees, they don't say "it made me feel ignorant" or "I didn't have enough knowledge". They say "I was too stupid". The author is expressly trying to address those people, and the people who might be able to intervene in their lives. "Yes! We're all stupid! That's part of what it means to learn and research math and science!"
On the contrary, the problem with elementary mathematics education is that teachers don't tell students that they're supposed to not feel stupid at the point that they understand something. Students think it's fine that they mechanically do long division without understanding how it works. Then the next year, they have to be taught how to mechanically do long division again, and they still don't know why it works. Eventually, their foundation is so shaky that they don't understand why anything they're doing works.
I send this to students who feel discouraged by university-level topics. If math professors find things difficult, then you're probably OK... just keep hacking at it!
And how do we formalize stupidity aka human beehiveour?
We write linq-pad queries against the planetary NSA Meta+C db collected by those neat seeing stones everyone carries since 2008. Its anonymous, its collected unaware, its omni-present, its not deformed by the questionnaire, its obvious the conclusion of the science of neurons and the model of the mind.
One of my wife's superpowers is that she isn't afraid to look stupid. When we were about to have a kid, my wife plied my mom with a lot of stupid questions. "Do I have to play with the baby all the time? What happens if the baby annoys me?" The result was that she now has an extremely solid baseline of knowledge about how to deal with babies.
[+] [-] gwd|1 year ago|reply
When I started my PhD program, a group of us were given a little talk by the department secretary.
She told the story of how she went to audition for Jeopardy!, a trivia game show. She saw a whole bunch of other people at the audition get really nervous and choke up; her take on it was that they were used to being the most knowledgable in the room -- they were used to sitting in front of the TV screen with their friends or family and knowing every fact, and when they were suddenly confronted with a situation where everyone was as knowledgable as they were, they were suddenly very intimidated.
She, on the other hand, was completely relaxed -- she spent her days working with Nobel prize winners and loads of other people for whom she had no doubt were smarter than her. Being confronted with loads of people smarter than her was a daily experience.
She told this story to us to say, a lot of you will experience the same thing: You were used to being the smartest person in your High School, you were even used to being the smartest person in your classes at the prestigious university you attended. Now you'll encounter a situation where everyone is like you: the best and most driven people in your classes.
You'll feel stupid and inferior for a bit, and that's normal. Don't let it bother you. Eventually you'll notice while that most of these other people have areas where they're better than you, they have areas where you're better. And there will still be the occasional person who seems better than you at everything: that's OK too. You're not the best at everything, and you don't have to be.
[+] [-] tombert|1 year ago|reply
I went to ICFP in 2019, and I can say with a high degree of confidence that I was the dumbest person there [1]. Everyone was speaking on four-syllable mathematical notation that I had never heard of, and talking about intricacies in GHC that I wasn't really familiar with, and different aspects of type theory that were completely foreign to me.
It was very humbling; it didn't depress me or anything, but made me realize that there's a lot to learn and improve on, and the people there were actually extremely nice and gave me some pointers so I can get incrementally closer to being as smart as they are.
I think 2024 Tom would be the second dumbest guy in the room if I went again.
[1] Knowledge-wise, I have no idea about IQ or anything.
[+] [-] andai|1 year ago|reply
[+] [-] mkleczek|1 year ago|reply
As a 50 years old person that some time ago was one of these brightest in class I can say that for most of us, people, it is:
You're not the best at anything, and you don't have to be.
[+] [-] wileydragonfly|1 year ago|reply
[+] [-] scruple|1 year ago|reply
I'm a college dropout who has managed to work professionally, in software, in RF / embedded development, medical robotics, all over the web, and most recently in AAA games. I've called PhDs colleagues, people with multiple Masters, people with decades of industry experience at the top of their fields...
I always feel like the odd-man out, and, while it used to bother me a bit, I'm pretty content with the fact that I probably always will. I frequently feel like I'm inferior to my colleagues, because of the sheer depth of their knowledge as it relates to whatever the particular domain is.
But I have the sense that I'm doing something right because I get great reviews, I frequently find moments where I can teach my colleagues something they didn't know, and they come to me for help, advice, and say good things about me (and vice versa).
But it is still a very odd feeling and I think it'll be with me for however long I work in this industry.
