Four Ways of Thinking: A Journey into Human Complexity

by David Sumpter

Acclaimed mathematician David Sumpter shares practical and insightful solutions for navigating the chaos and complexity of our lives

What is the best way to think about the world? How often do we consider how our own thinking might impact the way we approach our daily decisions? Could it help or hinder our relationships, our careers, or even our health?

As acclaimed mathematician David Sumpter shows, thinking about thinking is something we rarely do, yet it is something science questions all the time. He has spent decades studying what we could all learn from the mindsets of scientists, and Four Ways of Thinking is the result. Here he reveals the four easily applied approaches to our statistical, interactive, chaotic, and complex. Combining engaging personal experience with practical advice and inspiring tales of groundbreaking scientific pioneers (with a tiny bit of number crunching along the way), Sumpter shows how these tried and tested methods can help us with every conundrum, from how to bicker less with our partners to pitching to a tough crowd—and in doing so, change our lives.

Genres: Nonfiction, Science, Psychology, Self Help, Mathematics, Logic

303 pages, Kindle Edition

Published August 27, 2024

Reviews

[Mauricio · Rating 3 out of 5]

TL:DR True rating: 3.5. Book has a lot of interesting stuff, but buried in unnecessary fictional narration, which made it harder to read.

Expectation: I bought the book expecting a "dry" pop-science (or rather pop-math-y) book, explaining the maths in intuitive ways with well thought out examples.

Reality: The book ended up being something like:
* 60% my aforementioned expectations,
* 30% stories of fictional & historical characters to bridge / introduce / contextualize the mathy topics
* 10% self help.

The author sets the book as a protagonist telling the story of his experience in a Santa Fe Complex Systems summer school, introducing the topics, as he was learning them in the daily classes, and thorugh the interactions with his peers. Personally, I would have enjoyed way more this book without this overarching summer school narrative arc. It felt like a lot of boilerplate to have to go through to get to the interesting bits. And it really took some willpower to get me through those just to finish it.

There are some other small stories concerning relevant historical characters, which I did appreciate very much. The self-help bits, how these "formal" ways of thinking can be applied not only to science but to our personal life, were nice, but maybe the last chapters that emphasized just that felt too repetitive from what was already said during the book.

As a final observation, I see that the book's subtitle here is "A Journey into Human Complexity", which I guess hints at the self-help reflection bits. Funnily, my edition's subtitle is just "Statistical, Interactive, Chaotic and Complex". So maybe the former title was more honest :)

[José · Rating 5 out of 5]

One of my favourite stats/science communication books. Beautiful narratives comprising not only how to use statistics when talking with people, but also on how to be understanding and understood while communicating. Inspired by Wolfram's four behavioural patterns for cellular automata, Stumpter derived his four ways of thinking from different figures in statistics and provided them with ample context on when they should be of guidance and when their ways of thinking also fell short - hard data has a place in conversations, much like your own personal experiences and those of others. I highly recommend this.

[Cheryl]

Oh man. This should be perfect for me. I like statistics and hard science, but also know that there are other ways to study, learn, and communicate. Some facts can be pinned down, like a fair coin has a 50/50 chance of being flipped heads. Some statistics are relevant, like eating more vegetables and less meat will mean that it's very likely you will live longer. And some things can't be pinned down at all, because people, relationships, the world... all is complex.

By p. 52 I have no idea whether that's the kind of thing Sumpter is talking about at all. I mean, the title and blurb say that he should be enriching my understandings, but all he's doing is confusing me with stories.

Jan. 2025

[Kavalaksala · Rating 1 out of 5]

Set of stories "one of my colleague believes in astrology, another colleague is very rational - people are different, and that's normal. You know what's also different? Math formulas!"

Are you serious? I expected more science as researches, new ideas of behaviourisms or anthropology mixed with math... But all you get - personal stories and a bit of basic statistics.

Disappointed.

[Nara · Rating 5 out of 5]

“It was this type of life that Kolmogorov yearned for. A life of experience. Of mathematical mornings. Of swimming feely in lakes. Of poetry and music. Of travel. Of friendship. Of love…” This is a delightful way to finish 2023 with such an insightful book. Reading some negative reviews, I was hesitant to go forward with 'Four Ways of Thinking,' yet I do not regret doing it.

