How Long Is the Coast of Britain?

That’s a strange title, I know. I’ll get to it.

But first, a brief personal story and an update on my book, The Stoic Systems Thinker.

If you want to skip ahead to the main essay, click here.

Last week, the University of Michigan won the college basketball national championship — its second overall and first since 1989.

I moved to Ann Arbor six years ago. Living in a college town with a major university’s sports program is fun. It’s like having your own set of pro sports teams to cheer on.

When things are going well — like when the football team won its national championship two years ago — the town buzzes. When they’re not — like when Sherrone Moore was dismissed as football coach several months ago — a fog settles in.

So it was nice to experience more of the buzz than the fog. This one felt particularly good because I’d been waiting so long to see it.

I grew up in New Jersey and attended the University of Maryland. But as a kid, I was a Michigan sports fan.

My first favorite team was the 1991 Michigan football team. One of my clearest early sports memories: a 10-year-old me watching Desmond Howard strike the Heisman pose against Ohio State. The cool helmets drew me in, and Howard closed the deal. I was a Michigan fan.

As football season ended, I started watching college basketball. Not knowing any other teams, I followed Michigan. As it happened, that was a good year to do it — it was the first year of the Fab Five.

The Fab Five were unlike anything college basketball had seen to that point. They started five freshmen, wore black socks and baggy shorts, and played the game in a way that was fun, loose, and magnetic for an impressionable kid.

I stayed up late in 1992 to watch them play a better, more experienced Duke in the championship game. Michigan kept things close in the first half, but Duke pulled away in the second for a 20-point win.

The next season, I was all-in. I followed every Michigan game I could — live when they were televised and via highlights on SportsCenter when they weren’t. They dominated college basketball all season. I expected them to win it all, and was devastated when Chris Webber called the infamous timeout that sealed their fate against North Carolina.

Over the years, I kept rooting for the Wolverines. I was lucky enough to see a national championship season when Maryland won the basketball title in 2002, but I never saw Michigan cut down the nets.

When Michigan made the championship game as underdogs in 2013 and again in 2018, I rooted for them, knowing they were long shots to win.

That’s what made this year’s team so unexpected and special. I don’t watch as many games during the season as I used to, but I always jump back in when the calendar turns to March. And this March was something else. This was the most dominant Michigan team I’ve seen since the Fab Five days — a joy to root for.

Since moving here, I've become embedded in the UM culture. Despite never attending the university, it feels like my home team — which is why this one felt extra good.

On to the book. The Stoic Systems Thinker is nearly done.

My manuscript has cleared copyediting and proofreading. The words are locked — I can’t add or change anything at this point. A few steps remain before it reaches the printer. I need to finalize early praise, select fonts, lock in the layout, and wrap up a handful of other tasks over the next few weeks. But the finish line is visible and rapidly approaching.

And today, I’m excited to share the final book cover with you.

I’m grateful to everyone who’s been following along. More details on the launch coming soon.

And now, on to today’s essay.

Here’s the thing about writing a book: you produce far more than you keep. Across multiple drafts, I cut more than 30,000 words from the manuscript.

Most of that material will never see the light of day. But some of those ideas didn’t fail on their merits. They just didn’t fit the book’s structure.

One of those ideas was about the fractal nature of knowledge.

In one of the book’s interludes, I wrote about how knowledge follows a Pareto distribution, with 80% of understanding in any topic coming from roughly 20% of the effort. What I love most is the idea that the remaining 20% has a fractal quality. 80% of that slice takes 20% of the effort. The next layer does the same. And the next. And so on, infinitely. I found the idea fascinating, but I couldn’t fit it naturally into the interlude, so I cut the section.

The concept, though, never left me. It’s been rattling around in my head for months.

In 2023, I read Nassim Taleb’s Incerto series. A name kept appearing in the margins of Taleb’s thinking: Benoit Mandelbrot. I’d heard the name before — the fractal guy — but I’d never dug in. So I circled it in my notebook, bought two of his books (The Fractalist and The (Mis)Behavior of Markets), and headed down the rabbit hole.

Mandelbrot was a mathematician best known for coining the term “fractal” to describe complex, self-similar shapes found throughout nature. His work has significantly influenced how I see the world.

After reading Mandelbrot, I started seeing fractals everywhere:

The idea was one of those lenses that, once you put it on, you can’t take off.

Then, while researching my book last year, I came across a paper Mandelbrot published in 1967: “How Long Is the Coast of Britain?”

