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My new essay on the use of digital media to explain science.  
Aaron Meyer's profile photoMichael Nielsen's profile photoCurtis SerVaas's profile photoJens Petzold's profile photo
Nice article. There's another paradox, which is that if you explain something too well, it doesn't stick as well as if you explain it 90% well. Forcing the student to struggle through the last 10% is an important part of learning. Feynman is a spectacular explainer, but I've found that I don't learn as much from him as I do from inferior teachers. I think the struggle is the key. Unfortunately this works against your goal of creating the best explanations you can make. If you succeed, you may find that everyone walks away from your stuff thinking, "I learned so much!" and not remembering much of it a week later.

There are other approaches, like the one taken by Lewis Carroll Epstein in "Thinking Physics", where the quiz comes before the explanation. That might get you the struggle you need without having to actually explain something sub-optimally.
"I think the struggle is the key. " Nicely put, +Lawrence Kesteloot.  I quite agree.  A couple of observations:

(1) Often, we fail to deeply engage (i.e., struggle) with a subject simply because it's hard and a bit boring to do so.  One of the things I like about Bret Victor's prototype is that it makes it easy to play with difference equations.  That ease of play seems crucial to me, and a highly desirable goal for a good medium for thought.

(2) Even with such a medium available, we still need a strong emotional engagement to struggle with  a subject. Otherwise, it's more fun to just go and do something easy (browse Google+!)   It seems to me that such engagement is often obtained as a consequence of extrinsic circumstances ("learn this material or you'll fail your course").  But it'd be nice to have better intrinsic techniques.
Great essay Michael. I was confused though when you introduced Simpson's paradox, and I think I know why. I like the explanation (from "the nature and direction of association changes due to  presence or absence of a third (possibly confounding) variable" and where I think I was set off on the wrong path was when reading in your example "... regardless of whether you have large or small kidney stones." Rather, shouldn't it be "... when whether you have large or small kidney stones is explicitly regarded." in other words, when the extra conditional variable is included. In hindsight I know what you're getting at and how to interpret your sentence, but my plain English explanation says exactly the opposite to yours (yet is surely equally confusing). Perhaps there's a plainly worded sentence that would make this clearer.
Along similar but less ambitious lines: ever since I learnt javascript, I've been wishing I had time to create a good explanation of the Kochen-Specker theorem.
I like questions-first too. But it's worth noting that in a computing medium an explanation can come with its own 'resistance' -- most obviously in the form of a game or puzzle.
Ooh, this is a fascinating topic. Methods of explanation...

I'm definitely interested to see collections of related-examples and any generalizations that can be drawn. Tufte's books (e.g. Visual Explanations) might be a good model.

I personally keep returning to Isaac Asimov's explanations (e.g. the monthly essays he wrote for F&SF, for over 30 years). He had several recurring explanatory techniques (e.g. biography, etymology, anecdote). Most of his essays were collected into books.

It's also worth noting that a particular explanation will work fine for one person but poorly for another. Imagine software that determines the explanatory style that works best for you (and not just what you've mastered so far).

I agree that the words "game" and "educational" are culturally loaded and should probably be avoided. Maybe invent some new words :D
Is it a coincidence that you wrote your explanation of bitcoin in the way you did?

Since you published it, I've been reflecting on how it works to set up a series of problems you can mentally (emotionally? imaginatively?) engage with.

Tentative conclusion: you have to want to understand something. Asking the question first, as Lawrence suggests above, seems sound.

However, it has to be an interesting question. In maths, it's traditionally been things like when oncoming trains will meet, or how much a bath leaks. Not brilliant. I'm not interested in how fast your bath is leaking.

Lawrence Gowers has been thinking along similar lines...
Great essay. Worth noting that such interactive tools could be extremely valuable to research itself. For example, the main audience of systems biology is often biologists/clinicians, and yet results are communicated in a manner that requires computational/modeling knowledge for interpretation.
+gary ruben I see your point.  On the other hand, I find your suggested replacement hard to parse, too - I can't imagine someone coming to this for the first time will understand what "is explicitly regarded" means.  Need to give it some more thought.
+Carlos Scheidegger The Wason Card Test is very interesting, but my point is somewhat different.  At least as I've had it explained to me, the point of the Wason Card Test is that our ape brains find it much easier to reason about social contexts that are formally identical to some abstract problem than to reason about the abstract problem itself.

My point about emotion is much broader and less specific.  What I think is perhaps most important is the (very obvious) point that the more we care about something, the more effort we're likely to put into it [*].  While this is obvious, many approaches to pedadogy (indeed, to life) ignore it, or act in a way that is opposed.  I find this a lot in my own work - regularly revisiting questions like "Do I really care about this?" and "Why care about this?" helps a lot; I find myself going down wrong paths when I don't do so.

([*] With some obvious caveats.  People sometimes care so much about something that they tie themselves up in knots about it, and can't work.  But I'm speaking in the more typical case.)
+Troy McConaghy On software figuring out what learning style works best: it sounds like a great idea.  But as a practical issue I wonder about how much content needs to be created in this case?  There's a huge overhead involved in catering to multiple learning styles.  Not that it's not a great idea, in principle, of course!
+David Harbottle +1 for the "bath leaks" comment alone, it gave me a smile!

On the "series of problems" approach, I've believed since undergrad that the right way to understand something deeply is to be able to reinvent it from scratch (preferably in more than one way).  It's often not real reinvention, of course - one picks up various hints and facts along the way, and those things help tremendously.  Still, it's a useful mental discipline, and sometimes leads to original creative insights.

The writing approach in the Bitcoin post (and several of my other essays) is simply a cleaned-up, narrative form of this reinvention process.  It is cleaned up a lot, of course, and uses a fair bit of dramatic license to make things easier to read. Some people enjoy the style; others hate it.
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