[+] [-] sandspar|1 year ago|reply
[+] [-] tapanjk|1 year ago|reply
[+] [-] madcaptenor|1 year ago|reply
[+] [-] dahart|1 year ago|reply
He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing. But one of the big problems with math education is that we force students to struggle to a far greater degree than other subjects, under a belief that personal struggle, the “trying”, is the only way to truly get it. This is a pervasive cultural belief that extends to work and money too. And we force it from the beginning when kids are very young, without taking the time to develop their curiosity, and without setting up the system to gracefully nudge people who for whatever reason don’t see why they should try so hard.
Personally I suspect there are lots of things that could help motivate many more students than we do using our current system of demanding kids “try” to grok abstract rules using Greek letters. A combination of more visual storytelling, math history, and physical less abstract problems, along with a grading and progression system that ensures kids get it before moving to topics that depend on having got it might help a lot of people; too often kids are pushed to progress without ensuring they’re ready, and once that happens, “trying” is a fairly unreasonable expectation.
Think about how you learned your first language. Your mom taught it to you by rote repetition. She didn’t expect you to come to any of it on your own, and you weren’t expected to struggle with grammar or understand the rules or judged for getting them wrong, you were just gently corrected when wrong and celebrated when right. I don’t know if first language learning is a good way to learn math, but it is obvious that we have alternatives to today’s system and that today’s system isn’t serving everyone who’s capable of doing math.
[+] [-] ColinWright|1 year ago|reply
The "being curious" thing is independent of the "feeling stupid" thing. It definitely exists, but it's absolutely not the same thing.
Looking at the rest of your comment, maybe we have a lot in common, but I definitely disagree with a lot of what you've written here, so no doubt our experiences are wildly different. Perhaps over a coffee[0] we could talk constructively about education, math, struggles to understand, and work ethics, but suffice to say here that even if we do have substantial common ground, I think we might have very different points of view.
[0] Other beverages are available.
[+] [-] glitchc|1 year ago|reply
[+] [-] wwarner|1 year ago|reply
[+] [-] derbOac|1 year ago|reply
One of the central problems of our time in research and academics, I think, is an incentive to focus on areas that are well-established because we know they are likely to produce results that we have confidence in (according to whatever inferential criteria we use). The idea of it being ok to not know something a priori, to have lack of confidence in it, seems sort of discouraged in the current climate, because it's too risky.
[+] [-] bonoboTP|1 year ago|reply
I disagree. In fact, I found that often the better and more didactically streamlined the exposition is in a book, the less deeply I end up learning the material. It is precisely the personal struggle, having to make my own sketches and derivations, starting out with a misconception because of bad phrasing in the book and having to explore that misconception until I find what I misunderstood etc. makes the knowledge stick much better because it now feels my own, like an intimate friend.
Spoonfeeding may get people quicker to the point of solving the standardized quiz at the end of the chapter but that's not the same as learning and understanding. Another instance of metric-chasing in action.
It's a bit like how I learned MS Office or Photoshop by trial and error as a kid, or programming by mucking around trying to make a website do what I want. And you bet it was a struggle. Struggle but with reward at the end. Compare that with a handholding tutorial where you do learn how to do whatever the tutorial makers had in mind, but it won't generalize as much. Sounds totally dry. I loved computers, but hated school lessons that tried to teach us MS Office in the handholding spoonfeeding way. It's the death of the subject.
It's a safari in a safe car, looking at the animals through binoculars vs running around in the jungle in your own adventure amongst the beasts.
[+] [-] kragen|1 year ago|reply
i think we can do better than we are doing at math education, much better, but there is no way to learn math, or anything else, without diligent effort. it won't happen by passive absorption. you can listen to people speaking spanish all day every day for years without learning more than a few words of spanish if you don't make any effort
curiosity is one possible motivation for making that effort, but the immediate result of the effort is, at first, failure. that's true of language, it's true of playing the guitar, it's true of programming, it's true of throwing clay on a potter's wheel. that failure feels like being clumsy, weak, or stupid, depending on the form it takes
and that's what the article is talking about. trying to do things that are beyond your mental ability makes you aware of, and frustrated with, that mental ability. that's not curiosity, it's feeling stupid. it's also how you increase your mental ability!
