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The Great Mental Models #3
The Great Mental Models Volume 3: Systems and Mathematics
The much anticipated third installment in the Wall Street Journal Bestselling series 'The Great Mental Models'. The secret to better decision-making is learning things that won’t change. Mastering a small number of versatile concepts with broad applicability enables you to rapidly grasp new areas, identify patterns, and understand how the world works. Don’t waste your time on knowledge with an expiry date - focus on the fundamentals. In part one, you’ll learn mental models from systems, helping you see unexpected connections and avoid costly mistakes. You’ll discover how these concepts govern the behaviors and interactions in your life. In part two, you’ll learn mental models from mathematics that reveal logical patterns in the world. This isn’t your high school math class. Mastering The Great Mental Models helps you thrive in an uncertain world. The right cognitive tools prepare you for any type of challenge. From parenting to healthy eating, relationships to personal productivity, and from learning to product design, this book will give you new lenses for understanding life.
364 pages, Kindle Edition
Published September 12, 2021
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3494 people want to read
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Displaying 1 - 30 of 54 reviews
September 12, 2021
Each entry in these series is stronger than the last.
This is my favorite entry in the series so far.
This is my favorite entry in the series so far.
Read
March 5, 2022Integrating mental models from systems and mathematics can help you overcome blind spots in your thinking. Challenge your perspective on the world by reflecting on it through the lens of systems theory. Models from mathematics can also help you become more tolerant and enhance your creative capabilities. By integrating models from these disciplines as much as possible, you’ll be sure to sharpen your problem-solving and decision-making skills.
Actionable advice:
Put your mental models into practice.
The first step in learning is to expose yourself to new information. But if you want to benefit from the knowledge in any practical way, you also need to put the learned concepts to the test. Every week, pick one mental model, and start looking at your life in that context. What do you see? What appears new or different? Write down your observations. By taking the time to reflect on your experiences through each set of insights, you’ll be able to apply that wisdom more easily.
---
Construct reliable algorithms in your mind to improve your chance of success.
Let’s say someone asks you to press “enter” on your keyboard every minute, for eight hours a day. Doesn’t sound like a terribly exciting way to spend your time, does it? For most people, engaging in repetitive actions over and over again gets boring very quickly.
That’s why we codify machines to do tasks for us. To tell those machines what to do, like press a button every minute, we use one of the most important models in human civilization: the algorithm.
In fact, all systems – not just computers – need algorithms to function.
Here’s the key message: Construct reliable algorithms in your mind to improve your chance of success.
Algorithms are developed to produce a certain output in response to a given input. You can think of it as an if-then process that is consistently repeatable.
An algorithm can be simple, like a clear set of instructions for a recipe. You put the ingredients together, run them through a process, and, in the end, you get a cake. An algorithm can also be complicated, like a computer algorithm designed to predict future crime locations.
For the best chance of achieving a predictable outcome, all the parts of an algorithm need to be aligned toward the same goal. The question is, how do you know which inputs will result in the desired outputs?
Well, you can actually use “algorithmic thinking” to help you decide what inputs to feed into your system in the first place.
In the 1920s, Bayer, a German pharmaceutical company, exemplified the power of algorithmic thinking as it pursued a cure for major bacterial infections, including tuberculosis and E. coli. Until then, almost no antibacterial compounds had been discovered. So Bayer’s scientists decided they would test every single chemical compound against the most deadly bacteria.
During the research, thousands of mice died. But despite the negative results, the scientists at Bayer did not change their method. They continued to test every chemical, keeping careful records of each test. Finally, in 1932, the methodology paid off when Bayer created the world’s first broad-spectrum antibiotic.
This goes to show that as long as your algorithmic process is accurate, it will eventually produce results that will help you refine your inputs.
In other words, you don’t need to know the answers – you just need a good algorithm for finding them.
---
Expand your understanding of the world through the power of sampling.
Imagine you want to investigate the color of swan populations. If you go out to your neighborhood ponds to collect data, you might conclude that all swan populations are white. But if you were to expand your research sample and study a larger number of swans from across the country, you would discover that some are actually black.
When you want to get representative information about a population, you usually need to look at a sample – meaning a part of that population. But if that sample is not truly representative, you risk being misled.
Here’s the key message: Expand your understanding of the world through the power of sampling.
Sampling is a particularly common measure in scientific studies of people, especially statistics. In many societies, statistics often determine how resources are allocated. That’s what makes it so important for measures to be accurate.
Thinking about sample size shows how samples can counter some forms of bias. For example, if you move to a big city where you’re exposed to a large sample of diverse people, you may end up with fewer prejudices. Similarly, if you read books from across various disciplines, you may become more open-minded.
But gathering representative samples takes effort. In fact, sampling can reinforce bias if it’s done haphazardly.
The first factor to take into consideration is sample size. The higher the number of participants in a study, the lower the margin of error – and the more likely it is that the study accurately generalizes the whole population.
It’s important to acknowledge that one measurement isn’t enough. For example, most people tend to rely on anecdotes to get a sense of the world. But they forget that an anecdote is just a sample of one – so it can’t be a reliable representation.