The paper explores what’s known as the Infinite Coastline Paradox, and it opens with a seemingly straightforward question: how long is the coast of Britain?

The answer is anything but. If you measure the coastline with a 100-mile ruler from a satellite, you get one number. Switch to a 1-mile ruler, and suddenly you’re tracing every harbor and bay. The number gets larger. Use a foot-long ruler, and you’re following the contour of individual rocks. The length grows larger still. Use a micrometer, and you’re measuring grains of sand.

The shorter the ruler, the longer the coastline. The number never converges.

Mandelbrot revealed something fundamental about measurement: the answer depends entirely on the resolution of your lens. What appears finite from a distance becomes infinite up close.

The concept is perfectly Mandelbrot. A fractal insight about the fractal nature of things. And while the paper is about geography, the coastline paradox applies to far more than coastlines. What interests me most is how it applies to knowledge itself.

When we first encounter a new subject — poker, fitness, leadership, cooking, parenting — we see it from the satellite view, examining the landscape from orbit. From that altitude, the coastline of the topic looks smooth and manageable. We learn the basic rules, absorb the major frameworks, and memorize the key vocabulary. The broad strokes come quickly.

And it feels like understanding. The shape of the coastline is clear. You can trace it with your finger on a map. You think: I’ve got this.

I mentioned above that knowledge follows a Pareto distribution. In other words, roughly 80% of a subject is accessible with the first 20% of effort. Here’s how I visualized it in the book.

That initial burst of learning is real. You’re gaining ground quickly. And the acceleration is seductive because it feels like the whole journey will move at this pace.

Psychologists call this the Dunning-Kruger effect: the peak of confidence that arrives after you’ve learned just enough to feel competent, but before you can see what you’re missing and how long the road to mastery really is. The satellite view shows you a smooth coastline and lets you believe that’s all there is.

We’ve all sat on “Mount Stupid” at some point, believing we’re far more competent than we actually are.

I lived this early in my poker career. In 2003, the game was flooded with newcomers. Chris Moneymaker had won the World Series of Poker as an amateur, and an avalanche of amateurs followed him in. This niche game became a massive phenomenon overnight.

It didn’t take much work to develop winning strategies in the early days. Players could memorize good starting hands, learn basic position concepts, and play aggressively. This simple strategy was enough for a real edge at most tables. From orbit, the coastline of poker looked finite.

It’s important to note that there’s nothing wrong with stopping at the satellite view. We don’t have the time or energy to become experts in everything. In many ways, this is what generalists are: people who’ve mapped the satellite view and moved on, spreading across many domains. It’s a perfectly valid approach to learning.

Stopping at that level only becomes a problem when we assume we’ve grasped all the details from that satellite view. This is where the phrase “know enough to be dangerous” originates. People are dangerous when they think they know more than they do. A smooth coastline breeds overconfidence, and overconfidence leads to blind spots.

Over time, I zoomed in. And everything changed.

Looking back on my poker career, I can see that I didn’t accumulate knowledge the way a beginner expects, with a steady march toward some finish line of mastery.

Every concept I learned revealed ten more beneath it. Learning about position led to deep dives into bet sizing. Bet sizing opened up into range construction. Range construction raised questions about risk tolerance. Risk tolerance tied directly to bankroll management. And bankroll management circled back to psychological resilience and identity: who I am at the table when the math turns against me.

The coastline kept getting longer. I never fully reached the end — it’s always a point on the horizon.

Eventually, with enough work, you become an expert, standing on the beach with a micrometer. You see the inlets, the rocks, and the grains of sand that are invisible from space. That remaining 20% of any domain — the part Pareto says will cost 80% of the effort — unfolds endlessly the closer you get. And it unfolds fractally: 80% of that remaining knowledge takes 20% of the effort, and the next layer does the same, and the next. A fractal edge. Self-similar complexity at every scale.

Here’s the paradox Mandelbrot’s paper illuminates: the more you know, the more coastline you can see. The beginner’s confidence comes from a smooth map. The expert’s humility comes from standing close enough to see that the map was always an approximation.

Socrates may have been the first person to stand on the beach and report back honestly. “I know that I know nothing” reads like a riddle until you understand the fractal nature of knowledge. He was being precise. He had zoomed in far enough to see that the coastline of wisdom has no endpoint.

The ancient Greeks had a word for the opposite state: amathia. Often translated as ignorance, it captures something more specific: the state of thinking you know enough. The person viewing from the satellite has mistaken the smooth outline for the full picture. Amathia closes the door to further learning because the coastline already looks complete.