Sumpter speaks about math, mind frameworks, randomness, order/chaos, and, above all, the purpose and beauty in life. In an era when AI transforms our lives, this book comes as a relevant work to remind us where to One impressive question, understand, and expand our horizons. part was a dialogue between the protagonist and Esther, who argues that the meaning behind Dostoyevsky's plethora of words and the waves in the ocean can be reduced to the coding language of zero and one. Is it?

Another point the author makes is asking questions, which reminds me of 'The Inevitable,' a book on the transformative power of AI, as a pinnacle of human quest to change the world around us and to better understand life phenomena. It may be a cliche, but the value of the book lies in how Sumpter explains it.

This book is also written in what I call American style (perhaps a more precise term can describe it): referencing big ideas, projecting a great mind style, and sharing personal stories such as a summer course in Santa Fe. What makes it special is that Sumpter describes cases across the world, from Russia to South Africa, from the US to Poland."

[Markus Hachenberg · Rating 4 out of 5]

Ich liebe die Art wie das Buch geschrieben ist. Die Geschichte und die Charaktere die um das Inhaltliche gestrickt sind, verleihen dem Buch einen auflockernden roten Faden, ohne dass es vom inhaltlichen ablenkt.

Inhaltlich geht es darum, dass wir die Welt auf 4 verschiedene Arten beschreiben können. Diese Sichtweisen werden sehr intuitiv und spannend erklärt. Man bekommt Einblicke in verschiedene Mathematische Theorien, die dabei helfen (können) die Welt um uns herum zu beschrieben.

Der Autor regt uns an, Situationen unseres Lebens im Hinblick auf die 4 Systeme zu analysieren und durch die Unterschiedlichkeit und Kenntnis dieser, einen besseren Zugang zu einer möglichen Lösung zu bekommen.

Ich hatte während des Lesens keinen großen Aha-Effekt und habe auch nicht das Gefühl, dass ich nun anders auf die Welt blicke. Ich habe nicht wirklich was essentielles aus diesem Buch mitgenommen. Daher 4/5.

Aber meist entdeckt man ja auch erst im Laufe der nächsten Zeit, ob ein Buch Einfluss auf einen genommen hat. Vielleicht finde ich mich bald in Situationen wieder, wo ich plötzlich einen Zusammenhang zu diesem Buch entdecke und die Situation anders löse, als ich es ohne die Lektüre dieses Buches getan hätte.

[Emily Feldman · Rating 2 out of 5]

2.5. not sure if I’m just too dumb for this book, but I feel like he made things that I understand harder to comprehend. His stories were difficult to grasp because names are not easy for me to remember. I do not appreciate the flow of incredibly short chapters. i’m sure this is a great book for some people. If you are interested in reading about math, I would suggest the book math ish

[Charles Reed · Rating 4 out of 5]

82. It's not that this is revolutionary or anything, but it does give us some background into mathematical Concepts mathematicians their lifestyles. How they work together in Academia? I enjoy this because it's reinforces Concepts and the big reinforcement concept. I want to say here that this wasn't directly point out is complexity, doesn't actually mean hard. It means multi-step. Anything that's complex just means that there's More than one step to it. So increasing levels complexity. So one on top of one on top of one on top of one and then you get variables in there, because one can go into a b, and then if a b triggers, you know, then it's in a more past more past more paths. Because I can go to a b and then B can go to a b

Of its own. And sometimes those paths end up reconverging, and sometimes they end up re-splitting, we can use this type of modeling.

With AI specifically which just makes me excited to make these much simpler to understanding our heavily digestible. So we can use these mathematical Concepts for probability. And calculating different matrix. So while we say chaos, chaos is very broad. It's not exactly. Chaos is more of unpredictable, the unknown unknowns. Is what we need to account for. So if you can account for unknown unknownst to a certain degree, You can predict like okay something that I don't know is going to happen is going to happen today. There's like this.

Five percent chance, for example, in a week given week. It's like go Rises, two, for example.

Uh, 35 chance.

So, that's why you can use these algorithms to actually Uh, do predictive reasoning for different states of matter. Etc. Social conditioning, everything. And that's why. Such as we say, you can't predict these things. No, you actually definitely can. It's just

Complex.

Great example is the billiard bar analogy here.

But there's ways to narrow that down. So, you know, it's like the range An LG here.

You say, okay. So,

Based off from the maximum and the minimum that has ever been recorded for billiard bars shots. We can determine That it's going to fall off within this range and then we look at median data and mean data,

And that helps us to determine. What's the most probable shot. That's someone's going to make, especially we can narrow that down even more if we have records of the individual's projections.