In addition to being large, samples need to be random in order to be representative of a varied population. This means every subject within the population should have an equal chance of ending up in the sample. You can’t study the behavior of three-year-olds in California and then make universal deductions about children. Rather, you have to expand the variety of your sample.
The same applies in your personal life. Remember to scrutinize the quality of your samples, including your generalizations about the world. When your decisions affect others, ensure that you’re equipped with information that is truly representative of those people. This way, you’ll minimize risk and maximize reward.
Actionable advice:
Put your mental models into practice.
The first step in learning is to expose yourself to new information. But if you want to benefit from the knowledge in any practical way, you also need to put the learned concepts to the test. Every week, pick one mental model, and start looking at your life in that context. What do you see? What appears new or different? Write down your observations. By taking the time to reflect on your experiences through each set of insights, you’ll be able to apply that wisdom more easily.
---
Construct reliable algorithms in your mind to improve your chance of success.
Let’s say someone asks you to press “enter” on your keyboard every minute, for eight hours a day. Doesn’t sound like a terribly exciting way to spend your time, does it? For most people, engaging in repetitive actions over and over again gets boring very quickly.
That’s why we codify machines to do tasks for us. To tell those machines what to do, like press a button every minute, we use one of the most important models in human civilization: the algorithm.
In fact, all systems – not just computers – need algorithms to function.
Here’s the key message: Construct reliable algorithms in your mind to improve your chance of success.
Algorithms are developed to produce a certain output in response to a given input. You can think of it as an if-then process that is consistently repeatable.
An algorithm can be simple, like a clear set of instructions for a recipe. You put the ingredients together, run them through a process, and, in the end, you get a cake. An algorithm can also be complicated, like a computer algorithm designed to predict future crime locations.
For the best chance of achieving a predictable outcome, all the parts of an algorithm need to be aligned toward the same goal. The question is, how do you know which inputs will result in the desired outputs?
Well, you can actually use “algorithmic thinking” to help you decide what inputs to feed into your system in the first place.
In the 1920s, Bayer, a German pharmaceutical company, exemplified the power of algorithmic thinking as it pursued a cure for major bacterial infections, including tuberculosis and E. coli. Until then, almost no antibacterial compounds had been discovered. So Bayer’s scientists decided they would test every single chemical compound against the most deadly bacteria.
During the research, thousands of mice died. But despite the negative results, the scientists at Bayer did not change their method. They continued to test every chemical, keeping careful records of each test. Finally, in 1932, the methodology paid off when Bayer created the world’s first broad-spectrum antibiotic.
This goes to show that as long as your algorithmic process is accurate, it will eventually produce results that will help you refine your inputs.
In other words, you don’t need to know the answers – you just need a good algorithm for finding them.
---
Expand your understanding of the world through the power of sampling.
Imagine you want to investigate the color of swan populations. If you go out to your neighborhood ponds to collect data, you might conclude that all swan populations are white. But if you were to expand your research sample and study a larger number of swans from across the country, you would discover that some are actually black.
When you want to get representative information about a population, you usually need to look at a sample – meaning a part of that population. But if that sample is not truly representative, you risk being misled.
Here’s the key message: Expand your understanding of the world through the power of sampling.
Sampling is a particularly common measure in scientific studies of people, especially statistics. In many societies, statistics often determine how resources are allocated. That’s what makes it so important for measures to be accurate.
Thinking about sample size shows how samples can counter some forms of bias. For example, if you move to a big city where you’re exposed to a large sample of diverse people, you may end up with fewer prejudices. Similarly, if you read books from across various disciplines, you may become more open-minded.
But gathering representative samples takes effort. In fact, sampling can reinforce bias if it’s done haphazardly.
The first factor to take into consideration is sample size. The higher the number of participants in a study, the lower the margin of error – and the more likely it is that the study accurately generalizes the whole population.
It’s important to acknowledge that one measurement isn’t enough. For example, most people tend to rely on anecdotes to get a sense of the world. But they forget that an anecdote is just a sample of one – so it can’t be a reliable representation.
In addition to being large, samples need to be random in order to be representative of a varied population. This means every subject within the population should have an equal chance of ending up in the sample. You can’t study the behavior of three-year-olds in California and then make universal deductions about children. Rather, you have to expand the variety of your sample.
The same applies in your personal life. Remember to scrutinize the quality of your samples, including your generalizations about the world. When your decisions affect others, ensure that you’re equipped with information that is truly representative of those people. This way, you’ll minimize risk and maximize reward.
October 2, 2023
Originally published at myreadinglife.com.
I've been listening to the Knowledge Project podcast for a number of years now. It is put out by an organization called Farnam Street. As part of their mission they have published a series of books called The Great Mental Models. I've most recently read the third volume in the series. Each volume covers a few areas that it focuses on. For volume 3, these are systems and mathematics.
The book is divided into two section (systems and mathematics, naturally). Each chapter delves into a particular aspect with examples for how it is applied as a model. These are written in clear, easy-to-understand prose.
While I liked this volume, I feel like I didn't really learn much new. As a result, I don't rated as highly. But I highly recommend this volume and the previous two for building up a set of models for how to look at and interact with the world. These might be particularly helpful to teenagers.
