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14 min 25 sec
Available in:English

The Great Mental Models Volume 3: Systems and Mathematics

Shows how seven ideas from systems thinking and mathematics, from feedback loops and bottlenecks to sampling and compounding, widen the way you see problems, so you fix them sooner and prevent many before they start.

Table of Content

If you only think about problems with the tools of your own field, you will keep missing the ones that sit outside it. In The Great Mental Models Volume 3, Rhiannon Beaubien and Rosie Leizrowice of Farnam Street borrow a lesson from driving: a single windshield leaves blind spots, so you check every mirror. A psychologist tends to see incentives, an engineer sees systems, a biologist sees evolution, and each view misses what the others would catch.

This volume adds models from two disciplines, systems and mathematics, and turns them into everyday tools. The case running through every chapter is simple. Each new model lets you look at the same problem from a fresh angle, so you can fix trouble faster and often prevent it entirely.

The examples range from a museum director who emptied the Louvre before the war to a drug company that tested every chemical it could find. Each model ends with a question you can put to your own work or life this week.

A walk around the local ponds can convince you of something false about every swan alive. The same trap hides inside anecdotes, surveys and first impressions, and two simple checks decide whether a sample deserves your trust.

Ask a crowd for a random number and a magician can guess the answer. That predictability reveals how the mind fights chance, and why sitting at a desk waiting for ideas may be the least creative habit.

A thermostat and the cycle of poverty run on the same principle, pushed in opposite directions. Knowing which kind of loop you are in changes how you learn, and which signals you should ignore.

Russia’s builders solved one delay after another on the world’s longest railway and still had to rebuild it several times. A German doctor facing wartime hunger shows the other side of the same problem.

Many in Paris believed the Nazis would never touch its museums. One official refused to take that bet, and the cost of his caution looks very different once you know how the war ended.

Thousands of failed tests and no breakthrough in sight would make most teams change course. A German drug company stayed with its method instead, and the reason it worked applies to problems with no obvious answer.

A wildlife reporter waist-deep in Tanzanian mud got through it by drawing on a moment from high school. Her story, and a thousand years of one culture’s schooling, show what lies behind most lasting success.

The thread through this volume is that the worst problems are often the ones you never see forming. Russia’s railway was rebuilt several times because each fix ignored the next delay down the line. Jaujard saved the Louvre’s collection by acting on a danger nobody could prove. Both sides were capable people. What separated them was how many angles they were willing to look from.

The authors argue that systems and mathematics, abstract as they sound, explain much of daily life, and that the two fields feed each other the way the models do. Reading about them is only a start. Their advice is to pick one model each week, look at your life through it and write down whatever seems new or different. One week you might ask which feedback you actually trust. Another, you might count how many cases your firmest opinions rest on, or find the plan that matters most to you and ask where its buffer is.

None of this changes the road you drive. It changes how much of that road stays hidden.

About this book

What is this book about?

Most people think with the tools their own field handed them. A psychologist sees incentives, an engineer sees systems, a biologist sees evolution, and each lens leaves blind spots. Rhiannon Beaubien and Rosie Leizrowice argue that the fix is to collect more models, the way a driver checks every mirror before changing lanes. This third volume of The Great Mental Models takes its tools from systems thinking and mathematics. The authors cover feedback loops, bottlenecks, margins of safety, algorithms, randomness, compounding and sampling, and show how each one applies to ordinary decisions. Their examples include the troubled building of the Trans-Siberian Railway, a museum director who emptied the Louvre ahead of a feared Nazi invasion, Bayer's long search for the first broad-spectrum antibiotic and a mentalist who found that most people asked for a random number between one and five choose three. Readers get a set of practical questions to run on their own work and life: which feedback deserves trust, where a system will jam, how much buffer a plan needs and whether a conclusion rests on a sample worth believing. The authors close with a simple weekly habit for turning the models into instinct.