[Edward Pashkov · Rating 5 out of 5]

I loved this book and love it still. I ended in my books of notes with a question: what is the point of this book? Far from polemical I was trying to synthesize a main theme or idea. This book is about how stepping outside of the box of ordinary thinking can help to solve challenging problems. The important part is figuring out where the limits of the box are and then challenging ourselves to step out of it. David does this masterfully throughout the book while he provides an expose of 4 types of thinking: Statistical, Interactive, Chaotic, and Complex.
Perhaps my cat is annoying, always clawing me in the morning. No matter what I do, she claws at me. Thinking type one may prompt me to look up the statistics of how often cats claw. As I get more information I bring myself into the problem and attempt to see my cats behavior as a byproduct of how I wake up in the morning. My cat can feel my breadth change from deep to light sleep. This itself is fascinating. There is something very deep coming out of shifting my thinking from statistical to interactive. I bring myself into the puzzle. This is just one example of an application of the ideas in this book.
I also love how the Santa Fe institute creeps up on me. In my research I've been drawn recently into complex systems science. I see is at a gateway into understanding more about my research topic. Although I don't know how it may be used, I know that once I can think up a way it will be an invaluable addition to the way we understand memory organization in society. This book brought me closer to thinking in interactive, statistical, chaotic, and complex ways.
At first this book was to receive 4 starts. After I finished though, there is no way that I can rate this book less than 5 starts. The way stories are mixed with math and punctuated by existential philosophical thought is just brilliant. I look forward to sharing this book with everyone I know that may have even a remote interest in thinking, living, math, self-help, and stories, because that is really what this book is, a story about how chaos and complexity science emerged... thank you Dave and Lovisa. To be sure I will be reading your other books. It take a great mind to take complexity and make it digestible, that is exactly what you've done in an original and tasteful style. Thank you, thank you, thank you.

[Lothbrok · Rating 2 out of 5]

It should be 1.5 stars, but I give it 2 instead of 1 because this style is really not for me and I don't want to discourage people who are interested in this topic if they don't have an issue with this type of writing structure.

I started reading this book in January and within 2 days I had already read 2/3.
That's when everything shifted from a joyful read to an excruciating challenge of overcoming boredom.
I dropped the book and every so often I would painfully read through 10 pages or less. It became a mental workout, one that I hated performing, and worse, one that I felt might be a waste of my time.
The only reason I kept reading was to prove to myself I was able to finish a project that I hated.
Just to illustrate the pain I went through: I finished reading this small 291 pages book by the end of August, EIGHT MONTHS.

Credit were credit is due, the content is interesting, nice even.
I liked some parts especially the ones referencing the achievements of mathematicians such as Fisher and Kolmogorov.

What I really disliked is the chaotic plot with so many useless characters that pop here and there and inter-mix with real historical figures throughout very small sections (chapters of 4 pages usually). The anecdotes are boring and take too much space compared to the actual message the author wants to deliver. I don't care about Chris and his Gherkins and Antonio and his stupid ants. Instead of creating an entertaining supporting story-line, it felt like a spatio-temporal-travel mind fuck where as I always forget who I the people are, where this is happening and OH MY GOD did I just read all this bullshit to for this simple concept?

Paradoxically, I am very happy I read this book, because I proved to myself I had the mental endurance to survive this experience.

[Anna Olivia Burkholder · Rating 5 out of 5]

'Four Ways of Thinking' by David Sumpter is a wonderfully thought-provoking book about not only applied mathematics and statistics but also on how to become a better versions of ourselves and what it means to be human. Sumpter does a fantastic job at explaining each example in a way that is easy to understand regardless of one's prior knowledge of mathematics. The book is composed neatly of four sections, each containing many short chapters. I really enjoyed reading a blend of mathematical situations, historically famous figures, and a bit of David's own experiences at a prestigious summer program in Santa Fe, New Mexico during a study abroad experience. Throughout the book, I found myself pondering over each example carefully, analyzing the graphic models deeply, and drawing my own connections. The variety of topics in the book truly made each page a joy and surprise. Sumpter does an excellent job bridging the sciences with the humanities, but also emphasizes the importance of keeping barriers between them as well. An aspect of the personal experience chapters that I appreciate is how each PhD student came from a different field of study, showing how mathematics can work as an explanation for a variety of subjects. Reading the thoughts of different scientists, from biologists to philosophers, added many important insights on how we as humans come to understand the world in different ways. After completing this book, I feel that I have gained essential skills moving forward in life. I have really become fascinated by applied mathematics as well. As a philosopher, I find the information I learned extremely helpful for my studies. Overall, I highly recommend this book to anyone looking to gain a better understanding of science, society, and our existence.

