His motto "What I cannot create, I do not understand" has been one of the driving forces in my own quest to understand more about the world around me. A good friend had picked up a corollary which was "What I cannot teach, I do not understand" which I think was quite similar. Definitely one of my heroes.
And the corollary to that, from 17th century French writer Nicolas Boileau: "Ce que l'on conçoit bien s'énonce clairement, et les mots pour le dire arrivent aisément." - What we understand well, we express clearly, and words to describe it flow easily.
I'm french and I have a great memory about that quote. In high school my litterature and physics teachers had a disagreement about it, although I believe they didn't know about each other's point of views. Only us the students did, as they each hand waved great insights about the world with this quote. One was arguing, much like you, about the profound truth there is to it. The other was quick to explain that they perfectly conceived how to ride a bicycle, but like most of us couldn't possibly teach it at a blackboard. I leave it to you to guess which was which :)
I took up social dancing in my 20s, including salsa and Argentinian tango. I think that it is a very good way to experience the difference between being very good at something and being able to teach.
I've been on courses with some people that are clearly exceptionally good at dancing but are a bit lacking when it comes to teaching. Then I've had the pleasure of having teachers that, while still very good at dancing, would not win the high level competitions. When it comes to teaching though, they are just wonderful to be around. They are exceptionally good at spotting what you are doing wrong and giving you an explanation of how to fix it. Not only that, but they make you feel good about learning.
One concrete memory I have is from a cuban salsa dancer trying to teach me, a poor northern European, how to move like a cuban. His frustration was very noticeable and not making it easier for me! Then an example of the other type of teach, is the crazy Australian tango dancer that not only had fantastically fun and simple workshops, but also spotted and explained simple fixes. When I was struggling with a move, he told me to rotate my foot, which I did, and I stopped struggling. When us attendees in the class talked about some high level move being complicated, he said that it is not at all complicated, and showed us how it's simpler than it appears.
I think teaching requires not only that you understand how to do something, but also what someone else's incomplete understanding is. You need to address the root cause as to why the other person's understanding is so lacking, like your examle with the tango dancer, instead of pointing out that a move is wrong and not giving the tools to prevent it. There may be many paths to reaching similar understandings, and a teacher needs to be able to tame this sprawling diversity. That's one reason why we don't just get blog posts or films that are exceedingly short, because if everyone could just understand a dry delivery of the core points instead of needing to think through multiple examples and reasons, we wouldn't be so pressed about teaching.
> I think teaching requires not only that you understand how to do something, but also what someone else's incomplete understanding is.
This 100%. I have been playing guitar since around 1972, and am really good at it. I will never offer lessons to anyone, at any level, because that is a completely different skill than just being able to play a guitar.
I also know instructors at bootcamps that are not master programmers, in fact more than a few don't meet senior-level expectations; but they are exceptional at explaining the basics, triggering those "lightbulb" moments in their students, that makes them a far better instructor than someone with vastly more experience and expertise.
Great insight, it actually aligns with the conversation above: Yes, teaching is its own skill regardless of the subject matter, but to teach you really have to understand the subject matter really well, and isn’t at all related to “doing it well” in some cases.
For example, in film, being a great director requires a deep insight about acting, so they can explain what’s needed from a performance to an actor. A director may know what they need despite being unable to perform it themselves.
All my best teachers were trained as teachers, and weren’t necessarily content experts.
One of the worst teachers I ever had, was a genius Calc II teacher, who was an abusive asshole, and would humiliate students for asking questions he deemed as “stupid.”
Since a significant part of my learning, is asking “stupid” questions, this did not go well for me, and I took an Incomplete. I had a 4.0, to that point.
> “The only stupid question is the one you don’t ask.”
From a poster in one of my tech school classrooms.
If you consider professional sports as an example, the best coaches were not the best players and vice versa. The saying "Those who can't do, teach" is such a shallow representation of reality perpetuated by those who can do neither.
I would say that if you can't explain on a blackboard how to ride a bicycle, then that simply means you do not understand how to ride a bicycle. You can do a thing without understanding it. I would guess very few bike riders really understand what all makes the act work even though they all can perform the act.
