How to learn and master complex concepts

In a previous post I wrote about the power of explicitly stating the obvious fact that there is no magic. The idea being that, once you convince yourself of this, there is nothing stopping you from learning and understanding what previously seemed magical.

If you were, for example, trying to reverse engineer a technology or learn a new scientific or engineering discipline, this exercise can quickly give you the positive affirmation you need to get started. Can I learn how this works? Well, there is no magic… So, yes I can!

Once you convince yourself that you can do something, however, there's still the little matter of actually doing it. And when it comes to learning and mastering complex concepts, that is usually a daunting challenge.

How to unravel the Magic

Occam's razor is a great problem-solving principle. In general, it states that when you have multiple theories to explain the same outcome, you should pick the simplest one. Of course, your range of theories and judgement as to which is the simplest one requires some understanding of the problem at hand. Imagine a normal person, just like you in every way, but lacking any sense of understanding at all about the concept that something solid can melt and turn into a liquid. If this was an actual knowledge gap for our hypothetical person, how would they explain the fact that a layer of snow that was on their front lawn last night has disappeared in the morning, leaving nothing but wet grass. One possible explanation, keeping in mind that melting is not in their catalogue of mental concepts, is that it must have rained and the rain washed away the snow. That seems like the simplest theory. But can you imagine the little seeds of doubt starting to grow in the hypothetical mind. Where did the snow go? Was it washed down to the nearest stream? Does snow float on water, or sink to the bottom? How come I've never seen piles of snow floating down the river before?

This example is contrived specifically because the answer is so obvious. It's just one concept we are missing: solids can melt and turn into liquids. No advanced degree in thermodynamics is required to understand that fact. One missing concept has led our hypothetical person to start questioning a lot of different things related to snow and water.

If you ever find yourself utterly lost when trying to learn a complex concept or subject (after reminding yourself there is no magic, of course), it's best to take a step back and identify at which level of complexity you are unable to explain the concept to yourself. Once you know where your mind is struggling to make the leap, it is a simple matter of identifying what foundational knowledge you are missing, working your way back until you come to a spot where everything makes sense.

Here are a few ideas for how to go about that.

1. The Feynman Technique

Richard Feynman was a Nobel Prize winning physicist and considered by many of his peers to be the brightest mind since Albert Einstein. Outside of physics, he is still remembered today for his lively writing, funny stories and captivating lectures. The so-called Feynman Technique is the method he used to master complex subjects and understand the underlying principles with such clarity that he could explain them using plain language to a non-scientific audience.

The idiom "… wrote the book on …" is a cliché way to say that somebody is an expert in a specific field. In one sense, the Feynman Technique involves becoming an expert by writing a book on the subject. Only the book can be anything from a long note scribbled in a few minutes to a whole collection of notebooks compiled over a lifetime of learning. The core concept is that you have a dedicated spaces to write things you have learned about a subject, using simple language and coherent thoughts. And when you learn new material, you add it to the notebook. And while doing all of this you have to continually figure out what you are missing and organize your prior knowledge to draw connections with the new concepts your are studying.

Feynman Technique

  1. What is the subject and what do I know? Starting a new notebook or at least a new page, write down the name of the subject, followed by everything you know about it. Be clear and concise. When you come across new information related to this subject, make sure you understand it and then add it to the notebook, again, using your own words.

  2. Can I teach it to a child? Using your accumulated knowledge on the subject so far, try to write a note you could use to teach it to a child. This means you have to use simple words, clear analogies and do it in a short amount of time. If you find yourself struggling to turn thoughts into words, you probably have some gaps in your knowledge.

  3. What am I missing? This is the hard part. By definition, it is difficult to identify what you don't know since you can't name it or describe it (remember the snow-to-water analogy from earlier). You should review your notes and try to sniff out any areas where your understanding starts to get hazy. Find the lose threads in your mind and start pulling on them. Refer to a different source covering the same material. As you are reading and studying, you should have a mental trigger set to warn you when something looks like a candidate for filling in your knowledge gaps.

  4. What is the whole story? This is the step where you try to write the book on the subject. Organize your notes. Start drawing analogies and comparisons that can illustrate specific concepts. Map out the big pieces and how they are connected. Ideally you want to be so comfortable with the subject matter that you can stand in front of a room of people and explain it in a concise narrative without having to refer to your notes.

2. Knowledge Stage Table

The Feynman Technique is powerful, but it may not work for every person and every use case. For one, it tends to work better for studying and mastering whole subjects. Sometimes we don't have time to start a new notebook and write multiple pages of concise prose. One thing that I have found helpful is to use what I call a Knowledge Stage Table. This is something I started doing a few years ago, and it very well may have a different name (if so, please leave a comment so I can give proper credit).

