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The Art of Learning: Fractals, Water Polo and Marketing Templates

“We do not learn from experience, but from reflecting on the experience.” – John Dewey

[This post started out as a book review and became a reflection on my own experiences of learning. The idea of fractal learning is one that I would love your feedback on in the comments. Is it useful? Could it be applied in a way that helps us to learn more rapidly or teach more effectively? With more depth or more focus on the passions we have?]

Josh Waitzkin has a fascinating story. He is:

I’ve read his book, The Art of Learning: An Inner Journey to Optimal Performance and loved it.

The Art of Learning:

The book explores Josh’s journey from US Junior chess champion to world champion as a martial artist in Tai Chi Push Hands. As he learned TaiChi, Josh began to see how his deep understanding of chess was influencing his learning process and vice versa. Josh subsequently spent years deconstructing his learning process across the 2 pursuits and shares his universal themes in the The Art of Learning.

Josh’s principles of learning:

Fractal Learning

As I was trying to understand these principles, I started to draw. This is my original drawing and notes:

 My notes on the side tie it back to Josh’s themes:

This drawing – of smaller and smaller circles within circles – immediately reminded me of fractals.

From Wikipedia: A fractal is a mathematical set that typically displays self-similar patterns. Fractals may be exactly the same at every scale or they may be nearly the same at different scales.

I started to look for a fractal that would help me visualise Josh’s concept of “making smaller circles”. I found the Apollonian Gasket. Here is an animated version:

As the animation proceeds, it is exactly the same at each level – a bit like the drawing in my initial notes although with much more detail.

On the other hand, The Mandelbrot Set – one of the most famous visualisations of a fractal pattern – varies at each level:

Here’s an animated zoom of it (you don’t need to watch the whole thing):

You’ll notice that as you zoom into the structure, you don’t get an identical pattern repeating. Unlike the Apollonian Gasket, you get something different at each level. BUT it is still related to the whole.

Fractals really helped me to visualise Josh’s principles. So I wanted to step through 2 examples from water polo and web marketing to make these ideas more concrete.

Water Polo

I created a simplified water polo example:

Level 1 – A beginner, keen to learn, watches a game of water polo and sees 3 circles of skills she will need to learn to be able to play the game:

So a branch of this water polo example might look like this:

Drawn out, the pattern of smaller circles looks like this:

It looks a bit like a very simple Apollonian Gasket. In reality, there a more than 3 circles at each level of water polo, so let’s look at web marketing to provide a more detailed example.

Web Marketing and Templates

We started to create web marketing templates to help us teach our clients how web marketing worked and how all the various pieces of the puzzle fitted together. In hindsight, we were deconstructing the relevant skills as we learnt them.

So let’s consider web marketing as a skill set you might want to master.

The visual side of the Web Strategy Planning Template works as a good representation of the broadest level of web marketing.

Level 1: In the above image there are 5 areas that will need to be understood:

Level 2: Let’s zoom in on one – Search. There are 2 skills to learn in Search:

Level 3: Let’s zoom in again – SEO. The Web Strategy Planning Template doesn’t give more detail, so we can use the SEO planning template to explore the smaller circles:

SEO can be broken down into:

Level 4: Let’s zoom in one final time – On-page SEO. Again, the template helps us to clarify that we need to learn:

So one branch of Web Marketing might look like this:

Web Marketing:

Imagine if you expanded each of these – it would be complex right? Visually it might start to look more like the Mandelbrot Set with related but not identical patterns at each level.

In order to progress through the levels of either of these skills and “make smaller circles”, we need to look back at Josh’s principles:

All with the purpose of making smaller circles as we learn to condense our technique in order to enhance our perception.

So thanks to Josh for an incredibly thought provoking book that inspired me to explore and reflect on my own learning journeys. I can’t recommend The Art of Learning highly enough.

Finally I’d be really interested to hear what you think:

Let me know your thoughts in the comments below. Thanks!

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