Maybe no one can learn how to ride a bike purely from a blackboard but that is a seperat issue about physicality.
But the quote is really about understanding, and the forces and effects that go into the act of riding a bike are both understandable and explicable. Anyone who understands them can describe them on a blackboard. So the quote holds water even in the case of riding a bike.
I would say anyway.
Maybe there are other examples and bike riding just wasn't the best example to invalidate the quote.
That's were I put my money, but I could see it going either way.
This can devolve into a definitional argument, but I actually think it's fair to say we don't understand how we ride a bike. We have many abilities and fluencies we don't understand, or only partially understand, in the sense that we can't break them down into pieces easily and transmit the information. That perspective feels more accurate to me than saying I understand how I ride a bike because I can ride a bike, though in common usage the phrase "I understand how to ride a bike" would be perfectly acceptable.
The subtle distinction between the phrase "knows how to" and "understands" hints at the difference here.
We(by which I mean a person who knows how to ride a bike) do understand how to ride a bike. The problem in communicating that is a riding a bike is a skilled act. that is you cant get good at riding a bike by reading about it, and it is very hard to describe a well trained skill, it boils down to "practice a lot" which makes nobody happy.
One of the reasons you can’t get good at riding a bike by reading about it is that we literally don’t understand the mechanics of bike riding. It’s a currently unsolved problem in physics. Google it if you do t believe me!
So I get what you’re saying, but it is maybe not the optimal example.
Even if we could perfectly and accurately explain the mechanics and mathematical representations of riding a bike, it would still be useless knowledge even to the few people capable of understanding it in terms of utility in riding one.
> This conservative non-holonomic system has a seven-dimensional accessible configuration space and three velocity degrees of freedom parametrized by rates of frame lean, steer angle and rear wheel rotation.
I always adore the split between how my brain does things instinctually, but making it arbitrary completely demolishes the 'natural' flow of it. Same with complex ball throwing / bouncing trajectory calculations.
It also immediately makes me angry about how we teach math. When you learn about powers (squares, cubes, roots, etc), these things are just written out as arbitrary concepts instead of displaying them geometrically.
Hell, when I was first taught the Pythagorean theorem, it was just explained by drawing a triangle with A² + B² = C², without also drawing out the related squares of each side. Immediately doing that would instill so much more intuition into the math. In general, mathematical concepts gain so much clarity by doing them geometrically.
Sounds like a problem with your early math tutors: especially with geometry, all the examples you bring up have been taught with "what it means".
I mean, squares and cubes are just multiplication by the same factor: I distinctly remember even trapezoid surfaces, pyramid volumes being demonstrated by chopping and piecing parts together.
In the US especially, too many programs have an insistence that doing things with symbols and doing things with shapes and solids are completely different things and don't relate the two.
Primary school programs? Secondary school programs?
I could understand that in high school and uni when you need to move past "intuitive" maths into abstractions, but I'd be perplexed if this is really the "program", and not just an individual teacher (and surely, a big chunk of them too)!
We've started to swing back towards visual and geometrical models with common core/new math.
But I have a big collection of math textbooks from all over the world, and math 6, pre-algebra and algebra texts in the US have far less geometrical content and pictures than the non-US equivalents that I have. I also think that the increased emphasis on getting students through standardized tests ended up dedicating a lot of class time towards rote with short term benefits.
Sibling comment to yours points to a relatively recent (this century) article with a mostly complete theoretical model for bike self-stability. There are other theories though, some more or less developed than others. It turns out to be a fiendishly hard control-theory problem, and at least one aspect is chaotic. Which theory is correct has not, to my knowledge, been definitively determined by experiment. Until it is, I think it is fair to say that it is unsolved.
Unlike lift, which is very well understood but often poorly explained.
That's easy! It pushes air down, and the reaction force is what we call lift!
... now, why it pushes air down... there be many computational fluid dynamics PhDs... though "angle of attack" covers a lot, and the rest is just efficiency tweaks.
