The Everyday Magic of Models

I have a couple posts in the queue that describe interesting models that have popped up in my head for various problems, situations, or relationships.

I'm having a lot of trouble finishing them. Models are complicated, and you're never quite sure if they're right or helpful or universal.

But I love the whole art and practice of modeling. That's what I want to talk about today.

What's a model anyway?

I think sometimes just associating the word model with something makes it feel complex and inaccessible.

It's really not. A model is just an analogy to help you think. It's a representation of something that's hard to think about—in a shape or size that's easier to think about. Think of an architect's model of a building, or a toy model of an airplane.

We model the world around us naturally every single day. We explain things to people by analogy, use a to-do list to represent real-life tasks, make long-term decisions by looking at a calendar representing time scales we can't truly perceive in the moment.

Here are some examples you might not even think of as models.

All of these are everyday things we use to make sense of something larger or more complex.

What makes a great model?

Great models help you think through something large that wouldn't otherwise fit in your head, and make sense of it. What does it take to do that?

First, a great model must be a working bridge between the thing it represents and its intended purpose. An abstract painting may represent a person, but it would not be a good model for a medical anatomy course. A piece of music may represent an emotion sublimely, but it may not be a great model for psychoanalysis. A model's quality is contextual, and the model itself needs to be true to the context.

Second, great models are close enough in level to jump the gap in understanding easily. A map of the solar system may be a model of location, but it's too distantly removed to be useful for driving to the supermarket. A model of the circulatory system may be technically accurate, but it's irrelevant for making nutritional decisions.

Finally, great models fit in your head. They're simple enough to think about all at once, even when the reality they describe may not be. The equations that describe gravity and Newton's three laws of motion are easy to see all at once, even as the emergent behavior from them is not. An org chart helps you understand a whole company in one sense, even though the reality is much more complex. A great model helps you zoom out and focus.

Basically, great models are appropriate, facile, and simple. Of course, there are fantastic models that break all these rules: scientific ones abound. But I continue to find this applies to the ones that help me think clearest and most productively.

My first encounter with models

I remember grappling with two models early on in my life, and they each stuck with me in different ways.

The first was poetry.

The complexities of human life and how we feel about being in one are hard things to pin down: they are the sum of so many small and large events, relationships, and feelings.

Poetry is a way to make a map of that often confounding human experience. It's a model of the human soul, and we can use it to understand ourselves better and navigate our lives.

My dad used to read us Robert Frost and other poets often, almost every week it seemed, and we'd always talk about it and try to figure out what the poem meant and why. We'd look at metaphors:

So was I once myself a swinger of birches.
And so I dream of going back to be.
It's when I'm weary of considerations,
And life is too much like a pathless wood
Where your face burns and tickles with the cobwebs
Broken across it, and one eye is weeping
From a twig's having lashed across it open.

— from “Birches,” by Robert Frost

I mean, the whole poem reads about playing in the woods as a kid. But you get to that point, and Frost compares carefree play with the realities of life, and you see that it's might be about something larger: the conflict between your inner playful child and the pains of life and love as they really are—and all in the same woods!

The metaphor is a sublime model that puts this perennial human conflict (something incredibly difficult to grasp in the abstract) into a picture that's easy to see: the difference between playing in the trees and being lost in those woods.

And we feel it, and we have a chance to understand it.

The best poems do this expertly. They identify a core analogy or metaphor, or just paint a picture of something seemingly insignificant and unrelated—and then whack you upside the head with how it's a mirror image of something else crucially important to the human experience.

One would do well to study poetry and literature to learn this incredibly useful skill.

Scientific models

The second kind of model I latched onto when I was young was scientific.

I used to love Microsoft Encarta, the amazing multimedia encyclopedia that came on 2 CD-ROMs and was packed full of fantastic curated content: illustrations, videos, and wonderful articles.

I soaked up the articles on science like a sponge, and the pictures were particularly interesting. I was able to understand more by looking at an illustration of a cell than I ever could reading about mitochondria and membranes. I explored both history and physics through animated examples of Newton's three laws. It was a blast.

One that stuck with me, maybe because of its mystifying difficulty to totally understand, was the wave-particle duality of matter.

The video accompanying the article was great: it laid out the basics, and then showed Young's double-slit experiment, right there from the top down: an emitter, the two slits with doors, and a detector.

They showed the experiment for marbles (particles), then water (waves), with the pretty easy to understand results. Then they showed it for electrons—and revealed the totally unexpected outcome.

“This is the question that makes quantum theory non-intuitive. It may not seem possible, but this is the way nature works.”

What a perfect example of using a model to reveal the mystery of something so abstract and complex—quantum theory—with something simple and comprehensible—rolling marbles down a ramp through a couple doors.

The idea that the world is actually not orderly or predictable in some cases was so powerful.

I still didn't totally get it, but I understood that it was  true, and one level of why it was true, which was pretty damn good for a twelve year old.

The art of abstraction

When I got to college, I started to get a glimpse of what made these models work.

In my second or third year computer science class, our professor was adamant: abstraction was the most important idea in computer science.

I didn't get it at all to begin with: he wasn't very good at teaching with models.

But looking back, it was the most important lesson I learned, not only for the practice of creating software programs, but for the idea of abstraction itself.

Abstraction is the art of jumping levels.

In computer science, it's driven the whole of the field and industry: computers started out as vacuum tubes, and programming was as much about configuring which wires connected to which circuits as it was considering the purpose and output of your program.

Computers got a lot easier when we jumped levels: we cleanly packaged up the part that was about connecting wires and managing vacuum tubes, and said "OK, we'll put that behind the curtain, and in front of the curtain will be this punch card reader." Now you could think about punch cards and order of commands, and programming became multiple times easier.

Then came assembly language, then Basic, and C, and JavaScript, and Python—and these "higher level" languages (called such because they're at a higher level of abstraction) cleanly separated the layers below them—abstracted them away, they call it—so the programmer never had to worry about them.

The multiplying power of models

This idea of abstraction never left my head: you can bundle up all the complexities of reality, and on top of it, place a model that describes some part of it cleanly.

Which is maybe the reason I love models the most: they are powerful.

Models are great levers for thinking. They reframe the world, reduce the work it takes to think about some part of it, and make it possible to make progress.

This is not some heady in-the-clouds practice of descriptive analysis, but instead a way to unblock your progress in a complex system or an unworkable corner.

If you're working at too detailed a level, going in circles in the maze of your actions, you can zoom out, see how they relate and what things look like from above, and find your way.

Models are really useful.

And from poetry, to science, to programming, they've been one of the most consistent ways humanity has made progress as a civilization. Each step, artfully jumping levels and collecting or abstracting something to make the next step easier; on the shoulders of giants.

Think about that the next time you use a map.