> Still, after finishing the article, I'm impressed by not just the the number visualizations, but by their legibility and smoothness

I think the author probably had to try a lot of things
before hitting on such a well-balanced set of visualizations: not too much detail, not too little, not too many degrees of freedom, not too few, usable on hand computers, usable on laptops. But I think that if you gave someone the web page to look at and asked them to make similar visualizations, it would probably take them a day or two.

> I would say you can go a lot further than you think in bridging the gap.

You might be right, but I'm kind of cynical about it. I think it's easy for people to fool themselves into thinking they understand things after seeing a good explanation. Nova on PBS resulted not in rapidly advancing physics from the generation of kids who grew up watching it, but instead Deepak Chopra and The Secret — the fruit of the illusion of fluency without the corresponding skill.

Worse, the educational system is in many ways optimized to promote the illusion of fluency. You have textbooks of the variety Feynman complained about, with the wakalixes. You have semester-long self-contained courses, discouraging spaced learning. You have pre-announced big-bang exam dates for those courses, so students game the system by cramming to get better grades. In many cases you have multiple-choice tests to make grading easier, so guessing the teacher's password is the highest-return gaming strategy, even if often insufficient by itself. The whole educational experience is compressed into a degree program of four years or thereabouts, further discouraging spaced learning. Students rarely attend any classes they aren't getting credit for, even though this is technically permitted at most universities I've visited. It's a commonplace observation that students forget almost everything they "learn" within a few years. So the idea students get of learning is very different from what learning is; schooling systematically distorts their ability to evaluate whether they are learning or not.
(Paul Graham has explored this theme from a different angle in http://www.paulgraham.com/lesson.html as well.)

How would we distinguish a universe in which this beautiful post on gears successfully transmitted learning to its readers from a universe in which it only transmitted the illusion of learning to them? In both universes the post is popular. In both universes people say things like "I wish I had this in high school!" But in one universe people are able to do things they couldn't do before; perhaps design gear trains for 3-D printing that show up in Hackaday projects, or perhaps laser-cut unusual gear-tooth profiles with different pressure angles or different depthing/ripple tradeoffs or something. But that could take a while, and it might be really hard to trace back. Is there a lower-latency indicator we could observe, even if it's something hackable like school exams?

I don't want to sound like I'm above all this. I feel like I have new gear knowledge from reading this post, despite having read hundreds of pages about gears and watched hours of gears videos previously; it happens to be something I can state, namely that the pressure angle always needs to point at the point of tangency of the pitch circles. But I'm not yet sure if that's really true or what happens if it's false (you can definitely design gears for which it is false). I'd need to struggle with the problem for a while in order to really understand it.

(A different learning effect would be that people learn that posts like this are very popular and make more of them, having been inspired by this one. I'm pretty sure that will happen whether or not people learned things about gears from this post.)

> This ties in nicely to your Dercuano notes which I have had open in my browser for awhile! There are many interesting topics there. But I also feel like you went to the other extreme and there's a lot of interpretive labor involved in reading them :)

Thanks, that's flattering! I'm glad you're enjoying it. Are you using the HTML version or reading the raw Markdown?

> Why did you decide to polish and publish the "memory models" post?

I don't know. I think it was just random chance. I enjoy doing that kind of thing but I don't do it very often. Even memory-models is pretty unfinished and has some parts that are pretty raggedy.

> I could send you the notes that jumped out at me if interested.

Sure, that would be wonderful! If you wanted to commit to commenting on further drafts within some timeframe, that would probably help motivate me to work further on them.

----

I want to be careful to disclaim a particular interpretation here. In "Real Programmers Don't Program in Pascal" it says, "If it was hard to write, it should be hard to read." I don't believe that. I don't believe that if something was hard to discover, it should be hard to learn. I think we should make learning as easy as possible, and I agree with the post you linked that this benefits from improved explanations, and that improving those explanations takes a great deal of work.

But I have been burned many times even by my own illusion of understanding, let alone those of Freud and Chopra, to the point that I am wary of it. It is well that we remember, as Euclides said, that there is no royal road to geometry; a good tutor can save a student from remaining in error and from failing to notice the importance of something they could learn, but ultimately the student is the one that must do the hard work of constructing the knowledge within their own mind.