My rating: 3/5
I've been listening to the Knowledge Project podcast for a number of years now. It is put out by an organization called Farnam Street. As part of their mission they have published a series of books called The Great Mental Models. I've most recently read the third volume in the series. Each volume covers a few areas that it focuses on. For volume 3, these are systems and mathematics.
The book is divided into two section (systems and mathematics, naturally). Each chapter delves into a particular aspect with examples for how it is applied as a model. These are written in clear, easy-to-understand prose.
While I liked this volume, I feel like I didn't really learn much new. As a result, I don't rated as highly. But I highly recommend this volume and the previous two for building up a set of models for how to look at and interact with the world. These might be particularly helpful to teenagers.
My rating: 3/5
December 6, 2024
5 para personas mentales. Creo que no sería tan útil para personas emocionales.
July 26, 2024
The great mental models part three
Systems
1. Feedback loops - two kinds balancing and reinforcing. Balancing is like your thermostat, it receives information on the temperature and adjust to meet the setting you set it too. Then reinforcing which amplify a process you can think of learning to ride a bike you fall you get back up try different things and keep improving until you become a champion. This system is everywhere from our legal system to economic system.
2. Equilibrium - systems are rarely static they continuously adjust to reach equilibrium, be ready to adjust and let your feelings guide you
3. Bottlenecks are the limiting factors sometimes you need to think of the bigger picture in the system as changing other parts of the system may only magnify the bottlenecks. Yet bottlenecks are not a constraint so they can be alleviated and can lead to innovation such as during ww2 the development of nylon and artificial rubber given the loss of trade/supply from Japan to the US. Constraints are like 24 hours in the day you can't change that. Be aware of bottlenecks of our own creation like if I had this then I could do that. Get to the root cause and find alternatives.
4. Scale - being larger magnifies changes in variables in the system as some things may not be able to grow at the same pace. Staying smaller may allow you to stay more nimble. Neither one is right or wrong just be aware of scale typically not being a linear system.
5. Margin of safety - preparation for the unknown is a margin of safety you might never need it but that's the point you never know
6. Churn - Replacing components of a system is an inevitable part of keeping a system healthy. New parts can improve functionality. When we use this model as a lens, we see that new people bring new ideas, and counterintuitively, some turnover allows us to maintain stability. Replacing what is worn out also gives us a chance to upgrade and expand our capabilities, creating new opportunities.
7. Algorithm - a clear set of rules that provide instruction on what to do. We can also conceptualize them as if–then processes that are useful because they can help us ignore variables that don’t matter and focus on requirements. Algorithms as a model suggest a way of thinking that explores what processes can be put in place to get us the results we want.
8. Critical mass - basically the tipping point when does everything change being aware of tipping points can help you understand catalyst for change - sometimes it takes generation like womens rights
9. Emergence - organization without an organizer another way to look at it is acknowledging the sum of the micro doesn't always translate to a replica in the macro new patterns/behaviours may emerge.
10. Irreductibility - make thing as simple as possible but no simpler - this is all about understanding that simplicity is a way to strip fluff and noise from a message like what is bare minimum to get the point across. This helps in being able to adjust and get to first principle thinking as well
11. The law of diminishing returns - everything reaches a point of diminishing returns that's why its important to consider change as the rewards from certain actions is reduced new methods are needed to increase output.
Mathematics
1. Distributions - try to understand what sort of distribution you are experiencing is it normal then you can think of constraints and likely outcomes or is it a power law where things keep magnifying
2. Compounding - keep this framework in mind as all returns in life come from compounding (experience, knowledge and relationship)
3. Sampling - samples are used to inform so many of our heuristics we need to be aware of what the sample represents just large size doesn't indicate proper sampling need to consider the diversity of the samples
4. Randomness - when stuck in a creative process add randomness to get unstuck because all of life is random so the more events we experience the more sources of inspiration we can draw on. Randomness as a model reminds us that sometimes our pattern-seeking, narrative-building tendencies can be unproductive. Using randomness as a tool can help us get a fresh perspective and lift us out of the ruts we have built. It also gives us an appreciation of the value that the unpredictable or the unexpected can sometimes have.
5. Regression to the mean - We all have an average. When luck is a factor, instead of trying to replicate an unusual success or giving up after an exceptional failure, we can instead try to find the mean and build from there.
6. Multiplying by zero - this is more about thinking what is the weak point in your system for example if you have a restaurant with all the best ambiance and service but have crap food then likely won’t survive that’s your zero same goes for your skills something might look like a zero but you just need to get it to a 1
7. Equivalence - People in similar situations facing similar incentives are likely to behave in similar ways. Being equal doesn’t mean being the same. Different inputs can produce identical results, and there is more than one way to solve most problems. Using equivalence as a lens helps us appreciate the richness of the solution space. We can better appreciate the efforts of others who took a different path and find a common language to share information and experiences.