Physicist John Archibald Wheeler, the man who popularized the term “black hole,” captured this idea with a metaphor I keep returning to: “As our island of knowledge grows, so does the shore of our ignorance.”

Imagine your knowledge as an island in a vast ocean of the unknown. As you learn more, your island gets bigger. But a bigger island also means a longer coastline. More contact with the ocean. More awareness of what you don’t know.

Wheeler’s metaphor is powerful on its own. But Mandelbrot’s coastline paradox adds a dimension Wheeler didn’t account for.

The shore of our ignorance is a fractal edge. The closer you look, the more complex it becomes. Every bay of understanding reveals a dozen inlets you hadn’t noticed. Every answer generates questions that branch and branch again.

This is what happened to me after reading Mandelbrot. The lens I couldn’t take off. And once you see it, it shows up everywhere:

Health and fitness. The beginner thinks in terms of calories. Zoom in, and you find macronutrient balance, metabolic function, and the relationship between sleep and energy levels.

Leadership. The new leader thinks about communication and delegation. Zoom in, and you find incentive structures, organizational feedback loops, second-order effects of every decision, the invisible culture that shapes behavior more than any meeting ever could.

Parenting. The young parent thinks about loving their children and setting boundaries. Zoom in, and you find attachment theory, developmental psychology, the way your own childhood shaped your instincts, the feedback loops between your emotional regulation and your child's behavior.

The pattern repeats everywhere. The smooth coastline was always an illusion of distance. And the shore of ignorance — that fractal boundary between what you know and the vast ocean of what you don’t — grows more complex with every step forward.

Some people spend twenty years at the satellite view. Others reach the beach in five because they choose to look closer. The difference is intention.

Four principles I’ve found useful along the way:

Follow the question behind the question. When you think you understand something, ask what it depends on. Every answer reveals a new bay. The person who asks “why does this work?” after learning “how it works” is zooming in by one order of magnitude. In systems thinking terms, they’re moving from events to patterns to structures, each layer deeper than the last.

Seek out the uncomfortable edge. The fractal complexity lives at the boundary of your current competence. If everything in your domain feels smooth and known, you’ve stopped zooming in. Deliberately find the topics within your field that make you feel like a beginner again. That discomfort is the coastline revealing itself.

Let uncertainty be the signal. That persistent sense that there’s more to know is the most honest relationship you can have with any subject. The Stoics understood this. Epictetus taught that we cannot learn what we think we already know. This is the daily discipline of standing on the beach and looking at the ocean honestly.

Know when the satellite view is enough. You don’t have to zoom in on everything. Some domains deserve your micrometer. Most deserve a glance from orbit and nothing more. Wisdom lies in knowing the difference. If deeper knowledge in a domain won't meaningfully change your decisions or your life, the satellite view is probably the right altitude. Zooming in for its own sake is just another form of overconfidence: the belief that more information always equals more value. Sometimes the 80% is all you need, and the remaining 20% belongs to someone else’s coastline.

Wisdom has never been about reaching the end. It’s about having the humility to go deeper into the coastlines that matter and accept the satellite view for everything else.

The coastline of Britain hasn’t gotten any shorter since 1967. Better tools have only revealed more complexity. The same is true for every domain worth caring about: your career, your health, your relationships, the way you think.

I read Jorge Luis Borges’s Labyrinths recently, and his short story “The Library of Babel” has been stirring in my head as I’ve worked on this piece. In it, Borges imagines an infinite library containing every possible book, every combination of characters that could ever be written. All knowledge exists within it. And yet the librarians are driven to madness, because the Library is infinite and they are finite. They wander through an endless series of hexagonal rooms, searching for meaning, unable ever to find it.

That’s the coastline paradox from the inside — what it feels like to stand on the fractal shore.

Since reading Mandelbrot, I no longer expect subjects to resolve into neat, finite shapes. I now welcome the moment when the smooth coastline breaks apart into bays and harbors and grains of sand. That moment used to feel like a setback. Now it feels like progress.

The goal is never to reach the end of the coastline. There is no end. The goal is to keep zooming in and to find peace in the fact that the closer you look, the more there is to see.

Mandelbrot measured the coast of Britain and found infinity. The same infinity lives inside every subject you care about. The only question is whether you’re willing to pick up a smaller ruler.

I’ll be back in your inboxes later this month with more updates on the book.

All the best,
-Michael