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Day 3: Develop the deep intuitions that allow you to “get” any subject

In yesterday’s email, I talked about how you can memorize things. This works well if there are far too many facts and figures to understand deeply–or if the way you need to use the knowledge doesn’t require an in-depth understanding.

That won’t work on most subjects. Why? Because remembering isn’t the only problem you face–understanding matters even more.

In today’s email, I’m going to tell you how to build those deep intuitions so that you can “get” any subject.

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Why would I share a technique with you yesterday that doesn’t work for most subjects? The reason is that mnemonics can be incredibly powerful when specially designed for the subject at hand, doubling or tripling your recall.

This method, in contrast, is the Swiss Army knife of learning methods. I use this in almost every subject I learn. Best of all, the more difficult the subject, the better the method works (because it gives you an intuition your peers often lack).

Before I talk about the method, I want to briefly explain the principle behind it.

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Every day I get emails from students complaining about all the things they need to memorize. However, when I ask them to tell me what they’re studying and how they’re being tested, the majority of the time memorization isn’t their problem.

Students are quick to blame memorization, when really it’s a poor intuition that’s often to blame.

Cognitive scientists call this inflexible knowledge. Inflexible knowledge is when you remember superficial details of a problem or subject, but not much else. It’s inflexible, because you can only answer very narrowly prepared questions. You’re not equipped to use the knowledge outside of a specific context.

Take cognitive psychologist Daniel Willingham’s example:

“In his book Anguished English, Richard Lederer reports that one student provided this definition of ‘equator’: ‘A managerie lion running around the Earth through Africa.’ How has the student so grossly misunderstood the definition? And how fragmented and disjointed must the remainder of the student’s knowledge of planetary science be if he or she doesn’t notice that this ‘fact’ doesn’t seem to fit into the other material learned?

“All teachers occasionally see this sort of answer, and they are probably fairly confident that they know what has happened. The definition of ‘equator’ has been memorized as rote knowledge. An informal definition of rote knowledge might be ‘memorizing form in the absence of meaning.’ This student didn’t even memorize words: The student took the memorization down to the level of sounds and so ‘imaginary line’ became ‘managerie lion.'”

(Source)

Willingham explains that such inflexible knowledge is an important step to later acquiring expertise. That is, all knowledge starts out inflexible, but it gets more flexible as we work with it.

The problem is that when you have a lot of inflexible knowledge, ideas seem arbitrary. Definitions seem to be about managerie lions instead of useful concepts that you understand intuitively. So, when testing time comes, it seems to be full of very specific facts that you can’t remember.

The difference is that the smart students weren’t memorizing superficial details. They were building deep intuitions about the ideas so that they didn’t need to.

When you have a deep intuition, what Willingham would call flexible knowledge, you don’t need to memorize nearly as much. For every forgotten fact, the possibilities of what it could be are heavily constrained. As a result, you may forget many superficial details before a test and still perform well by reasoning them through on the exam.

The first principle of my books and courses is: never memorize what needs to be understood. However, it could have easily been: understand things deeply so you don’t need to memorize most things.

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How can you develop a deep intuition, which allows you to avoid a lot of memorization?

If deep intuitions are based on flexible knowledge, then to get that knowledge, you need to stretch out your inflexible knowledge so it can bend and adapt to other situations. I cover quite a few methods for doing this in Learning on Steroids, but here I just want to cover one: the QAT method.

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The QAT Method

This method has three parts: Question, Analogy and Test. Essentially, it is a method for flexing the brittle knowledge you have on particular topics, until you can build robust intuitions about the ideas that never require memorizing.

Step One: Question

The first step is to take the topic or idea you want to understand more deeply and ask a question about it. Even better if these are questions drawn from actual assignments, quizzes or past tests, since then you’ll optimize your coverage for what will be tested later.

If you can’t get questions from a prior source (or the questions on future exams will be a different format) then make up your own question involving the topic. The question should be something you don’t currently understand about the idea, or an example to apply it in a different context.

