Thinking in models

When I want to understand something complicated, I don’t start by reading harder. I start by drawing.

A model is a deliberate simplification. You throw away almost everything about a thing and keep only the few parts that matter for the question you’re asking. That sounds like cheating. It’s actually the whole trick. The real thing has too many moving parts to hold in your head at once; a good model has exactly as many as you can reason about, and no more.

Take a black hole. The full description is general relativity — field equations most people, including me, can’t solve by hand. But there’s a model hiding inside the math that anyone can hold: the event horizon. Picture a boundary in space with one rule. Cross it going in, and no path leads back out, not even for light. That’s it. You don’t need tensor calculus to reason with that picture. You can ask real questions and get real answers. Why is a black hole black? Because light that crosses the horizon can’t return to your eye. What happens as you fall toward it? The paths back out get narrower until there are none. The model doesn’t replace the math — it makes the math worth learning, because now you know what it is describing.

Here’s the shape of what I mean:

The arrow in the middle is where all the work happens. Choosing what to discard is the hard part, and it’s a skill you build by doing it badly a few times first. Keep too much and the model is as confusing as the original. Keep too little and it lies to you. Every model is wrong in some corner, and knowing where yours breaks is part of using it honestly.

This is most of what this blog will be. I take something that feels too big to grasp — a piece of technology, a market dynamic, an idea from philosophy — and I look for the small picture hiding inside it. Sometimes I get it wrong and have to redraw. That’s fine. A wrong model you can see beats a correct one you can’t.

If you can draw it, you probably understand it. If you can’t, you probably don’t yet.