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Is there a secret formula for getting rich? For going viral? For deciding how long to stick with your current job, Netflix series, or even relationship?
This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthfully, and see through scaremongering. They are known by only the privileged few - until now.
With wit and clarity, mathematician David Sumpter shows that it isn't the technical details that make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn.
Empowering and illuminating, The Ten Equations shows how math really can change your life.
This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthfully, and see through scaremongering. They are known by only the privileged few - until now.
With wit and clarity, mathematician David Sumpter shows that it isn't the technical details that make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn.
Empowering and illuminating, The Ten Equations shows how math really can change your life.
316 pages, Hardcover
First published June 4, 2020
307 people are currently reading
2689 people want to read
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October 10, 2020
David Sumpter makes it clear in this book that a couple of handfuls of equations have a huge influence on our everyday lives. I needed an equation too to give this book a star rating - I’ve never had one where there was such a divergence of feeling about it. I wanted to give it five stars for the exposition of the power and importance of these equations and just two stars for an aspect of the way that Sumpter did it. The fact that the outcome of applying my star balancing equation was four stars emphasises how good the content is.
What we have here is ten key equations from applied mathematics. (Strictly, nine, as the tenth isn’t really an equation, it’s the programmer’s favourite ‘If… then…’ - though as a programmer I was always more an ‘If… then… else…’ fan.) Those equations range from the magnificent one behind Bayesian statistics and the predictive power of logistic regression to the method of determining confidence intervals and the kind of influencer matrix so beloved of social media companies. Each is well-described with often personal examples. While it’s hyperbole to suggest that these ten equations rule the world of applied mathematics, let alone the real world, they are certainly key components of the applied mathematics toolbox.
Let me make it clear, I should have absolutely loved this book - it should have been the best book I’ve read all year. The introduction and clear explanation of these equations gives me exactly the same thrill I remember doing my Masters in Operational Research and discovering the power to do remarkable things for people and businesses that these kind of techniques bring. Wonderful. But.
The lesser problem I have with the context is that almost all of Sumpter’s big examples of applications in the world were either trivial (in sports or games, for example) or morally dodgy, such as betting, stock market trading or social media and advertising manipulation of people. Sumpter suggests at one point that though these tools can be used for good or evil, those who use them are mostly on the side of the angels - it hardly seems to be the case with the examples he uses.
The bigger problem is that Sumpter frames all this with applied mathematicians being described as members of TEN, a secret illuminati-style set of people who rule the world through their ability to understand and make use of these equations. This comes across as both silly and intensely smug - I really don’t think it does anything to win across those for whom any equation is a turn-off. Instead it just underlines any existing prejudice.
The frustrating thing is that Sumpter makes passing reference to lots of real research with positive implications where these approaches are taken - but all his big stories are about things like sports betting which hardly comes across as a positive thing to do. The downside of the smugness is that it’s difficult not to look for opportunities to turn some of his comments against him. So, for example, he criticises 60 to 69 year olds who criticise Greta Thunberg for damaging the environment by flying off on holiday without pointing out that academics like Sumpter are always jetting off around the world to conferences - a touch of the glass houses equation required there.
This was truly a hard review to write. I really like David Sumpter’s work and looked forward to reading this book as soon as I saw it. Somehow it manages to be excellent and an opportunity missed all at the same time.
What we have here is ten key equations from applied mathematics. (Strictly, nine, as the tenth isn’t really an equation, it’s the programmer’s favourite ‘If… then…’ - though as a programmer I was always more an ‘If… then… else…’ fan.) Those equations range from the magnificent one behind Bayesian statistics and the predictive power of logistic regression to the method of determining confidence intervals and the kind of influencer matrix so beloved of social media companies. Each is well-described with often personal examples. While it’s hyperbole to suggest that these ten equations rule the world of applied mathematics, let alone the real world, they are certainly key components of the applied mathematics toolbox.
Let me make it clear, I should have absolutely loved this book - it should have been the best book I’ve read all year. The introduction and clear explanation of these equations gives me exactly the same thrill I remember doing my Masters in Operational Research and discovering the power to do remarkable things for people and businesses that these kind of techniques bring. Wonderful. But.
The lesser problem I have with the context is that almost all of Sumpter’s big examples of applications in the world were either trivial (in sports or games, for example) or morally dodgy, such as betting, stock market trading or social media and advertising manipulation of people. Sumpter suggests at one point that though these tools can be used for good or evil, those who use them are mostly on the side of the angels - it hardly seems to be the case with the examples he uses.
The bigger problem is that Sumpter frames all this with applied mathematicians being described as members of TEN, a secret illuminati-style set of people who rule the world through their ability to understand and make use of these equations. This comes across as both silly and intensely smug - I really don’t think it does anything to win across those for whom any equation is a turn-off. Instead it just underlines any existing prejudice.
