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Comment by fouronnes3 | Hacker News Reader

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 :)

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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.

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.

It is not sufficient to understand the content very well, you also have to understand the state of the mind of your pupils very well.

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.

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.

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.

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.

Literature professor = bike argument?

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.

Looks like here's an opportunity for a language to express the riding of bikes

Headstart (modelling the non-riding of bikes): http://ruina.tam.cornell.edu/research/topics/bicycle_mechani...

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.

It's not unsolved per se, just a complex topic that resists simple explanations. (see also: what causes lift in an airfoil)

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.

> (see also: what causes lift in an airfoil)

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

https://royalsocietypublishing.org/doi/10.1098/rspa.2007.185...

MATLAB Code from the authors:

(There's no rider however)

http://ruina.tam.cornell.edu/research/topics/bicycle_mechani...

> 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.

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.

It’s not. Google harder.

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".

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