The value of this step is that it’s supposed to probe out weak points in you understanding. It should reveal some of the brittleness in your current knowledge by asking “why?” and drawing blanks.

Here are some example questions you could ask:

• Why is there a negative sign in the Fourier analysis equation?
• How is DNA copied during mitosis?
• Why was Socrates executed?
• What are the necessary parts of a contract in common law?
• Why would the consequences of an act not be important for Kant’s morality?
• How can matrix operations give a least squares regression?
• Why is a 2×3 cell structure necessary for the Cook-Levin theorem of NP-completeness of SAT?
• Why does resistance go down when more resistors are added in parallel?

The questions should be more specific if you know more. That is, if a question is too easy, try asking a more specific one that you currently don’t know. Flexibility is relative, so what might be flexible knowledge for an intro calculus class, could be very inflexible for a PhD student.

Step Two: Analogy

Once you’ve come up with a question, now you need to answer it. But answering the question isn’t really enough. Often we can answer a question, but never develop an intuition for why it is the case.

I could solve a complicated set of math formulas, for example, and derive an answer to a question I have. But that process likely won’t yield an intuition. It’s buried beneath too much abstraction.

The key is to answer your question (by looking at the textbook, asking a professor, derivation, Feynman technique, etc.) and then try to come up with an insight for explaining your answer in an easier way.

Sometimes the best way to do this will be in the form of a picture or diagram. When I was trying to learn the different spaces associated with a set of linear equations, I tried to visualize what they were and what their counterparts were.

Other times, the best way to do this is to create an analogy. When I was learning about voltage, I asked myself the question of what it was analogous to in terms of gravity. The answer was height–higher voltage was like troughs of water being at a higher level, with resistors being pipes where water on higher levels flows to lower levels.

If those methods don’t work, you can always use multiplicity of examples to help you reason about deeper features of an idea. Walking through different possible cases helped me remember the elements of a contract when learning law.

The end product of this step should be not only that you understand an idea, but that you can get an “aha!” feeling that it appears somewhat obvious.

Step Three: Test

The final step is to test your analogy and see if it works beyond the small case that you derived it for. Is voltage really like height? Do the spaces in linear algebra really correspond to the mental image you’ve created? How would you handle a new example of a possible contract?

This final step helps you double check whether your insight is correct, and quite often, it allows you to generate a better, more exact insight.

If your question was from a problem on a test, try finding a different, similar problem, to test your intuition against. If your question was self-generated, look for examples that are markedly different from your original one.

Even if your analogy breaks down, it might not be a bad analogy. Some insights are imperfect, but the can still be useful. What matters more is knowing where your insights break down, so you don’t get into conceptual traps later on.

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Using the QAT method isn’t terribly fast, which may make you wonder why I’ve included it in a bootcamp on learning faster.

The reason is that it is much faster than the alternative. By deeply understanding a few core ideas, you can easily associate hundreds of related facts. Spending an hour or two to understand a deep equation is much better than memorizing it and hoping nobody will give you any tricky questions on the exam.

If you look at your learning over the course of your entire degree (or your entire life) then this method is lightning quick compared to the alternative. Because you’ll have built deep intuitions about ideas, they will stay with you longer and provide a foundation for anything else you learn that builds off of them.

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Day Three Homework Assignment

Now it’s your turn to use the QAT method to better understand something you’re trying to learn. Follow these steps:

1. Pick an idea you’re trying to learn.
2. Ask yourself a question about the idea (either from past exams or of your own creation).
3. Answer the question.
4. Explain why the answer is correct, using a simplifying analogy, visualization, diagram or example.
5. Test your simplifying insight on a different problem or question. Does it still hold?

Walk through these five steps and hit REPLY when you’re done with a one-sentence answer sharing the idea you learned from step #1 and the insight you generated in step #4.

Best,
-Scott