[+] [-] Arisaka1|1 year ago|reply
Feeling stupid is when you're confronted with an external you cannot understand why it works.
Curiosity can help push through feeling stupid, but you can be curious about something you won't struggle understanding it at all.
[+] [-] Gupie|1 year ago|reply
[+] [-] thomastjeffery|1 year ago|reply
I disagree.
How can you be curious without something you don't understand?
The point, as I see it, is that if you find yourself in a position of complete understanding, then you must also have a complete lack of curiosity. If you think you are in that position, then the way to revive your curiosity is to deconstruct your position of expertise, i.e., recognize your position of stupidity.
---
Curiosity is step 2. Stupidity is step 1. Learning moves us from step 2 to step 3. The important thing to recognize is that step 3 is actually a new instance of step 1. Expertise is the base case of this recursive tree traversal: it's how you stop the learning process.
[+] [-] spookie|1 year ago|reply
But alas, I never thought as a kid that I didn't have time for other things. I was always into something.
[+] [-] seanhunter|1 year ago|reply
> He’s really talking about curiosity. Calling it stupid is a cheeky glass-half-empty framing.
One of the most important characteristics to succeed in maths is the ability to acknowledge things you don't understand, to fail, and to persist in spite of failure. Trying really is the only way to understand some hard things, because there are some things that are conceptually extremely difficult.
He's not talking about relative stupidity where there are other people you feel are smarter, he's talking about stupidity on an absolute basis. You don't know. You don't understand. But somehow you have to find a way to carry on, and then later on, looking back once you do understand, you're baffled by why you didn't know/understand or couldn't see some crucial things. You have climbed up a ladder and pulled it up behind you and it's hard now to imagine what it is like to be on the ground.
It's not about curiousity. Of course you have that - if you didn't you wouldn't be there in the first place.
[+] [-] taeric|1 year ago|reply
The problem, I think, comes from the weaponization of "stupid" against people. The XKCD of the lucky 1000 plays a good role here. If you are constantly deriding others for stupid takes, then anyone that derides one of your stupid takes will hit hard. And that seems to be getting worse.
[+] [-] enriquto|1 year ago|reply
Sounds a bit like Kernighan's lever: "Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it. Yet." [0]
[0] https://www.linusakesson.net/programming/kernighans-lever/in...
[+] [-] rossant|1 year ago|reply
[+] [-] norir|1 year ago|reply
[+] [-] jimhefferon|1 year ago|reply
[+] [-] maroonblazer|1 year ago|reply
To be able to truly learn any given concept means being capable of answering a practically infinite number of different questions about that topic. The process of teaching is essentially trying to uncover which questions the student can't answer. The challenge, of course, is that the student doesn't know what questions they can't answer, because the questions haven't occurred to them. That is, until they start testing themselves, to see if they really do understand the concept.
Problem sets in textbooks are the canonical way of addressing this teaching challenge, but there are only so many pages in a textbook, and there are other concepts that need to be taught, so the scope of the problem sets are necessarily finite.
How many times have you nailed all the problems in a book, only to discover that there was some aspect of the topic you didn't understand, despite getting all the right answers?
[+] [-] chefandy|1 year ago|reply
[+] [-] nicholasbraker|1 year ago|reply
[+] [-] sureglymop|1 year ago|reply
[+] [-] bongodongobob|1 year ago|reply
I had a junior helpdesk employee that I was training/mentoring years back. He was 20 years old, fresh out of tech school. He was good at what he did, but he only did things he knew how to do. When he didn't know something, he'd ask me. Which is great. I'd say "Well, this sounds like DNS, it's like a phone book..." or "That's an APIPA address, it must not be getting DHCP. The computer shouts out to the network asking for an address..." and so forth. However, he kept asking the same questions.
After a few months in one of our monthly meetings he kind of broke "I don't understand what I'm doing out there, you need to train me! I need to be trained!" Completely perplexed I asked him what he was talking about. "You just answer my questions, but you're not training me!" I realized he was expecting me to learn him the answers to everything. I had to explain to him that the responsibility of learning was actually on him. "This isn't school, there's no study guide. We have documentation and Google. It's your responsibility to read it and make sense of it."
I told him that I can give him all the puzzle pieces but I can't put them together for him. To be fair, helpdesk is kind of about making things work and remembering the quick fixes and tricks for things to close out your tickets.