What is a Knowledge Stage Table? It's a simple 3-column table that allows you to track the things you don't understand and the visualize the process through which you learn new facts and concepts. You start with a list of questions or things you Don't Understand in the left column. Next to that, you have a column of thing you Know About. These are related concepts and facts that you sort of know, but don't truly understand. The column on the right is a list of the things you Known & Understand.

With this setup, the name of the game is add new concepts and terms to the middle column as you come across them in your studies/reading, and then move them to the right column as you gain mastery of the material. And the entire time you are doing it, you look for connections or answers the newfound knowledge may have brought you in regards to the questions in the left column.

The nice thing about a Knowledge Stage Table is that you can quickly create one for a specific topic, even just to answer a specific question you have. Using a table format and short bullet points lets you quickly map out the general questions and concepts. If you are a visual learner, the ability to draw lines and arrows to connect different bullet points is also a benefit. Personally, my favorite part is crossing out the items in the left and middle column as things finally click in my head and I can add new points to the known and understand column.

Let's see this method in action on a simple concept in physics: Why do astronauts in space experience weightlessness?

If you're a bit fuzzy on physics, your Knowledge Stage Table may look like this:

Don't Understand Know About Know & Understand
What is “weightlessness” exactly? Einstein, Relativity
Gravity Newton and his apple?
Is there gravity in space? Those planes that fly up and down to simulate weightlessness
There is less gravity on the moon, Mars, etc.

As you start looking up Wikipedia pages and reading different articles online, you may quickly fill up the middle column with new ideas and concepts. And as you come across multiple versions of the same information from different sources, you can start to expand your list of things you know and understand. Through this process the things you don't understand in the left column are linked to the general concepts and big ideas in the middle column. And once you understand exactly how they are linked and can explain it to yourself, you should be left with a list of simple sentences and facts summarizing everything you have learned in the right column.

3. Chunking

Chunking is a powerful technique I picked from Dr. Barbara Oakley's excellent book A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra). It is also one of the core techniques covered in her highly popular Coursera course Learning How To Learn.

The general concept behind chunking is to break a big and complex subject down into chunks that represent the core concepts you have to master. Each chunk represents one piece of the larger puzzle, and once you learn the chunks and you learn how they fit together into the larger picture, you can put all of the puzzle pieces together to understand the whole.

The way you do this is by surveying the subject and priming your mind. Surveying is the act of looking over a course syllabus, reading the table of contents in a book and skimming through the pages and looking at the headers, sub-headers and illustrations. In other words, surveying is something you do to get a sense of what material you are about to dive into.

As you are surveying the subject, you can take notes or just make mental observations on how the material is covered, what the names of the chapters are and how they are ordered. This is how you prime your mind and start drawing associations about the material to get an outline of what the big picture looks like.

If you want to learn Calculus, for example, most books or courses will follow a similar kind of sequence in introducing the basics and moving through more complex subject matter. And each resource you survey will use different ways to explain it, with various analogies and visual aids. If you look at several resources during the surveying and priming stage, you will quickly get a sense of what the big picture looks like and your mind will be ready to fill in the details.

After you survey the subject and prime yourself, the second phase of the chunking technique is to start learning the ins and outs of the individual chunks. For each concept, you have to read/watch the material and observe an example, then try to apply it yourself. This works great for some subjects and not so well for others. If you're learning Calculus, you can see an example of how to solve an equation and then solve one yourself from a workbook. If you're learning the gritty details of integrated circuit design, it's probably a little harder to directly apply the knowledge. In such cases, you can substitute this step with writing, in your own words, how it is done or what the core concept is.


He who learns but does not think, is lost! He who thinks but does not learn is in great danger. -Confucius

  • Becoming an expert at any skill or subject matter requires time and a focused learning approach.
  • Acquiring knowledge, as in rote memorization, takes a lot of effort and may not guarantee that you actually understand how all of the pieces of the puzzle fit together.
  • If you improve your technique for learning and mastering complex concepts, you can significantly decrease the amount of time it takes to gain mastery.
  • Some of the methods outlined above can help you not only acquire knowledge, but gain deep understanding of the topic.
  • The most effective methods for learning and mastering complex concepts share a fundamental characteristic: as you learn, you have to apply the knowledge in a way that requires actually understanding it. Don't just try to memorize what you read. Read a little, then turn the ideas and facts around in your head, make sense of them in your way, rewrite what you read in your own words.
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