Puzzle Theory
Summer 2024
Lately I’ve rekindled a love of jigsaw puzzles I first developed in childhood. My wife and I bought a David Bowie puzzle shortly after our beloved dog Chewie passed away last January. We also got a puzzle as a gift from some friends a bit before that. This year, being a mature, middle-aged man, my wife bought me a He-Man puzzle for an early birthday present. Just about everything I love to do has a “puzzle” element to it; there’s a way that putting together puzzles makes your brain work that really appeals to me and that reflects in my other goals.
Like writing: I recently signed a contract for my second book (which I have already written between a third and half of). Writing, especially writing theory, is a lot like putting together a jigsaw puzzle. You have a lot of elements, a lot of pieces to fit together and try to make a coherent picture out of them. Except with theory there isn’t a picture on the box that tells you what it’s supposed to look like when you’re done. That’s what a “theory” is, a way to organize a large amount of factual information. It’s possible to have more than one theory that fits the facts, but the “better” theory in the world of science is the one that fits the most facts together, makes the fewest assumptions, and also carves out new space for new questions and areas of research.
I also “have a passion for statistics” which I guess is a weird thing to have a passion for. Statistics as a field is often misunderstood—people think math conveys some kind of otherworldly certainty, and when they learn in a field like statistics that there are a lot of uncertainties and educated guesswork going into it, there is often this sense of disillusionment, because people who don’t work with patterns regularly think there either “is” or “isn’t” rather than a gradient of (un)certainty and ever-present margin of error. So, when people learn statistics underpins most of scientific research they might imagine that science, too, is “mathematical therefore certain” and when they find out that’s not how it works, think maybe there’s something wrong with the project overall. I have these experiences from teaching students in a classroom as well as from watching how people approach, or ignore, critical thinking best practices on the internet.
Statistics is fundamentally about finding patterns in the noise, and it is applied in the world of science to keep us from fooling ourselves into thinking there is a pattern where there probably isn’t. A work of theory is going to combine hundreds of little “fact-finding missions” or things learned through careful scientific study of the world (in my case the social world). Each of those bits of factual information that are fitted together like the pieces of a jigsaw puzzle to form a theory come from careful and painstaking research which itself involves separating “signal”—a meaningful pattern or relationship—from “noise,” or random variation that may or may not look like a pattern. Humans use intelligence to find patterns, but we are also prone to find patterns that aren’t really there. I do it too, staring at walls or tile floors or clouds and finding images and shapes in them. Statistics and theory sharpen that intelligence to help ensure that the patterns we find are really there and that we’re not simply fooling ourselves.
Music is a lot like putting together a jigsaw puzzle too (and definitely overlaps with applied math). I have been composing music on my own on and off since 2000. YouTube calls my most recent work “progressive rock” or “post-punk” but I have never been fully comfortable any label (and get bored being pigeonholed in a genre). Figuring out where the guitars, bass, drums, keyboards, and vocals fit together is an ongoing challenge. Songs can take years to write. I spent some time recently recording new music and have been releasing back-catalog stuff on streaming. It’s been an eye-opening experience learning how the streaming culture and influencer economy work; and I just got a scholarly paper accepted for publication on the topic to date combined with my interest in theory (first try, without revisions—still shocked by that).
Putting together a puzzle is all about finding patterns. It’s of course easier, so goes the conventional wisdom, to find all the edge pieces first, because there are a lot fewer of them and a lot fewer possible matches between them; and they also carve out the space for putting the rest of the puzzle together. They’re like defining approach and parameters in building a statistical model or defining the topic of a book in the first chapter or building the basic skeletal structure of a song, to figure out the tempo and what key it’s in and about how long it's going to be. Every other piece goes within the confines of this rectangle.