So I said, "Ok, I think you need a project. What do you do at home for fun?"
"Well I play a lot of video games."
"Perfect, we're setting up a Minecraft server". He laughed.
I said "No, I'm serious. We're using like 5% of this massively overblown server that was sold to us. Maybe this will help you put the pieces together."
I gave him a restricted vSphere account for his DMZ'd VM, sent him a guide and unleashed him.
"Well, I've never done this before..."
"Exactly. That's how you learn my dude."
"But..."
"RTFM"
"This VM doesn't do anything."
"Right, it needs an OS."
"We'll how do I install one?"
"Here's a guide."
"I installed the OS, how do I get into it?"
"SSH"
"No I mean the desktop."
"There isn't one."
And so he learned that a computer isn't the Windows desktop.
"I can't SSH in, it says connection refused."
"Right, that's the firewall."
"Well what do I do?"
"Google UFW"
"I can't SSH in anymore, it says connection timed out."
"Can you ping it?"
"No."
"Check the IP address in vSphere"
"It changed..."
"Why?" I asked.
"DHCP...! That's what a static IP is for!"
From then on he finally understood that learning actually takes a little effort and curiosity AND yes, it's OK to Google things. He had this idea that he had to know everything, memorize everything, and looking things up was "cheating". Not knowing something and feeling dumb is actually where learning happens rather than pure repetition.
About a year later he thanked me and said that he completely misunderstood my motivations initially and that he thought I was brushing him off and being lazy, when in reality I was giving him the opportunity to learn by not feeding him every detail. He felt like he was failing because he didn't know all the answers and said that he looked back at himself a year ago and couldn't believe what he was doing now and how far he'd come. "I had no idea what an IP address was but now I understand how the packets move through the switches, request an address..." etc.
We both ended up quitting and going our separate ways as the IT department there was an absolute shitshow. He's now a sysadmin and we chat now and then and he's mentioned that he's actually glad he learned in such a fucked up environment because you were absolutely forced to understand due to all the ridiculous hacks and workarounds that had been piled on over the years. Nothing could be taken for granted.
I learned in a similar way and I think trial by fire may be one of the best teachers. "Smooth seas never made a skilled sailor."
[+] [-] mjburgess|1 year ago|reply
Very little of anything worth knowing, in practice, can be given this account or a reliable one at least (physics sure,.. teaching?). Say, after decades of teaching, an exceptional teacher is not going to be able to (in general) report their methods in terms of the explicit accounts of methods as established in books. These are highly varied anyway, and full of rival theories.
Indeed, a person who could give such a count is most likely to be a poor teacher by comparison: since all their labour has been in the creation of these accounts, not in teaching (or far less).
You cannot do both. You cannot both acquire a vast depth of expertise that grounds good judgement (risk/reward, problems that arise in practice, context-sensitive question, intuitions for failure/sucess, etc.) -- and develop baroque accounts of that knowledge (its origins, remembering which papers you read, remembering all your projects, all the theories developed by academics, their history, and so on).
If knowledge is only, as academics say, just their own sort of accounting -- then one would feel stupid all the time. Since almost nothing can be thus accounted for.. and yet the world is replete with highly practiced experts in a very large number of domains.
[+] [-] alphazard|1 year ago|reply
But at the end, there is a question about sharing a graham cracker, which I am 100% sure a child of that age understands. They want at least the same amount of graham cracker as the other person. The kid also gets that one wrong, at the cost of his own bottom line. That really sold it.
[+] [-] api|1 year ago|reply
[+] [-] 082349872349872|1 year ago|reply
The way I currently think about it is that a learning space is a sort of skill tree (poset), and the easy concepts/skills are the ones where we can learn all the prereqs, and then just combine them (join reducible elements), whereas the tricky concepts/skills (the ones which make us feel stupid) are the ones that only have a single prerequisite, so we can't just combine things we already know, but have to do something novel[2] in order to acquire them (join irreducible elements).
[0] and both of them were probably confident all along that they'd make it, the former because they had already sketched out a few likely paths in their mind, the latter because they've always managed to muddle through before
[1] furthermore, having travelled from A to B multiple times, it's difficult for a teacher to empathise with those who are not following
[2] to https://news.ycombinator.com/item?id=41566945 I'd say maybe that's why traditionally we've waited until people are in their late teens/early twenties, significantly ego-invested in research as a career path, and have an experienced mentor, before we throw them overboard into the lake of obligate stupidity[3]?