8. Surface area - need to understand what the surface area of your system means for how it can scale or decay. An interesting passage that I can see parallels to gaming in “during the eighteenth and nineteenth centuries, well after the rise of public education, circus performers continued to educate their children themselves.” This resulted in a situation where “they didn’t just learn their skills, they lived them, an intuitive experience that translated into astonishing ability.”1 From very young ages, circus performers could accomplish the amazing feats presented in a circus show. However, this family system led to a problem. Circus acts became predictable. They may have required great athleticism, but they were always the same. As Wall describes, “Beholden to tradition, each generation mindlessly duplicated the work of the last,” creating an artistic bubble where “technical ability continued to rise, but the art as a whole stagnated, [and] a cheap uniformity ensued.”2 Eventually the circus became synonymous with nostalgia and directed its marketing at children because they were the only group to whom the circus was new and exciting. Overall ticket sales went down, and the circus was well on its way to becoming history. How did this decline happen? One of the reasons was that, as Wall explains, “the family system defined the circus for centuries. But while it provided the source for much of the circus’s strength and allure, it also had a fundamental flaw. Ruled by families, the circus was what physicists call a closed system. Although the troupes traveled widely, they remained almost totally isolated from the outside world.”3 The surface area of the circus community was small. The borders were not around individuals but the whole unit. Interactions with anyone outside the circus were kept to a minimum. Thus there were minimal opportunities for creative reactions to occur. They were able to get out of this challenge by the core of circus education becoming multidisciplinary effectively increasing the surface area to promote more creative reactions, increasing the pace of innovation. When you have a narrow knowledge set to draw on, it’s harder to come up with new ideas. Exposure to different disciplines sets up circus performers to be creative in the execution of their art. Increasing our own knowledge surface area is a solution when lack of creativity or fresh ideas is a problem.
9. Global and local maxima - can be used in different ways to help us make the changes we need for success. It encourages us not to see achieving our goals as a steady upward trajectory but as a path full of peaks and valleys. Understanding that sometimes we have to go down in order to climb even higher helps us make short-term sacrifices to play the long game. This model also offers insight on how to optimize to find our global maxima. It’s more powerful to make the big changes before we try to optimize the details.
Systems
1. Feedback loops - two kinds balancing and reinforcing. Balancing is like your thermostat, it receives information on the temperature and adjust to meet the setting you set it too. Then reinforcing which amplify a process you can think of learning to ride a bike you fall you get back up try different things and keep improving until you become a champion. This system is everywhere from our legal system to economic system.
2. Equilibrium - systems are rarely static they continuously adjust to reach equilibrium, be ready to adjust and let your feelings guide you
3. Bottlenecks are the limiting factors sometimes you need to think of the bigger picture in the system as changing other parts of the system may only magnify the bottlenecks. Yet bottlenecks are not a constraint so they can be alleviated and can lead to innovation such as during ww2 the development of nylon and artificial rubber given the loss of trade/supply from Japan to the US. Constraints are like 24 hours in the day you can't change that. Be aware of bottlenecks of our own creation like if I had this then I could do that. Get to the root cause and find alternatives.
4. Scale - being larger magnifies changes in variables in the system as some things may not be able to grow at the same pace. Staying smaller may allow you to stay more nimble. Neither one is right or wrong just be aware of scale typically not being a linear system.
5. Margin of safety - preparation for the unknown is a margin of safety you might never need it but that's the point you never know
6. Churn - Replacing components of a system is an inevitable part of keeping a system healthy. New parts can improve functionality. When we use this model as a lens, we see that new people bring new ideas, and counterintuitively, some turnover allows us to maintain stability. Replacing what is worn out also gives us a chance to upgrade and expand our capabilities, creating new opportunities.
7. Algorithm - a clear set of rules that provide instruction on what to do. We can also conceptualize them as if–then processes that are useful because they can help us ignore variables that don’t matter and focus on requirements. Algorithms as a model suggest a way of thinking that explores what processes can be put in place to get us the results we want.
8. Critical mass - basically the tipping point when does everything change being aware of tipping points can help you understand catalyst for change - sometimes it takes generation like womens rights
9. Emergence - organization without an organizer another way to look at it is acknowledging the sum of the micro doesn't always translate to a replica in the macro new patterns/behaviours may emerge.
10. Irreductibility - make thing as simple as possible but no simpler - this is all about understanding that simplicity is a way to strip fluff and noise from a message like what is bare minimum to get the point across. This helps in being able to adjust and get to first principle thinking as well
11. The law of diminishing returns - everything reaches a point of diminishing returns that's why its important to consider change as the rewards from certain actions is reduced new methods are needed to increase output.
Mathematics
1. Distributions - try to understand what sort of distribution you are experiencing is it normal then you can think of constraints and likely outcomes or is it a power law where things keep magnifying
2. Compounding - keep this framework in mind as all returns in life come from compounding (experience, knowledge and relationship)
3. Sampling - samples are used to inform so many of our heuristics we need to be aware of what the sample represents just large size doesn't indicate proper sampling need to consider the diversity of the samples
4. Randomness - when stuck in a creative process add randomness to get unstuck because all of life is random so the more events we experience the more sources of inspiration we can draw on. Randomness as a model reminds us that sometimes our pattern-seeking, narrative-building tendencies can be unproductive. Using randomness as a tool can help us get a fresh perspective and lift us out of the ruts we have built. It also gives us an appreciation of the value that the unpredictable or the unexpected can sometimes have.