Good question for teachers who insist it's the Bernoulli Principle: "But my paper airplane has flat wings and flies just fine!" toss across classroom
That's a great rebuttal. But if the actual claim is "I cannot teach..." It is still consistent. No one is claiming to teach you how to ride a bike or be in a relationship or know when to leave a party. "I cannot teach what I cannot understand" is not the inverse: "I can teach everything I understand".
I'm a native English speaker who, a lifetime ago, moved to Shanghai to teach English to adults. One of my biggest struggles when I first started was explaining to students not just what the correct English should be in a given situation, but why that was the correct English. This had a profound effect on my view of expertise and experts in general.
As someone that speaks English as my second language, the trick of English is to memorize all the exceptions and then accept that the English spelling is just made up to mess with foreigners.
Looking at you, the "b" in debt, that I was pronouncing for a long time growing up and learning a lot of words from reading.
A big one is also "ed" like "jogged". It looks like jog ged, so surely it's pronounced that way. Bahaha, no - gotcha! It's jogd! But we like extra letters and there must be vowels even when completely and absolutely unpronounced. Not sure if this is better or worse than Russian which seems to have no problem with squeezing a half dozen consonants side by side and saying, 'good luck.'
Honestly English spelling is the worst at least of Western Europe. Its so bad it that unless you know some IPA and learn the words pronunciation one by one youre misunderstood all the time. Its also imposible to guess with 100% accuracy how a word is said unless being told.
Schwas everywhere randomly (why is it adjust (uhd 'juhst) and not ad 'juhst when we have accept (ak 'sept). In German this is way more consistent.
Diphthongs everywhere, almost no pure monophthongs. Which is a language feature but in written form is also fucked. I tend to have problems with oh vs aa sounds. E.g. poland is pou luhnd and polish is paa lish.
Stress isnt written.
Consonants not only can be spelled differently but also said differently. Gif vs djif, cell vs celt, china vs machine
This makes the language way harder in a high level than it should be if it had had some spelling reform at some point.
Sorry for not using IPA Im on the phone.
There's two pronunciations of 'polish' though: the one you mentioned being what one does to grandmother's candlesticks, and 'pou lish' referring to someone or something from 'pou luhnd'.
As an ESL speaker living among native speakers, my take: No human language has "the correct [expression]". What is best suited is the thing that's often used, or an interesting but understandable twist on it that will be familiar to the audience, and grammar should be viewed as descriptive not prescriptive. Grammar is just some OCD person's attempt to write down a simplification of reality, nothing more.
The best way to learn written English is by reading English books[1]; the best way to learn spoken English is to interact with native speakers, a lot. Build familiarity without ever trying to justify "why that was the correct [expression]". It'll just feel right when it's right, because it fits the statistical pattern your brain has picked up.
Grammar is to language like ballistics is to throwing & catching a ball.
[1]: For someone with a basic grasp of the language but not enough exposure yet, Young Adult content is often easiest to read. I read most of the Sherlock Holmes stories, some James Bond novels, and a lot of Heinlein growing up.
One of the big takeaways was not to over-value the knowledge I had gained learning English via immersion in an English-speaking culture, and conversely not to under-value that of the local teachers, who had gained their knowledge in the classroom. It's a cliche at this point to say that "street smarts > book smarts", at least in my culture. My teaching job taught me that there are situations where neither type of knowledge by itself is sufficient, and that both types have their place.
For example, as I mentioned I frequently ran into situations where I could tell whether a student's sentences were correct or not, but I struggled to explain why. One example from early in my teaching career was when students would place their adjectives out-of-order, for example "The German, red, old, large car..." instead of "The large, old, red, German car...". I intuitively knew that the former is incorrect and the latter is correct, but when students would ask me why, I struggled to articulate a reason.
But the local teachers on staff (i.e. native Chinese speakers) would chime in with "The order of adjectives in English is opinion, size, age, shape, color, origin, material, and purpose." They (the local teachers) still made mistakes in their English, but they had mostly memorized the rules from classroom study, and could recite them better than I could. Which was helpful to both us as native speakers (who wanted to give the students concrete answers to their questions) and to the students (who wanted rules to govern future scenarios they might encounter).
