Learning Breadth-First

Forgoing Every Question Unanswered

My life's philosophy in one word: breadth. Breadth wins arguments, perpetuates learning,  carries conversations, supplies surprise,  enables agility,  increases connection-density of thoughts, and can be obtained in independent and immediate chunks.

Breadth enables and compounds. Depth isolates and narrows.

Information Digestion

Achilles* and the Shark are sitting on a park bench on a radiant day.

Achilles: Do you know why is the sky blue?
Shark: Great question! First, sunlight is actually made of all colors mixed and -
Achilles: Wait, if you mix all the colors you get bright white?
Shark: Yes. We perceive white light when photons of varying wavelengths bombard the receptors in our eyes and -
Achilles: Photons? What are those?
Shark: Little packets of light that are emitted by atoms and -
Achilles: Packets of light? I've never heard of them. What are they like?
Shark: Well, that's a tough question. There are particle, quantum mechanical, optical, electromagnetic, and many more interpretations of them and their behavior. Let's start with -
Achilles: This is why the sky is blue?
Shark: It is indeed! And if you keep listening you'll find the depths of science! Eventually.

In less than a minute Achilles gives up and changes the subject.

The next day, while relaxing with the Tortoise, he decides to ask the same question.

Achilles: Why is the sky blue?
Tortoise: The sky is made of stuff that makes all colors except blue disappear. Might you guess why grass is green?
Achilles: I'd guess because it's made of stuff that makes all colors disappear except green. Is that correct?
Tortoise: Precisely. That is why blood is red, carrots orange, lemons yellow, hamsters golden, and my shell green.
Achilles: So that explains the color of everything. That's pretty cool!
Tortoise: It's not actually true for purple, heh, but that's sideways of your question. I'm glad to answer if you'd enjoy more breadth to your new understanding.

Depth-First Drowning

The Shark  answered none of Achilles' questions and was interrupted in each attempt. The Tortoise, on the other hand, gave a response that empowered Achilles with intuition and the ability to correctly apply the new knowledge.

Given the Shark's answers it should be obvious that he has a deep understanding of Physics. Unfortunately, all of his answers are all depth-centric and try to answer the question based on the concepts of the lower abstraction (the true, derivable answer). This approach to teaching and learning is incredibly flawed; you have not yet learned the lower abstraction and so will attempt to digest it through yet another abstraction lower. Repeat this process and no understanding is attained at any level until each is firmly understood from the very bottom and the learner can reapply the knowledge back up to the top. In reality, this takes forever. One must concede and select a level at with to attain intuition before continuing onward.

In depth-first learning the first question takes the longest to answer.


Recall the Tortoise's answer:

"The sky is made of stuff that makes all colors except blue disappear."

To any learned person this answer should look terrible and sounds childish or perhaps, even ignorant.

  • Why say "the sky is made of stuff" instead of "the atoms in the sky" or simply "the sky" and not distinguish it from its components?
  • Why "all colors except blue disappear" instead of mentioning absorption, scattering, or the source of the colors themselves?
  • Why is "The sky scatters blue light" not just as good, if not a better, answer?

The answer: assumptions.

Each of the above questions try to slip extra words and concepts into the answer, burying the assumption that the questioner knows them. The Tortoise's answer could understood by a child, and I can tell you, from experience, that I have had the Tortoise's conversation with children and they can indeed immediately tell you why grass is green, and without hesitation. I wonder, by chatting with the Shark, how long it would take for a child to have any understanding of why the grass is green. The answer is easy: not until college, or for most people, never.

The argumentative reader may interject, "what if the listener already knows what atoms and scattering are?" Well, a person familiar with atoms and the scattering of light does not ask why the sky is blue, and if he or she does, then clearly atoms and scattering are actually not understood. Though, with the depth-based approach to learning it is quite possible for someone to have some understanding of atoms and scattering and have lost all context of the high-level implications.

What kind of person asks the question why the sky is blue? What might he or she already know? What is the context to the question? And most importantly what will be done with the answer? 

Context trumps assumptions. Context is breadth.

Per-Level Intuition

Looking at Achilles and the Shark it is apparent that every answer is just a waste of time. The conversation quickly dives to the deepest depths of human knowledge with every fragment of understanding thrown out along the way.