5. Regression to the mean - We all have an average. When luck is a factor, instead of trying to replicate an unusual success or giving up after an exceptional failure, we can instead try to find the mean and build from there.
6. Multiplying by zero - this is more about thinking what is the weak point in your system for example if you have a restaurant with all the best ambiance and service but have crap food then likely won’t survive that’s your zero same goes for your skills something might look like a zero but you just need to get it to a 1
7. Equivalence - People in similar situations facing similar incentives are likely to behave in similar ways. Being equal doesn’t mean being the same. Different inputs can produce identical results, and there is more than one way to solve most problems. Using equivalence as a lens helps us appreciate the richness of the solution space. We can better appreciate the efforts of others who took a different path and find a common language to share information and experiences.
8. Surface area - need to understand what the surface area of your system means for how it can scale or decay. An interesting passage that I can see parallels to gaming in “during the eighteenth and nineteenth centuries, well after the rise of public education, circus performers continued to educate their children themselves.” This resulted in a situation where “they didn’t just learn their skills, they lived them, an intuitive experience that translated into astonishing ability.”1 From very young ages, circus performers could accomplish the amazing feats presented in a circus show. However, this family system led to a problem. Circus acts became predictable. They may have required great athleticism, but they were always the same. As Wall describes, “Beholden to tradition, each generation mindlessly duplicated the work of the last,” creating an artistic bubble where “technical ability continued to rise, but the art as a whole stagnated, [and] a cheap uniformity ensued.”2 Eventually the circus became synonymous with nostalgia and directed its marketing at children because they were the only group to whom the circus was new and exciting. Overall ticket sales went down, and the circus was well on its way to becoming history. How did this decline happen? One of the reasons was that, as Wall explains, “the family system defined the circus for centuries. But while it provided the source for much of the circus’s strength and allure, it also had a fundamental flaw. Ruled by families, the circus was what physicists call a closed system. Although the troupes traveled widely, they remained almost totally isolated from the outside world.”3 The surface area of the circus community was small. The borders were not around individuals but the whole unit. Interactions with anyone outside the circus were kept to a minimum. Thus there were minimal opportunities for creative reactions to occur. They were able to get out of this challenge by the core of circus education becoming multidisciplinary effectively increasing the surface area to promote more creative reactions, increasing the pace of innovation. When you have a narrow knowledge set to draw on, it’s harder to come up with new ideas. Exposure to different disciplines sets up circus performers to be creative in the execution of their art. Increasing our own knowledge surface area is a solution when lack of creativity or fresh ideas is a problem.
9. Global and local maxima - can be used in different ways to help us make the changes we need for success. It encourages us not to see achieving our goals as a steady upward trajectory but as a path full of peaks and valleys. Understanding that sometimes we have to go down in order to climb even higher helps us make short-term sacrifices to play the long game. This model also offers insight on how to optimize to find our global maxima. It’s more powerful to make the big changes before we try to optimize the details.
November 14, 2021
Mental models are a representation of how something works. The Great Mental Models series is meant to provide public models from various fields of discipline to help us make better decisions in our lives. Systems and maths provide a nice group of mental models for everyday life. Here are a few models from the book that really resonated with me.
1. Bottlenecks (the specific process of a workflow that limited that amount of output from an overall workflow)
2. Algorithms (clear set of rules that process inputs and produce expected results in a logical and repeatable way)
3. Critical Mass (an incremental point that leads to a drastic change in the system state—for the better or for the worse)
4. Law of Diminishing Returns (threshold where the effort and reward relationship becomes non-linear)
5. Compounding (daily reinvestment of resources can lead to large growth on a long time scale)
6. Surface Area (considering the number of dependencies or assumptions something has.)
I really enjoyed the wide practical use these models have to offer in the personal, professional, and spiritual aspects of my life.
my rating - overall Score: 4.0/5.0
- quality of writing (4/5)
- quality of the content (5/5)
- impact on my perspective (4/5)
- personal resonance (4/5)
- rereading potential (3/5)
1. Bottlenecks (the specific process of a workflow that limited that amount of output from an overall workflow)
2. Algorithms (clear set of rules that process inputs and produce expected results in a logical and repeatable way)
3. Critical Mass (an incremental point that leads to a drastic change in the system state—for the better or for the worse)
4. Law of Diminishing Returns (threshold where the effort and reward relationship becomes non-linear)
5. Compounding (daily reinvestment of resources can lead to large growth on a long time scale)
6. Surface Area (considering the number of dependencies or assumptions something has.)
I really enjoyed the wide practical use these models have to offer in the personal, professional, and spiritual aspects of my life.
my rating - overall Score: 4.0/5.0
- quality of writing (4/5)
- quality of the content (5/5)
- impact on my perspective (4/5)
- personal resonance (4/5)
- rereading potential (3/5)
December 29, 2021
As a fan of Farnam Street, and the first couple volumes of The Great Mental Models series, I was definitely looking forward to reading Volume 3. I have a degree in Mathematics, and it has been my favorite school subject for as long as I can remember. This started likely due to the fact that I was quick with my arithmetic and mental math skills in elementary school, and that progressed all the way to college courses I took on logic that has helped my way of thinking post-graduate. This book showcases mental models not only in mathematics, but also in systems, and it is a book, like the other volumes, that does a great job in explaining concepts without the repetitious problems of normal schooling. Following up this book, I am planning to take one model per week from all the volumes and focus on using it in my day-to-day activities to establish my own latticework of mental models, instead of only reading the concepts and moving on. This is a book that high school math teachers should read because some of the concepts, like compound interest, should be taught in schools as it is something that can help everyone in many avenues of life. Already looking forward to the next volume of The Great Mental Models series.