I was admittedly a bit cocky coming into that job, thinking I was qualified simply because I was a native speaker. I quickly learned that teaching a subject is a skill unto itself. It requires abilities like gauging levels of understanding by asking comprehension questions, and tailoring the subject matter to those comprehension levels, so as not to either talk down to the student or talk over their head.
Exactly correct, but I would say 'Where it gets interesting ...' as opposed to complicated. Like the bike riding comment in a peer to the parent of this comment, there is a difference between 'operating' and 'creating' right? Knowing how to ride a bike tells you nothing about how to design a bike. It is not uncommon in my experience that people mix up these two things all the time.
One my personal trick: imagine that you are magically transported into the 19-th century (or earlier). Can you teach the subject to a well-known scientist of that era?
E.g. if you want to explain radioactivity to somebody from 1860-s, how would you do that? Or for math, how would you explain calculus to Archimedes?
In 1860 Lavoisier and Dalton have already published their work and died, so they know chemistry and atoms. Napier is much older, so they will understand exponential decay. It looks easy to explain.
I'm worry about getting some samples. Let's go to Poland and dig in random sites? Before the time travel I need a few days to study in Wikipedia where I should go and what mineral to look for.
I can try to guess how to purify it because I went to a high school with and specialization in Chemistry. (Let's dissolve everything with Nitric Acid, and then use Sodium Carbonate to precipitate Calcium and then Sodium Sulfide to precipitate all heavy metals including Uranium. I'm not sure if it works.) Anyway, one extra day to study this will be helpful.
To show the radioactivity I guess I can use a photographic plate. Luckily, it look like they already have some. (I was going to use Silver Nitrate and hope the best, but the chances of success are better if some of them already know what they are doing.) Add another day of preparation just in case.
Also, as an application, I'd try to irradiate food. 1860 is just in time for Pasteurization. Can I get enough radiation??? Is it safe???
---
Calculus to Archimedes:
That's easy. Archimedes was using Calculus 2000 years before it was cool. The guy calculated the area of a parable slicing it in small parts. Also the volume of a sphere slicing it in small parts. (And then the surface of a sphere with a trick.)
I taught Calculus in the first year of the university, and also in more advanced courses and also in high school. (It will be necessary to start explaining formulas or a translation of formulas to geometric figures. Also, the idea that a formula is related to a graphic in paper is hard, so it will take some time.) I guess I can enter the time machine on the spot.
Those both seem much easier to me than what I usually struggle with: Transported back to a pre-industrial time, is any of my technological knowledge or understanding even remotely useful?
Like, sure, germ theory is great I guess, but I have no idea how I'd begin to explain the internal combustion engine (which I'm fairly sure requires pretty advanced metallurgy) let alone something as esoteric as solar panels. Hell, how do you generate electricity? I could mumble something about waterwheels, a coil of wires, and a large magnet, but I have no idea how you'd begin to go about sourcing a large magnet. Industrial-scale mining of Africa/Australia, maybe?
Like, I know a lot, and I could explain a good amount about how a lot of this works conceptually, but I couldn't even begin to explain how to actually engineer it. As far as I'm concerned, solar panels come from factories.
This thought experiment reminds me of Mark Twain's novel "A Connecticut Yankee in King Arthur's Court", in which the main character is a 19th-century American man transported back to 6th-century Britain. He used his experience in firearms manufacture to introduce modern weapons and had bicycles constructed for the knights to ride around on. I always thought it was pretty farfetched that he'd be able to recreate such complex technology without the aid of modern tools, much less set up factories to manufacture it in pre-industrial times. But it is a bit fun to imagine someone using knowledge of modern technology to pose as a wizard. As Arthur C Clarke famously said, "Any sufficiently advanced technology is indistinguishable from magic."