Book Information

Rating:

Genre:

Personal Development

Topics:

Decision-Making, Mental Models, Risk Management

Publisher:

Penguin Random House

Language:

English

Narrator:

Julia

First published:

October 15, 2024

Pages:

384

Length:

14 min 25 sec

Get the book:

Amazon

Who it's for

  • Professionals wanting new angles

    Professionals who rely on the habits of their own field and want new angles on stubborn problems.

  • Running projects that stall

    Founders and managers whose projects keep stalling, breaking or running without a safety buffer.

  • Students and lifelong learners

    Students and lifelong learners who want systems and math ideas they can use in everyday decisions.

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About the Author

Rhiannon Beaubien

Rhiannon Beaubien researches and writes for Farnam Street, with a background that spans science and philosophy. With Shane Parrish she co-authors The Great Mental Models series, which aims to help readers from all backgrounds build better thinking habits. Rosie Leizrowice also writes for Farnam Street, producing articles and content for its members, and lives and works in Berlin. Together they turn ideas from systems thinking and mathematics into practical tools for thinking.

Ratings & Reviews

Ratings at a glance

4.3

Overall score based on 328 ratings.

What people think

Listeners find this installment to be a functional and eye-opening handbook that successfully breaks down complicated mathematical principles and systems thinking into understandable "lenses" for making better choices. Additionally, they value the practical illustrations and relaxed terminology that make the advice relevant to both career and home life, with one listener remarking that the tip to master a single model per week is exceptionally smart. They also emphasize the book's merit as a lifelong learning instrument, complimenting its reliable sources and its capacity to educate readers on how to think rather than just what to think. Furthermore, listeners consider the material highly adaptable for all life phases, while one reviewer notes how the work helps sort through excessive information to resolve routine obstacles.

Top reviews

Hassan

Finally got around to finishing the third installment, and it doesn't disappoint if you're a fan of the Farnam Street approach. The way it tackles systems thinking makes incredibly abstract concepts feel like tools you can actually pick up and use tomorrow. I found the "lenses" metaphor particularly helpful for my work in project management where everything is interconnected. It doesn't just give you facts; it teaches you a specific way to filter the noise of the world. While some might find the definitions a bit informal, I think that's exactly what makes it so accessible for a broad audience. It’s an essential addition to any lifelong learner's library.

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Pita

The chapter on mathematical models was probably the highlight for me, though I’ll admit some of the applications felt a bit stretched compared to my college stats classes. Despite that slight deviation, the book remains an enlightening guide for anyone trying to improve their decision-making frameworks. It’s beautifully written and clearly well-researched with strong sources throughout. Truth is, I preferred this volume over the second one because the focus on systems feels more relevant to my current stage of life. It’s a solid addition to the series that continues Charlie Munger’s legacy of multi-disciplinary thinking. I highly recommend it for the clarity it provides.

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Weera

As someone who has followed the FS podcast for years, I was eager to see how they’d handle the more technical aspects of mental models. This volume is essentially a masterclass in distilling huge, complex ideas into manageable frameworks for daily life. Each model is presented with clear real-life examples that keep the material from feeling like a dry textbook. Personally, the suggestion to focus on just one model per week has been a total game-changer for my self-reflection routine. It prevents information overload while building a genuine latticework of knowledge over time. Truly an indispensable tool for navigating modern life with a bit more wisdom.

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Wit

Wow. It’s rare to find a book that actually teaches you how to think rather than just telling you what to think about. Volume 3 hits that sweet spot by focusing on systems and math in a way that feels applicable to both your professional career and your personal relationships. The authors have a knack for taking obscure facts and turning them into "aha" moments that stick with you long after you close the cover. Not gonna lie, I’ve already started rereading certain sections to make sure I’ve fully internalized the concepts. It’s a dense read in terms of value, but the prose makes it go by quickly.

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Taw

This book is one of the better ones I’ve read this year because of its sheer versatility. Whether you’re trying to navigate office politics or solve a complex engineering problem, the systems thinking models provide a clear path forward. I love the composition of each chapter—the way they blend trivia with actionable wisdom is just brilliant. It helps you manage the massive amount of information we’re bombarded with daily by giving you specific filters to use. It’s an incredible exercise in cognitive discipline. I’d recommend this to anyone, especially young professionals just starting to navigate the messy realities of the business world.