January 16, 2022
I love their presentation of the ideas once again just as in Vol. 1 & 2! But I can’t help it but notice how little of an effort was and is yet again put into teaching the applying of these models in reality! For me, I have decided the informing part is their job and the application part is my job! So I can’t hate them for paying too little attention to the application part of these models!
I definitely recommend this book to anyone out there who is looking to challenge and upgrade their own thinking built upon principles and models that stand the test of time and that best represent reality.
A 5 because I believe they excelled at doing their job of informing thoroughly! I am however struggling with the application part of the models! The good news is that I have a draft version of framework that I can further build on! The challenging part is that I am dependent on the framework itself. I have to write things out to think…and I have to navigate through the models in the framework to find which applies best in or to my x situation/context. The fact that the process itself is challenging is just another good news! Because I wouldn’t bother do all this otherwise!
Lastly, the last & final model: Global maxima and local maxima was my favorite model of this book!
I definitely recommend this book to anyone out there who is looking to challenge and upgrade their own thinking built upon principles and models that stand the test of time and that best represent reality.
A 5 because I believe they excelled at doing their job of informing thoroughly! I am however struggling with the application part of the models! The good news is that I have a draft version of framework that I can further build on! The challenging part is that I am dependent on the framework itself. I have to write things out to think…and I have to navigate through the models in the framework to find which applies best in or to my x situation/context. The fact that the process itself is challenging is just another good news! Because I wouldn’t bother do all this otherwise!
Lastly, the last & final model: Global maxima and local maxima was my favorite model of this book!
October 20, 2023
The third volume of the series explores the topics of mathematics and system thinking - the latter has been on my radar for quite some time (check out my review of Donella Meadows' Primer to System Thinking).
The concept of system thinking isn’t well known, nor taught at school, which gets me thinking, why not? Awareness of systems, their behaviours (like feedback loops or bottlenecks) and our ability to notice them in the real world help us with understanding the world around us. The book does a great job of explaining systems.
The second part of the book is dedicated to mathematics, where timeless aspects are presented to us using real-world situations. Distribution, compounding, sampling or randomness, among others, are presented using practical examples.
Using system thinking and mathematics helps us with understanding of the world and as a side effect it improves our decision making process.
As with previous volumes, I’m amazed by its quality both content-wise and looks-wise.
My Reviews of other volumes:
- Volume 1
- Volume 2
The concept of system thinking isn’t well known, nor taught at school, which gets me thinking, why not? Awareness of systems, their behaviours (like feedback loops or bottlenecks) and our ability to notice them in the real world help us with understanding the world around us. The book does a great job of explaining systems.
The second part of the book is dedicated to mathematics, where timeless aspects are presented to us using real-world situations. Distribution, compounding, sampling or randomness, among others, are presented using practical examples.
Using system thinking and mathematics helps us with understanding of the world and as a side effect it improves our decision making process.
As with previous volumes, I’m amazed by its quality both content-wise and looks-wise.
My Reviews of other volumes:
- Volume 1
- Volume 2
January 26, 2025
All right, third time is the charm, it was a bit better than the second one, it tried to circle back to the first book's style. Less historical examples (or just more useful) from fields I don't usually engage in separately, so it did show some new stuff here and there. It could be that it's easier to make mental models out of these concepts, as in they better apply to or align with real life (or business). Things like scale, bottlenecks, diminishing returns, margin of safety, these from systems. Or compounding, surface area, or randomness, from math. Overall this was easy/easier to digest than the second one and almost as good (but more specific because of the two featured disciplines) as the first one. It is dense, though, and still needs some extra mental power to unpack. They even tell you how they think it's the best way to use the knowledge gained through this book (pick one model every week and observe the world through that lens). Not sure if it works that way, but this book was definitely among the more interesting non-fiction I've listened to lately, but not a life-changer.
Currently reading
November 23, 2021"The more moving parts you have in something, the more possibilities there are."
1. FEEDBACK LOOPS
People are driven by incentives. We do certain behavior in order to gain something or avoid losing something.
A feedback loop is a stimulus creating a response which response is the initiator of the other stimulus, which in terms creates a loop. Think, conversation.
There are positive and negative feedback loops. A positive feedback loop amplifies the response with a stronger stimulus (e.g. anxiety going in viscious cycle). A negative feedback loop is two responses acting in turns in order to keep the stimulus steady (e,g. body temperature).
!!-In Prisoner's Dilemma, trust first (cooperate) and then mirror your opponent's last behavior. This sends the first feedback loop that you are willing to be trustworthy.
Complex systems often have many feedback loops, and it can be hard to appreciate how adjusting to feedback in one part of the system will affect the rest.