For any knowledge-driven dive there are three possibilities:

  • The interrogator gives up
  • The dive hits bottom
  • A forced-stop occurs at a particular depth

The first is the most common and the reason why most conversations beginning with "Why" go unanswered - the answer is simply too complex, meaning full of assumptions and vacuous in context. The second possibility is insane. If the precursor to learning were understanding the lowest known abstraction (currently the standard model of physics) then it can be expected that no one will ever get anywhere. Try to teach a child quantum mechanics before allowing the chance to play with mirrors. It will not work.

That leaves the third possibility, stopping at a particular depth. Choose a level of abstraction and accept it as the basis of everything. But then, why not start at the highest level possible? Learn the implications and intuitions of the highest level of abstraction and then carve downward. This is one way in which current computer science education is a complete failure. Almost always it begins at the very bottom.

Intuition alone is not enough. If you tell someone "the sky makes every color other than blue disappear," the obvious response is that such a statement is the least intuitive idea ever, which is to be expected. If it were intuitive then no one would ever ask about it in the first place!

Intuition comes after that statement, when the inquirer treats it as fact. Given that it is true, via intellectual trust, what more can be ascertained about the world? The dialog above shows that statement providing a sufficient basis for guessing the cause of the color of all objects. The true win is that the conclusion is false. It fails to explain the cause of the color purple, but taking the over-reaching generalization is the first step to improving approximated understanding, instead of forcing the whole picture up front. And now, if anything, your curiosity is sparked to understand why your intuition failed and what is unique about purple.  

When the learner has enough context and breadth of understanding, the words "absorb" and "scatter" will come for free. There will come a point where there is enough intuition on the behavior of light to hear the definition of scattering and accept it simply as a name for a concept already known. That is breadth.

A Breadth-ful Life

How often have you found yourself in a conversation where you feel you have nothing to contribute and you are completely unable to comprehend? Where is your breadth? Where is your ability to pull the conversation, or steer it toward your context and away from their assumptions?

Breadth, and the ability to wield it, will allow you to enter any conversation and the more conversations you can enter, the deeper into each you can go. Breadth is the compounding force of learning. It will allow you to draw patterns across broad areas, helping to win arguments or contribute an idea. You will find yourself often surprised when a new connection forms between two apparent disparate ideas. Where is the surprise in depth? The surprise is at the top and to the sides, where the world appears to be a puzzle where you have to play the game to fit them all together, instead of carving one single piece into the perfect shape.

The more context you have the more free you will be. Agility at your job, potential at another, stories at Christmas, or arguments over coffee. Don't be the depth-er waiting for your moment to come where you inject a rush of depth and knowledge. Be the breadth-er balancing across the entire conversation, learning at some parts and dancing through the rest.

Go to the breadth and soak in it. Enter every conversation with as much context as you can bring, from every subject imaginable. Apply your imagination and the ways in which a raven is like a writing desk becomes infinite.

Breadth-First, Depth-Eventually

A person who grasps physics, chemistry, biology, mathematics, engineering, linguistics, psychology, design, religion, history, literature, and so forth is capable of seeing many more patterns and learning more quickly by integrating information into many already knowns. This increases the intuition gained per new concept. Breadth is implicit context supplied to every new idea. School will not provide you with this, no matter how much it promises. You will gain it from reading, exploring, conversing, teaching, guessing, and from every corner of life and your own creativity.

Go to a random Wikipedia page. How much of the first paragraph do you already understand? How many pages do you have to open, all of which reference one another, to comprehend it? Do you know enough to flatly accept all of the contents and have some form of intuition?

If this sounds difficult and you think it's best to scroll down the page and read the whole thing, then enjoy the depths to which you are diving; the farther down you go, the less of us you'll find. What's the rush to reach depth? You have clearly already forgotten all of the first paragraph. Are you diving or sinking? They both look the same.

Depth should be accidental. When you have enough breadth on a topic you will begin to learn words for the intuitions you already have. Then you will grow breadth, context, and intuition surrounding those words. Eventually all of that new understanding will be identified with more words and you will continue the iteration, learning forever. That is depth as the overflow of breadth, a pain-free route to it. Depth should be free.

Breadth is what you should be fighting for. Eventually you really can and will know everything, because you'll be around people who collectively understand it all and you'll have just enough breadth to always join in the conversation and get just a little more. A breadth-ful conversation will plant the seeds of the depth of the universe. Jump in a conversation. I'll see you there.

"Achilles and the Tortoise" is a reference to Zeno's paradox, the idea that if there are an infinite number of locations between here and there, how can one ever get there?

I'd argue: through breadth.