The Formula to Understand Anything

 

If you'd like to know what it feels like to bang your head on concrete, read a technical paper. Random math symbols, archaic jargon, dry prose, all mixed together, is the perfect cocktail of frustration.

As Elon Musk says, “It is important to view knowledge as sort of a semantic tree — make sure you understand the fundamental principles, ie the trunk and big branches, before you get into the leaves/details or there is nothing for them to hang on to.”

After sipping the cocktail of frustration for many years, I've concocted a sweet recipe for building this semantic tree in the form of questions. I’ve used this formula to self-teach myself 12 skills in 12 months, get 7 job offers during the pandemic, build ML systems, etc:

TLDR:

To build the tree trunk:

  1. What’s the intuition, in a single line?

  2. What’s the intuition, as an analogy, example or diagram?

  3. What’s the plain english definition, in my own words?

  4. What terminology do I need to know?

  5. How does this concept work, step-by-step?

  6. What’s the technical definition, in my own words?

Building the Branches:

  1. What are the assumptions of this concept?

  2. What are the pros/cons of this concept?

  3. What are the pitfalls/edge cases?

  4. How does this compare/connect with what I already know?

  5. When/Where can I use this concept?

Phase 1: Building the Tree Trunk

What's the intuition, in a single line?

The gist of any concept can be explained in a single line. By constraining the intuition into a single line, this gives me a simple mental hook for remembering the information.

For example:

  • Linear Algebra gives you mini-spreadsheets for your math equations.

  • Caching (in computer science) is like a short-term storage unit for your stuff.

Think of this idea like a key that unlocks the entire idea. If you have this key, you can access this idea anytime you want.

What’s the intuition, as an analogy, example or diagram?

Once we've developed the key that unlocks the idea, we'll need to build the tree trunk. If the details are like branches, we need to build the trunk first. To build the base, we need to make the idea tangible in our minds. Typically, this can be done through:

  • Analogy: What is this idea similar to?

  • Concrete Example: What's an example of this idea in the real world?

  • Diagram: What does a diagram of this idea look like?

Examples of each can look like:

  • Analogy: Caching (in computer science) is like a short-term storage unit for your stuff.

  • Concrete Example:

  • Diagram:

What’s the plain english definition in your own words?

Building the intuition first, allows us to immediately attach the idea to something we know. Once we can grasp this, we can start to translate the actual definition into our own words.

For example:

  • Caching is act of storing information in short term memory, for later use.

What terminology do I need to know?

Every idea has its own jargon. Whenever we read something new, unfamiliar jargon is the culprit to confusion/lack of understanding. In order to fully grasp the concept, we need to understand the jargon behind it.

I typically, will attempt to understand the jargon, until it no longer blocks me from the main concept.

How does this concept work, step-by-step?

Once I've built the tree trunk, now, it's time to dissect the tree trunk. This is where I break down the method into step-by-step. If this is a technical technique, I'll break the technique into chronological steps. If this is a non-technical concept, I'll break down the idea into its own lifecycle.

Examples using Decision Tress in Machine Learning:

  1. Look at feature A + Target

  2. Run through each row and keeping track of the value of the feature against the Target

  3. Look at feature B + Target

  4. Repeat

  5. Now, look at the mixtures for each feature

  6. Use these mixtures to determine which feature is the most predictive. Features that are solely one type, should be the the first node. This mixture is called impurity.

  7. For the specific node, repeat the process, reduce the impurity and re-split

The key here is to not touch any math and only make sure I understand the logic.

What are the technical details?

Now that we've broken down the logic, this should give us enough fuel to make the math less archaic. This is the step where I try to either break down the math formula or attach each step of the math sequence to the logic outlined earlier.

Phase 2: Building the Branches

What are the assumptions?

All model are wrong, but some are useful.

I'd even extrapolate this to all concepts are wrong, but some are useful. Somewhat cynical way of seeing the world. However, my point here, is that every idea will over-simplify the world due to some assumptions, thus making it "wrong."

Therefore, we need to make sure that we understand what any idea assumes about the world. By clarifying this assumption, then we can know when to trust the idea.

Even something as basic as "there are 24 hours in a day." The assumption here, is that we're living on earth. If we live on Neptune, does this actually hold? No it doesn't.

What are the pros/cons of using this idea?

I love coming up with pros/cons for an idea because this forces me to steel-man the idea. In speech & debate, steelman-ing is essentially thinking through the strongest arguments for the opposition.

What I love about pros/cons, is that thinking through the cons forces you to steel-man the concept. This helps me know where this concept may not work well and where I should avoid using this concept.

What are the pitfalls or edge cases?

Each concept has its own idiosyncracy that makes it less useful. This helps us avoid situations where we accidentally use the wrong concept for its context.

How does this compare/connect with what I already know?

By thinking through how this concept compares/connects with what you know, this expands your body of knowledge. This also allows you to contrast the details of the concept with what you know to identify specific idiosyncracies behind the concept.

When/Where can I use this concept?

Too often, I see students who take courses fail to extrapolate what they learn to the real world. This question forces you to think about the exact context in which you can use this concept. Therefore, opening the path toward application.