The Pigeonhole Principle
Why perfect organization is not possible.
I stare at the blank index pages of my new commonplace book, my pen hovering uncertainly. More than two decades of digital design work, and I’m stumped by the simple task of organizing an analog notebook.
Come on, I thought to myself, The commonplace book has been in use for centuries. This has been solved before!
And it has.
- John Locke, credited with coming up with the idea of the commonplace book, indexed his alphabetically, with a list of two-letter starts that could be completed with keywords. “Ar” would become “Art”, for example, and have the numbers of the page(s) with material on the subject listed next to it. The problem is, without knowing what you might write down, you’d have to expect that to be a long index.
- Renaissance bookkeepers used marginal notes to cross reference entries as they were added. This method was called “zibaldone.” Not a standalone index, but a distributed one. More maintenance required, I thought, than I want to commit to. Similarly, the “adversaria” method divided every page in half; the focus content written on one side and cross references on the other.
- The linguist Walter Ripman was pragmatic. He suggested that one’s commonplace book be focused on a shorter set of pre-defined subjects. He began a new book by dividing its pages among his chosen subjects and committing to a table of contents. Too risky for me; how would I not break that right away?
I’m going to leave some empty pages at the beginning and build an index as the subjects come up. We’ll see how that goes. I suspect that even if I’m conservative in categorizing my notes, I’ll run out of space.
This is, after all, a basic mathematical problem. How do you allocate space for an uncounted quantity?
This puzzle has a name in mathematics: the pigeonhole principle. Put simply, if you have more items than containers, at least one container must hold multiple items. It seems obvious, but it can be helpful in estimating things at scale without seeking confirmation. A classic example is this: In a group of 13 people, at least two people must have been born in the same month because there are only 12 months in a year.
But the principle reveals something deeper about how we think and organize — both on paper and on screens. My unfilled commonplace book is a good example of this: are the future notes the pigeons and the categories the holes, or is it the other way around?
My daughter was recently considering the organization of her library — yes, she is very much my child — and almost immediately got tripped up on categories. She had lined up all her chapter books in one place, and her comic books in another. “But what about this one, Dad? It’s a comic book, but it also has chapters?” I thought about my commonplace book’s index pages, about every digital filing system I’ve ever abandoned, about the fundamental impossibility of perfect categorization. I said, “Well, you’ve got one book and two places to put it. Which will you choose?”
Technology-makers have been trying to solve this problem for the duration. From hierarchical file systems to tags to AI-powered search, we’ve argued over increasingly cumbersome taxonomies and built increasingly sophisticated tools to organize our information. It all works, until it doesn’t. At some point, we’ve all run into that dead end that we know shouldn’t exist. With all of our tech, why does finding something sometimes feel harder than ever?
Modern photo libraries demonstrate both the promise and limitations of AI categorization. When I search for “Sue,” my phone finds not just portraits of my daughter, but group shots where she’s barely visible in the background. Facial recognition is so good it’s a bit scary, and has actually become something more like “form recognition.” A search for “shelves” surfaces every stack our home contains, including the ones my daughter was fussing over in her room. I just searched for “Happy Winter,” the title of one of our family’s favorite children’s books, and found several pictures where it is both the subject and very much in the background prioritized before several other images of happy people I know in the snow. The system seems almost magical in its ability to understand semantic meaning. Sometimes.
Amidst all my iPhone snapshots, I also keep a large collection of reference images. This is where categorization, at least for me, is more important. I’m rarely looking for a particular subject — like the name of a person — and much more often looking for an idea, a form, a texture, or a material. When I search for something abstract — “organization” or “array” for example — I can never be certain that the images I’m served are all the images I have that could be considered in that category. I’ve proven this out by running the same search twice, and getting different results each time. The pigeonhole principle suggests I should get much more overlap than I do.
One solution to this is to maintain my reference image collection locally, on my own machine, and either put images in categorized folders or use metadata to assign groups of tags to my files. Then, I can just use spotlight to find them. I can hear so many of you, saying, Duh! As I said at the start, This has been solved before! But it hasn’t and never can be fully, finally solved because our needs for organization change with every new question. It’s like Tolstoy said about unhappiness — everyone’s version of it is unique.
In my design practice, I’ve watched clients grapple with this same challenge: how to structure information when you can’t predict how it will grow or change. The bookshelf and the commonplace book make the problem tactile. Allocate too little space for one category, and you’re guaranteed to dislike the later squeeze. Too much, and you’ll be aware of the gaps and waste. Digital space may seem infinite (it’s not, and given the right scale of database, hard limits on space come up pretty often), but our attention isn’t — we still need new ways to find what matters.
What’s fascinating is that though this limitation can be a challenge, it isn’t a bug — it’s a feature of how human thought works. Our ideas don’t naturally organize themselves into neat, predictable categories. They overlap, evolve, combine in unexpected ways. My other child, just three years old, demonstrates this often by creating imaginative combinations that defy intended categories: a stack of blocks becomes a dinosaur, a wheel becomes a plate, and a tangram tile becomes its dinner. I find these scenes on the floor of his room all the time — no pigeons, no holes, no problem.
The digital world promised to free us from physical constraints, to create infinitely flexible organization systems. Instead, we’ve often replicated the limitations of physical filing cabinets in digital form. We still think in the way Ripman believed we do — shorter lists of concepts that suit our present focus in which we are prone to putting everything. Call it a category, a tag, or a folder — it doesn’t matter. What matters is how predictably our ideas and information overflow their boundaries.
Perhaps we’re still approaching the problem backward. Instead of trying to predict and pre-allocate space — whether in notebooks or interfaces — what if we designed systems that embrace the unpredictable nature of human thought?
Some of the most interesting digital tools I’ve encountered lately take this approach. They allow ideas to exist in multiple places simultaneously, to form organic connections rather than forcing hierarchical organization. They recognize that the value of information often lies in unexpected associations rather than rigid categorization. Especially for writers, programs like these are abundant — Ulysses, Obsidian, etc.
I often think about this during my slow walks with our aging dog, watching how nature organizes itself. There are patterns, yes, but they’re emergent rather than imposed. Trees don’t file their leaves into folders. Networks of fungi beneath the soil share information in ways that defy our tidy organizational charts. Life follows its needs, which are ever changing.
The pigeonhole principle isn’t just a mathematical curiosity — it’s a reminder of the limitations of rigid categorization. Whether we’re organizing notebooks, designing interfaces, or structuring information, we need to leave room for the future, which we know will bring change and surprises. The most useful systems might be those that help us discover connections we didn’t anticipate rather than enforcing organizations we can’t maintain.
Back at my desk, I’ve made peace with my commonplace book’s imperfect index. It’s not lost on me that establishing an organizational principle to a pocketable book of fewer than 200 pages is borderline absurd. But, you might say the same thing about using a book like this at a time when AI-driven note-taking apps are abundant. But the limitations of this little bundle of paper are its primary feature. It forces a focus that the digital space does not. It is a container made to receive what I put in it, whereas the digital space treats me as the container for an infinite number of pigeons.
Perhaps the future of digital organization lies not in better boxes, but in breaking free of them altogether — in designing spaces that flex and grow with our ideas rather than trying to contain them. After all, as any mathematician (or kid with a library) can tell you: life has a way of overflowing our pigeonholes.
Written by Christopher Butler on
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