Nineteenth century kit wouldn't really be all that difficult to replicate with the materials available in the early middle ages. Even the precision stuff of the time, you can make a surface plate just by scraping an iron sheet. With a surface plate you can make everything else you need. The hard part would be higher quality metallurgy, but it's certainly doable, the Chinese were making cast iron as early as 5th century BCE. Even steel was possible with even Bronze Age equipment.
> Those both seem much easier to me than what I usually struggle with: Transported back to a pre-industrial time, is any of my technological knowledge or understanding even remotely useful?
That's an interesting topic, and there's a whole community that is interested in this. Mostly for historical and educational reasons.
Surprisingly, there are quite a few things you can reasonably do. You will never be able to build a useful internal combustion engine starting in a pre-industrial time. But you'll be able to introduce the positional decimal notation (took 4000 years to invent!), double-entry bookkeeping, paper making, printing press.
If you know a bit of technology, then you can create water plumbing (just avoid lead), and at least some metalworking.
Germ theory is great, for sure. For the rest, aim a bit lower to reach things you can figure out how to manufacture in your lifetime: working with steel was just starting to be properly understood in 1850s, and pre-industrial seems to be defined as 1750-1850, so depending on exact timing you could perhaps become the greatest blacksmith in existence, or a rich industrialist/inventor. As a modern person, the simplest lessons you can take back on that topic are probably "add more oxygen to the fire", and that some combinations of metals burn in very specific ways (think fireworks, burning magnesium, etc).
> What we understand well, we express clearly, and words to describe it flow easily.
And the other side of the coin to both is a powerful trick to really nail a topic you feel like you have gaps on: get the basics and teach it / explain it to someone; you then have to explain it clearly thus have to fill all the gaps.
A similar thing I heard about the amish, is that it is not that they are anti technology, it is that they Don't want technology they can't control, basically if unable to make from raw materials they don't want it.
Now I don't think this is entirely the way things are, I suspect there is a core of truth with a lot of religion and tradition surrounding it. But I have a lot of sympathy for wanting to have the freedom that control over your environment grants you. Personally I would hate to give up my tech. and remain a willing slave to the manufactures.
It's impossible, even for Feynman, to understand how to create everything. In your example the Amish idea of "we" is religious bias — each Amish individual doesn't know how to create everything, they choose to rely only on other Amish, shunning the knowledge of others. "we" can also take on patriotic bias, as in, "we" don't build anything anymore because it's all made in China, thus excluding China from that "we". The fading globalist dream of the 90s was that "we" could include everybody on our little planet.
That's not really true about the Amish. I've never heard that interpretation. It is more complicated than and Amish do use technology in limited ways but it boils down to not wanting to disrupt their family with technology and also the complicated process of integrating new technology into their lifestyles.
> it is that they Don't want technology they can't control, basically if unable to make from raw materials they don't want it.
Lots of Amish farmers use a computer. They just keep it separate, and don't let it invade their home and decide their life.
Think landline phone on a farm, but also the phone is in an outdoor phone booth and used only for unavoidable things like ordering seeds, not socially.
I tend to agree, but teaching another person is also a whole different set of skills from being able to drive something yourself.
One prominent example is the "curse of knowledge"; it may take a lot of practice becoming a beginner to be able to teach for a beginner's perspective in your area of expertise.
God, thank you. I really dislike the old aphorism that if you can't teach something you don't understand it.
Teaching is a whole complicated skill unto itself, especially if one is teaching to beginners. Like (since we're on HN), how easy is it to imagine someone very good at programming but would be a terrible choice as a Comp Sci 101 prof? I'm guessing "very."
The whole idea deeply undermines teachers of all subjects.
I think that “teach” has a different meaning here. There is “understanding something well enough to elaborate it in its entirety” (the technical capacity to teach it) and then there is the former + “and have the skill/talent of being able to explain it to a wide variety of other people from different backgrounds.”
This is really more in line to some of the things Feynman communicated in many of his interviews. I feel like it more accurately reflects the way Feynman approached things.
This is even more relevant in the LLM era. LLMs can spit out an answer to a question. But if you cannot understand and assess those claims at a deep level, you are not adding any value to the process.
