Book Reviews

“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:

• 2 x US Junior Chess champion (his father wrote a book about his journey called Searching for Bobby Fischer which was turned into a feature film of the same name),

• Tai Chi Push Hands World Champion (2004) – the martial arts version of Tai Chi – and has subsequently coached others to that same title,

• and founder of The Art of Learning Project.

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:

• Cultivating a beginner’s mindset
  A beginner is open to all possibilities, is excited to learn and is not afraid of failing. As a beginner there is no expectation to succeed or produce results.

  As your skill level increases, so too does the expectation (often self-imposed) for you to produce results. We stop learning when those expectations make us too afraid of making mistakes. Cultivating a beginner’s mindset helps us overcome this fear of mistakes so we can continue to learn and improve.

• Invest in loss
  By training, practicing and competing with people who are better than you, you will be forced into making mistakes (losses). These losses become investments when you take the time to reflect on them to understand what happened and why. Through this reflection you can learn and then refine and improve your skills and performance.

• The study of numbers to leave numbers
  Another way of wording this principle might be to call it the study of a skill to make that skill automatic. By studying and practicing your skills, you gradually absorb them. They become intuitive, automatic, no thinking required.

  Remember the basics of how to catch a ball? Keep your eye on the ball and watch it into your hands. Do you repeat this to yourself every time you catch a ball? When you’re first learning – sure. However, after practicing for a while, you don’t think about it anymore. In fact, often you forget someone even taught that to you.

  This is one of the key difficulties for masters trying to teach beginners – they have forgotten what they have learnt and how they learnt it.

• Making smaller circles (condensed technique)
  Over time you work on finer and finer details within a skill, condensing your technique to use less effort to achieve the same result. To progress to smaller and smaller circles you’ll need to follow the above 3 elements every time:

• adopt your beginner’s mindset,

• invest in loss to understand and learn the finer level of a skill

• then reflect, study, and practice the new “smaller circle” of the skill until it is automatic. Then you can progress to even deeper levels.

• Slowing down time (enhanced perception)
  In a competitive arena, if you are “making smaller circles” by focussing on finer details of a skill than your opponent, you will feel like you have more time. The greater the difference in skill level, the greater the time difference will feel.

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:

• Level 1 Novice sees 3 skills to master

• Level 2 Intermediate sees 3 skills to master

• Level 3 Expert sees 3 skills to master

• And so on

• Cultivating a beginner’s mindset is about forever being open to, and then seeing the next 3 skills to master.

• To move deeper into the pattern and down a level to more condensed technique you must invest in loss.

• You progress to a deeper level when it is internalised by study, reflection and practice.

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:

• Water Polo:

  • Ball skills

  • Swimming

  • Game play

• Level 2 – When she arrives at her first training session, the player becomes aware (with the help of her coach) that these 3 skills can be broken down further. For example she learns that in Ball skills there are 3 more circles – Passing, Shooting and Blocking:

  • Water Polo:

    • Ball skills

      • Passing

      • Shooting

      • Blocking

    • Swimming

    • Game play

• Level 3 – This cycle of awareness of more detail (and capability to progress) then repeats and she then breaks each of these skills down even further.

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

• Water Polo:

  • Ball skills

    • Passing

      • Forehand pass

      • Backhand pass

      • Push pass

    • Shooting

    • Blocking

  • Swimming

  • Game play

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:

• Outcomes

• Website

• Search

• Backlinks

• Social Media/Content Marketing

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

• SEO – Organic searches

• SEM – Google Adwords

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:

• Keyword Research

• On-page SEO

• Off-page SEO

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

• Target Keyword

• URL

• Page Title

• Header tags

• Meta description

• Image alt tags

• SEO Yoast

• Web page copy

• Google Authorship

So one branch of Web Marketing might look like this:

Web Marketing:

• Outcomes

• Website

• Search

  • SEO – Organic searches

    • Keyword Research

    • On-page SEO

      • Target Keyword

      • URL

      • Page Title

      • Header tags

      • Meta description

      • Image alt tags

      • SEO Yoast

      • Web page copy

      • Google Authorship

    • Off-page SEO

  • SEM – Google Adwords

• Backlinks

• Social Media/Content 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:

• Cultivate a beginner’s mindset
• Invest in loss
• Study numbers to leave numbers

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:

• Could fractals help you to visualise your learning journey? Or to help you to teach others?
• How might your expertise or specific skill set look laid out as a pattern?

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