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Pim

Ever wonder why some people seem to make better decisions consistently while others struggle with the same recurring problems? This volume explains why by looking at the underlying structures of the world through a mathematical and systemic lens. The authors have done a fantastic job of making these "obscure" concepts feel relevant to the average person's day-to-day challenges. I particularly appreciated the focus on strong sources and the way they honor the original intent of these models. It's a fun, educational read that effectively simplifies the complex without being condescending to the reader. It is a must-have for your permanent shelf.

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Omar

After hearing Shane Parrish talk about these concepts for so long, it's great to have them organized in such a high-quality format. The book excels at providing informal definitions that strip away the academic jargon, making things like feedback loops and power laws easy to grasp. I did feel like some of the real-life examples were a bit brief, leaving me wanting more depth on the historical context. However, the overall utility of the book as a decision-making guide is undeniable. It’s a versatile resource that I can see myself returning to at different stages of my life as my priorities shift.

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Sing

Look, if you're into the whole "latticework of mental models" idea, this is a must-buy, even if it has a few minor flaws. The transition from systems to math is a bit jarring at times, and the pacing feels slightly uneven across the different chapters. But the core value is there: it provides a practical framework for anyone who values well-considered decision-making. The real-life examples are well-chosen and help to anchor the more abstract ideas in reality. It’s a very solid read that reinforces the habit of thinking through multiple perspectives before jumping to any major conclusions. Definitely worth the time and investment.

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Prapaiwan

To be fair, this is a decent book, but I didn't find it quite as revolutionary as the first volume in the series. Some of the sections felt a bit like they were treading familiar ground if you’ve already read a lot of systems thinking literature. The math concepts were simplified to the point where they lost some of their original nuance, which might frustrate those with a technical background. That said, the writing style remains engaging and the "lenses" approach is still a very practical way to view the world. It’s a good primer for beginners, just not a deep dive for experts looking for new territory.

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Isabella

Not what I expected given the high praise for the previous entries in the series. Frankly, the content felt a bit superficial and lacked the rigorous analysis I was looking for in a book about mathematical mental models. It felt more like a collection of blog posts than a cohesive, deep-dive exploration of complex systems. The examples were fine, but they didn’t provide the "latticework" depth that Charlie Munger famously advocated for. If you’re brand new to these ideas, you might find some value here, but seasoned thinkers might find it a bit too elementary and light on actual substance for their needs.

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Questions about this book

Rhiannon Beaubien and Rosie Leizrowice argue that everyone thinks with a limited set of mental models, usually from their own field, and that this leaves blind spots. Their third volume adds models from systems thinking and mathematics. Each one offers a different way to look at the same problem, so readers can solve problems more effectively and prevent many of them before they start.

The book covers feedback loops, both balancing and reinforcing, along with bottlenecks, margins of safety and algorithms from systems thinking. From mathematics it covers randomness, compounding and sampling. Each comes with an example, such as the repeated rebuilding of the Trans-Siberian Railway, Bayer’s search for an antibiotic or the magician Banachek predicting that most people pick three when asked for a random number between one and five.

A margin of safety is the gap between what a system has to handle and what it can actually handle, a buffer for the unexpected. The authors’ main example is Jacques Jaujard, who directed the French National Museums in the Second World War. He emptied the Louvre before any invasion was certain, and the collection survived while the Nazis looted about five million artworks elsewhere.

The authors suggest choosing one mental model each week and viewing your life through it, writing down what looks new or different. In practice that can mean asking whether a pleasant signal predicts long-term results, treating the first bottleneck as a warning about later ones, adding a backup to high-stakes plans, or checking whether an opinion rests on a large and varied sample or a single anecdote.

It suits readers who want practical thinking tools rather than theory: managers dealing with projects that keep stalling, founders planning for risk, learners trying to improve faster through feedback, and anyone who forms opinions from a few stories. The ideas from systems and mathematics are explained through concrete cases, so no technical background is needed to use them.

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The Great Mental Models Volume 3

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