The Geometry of Ideas

A little post I almost didn't publish on a little idea I almost didn't explore.

This post is about a small idea. In general, more posts ought to be. Posts based on small ideas are building blocks; I like to think of them as literal blocks. An idea in my head is a sphere. It’s tough to build things out of spheres, and it’s tough to connect ideas that are just floating around in my head. As I write about the ideas, the blocks take shape. They become cubes or pyramids — shapes that are easier to join with others. In my experience, it’s only through writing or discussion that ideas are defined and take shape. Edges and vertices form on what was once a sphere, allowing for physical connections and a more straightforward composition of ideas.

A writer surrounded by shapes

Simple ideas have fewer edges and vertices, like a pyramid. Complex ideas have more, like a dodecahedron (I promise I won’t introduce any more shapes; I just needed one with many syllables and vertices to make my point). The small pyramidal ideas are easy to combine with others in various orientations. Pyramidal ideas can be turned upside down to connect with a whole set of other shapes representing a new world of thought. They add structure to an argument, just as they would add structure to a … structure. The big ideas, like their shapes, are impressive but take a lot of work to define. After all, to define a dodecahedron, you merely need to provide 20 points in 3D space. That’s not the type of idea very many of us can just sit down and conjure up.

I used to shy away from posts premised on small ideas, the pyramids and cubes. I assumed that for my writing to be interesting, it had to either have significant explanatory power or be small yet surprising. Lacking both of these qualities, my writing should at least be entertaining and exceptionally clever.

Not true. While I haven’t given up entirely on the clever part, I am starting to embrace writing thorough posts on small ideas. The magic comes with fully exploring something - like a metaphor for how small ideas take shape and connect - to provide a solid foundation for more extensive arguments in the future. There’s still a (big) part of me that resists tiny posts like this. It feels trivial. Who cares about little ideas and whether they’re pyramids or spheres? Why am I looking at a Wikipedia page on dodecahedrons before I’ve had my coffee?

I don’t have a good answer to these questions. And I rarely write “I don’t know” to answer a question. Instead, I’ve made the very hard choice not to care. This little post exploring a little idea has served me. For example:

• Now, at work, I can refer to technical ideas as spheres, pyramids, and dodecahedrons, which will be a refreshing way for folks to wonder WTF I’m talking about.

• I can go through my backlog of drafts to identify the little thoughts worth finding the true shape of and the bigger ideas those shapes underpin. I can start now: I wonder how this geometry of ideas concept maps onto one of my favorite technical posts, Lucca Rossi’s thoughts on writing and connecting ideas for Refactoring:

  Introducing Brian • My Personal Workspace 🧠

• Also, look! I wrote a thing and published it. Which is a win unto itself.

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I wish you could see the real vague sphere of an idea this post used to be. It initially didn’t have any of the shapes stuff. I sat down to write something resembling satire of a little idea that was essentially about itself. Then I got frustrated trying to come up with a witty self-referencing definition of what a “little idea” is and bailed. And look where we are now! This is so much better. It's become a bonafide pyramid of a post that you’ll surely see in the structure of future essays!