The frustrating thing is that Sumpter makes passing reference to lots of real research with positive implications where these approaches are taken - but all his big stories are about things like sports betting which hardly comes across as a positive thing to do. The downside of the smugness is that it’s difficult not to look for opportunities to turn some of his comments against him. So, for example, he criticises 60 to 69 year olds who criticise Greta Thunberg for damaging the environment by flying off on holiday without pointing out that academics like Sumpter are always jetting off around the world to conferences - a touch of the glass houses equation required there.
This was truly a hard review to write. I really like David Sumpter’s work and looked forward to reading this book as soon as I saw it. Somehow it manages to be excellent and an opportunity missed all at the same time.
June 18, 2020
The Ten Equations that Rule the World : And How You Can Use Them Too (2020) by David Sumpter is a well written trip through ten equations that Sumpter describes as ruling the world. Sumpter is a professor of Applied Mathematics at the University of Uppsala.
The book starts by describing how the set of equations leads to being part of the TEN, a network of people who have some insight into the world. Sumpter describes this as being a bit like a member of a secret society.
The equations are described as, The Betting Equation, The Judgement Equation, The Confidence Equation, The Skill Equation, The Influencer Equation, The Market Equation, The Advertising Equation, The Reward Equation, The Learning Equation and The Universal Equation.
The Betting Equation shows how much odds can be adjusted against reality. The Judgement Equation is the basis of Bayesian statistics. The Confidence Equation comes from the Bell Curve. The Skill Equation originates with Markov Chains. The Influencer Equation shows how a network settles against certain weights with with the weight of each being the influence of each node, this is at the heart of Google's search algorithm. The Market Equation looks at how to find signal and noise in prices. The Advertising Equation looks at how things correlate and what clumps are formed by data. The Reward Equation describes how a variable reward yield can lead to chaotic but better behaviour. The Learning Equation is the start of gradient descent and hence machine learning. Finally the Universal Equation is an if then statement that describes how computer code can solve problems.
Each chapter provides thorough descriptions of each algorithm and lots of tales of the insights that can be gained from each one. Sumpter's experiences as an applied mathematician are used to great effect. There are also some branches out into philosophy and politics that are weaker than the tales of how the algorithms were developed and how they can be used.
The Ten Equations that Rule the World is a very good math popularisation that works well. Sumpter writes well, knows his subject and has created a fine book that shows some of the insight that math can yield.
The book starts by describing how the set of equations leads to being part of the TEN, a network of people who have some insight into the world. Sumpter describes this as being a bit like a member of a secret society.
The equations are described as, The Betting Equation, The Judgement Equation, The Confidence Equation, The Skill Equation, The Influencer Equation, The Market Equation, The Advertising Equation, The Reward Equation, The Learning Equation and The Universal Equation.
The Betting Equation shows how much odds can be adjusted against reality. The Judgement Equation is the basis of Bayesian statistics. The Confidence Equation comes from the Bell Curve. The Skill Equation originates with Markov Chains. The Influencer Equation shows how a network settles against certain weights with with the weight of each being the influence of each node, this is at the heart of Google's search algorithm. The Market Equation looks at how to find signal and noise in prices. The Advertising Equation looks at how things correlate and what clumps are formed by data. The Reward Equation describes how a variable reward yield can lead to chaotic but better behaviour. The Learning Equation is the start of gradient descent and hence machine learning. Finally the Universal Equation is an if then statement that describes how computer code can solve problems.
Each chapter provides thorough descriptions of each algorithm and lots of tales of the insights that can be gained from each one. Sumpter's experiences as an applied mathematician are used to great effect. There are also some branches out into philosophy and politics that are weaker than the tales of how the algorithms were developed and how they can be used.
The Ten Equations that Rule the World is a very good math popularisation that works well. Sumpter writes well, knows his subject and has created a fine book that shows some of the insight that math can yield.
November 17, 2020
Great book also for beginners where you can start to develop an understanding of several important equations. The writing style is catching and you don’t feel bored in any moment of the book. Nevertheless, he spends too much time trying to convince the reader about his own personal opinions.
May 7, 2022
I am quite disappointed with this book. I expected some deeper mathematical insights into the selected equations, how they are inter-connected or could be applied to some important real-life problems. But instead, author talks a lot about politics, social aspects, how to beat bookmakers. It looks like one of the main points of this book is to show how Jordan Peterson abuses statistics in his debates.
September 23, 2021
Good book, especially the first chapter. Could have done without the obvious attacks against Jordan Peterson and Ben Shapiro. I don't really want to read about 'systemic racism' in a book about mathematics.