2. EQUILIBRIUM
3. BOTTLENECKS
!- A bottleneck is also the point that is most under strain. It can be the part that is most likely to break down or has the most impact if it does. In trying to improve the flow of your system, focusing on anything besides the bottleneck is a waste of time. You will just create more pressure on the bottleneck, further increasing how much it holds you back by generating more buildup.
If bottlenecks are unavoidable, we at least want them to be in a less disruptive place.
Liebig's law of the minimum refers to the idea that a plant's growth will be limited by the nutrient that is least available. Yield is thus constrained by resource limitation.
!- In the long run, bottlenecks can make us better off because they promote innovation.
4. SCALE
1. FEEDBACK LOOPS
People are driven by incentives. We do certain behavior in order to gain something or avoid losing something.
A feedback loop is a stimulus creating a response which response is the initiator of the other stimulus, which in terms creates a loop. Think, conversation.
There are positive and negative feedback loops. A positive feedback loop amplifies the response with a stronger stimulus (e.g. anxiety going in viscious cycle). A negative feedback loop is two responses acting in turns in order to keep the stimulus steady (e,g. body temperature).
!!-In Prisoner's Dilemma, trust first (cooperate) and then mirror your opponent's last behavior. This sends the first feedback loop that you are willing to be trustworthy.
Complex systems often have many feedback loops, and it can be hard to appreciate how adjusting to feedback in one part of the system will affect the rest.
2. EQUILIBRIUM
3. BOTTLENECKS
!- A bottleneck is also the point that is most under strain. It can be the part that is most likely to break down or has the most impact if it does. In trying to improve the flow of your system, focusing on anything besides the bottleneck is a waste of time. You will just create more pressure on the bottleneck, further increasing how much it holds you back by generating more buildup.
If bottlenecks are unavoidable, we at least want them to be in a less disruptive place.
Liebig's law of the minimum refers to the idea that a plant's growth will be limited by the nutrient that is least available. Yield is thus constrained by resource limitation.
!- In the long run, bottlenecks can make us better off because they promote innovation.
4. SCALE
July 16, 2025
Lên đỉnh local maxima r nhưng muốn nhắm tới global maxima thì bước tiếp theo chỉ có thể là lao dốc, chạm đáy, trước khi leo lên đỉnh một lần nữa.
Compounding: một khi đã làm điều tốt thì bước tiếp theo là phải stick với nó thật lâu để có được thành quả.
Sức khoẻ, tiền bạc, mối quan hệ. Chăm chút càng lâu thì lợi ích cuối cùng càng khổng lồ (như tiền bạc với lãi suất kép)
Đừng bỏ cuộc khi mọi thứ mới bắt đầu và không tiến triển mấy
Churn: số người rời khỏi cuộc đời ta là không tránh khỏi. Khách hàng của 1 cty tới một thời gian sẽ dừng với nhiều lý do và nó là chuyện bt.
Bottlenecks: overall performance lại phụ thuộc vào điểm yếu nhất, điểm nghẽn. Cải thiện điểm nghẽn sẽ giải phóng tất cả. (Thực ra sẽ có 1 điểm nghẽn khác và ta cần phải giải nó tiếp)
Compounding: một khi đã làm điều tốt thì bước tiếp theo là phải stick với nó thật lâu để có được thành quả.
Sức khoẻ, tiền bạc, mối quan hệ. Chăm chút càng lâu thì lợi ích cuối cùng càng khổng lồ (như tiền bạc với lãi suất kép)
Đừng bỏ cuộc khi mọi thứ mới bắt đầu và không tiến triển mấy
Churn: số người rời khỏi cuộc đời ta là không tránh khỏi. Khách hàng của 1 cty tới một thời gian sẽ dừng với nhiều lý do và nó là chuyện bt.
Bottlenecks: overall performance lại phụ thuộc vào điểm yếu nhất, điểm nghẽn. Cải thiện điểm nghẽn sẽ giải phóng tất cả. (Thực ra sẽ có 1 điểm nghẽn khác và ta cần phải giải nó tiếp)
February 9, 2024
This provide a number of thinking models that can be used as metaphors in thinking about life. The is mainly a book of reiteration as a lot of the material was familiar to me. It is a book I am going to revisit via passively listening to as an audio book until I internalize the models contained in this book and the books previously written. I religiously listen to the Farnam Street Podcast and I am amazed at Shane Parrish’s generosity in allowing authorship to fall to Beaubien. This is a text book for thinking about life.
March 17, 2025
Ну что же, в третьей части нам наконец-то рассказали, как использовать книжки.
Эта часть состоит из двух разделов:
- системное мышление - которое лучше было бы прочитать у Медоуз
- и математики - где рассказывают совсем не про математику
Главное здесь то, что все принципы начинают растягивать на жизнь. В качестве примера "умножить на ноль - если одна из частей системы не даёт выхлопа, то вся система даёт ноль". Да математика так работает, но в реальной жизни состояние нуля труднопредставимо.
Эта часть состоит из двух разделов:
- системное мышление - которое лучше было бы прочитать у Медоуз
- и математики - где рассказывают совсем не про математику
Главное здесь то, что все принципы начинают растягивать на жизнь. В качестве примера "умножить на ноль - если одна из частей системы не даёт выхлопа, то вся система даёт ноль". Да математика так работает, но в реальной жизни состояние нуля труднопредставимо.