He was misogynistic and, by his own admission, did not hold women in high regard. I don’t remember exactly but I think he even admitted that at some point in his life he didn’t believe women could be scientists, or at least not as good as men. I think that by the end of his life he had matured and outgrown this.
He was deeply affected by the death of his first wife. I personally believe that he developed misogynistic traits as a way of self-defense and driven by the pain of her loss. They were deeply in love. His farewell letter to her is so beautiful and touching, and yet so pragmatic, in a way that only Feynman could be.
He is a personal hero but I do understand he was human and as such, a flawed individual like anyone else.
Given that his sister Joan was an accomplished scientist in her own right, and they got along well, I don't think your comment is accurate.
> “During the conference I was staying with my sister in Syracuse. I brought the paper home and said to her, “I can’t understand these things that Lee and Yang are saying. It’s all so complicated.”
> “No,” she said, “what you mean is not that you can’t understand it, but that you didn’t invent it. You didn’t figure it out your own way, from hearing the clue. What you should do is imagine you’re a student again, and take this paper upstairs, read every line of it, and check the equations. Then you’ll understand it very easily.”
> I took her advice, and checked through the whole thing, and found it to be very obvious and simple. I had been afraid to read it, thinking it was too difficult.”
All the first page results of my Google search are positive, except for the one video (not near the top of the results) that has a provocative title but is 2 hours long. I’m not going to watch that. Can you link to the negative stuff you’re seeing?
I’ve watched 2 Angela Collier videos on him albeit in the background — you’d probably have to watch the whole thing to truly understand the “bad rep” and I can’t speak to how widespread the bad rep is.
My memory is, misogyny, cringey stories that were surely greatly exaggerated and just happen to make Feynman the smartest guy in every room, kind of a jerk in general, divorce due to claimed domestic violence, never did the work of writing a book personally but has the reputation of being a prolific author, his pop appeal makes people elevate him to the very top minds of physics when the work of others was much more impactful.
I haven't watched this particular video, but Angela Collier's channel seems to be unfortunately going the typical way of pop-physicists, like Neil deGrasse Tyson, Sabine Hossenfelder, etc. - becoming famous for their physics-related content, and then assuming they're an expert at everything because they are physicists, and physics explains everything. It seems to be a rare physicist (possibly Sean Carroll) that's in the public eye, that doesn't succumb to this disease.
The fault lies partly with the viewers and commenters, ascribing a similar level of expertise to their platitudes and ill-informed takes on, for eg. AI, as to their actual field of expertise. But they don't exactly discourage that either, and in some cases lean into it actively. It's at least a hopeful sign that the descent into "physicist disease" isn't especially rapid in Angela's case, physics still being the primary topic on the channel, but it's still disappointing all the same.
She's the only youtube physicist I can stand, to be honest. Much better than Tyson, and much, much better than Hossenfelder, who's turning out to be a complete crank. Collier is matter of fact, cites her sources, and has non-hot takes on whatever non-physics topic she's talking about (e.g. AI). Sure, she gets the terminology wrong, but she gets the main thrust of the matter right. I say that as a computer science researcher who's concerned about AI ethics.
And her video on Feynman is detailed and worth watching. She goes through evidence from court cases of Feynman strangling his wife, of how Ralph Leighton created much of this myth of Feynman by fanboying him. And she gives him the benefit of the doubt as well, presenting him as flawed, but human.
He hasn't written a single book (surprising I know), I assume you're talking about "Surely you're joking, Mr. Feynman", which contains exaggerated anecdotes designed to make Feynman look like a hero. That one was written by a fanboy (Ralph Leighton) based on stories that Feynman told him, which have been revealed to be either fake or exaggerations (they found notes in his office of him writing and rewriting these hero stories).
Personally, I experienced a rude awakening when reading his book "Surely You're Joking, Mr. Feynman!". I've read part of his lectures, and heard great things about him in general. So I was extremely surprised when his own collection of anecdotes painted him as kind of a shitty human, in my opinion.
Very much an example of "never meet your heroes" for me.
