In Peak, two psychologists talk about the concept of "deliberate practice". The idea is that you don't just "spend 10,000 hours" to become good at something. Instead, it's about being deliberate about how you practice. You should have goals, you should be focussed and you should try and reflect on your weaknesses instead of repeating the one party trick that you're good at.

It's a really solid concept, but in this post I would like to propose a related alternative. Instead of doing "deliberate practice" all the time ... maybe consider doing "deliberate play" now and again too.

Linear algebra example

I recently made a tool called wigglystuff that ships a Matrix widget. It behaves like a numpy array but you're also able to change the numbers by dragging them around in the browser. It effectively turns a matrix into something that could be part of an online form. If you combine such a widget with a reactive notebook it's pretty easy to come up with compelling demos!

Here's a demo of a matrix that represents PCA. There's a n x 3 matrix of randomly sampled colors that I multiply with a 3 x 2 widget that you can control. This means that you're able to map colors unto a two dimensional plane. Here's what that might look like:

If you're good at curiosity, this might trigger some questions.

• When I move the first number in the matrix the points expand. Why?
• When I move the second number ... I introduce an angle away from the x-axis. Why?

The widget is great at the interaction bit, but if you're even mildly curious you'll immediately be able to check your knowledge. And you might bounce into things that you might not have expected.

Let's try one more.

Notice how we get into a perfectly straight line here? Why? There's more than one great argument to be made here: the columns are not independant, but you can also just do the algebra.

But notice how you just bump into great questions by just playing around? You have to be deliberate about it, mind you, curiosity needs to be activate. But when you do, you're really working on some great motivation to dive deep once you've spotted something curious. Playing can be an act to make something interesting that wasn't before. This feels especially for topics like linear algebra. That single matrix has tonnes of applications, and you should feel free to explore them with some deliberate play.

Don't get me wrong, there's loads of great YouTube videos now that will teach you linear algebra too ... but videos are a one way street. All you can do is listen. That's note the same as playing and being an active participant.

tldr

More educational notebooks need to leverage these widgets. They are a perfect method for deliberate play.

If you're interested in a longer demo, you'll enjoy this YT tutorial that does a deep dive on matrix widget.