January 15, 2022
The 3rd volume resonated with me almost as much as the first one.
If you're dealing with complex systems (and who does not these days!) - the models presented in this volume should be quite relevant for you.
This book series offers too much for a single pass, and as authors suggest in the end of each volume, the reader is expected to come back and revisit the models to build their own "latticework".
If you're dealing with complex systems (and who does not these days!) - the models presented in this volume should be quite relevant for you.
This book series offers too much for a single pass, and as authors suggest in the end of each volume, the reader is expected to come back and revisit the models to build their own "latticework".
March 5, 2022
Integrating mental models from systems and mathematics can help us overcome blind spots in our thinking. Challenge our perspective on the world by reflecting on it through the lens of systems theory. Models from mathematics can also help us become more tolerant and enhance our creative capabilities. By integrating models from these disciplines as much as possible, we‘ll be sure to sharpen our problem-solving and decision-making skills.
May 31, 2022
A continuation of the series, volume 3 looks at mental models in the area of systems and mathematics. Much like prior volumes in the series, each model is presented along with real-world examples of their application. This series continues to be required reading for anyone who's interested in the models by which the world operates. Reading these will make you better equipped to make important decisions.
July 26, 2022
Good addition to earlier volumes
Book-Level : Intermediate.
This volune adds good set of mental models on top of earlier volumes, so it's recommended, not restricted though, to read in sequence.
The book covers mental models from Science and Math concept, which are covered well, but i feel it does not have content appeal as good as earlier volumes, probably because of different area of topic. But nevertheless it could not have been covered better.
Book-Level : Intermediate.
This volune adds good set of mental models on top of earlier volumes, so it's recommended, not restricted though, to read in sequence.
The book covers mental models from Science and Math concept, which are covered well, but i feel it does not have content appeal as good as earlier volumes, probably because of different area of topic. But nevertheless it could not have been covered better.
September 5, 2025
4.5 stars
Been slowly working my way through this in between other books, which seems like a good way to digest this information.
Systems and Mathematics certainly seemed to resonate with me more than the chemistry one. I found several of these useful, if not a novel perspective, then putting words to a way I already view things.
Purchased #4 (WHY ISNIT BLUE AND SMALL?!) recently. It’ll probably be 10-12 months before I start it, but I look forward to it.
Been slowly working my way through this in between other books, which seems like a good way to digest this information.
Systems and Mathematics certainly seemed to resonate with me more than the chemistry one. I found several of these useful, if not a novel perspective, then putting words to a way I already view things.
Purchased #4 (WHY ISNIT BLUE AND SMALL?!) recently. It’ll probably be 10-12 months before I start it, but I look forward to it.
October 24, 2021
Good read on mental models. Volume three from the Farnam Street. I thought this one was good, but not as impactful on terms of the actual models. I thought the first two books were more insightful. Still, there is some really good stuff here: compounding, margin of safety, randomness to name a few. For anyone who likes the Farnam Street work, this is another good read.
December 7, 2022
Book 3. I can't wait to pass down these books to my kids. (Though I am not sure whether they would want it! Hah!) I love the 3 volumes. After a certain point, it is not about how many mental models you have ... but knowing how to find there in all the different places in life and using them. Love some of the examples and stories in the books.
February 4, 2023
For all the chapters, the conclusion is provided that gives us the point and take away. Most of the content in every chapter seemed to be filler at least for me. Not straight to the point, the examples quoted backing each model are not impactful IMO, could have been better. I still could not get why the word Mathematics is used in the book title.
May 6, 2023
A collections models that meet the Lindy effect criteria of applicability of across time and topic. Gals Law, Global and Local Maxima, Churn, and Critical Mass are all common understandings. However, I better understand with the stories of their discovery and application. I have enjoyed this entire collection making it to my reread list too.
December 30, 2025
Foundational knowledge, poorly explained at times. Volume 1 and 2, which I've read and own, were quite good. This one has examples that keep losing their way to a point where I kept skimming through and moving on to the next model / principle. Still, a recommended read, even if just to get an introduction to the overarching point of each model.
October 12, 2021
This is by far the strongest of the series so far and I really had some "aha" moments. Not all of the practical applications of concepts (i.e. mental models) are insightful or even accurate (IMHO) but the entire way to approach is is highly intuitively useful. Recommend.
December 5, 2021
A concise and easily accessible collection of the fundamental concepts in math and systems theory. The most valuable part is the application of these concepts in an interdisciplinary context and how you can use them for your life.
March 14, 2022
Another nice volume in the series, this time dealing with systems and mathematics. I felt the mathematics portion was lighter and can be more comprehensive. Continue to learn new historical facts narrated via the lens of mental models.
May 16, 2022
A really good book. I probably learned more from and liked this volume even better than the previous two in the series. The chapters on algorithms was especially interesting and thought provoking to me.
June 8, 2022
See the world differently and more clearly!!
Huge fan of all 3 books!! Systems and Math models are so interesting and I’m already finding them improving my decision making and life!!
Huge fan of all 3 books!! Systems and Math models are so interesting and I’m already finding them improving my decision making and life!!
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