[Satid · Rating 3 out of 5]

This book is a surprising disappointment compared to the author's two previous books I have read in that it contains much less enlightening substances to digest. (There still are good nuggets here but less than his two previous books I read.) And the life subjects discussed by the author are either so trivial or typical of general self-help books. I wonder why the author wants to discuss them? They appear to me a bit weird to discuss in association with mathematical ideas!

Although the overall structure of the topics in this book is interesting, the author mixes fictional and historical narratives and the former part appears confusing (too many characters involved which contributes to confusion) and even superficial in places. This book also reads like a self-help one in places which is also confusing as I sometimes cannot relate the mathematical notions discussed to the life topics the author try to make.

The first two parts of the book are interesting enough but it could have been better if the fictional part contained less fictional characters. The last two parts are mostly obscured to digest. Some life matters discussed are also quite superficial to discuss. For example, the way a small group of people forms a cluster while walking on road side was one such weird point to relate to mathematical notions discussed.

One observation of note here is that this is the second book I read that criticizes Angela Duckworth's book Grit: The Power of Passion and Perseverance in the sense that Duckworth overblows the benefit of her research that serves as the basis of her book. The previous book uses the word "educational hype". Soft Science is prone to such hype as I also remember another research on what was called Power Position by another researcher Amy Cuddy was also criticized as being disproportionately overblown. It did not help when in 2012, many social science researches were investigated and subsequently exposed on "replication crisis". To my perception, Dr. Sumpter's writing in this book also verges on such a border in a few places.

I can see better books by mathematician than this one that discuss similar topics in less confusing and more coherent and informative way, such as: Sync: The Emerging Science of Spontaneous Order and Do Dice Play God?: The Mathematics of Uncertainty.

[Wan Shoo · Rating 4 out of 5]

I  may not be mathematically inclined, but the author has certainly captured my attention by relating thinking patterns to numbers. David makes everything remarkably easy to understand, as if the numbers themselves are speaking to you. I am amazed by David's ability to convey his main messages through each lecture, narrated with clear examples using scenarios such as predator versus prey and the wedding planner versus mother at home (apologies for revealing too much). These examples, closely related to our daily lives, emphasise the practical applications of his concepts.

As you read, you'll feel as though you're walking amongst giants, gaining insight into the meaning of life and the strengths and weaknesses of humanity. At one point, the need for compromise when encountering indecipherable complexity struck a chord with me as a scientist. Understanding that letting go might broaden your horizons and preserve your sanity, rather than digging into a dark hole that could ruin your life, is a valuable lesson.

Immerse yourself in the world of numbers, journey through history to appreciate how numbers influence our thinking, and be sure to read until the end for an enlightening conclusion!

[Carlos Arellano · Rating 4 out of 5]

This book fell on my hands right on time as I have been introduced earlier, at work and through other books, to chaos theory. Here we are presented with four ways of thinking that can serve us to make decisions and understand more ourselves and the world around us. These ways of thinking are statistical, when we look at phenomena in terms of initial and final stable states; interactive, when we focus on the basic interactions that shape these phenomena and that make us realize that not always stable states can be reached, but sometimes cycles emerge; chaotic, when interactions analyzed do not arrive at repeated cycles or stable states, but rather jump to different cycles that may or may not repeat in time; and complex, when we accept that no matter how good our interpretation of phenomena could be, it will never completely capture the immense complexity that exists in nature.

This is a book not only for scientist, mathematicians, or data enthusiasts, it is a book for everyone that is looking for ways to understand the world around us in a systematic way that can lead ultimately to a happier and more fulfilling life.

[Shelton Kiana · Rating 3 out of 5]

David Sumpter's "Four Ways of Thinking" delves into cognitive processes through a mathematical lens, which, while intriguing, may not cater to everyone’s preferences. As a therapist, I found the book particularly insightful for understanding different approaches to problem-solving and information processing. Despite the strong mathematical orientation, Sumpter’s exploration of these cognitive strategies provides valuable perspectives that can enhance our practice and interpretation of clients' thought processes.

The mathematical focus was more pronounced than I had anticipated, but the underlying concepts remain relevant and thought-provoking. Sumpter's analysis encourages a deeper reflection on how we think and make decisions, which is beneficial for both personal growth and professional development.