(there are exceptions: Feynman habitually tested himself by attempting to self-derive [practising research mode] before allowing himself to read expository texts [entering spectator mode]. Somewhere he[?] claims something along the lines of him not being that smart, just that people were impressed after they asked him questions for which he could give answers he'd already spent hundreds of hours thinking about)
[3] everybody genius until it time to do genius shit, yo
[+] [-] thomasahle|1 year ago|reply
[+] [-] underlipton|1 year ago|reply
The lawyer friend who dropped out went into a field where her "bag was secured", to use a contemporary phrase. The author acknowledges that she was capable; perhaps the root issue wasn't "feeling stupid", so much as "feeling like I'm going to be broke even if I crack this nut."
[+] [-] bonoboTP|1 year ago|reply
[+] [-] User23|1 year ago|reply
To an extent the techniques are still woefully primitive too. The standout for me personally is the calculational proof. It’s arguably the biggest advance in how math is done since the equals sign, but despite that it’s still rather uncommon. I suspect it will be another generation or two before it really catches on. Thankfully mechanical checking will drive adoption.
[+] [-] Dove|1 year ago|reply
When I realized that, I realized that feeling dumb was actually normal, and that I should embrace it and expect to spend the majority of my career in that state. Not only did this dissolve my embarrassment, but it made me seek out ways to thrive in uncertainty and chaos -- which skills have been to my advantage for many years.
It is uncomfortable to admit you don't know things, or you don't know the best way to proceed, or you don't understand something. The temptation is to downplay that, to pretend you understand, to retreat toward the things you understand well. But poking at the unknown is how you get smarter, and ultimately how you solve problems. It takes courage, especially in a crowd, but it is also what solving problems normally feels like.
[+] [-] setopt|1 year ago|reply
But as long as I understand to some degree what we want to achieve, and have some vague idea of what corner I might start in, I usually don’t “feel” dumb even if I know very little about the final solution…
[+] [-] kzz102|1 year ago|reply
For the first type, I argue it's simply the resistance to a new mental model. The article's example of epsilon-delta language is a perfect example. It's a new way of thinking that takes time (and it did historically) to sink in. Competing on how fast you grasp this new concept is stupid. When the new mode of thinking becomes natural, it won't care how long you took to adapt to it.
For the second type, it's simply an impossible standard to reliably have eureka moments. Clearly, smarter people will have more of these than the average people, but no one can do this reliably. On the other hand, while it takes more work for us mortals to have these insights than a genius, there are plenty of ways to get there that don't require a super high IQ. Teachers should try to foster these moments because they are huge confidence builders, but try to minimise the impact of someone showing off their brilliance.
[+] [-] beryilma|1 year ago|reply
> Science involves confronting our 'absolute stupidity'.
I understand where the author is coming from, but these are just useless statements. Stupidity and knowing that you don't know stuff are not the same thing. The former involves an inability to understand or learn, whereas the latter involves an acknowledgment of our current state of ignorance and that we can do better.
I don't believe one can be successful in science by constantly feeling stupid and getting used to it. You have to be comfortable with not knowing stuff, but with the drive and self-confidence that you can discover new things and expand your knowledge, which is of course not easy either.
[+] [-] feoren|1 year ago|reply
[+] [-] lern_too_spel|1 year ago|reply
[+] [-] harrigan|1 year ago|reply
[0] https://www.manukapur.com/productive-failure/
[+] [-] ivansavz|1 year ago|reply
I send this to students who feel discouraged by university-level topics. If math professors find things difficult, then you're probably OK... just keep hacking at it!
[+] [-] InDubioProRubio|1 year ago|reply
We write linq-pad queries against the planetary NSA Meta+C db collected by those neat seeing stones everyone carries since 2008. Its anonymous, its collected unaware, its omni-present, its not deformed by the questionnaire, its obvious the conclusion of the science of neurons and the model of the mind.
And now for a word from our project lead: Peter.
[+] [-] sandspar|1 year ago|reply
[+] [-] wileydragonfly|1 year ago|reply
“Best I can do is a star.”