Then there’s the process of piecing together the rest. Different puzzles have different kinds of shapes that fit together in different ways. Unlike writing theory or building statistical models or composing a song, there is a picture on the box that tells you what the puzzle is supposed to look like when it’s done. I notice that getting wrapped up in the puzzle, there is a constant change of perspective; sometimes I “step back” and can see something from afar that I can’t when I’m too close. Other times, I fit pieces together in one very specific area, noting the texture and the color in ways that the picture on the box never does full justice. Something that attracts me to sociology specifically and science in general—the ability to take multiple perspectives from “closer” and “further away,” at each point being able to see things that would not be clear from a different vantage point. It’s like seeing the social world from the window of an airplane versus participating in it from the ground with all its messiness. Big, faraway perspectives and up-close, in-person perspectives make it possible to see different aspects of society and social interaction.
The biggest problem I have with pattern-seeking is that it’s almost impossible for me to shut it off. And that leads to other problems. Just as a puzzle is flat, two-dimensional, a statistical model, even a really complicated one with dozens or hundreds of “dimensions” is a useful simplification of a chunk of reality. The social world is too complicated to put everything, or even a significant fraction of all the variables, into one model. Even social theory is different from theory in the natural sciences because there are no “grand unified theories of society,” because, again, there are just too many variables, too many different things going on at once at too many levels. People also don’t ever behave as predictably as, say, molecules or solutions (which are never as straightforward in practice as one might imagine either). Theory organizes facts, and acts as a lens for bringing certain things into focus at a particular place and time or around a specific topic. And music—there are only twelve notes in “western” classical music, but they can be assembled in such a vast number of ways it can be hard to make decisions about what goes in a song and what doesn’t. In fairness to youtube’s “progressive rock” label, many of my songs start out being over ten minutes long and most of the work is deciding what they do or don’t “need.” Because I am old and grumpy (for a musician anyway) and think most songs that are over five minutes long are self-indulgent. In fairness to the post-punk label I’ve become more and more interested in minimalism, creating simple interlocking parts and using repeating patterns (partly because I’m not a very skilled singer and have an unusually deep singing voice, so it’s useful to write the music around the vocals).
It gets worse. Finding a pattern is not the same as experiencing what it is like to be a part of a pattern. Puzzles are usually made of cardboard; and cardboard is made from trees which means a jigsaw puzzle is really made up of a complicated set of organic molecules. But if I tried to study my He-Man: Masters of the Universe puzzle at that level, say by putting the pieces one by one under an electron microscope, I would literally lose sight of what the puzzle was “for” and why I wanted to complete it. In the same way, human beings are made of matter and energy, but we are also the product of a vast array of unique and ongoing life experiences. Knowing I’m made up of organic molecules that are actually similar in some ways to the organic molecules that made up the trees used to create the cardboard for my puzzle is an interesting and oddly uplifting feeling. But it gets me no closer to knowing what it’s like to be a human experiencing putting together a puzzle (let alone what it’s like to be the unfortunate tree that gave its life in the creation of this puzzle).
There is a lesson there too that I have had to learn over the course of my life (and need to be reminded of at least occasionally): being alive is not just some problem to be solved by fitting together facts or finding patterns. Knowing how to separate signal from noise, how to find the patterns, allows us to get it wrong less often and helps us become healthier, wealthier, safer, and wiser, as individuals and as a species. Patterns help us make more rational decisions with the limited time we have as living beings. But they alone don’t tell us what life is for, or why it is meaningful; and they don’t free us from the messy and complicated world of politics, of having to figure out how to live together and maintain a flourishing society full of people with conflicting interests and ideas. There is a vast gap of ignorance between knowing how a human body works and knowing what it is like to experience the world as another human being. That requires something else that doesn’t just fit into a pattern or become a puzzle to solve: Empathy.
Photo credit: completed 500-piece He-Man puzzle and nearly finished 1,000-piece constellations/northern lights puzzle, August 2024. Next, on to a 3,000-piece Star Trek: The Next Generation puzzle. Sensing a pattern here...