Thank you, NetGalley, for the opportunity to advance read this enlightening book.

[Man Ha · Rating 4 out of 5]

I love statistics and data. Using statistical thinking to understand and comprehend information in this noisy world makes sense. Information can vary over time and its distribution changes over time. As a result, more noise is created. Depending on the platform, the information will be disseminated. In this book, the author mentioned multiple examples to highlight his points about details about distribution, frequency, understanding, comprehending, perceiving, and sustaining. I like it because it makes me question how often, when, where, and why it was. If I dig deep, I find that not many people know the current information, but people receive it on the shallow surface. Moving from there, we have our principles for understanding information, which can be changed depending on how much we know.

[Evinpinar · Rating 4 out of 5]

It is an easy to read book about mathematics built around daily narratives. It can get sometimes a bit cheesy, but in general all stories and mind maps are relevant and meaningful. I would also love to read something more in detail about these topics, but then reading would probably not as smooth as this one, and it would require more dedicated time. I would not say that it is a self help book, even though it reads as easy as one, it’s rather more about integrating rational thinking into our daily lives and reasoning about events. It has bits on pop science since it provides some history/info about maths, but also not exactly because of the narratives. Anyways, I can suggest you give this book a go.

[Avinash · Rating 5 out of 5]

book was inspired by article written by Stephen wolfram , all natural phenomenon fall under one of the pattern based on his observation applied to modelling in thinking and decison making
statistical thinking (stable systems), interactive thinking(periodic systems) , chaotic thinking, complex thinking (emergence)

well written and loved of the book with lil burden of reading some unwanted drama which i felt boring for some time but that was okay given its compensated with interesting write up in other parts of book

I loved and discovered works of kolmogorov which i will read soon alongside another legend margaret hamilton whom I was not aware before

[Lin · Rating 4 out of 5]

A refreshingly original book about the four types of thinking: statistical, interactive, chatic and complex.

The writer gave brief and easy to understand ideas about deep concepts like the Chaos theory, golden ratio, social epidemics and entropy etc. I like how the author is able to infuse affectionate incidents of people around him and uses these complex ideas to describe their actions, findings and discussions.

[Kay · Rating 4 out of 5]

This book has some interesting information about different mathematical models and how they apply to the real world.

That is completely overshadowed by the (intentionally?) hilarious secondary plot used to illustrate the models. It boils down to 'what if the kids who were counting red and black marbles from vases in your math textbook grew up and became the weirdest group of friends'.

[Roy Kenagy]

Not in OCLC yet [Book review] Four Ways of Thinking by David Sumpter – safety in numbers? A mathematician tries to make sense of the world through different lenses in this surprisingly original book—Steven Poole / Guardian https://bit.ly/44DX4h3

[Emilie · Rating 5 out of 5]

A book about Mathematics (more than a Math book) but also a book about life and how the various experiences of life map to different mathematical thinking.
It reads like a novel and is very engaging. Not too much mathematicsl knowledge needed.

[Kate Pashevich · Rating 4 out of 5]

An interesting introduction to complexity, using mathematical theories of the previous century. Not sure which audience this book is meant for. I enjoyed a lot how well the author explains mathematics, although the philosophical and the self-help part of the book was too obvious for me personally.

[Duco Van Wallenberg · Rating 5 out of 5]

A unique non technical approach to the essence of mathematics. I really like the book, because it utilizes the flat charachters present in the book really well.

[Thomas Haverkamp · Rating 5 out of 5]

This was engaging and fun to read. And I got a much better understanding for predator-prey dynamics.

[Theodore Decker · Rating 4 out of 5]

Statistical, Interactive and Chaotic ways of thinking were clear, informative and ebjoyable to read. Complex thinking was as if written by another author. Overall, really worth reading!

[Urban Andersson · Rating 4 out of 5]

Fin och tankeväckande bok, om fyra sätt att tänka.
Lite osäker på målgruppen, och det tar ett tag att vänja sig med den berättande stilen med olika fiktiva personer

[Fathur Rizki · Rating 3 out of 5]

the four way but when I read this book I couldn't understand how the author explain the theories with some complicated example.

[Tommy · Rating 4 out of 5]

The initial parts were very well described and explained but, maybe by design, became more complex later on

[David Ireri · Rating 3 out of 5]

key concepts would have been summarised in a few chapters without many unnecesaary illustrations