Explorable Explanations

(Disclaimer: Most of what I say here has caveats and qualifications – hard to capture full nuance in a comment's space.)

One of the distinguishing features of computers is easy simulation. Humans learn well by direct, tight, interaction with a system – poking at a thing to see how it works. Tight feedback loops are how we quickly build intuitions.

Explorable Explanations [0] are a great extant example of what I mean, but we can do more... Imagine a "textbook" constructed around a well built-simulator (extant example, Earth Primer [1]). Sections of the textbook would present the simulator configured in a pre-set state, with various simplifications and initial conditions. Students can poke and prod these simulators, reset them, test out new states, and answer questions. Assignments could be on the order of "Given Sim[Initial Conditions] figure out what gets you to Sim[Desired State]".

Current explorables are lovely, but (usually) incredibly bespoke. One concrete improvement would be to produce an OpenSim standard, which would allow other content creators to embed and customize these sims to construct new narratives.

Another powerful computer affordance is extreme specificity – a system should be able to build a representation of a learner's current knowledge / skill graph, and figure out a (or many) shortest path(s) from current knowledge to desired knowledge, scoped to that user's interests. (Many LMS systems attempt this, but we're still in the early, clunky days).

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Yes, I agree! And also that a lot of the fun stuff is hidden behind historically opaque terminology. Although I'm also sympathetic to the fact that writing accessible explanations is a separate and hard to master skill. Once you understand something it can be really hard to step back into the mindset of not understanding it and figuring out an explanation that would make the idea "click".

I think a lot of maths is secretly a lot easier than it appears, but just missing an explanation that makes it easy to get the core idea to build upon.

For example, I've been meaning to write an explorable[0] for explaining positional notation in any integer base (so binary, hexadecimal, etc) in a way that any child who can read clocks should be able to follow. Possibly teaching multiplication along the way.

Conceptually it's quite simple: imagine a counter that looks like an analog clock, but with the digits 0 to 9 and a +1 and -1 button. We can use it to count between zero and nine, but if we add one to nine, we step back to zero. Oh no! Ok, but we can solve this by adding a second counter. Whenever the first counter does a full circle, we increase it by one. A full circle on the first counter is ten steps, so each step on the second counter represents ten steps. But what if the second counter wants to count ten steps? No problem, just add a third! And so on.

So then the natural question is... what if we have fewer digits than 0 to 9? Like 0 to 7? Oh, we get octal numbers. 0 and 1 is…

https://distill.pub is such a platform for articles about machine learning

https://explorabl.es is a more general hub.

> especially when you can tell that the 'teacher' is also the UI designer and developer in one and there's a very high level of quality and polish. There's nothing quite like it for learning a complex subject.

Agreed. Unfortunately I think this is the inherent limitation to the explosion of such material (Bret's seminal essay [0] was almost a decade ago) - it takes an insane amount of skill, in mostly orthogonal disciplines, as well as a lot of time and effort to make it. Some tools attempt to make them a little straightforward to program, but due to the nature of it you can't really have a one size fits all solution that isn't just a general programming language + rendering engine.

And there is no "explorables industry" to fund the production of those (unlike say, textbooks), so it ends up being mostly side projects for otherwise gainfully employed developers.

It would be amazing to have eg. attempts at building an entire K-12 curriculum around explorable explanations. It's also the kind of work that probably loses in clarity and value when done by a team/committee rather than a single person dedicated to their vision.

[0] http://worrydream.com/ExplorableExplanations/

Regarding the article itself: Brett Victor is amazing and so is Strogatz. They are both my heroes actually.

But I do think there is a difference between scientific professionals communicating amongst each other and scientific communication to the public. And if mathematicians understood Strogatz his paper at the time when it was published, and there were enough mathematicians to disseminate the knowledge, then should you require that you create algorithms as animations?

Part of the reason why mathematicians and computer scientists (as researchers) conceive of new algorithms in the first place is because a lot of them are very strong in visualizing algorithms and 'being their own computer'.

Though, if a scientist wants to appeal to a broader group of scientists, then I'd recommend her or him to use every educational tool possible. For example, they could create an interactive blogpost a la parable of the polygons[1] and link that in their paper.

On an unrelated note, it is such a pity ncase isn't mentioned at all in this article!

Also related is explorabl.es, not everything is science communication in an interactive way but a lot of it is[2].

[1] http://ncase.me/polygons/
[2] http://explorabl.es/

In case you're not aware, 3B1B has a Github repo for the engine he uses for the math animations so that others can use it to make similar things: https://github.com/3b1b/manim

There's also a loose group of people already doing the visual learners "explainers" thing over here: https://explorabl.es/ (you can scroll down for links to tools they use to make their explainers).

But yes, I also feel this is an important development and that this should be an ongoing way of teaching people things. Formal education has IMO stalled out around the printing press but there are massive opportunities on computers (and especially on globally networked computers) to take that a step further and leverage the capabilities of computers to make education even more engaging and information-dense.

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length.

The author's blog [1] has more of this style and has really helped me get deeper into category theory. Without it, I wouldn't have even begun to try and understand things like the Yoneda lemma (which still remains a mystery to me).

Does anyone know any other papers or resources with this style? Maybe something like "explorable explanations" [2]?

[1] https://www.math3ma.com/

[2] https://explorabl.es/