February 13, 2022
Interesting at first but quickly becomes tedious and preachy
June 15, 2022
I found this very useful. I work with data scientists and speak a lot of the language, but I confess that the math is often gobbledygook. This book is a great high-level guide to how mathematicians think about problems. I enjoyed Sumpter's tales and his historical perspective (such as his summary of the advancements in Big Tech). I also appreciate Sumpter's unabashedly pro-math approach, while I don't completely share it.
Sumpter's defense of the academy against Jordan Peterson was particularly good. Peterson says that colleges and universities are captured by liberal ideas. There is certainly some truth to this, but Sumpter says that it's not the case in those fields, such as sociology, that have learned how to use data. The way you distinguish the signal from the noise is by calculating confidence intervals to express your uncertainty. Otherwise it's just one talking head vs another. This is a similar point to the one Nate Silver makes in The Signal and the Noise. It wasn't hard for him to become a good political pundit, because it was all just BS before him.
As a trained philosopher, I also appreciated Sumpter's attempt to talk about the moral implications of the use of these formulas. Knowledge of them is often concentrated in the hands of few Big Tech companies which hold a lot of power. However, Sumpter turns to AJ Ayer, a logical positivist, for help. Ayer is a natural ally for hard-nosed analytical types, but the logical conclusion of his view is that we can't really talk about politics or morality. Sumpter appeals to our moral intuitions. But what if my moral intuitions are racist and sexist? Even if discussion of politics and morality is not verifiable in the same manner as science (which I don't think--you can set up moral axioms and see if behavior agrees or not with them, in the same analytical approach as math; and you can formulate hypotheses about what individuals or states should do in certain situations and then see if you're right, in the experimental approach of science), it doesn't mean we can't talk about them. Clearly moral and political statements have some meaning or humans wouldn't make them.
But the broader question is whether or not analytical training can help with the kind of critical thinking that is desperately needed today. I'm sympathetic to Sumpter's view that a STEM training is the way to go about this. After all, isn't stating your assumptions, proposing theories in an ego-less manner, and then verifying and revising them what critical thinking is about? However, it's not my experience that STEM education develops critical thinking. It's about rote memorization that is tested through well-defined problems. Sumpter argues that everyone should learn the 10 principles, in the same way people have argued that everyone should learn to code. Possibly, but I think a diversity of perspectives trained in critical thinking around different types of problems would be more useful.
In any case, the ten formulas are:
1. The obligatory Bayes chapter - New information should be judged in terms of how it fits in with old information.
2. Logistic Regression - 1 / ( 1 + aX^b) - I was surprised it wasn't linear regression, but the discussion of online betting was interesting.
3. Confidence intervals - h * n +/- 1.96 * o * n ^ 0.5 - It's very helpful to understand that a signal-to-noise ratio depends on the square root of the number of samples. So to find smaller and smaller amounts of signal (such as 1-3%), you need large samples (> 10,000).
4. The Markov Assumption - P(St+1|St)=P(St+1|St,St-1,St-2...S1) - Modeling is about eliminating variables that don't matter. Many problems can be modeled without considering the past and by focusing on a few parameters. I've often heard people talk about Markov assumptions, and I knew that it had something to do with each link in a chain being able to ignore previous links, but this chapter helped to clarify what this means.
5. Gaussian Elimination - A * p = p - Graphs are represented as matrixes and we find stationary transformations through elimination.
6. Feedback - dX = hdt + f(X)dt + o * e - Similar to the confidence interval, we have a signal and we have noise, but now we have feedback effects over time. This is what many market analysts before 2008 missed.
7. Correlation - (too complex to write) - The reason why many old algorithms (like YouTube's) weren't useful is they grouped people together and recommended things based on correlations with what other people liked. But just because I like art films and foreign language films doesn't mean that when you show a french speaker more advertisements for American art house films that they'll watch them.
8. Rewards and Decay - Qt+1 = (1-a)Qt + aRt - This formula will converge at infinity of the average reward. Change over time is modeled as a simple decay or reinforcement parameter.
9. Gradient Descent - -d(y-yx)^2/dx - Tuning models involves going in the direction that minimizes error the most.
10. If/then thinking - See discussion above about analytical and critical thinking
Sumpter's defense of the academy against Jordan Peterson was particularly good. Peterson says that colleges and universities are captured by liberal ideas. There is certainly some truth to this, but Sumpter says that it's not the case in those fields, such as sociology, that have learned how to use data. The way you distinguish the signal from the noise is by calculating confidence intervals to express your uncertainty. Otherwise it's just one talking head vs another. This is a similar point to the one Nate Silver makes in The Signal and the Noise. It wasn't hard for him to become a good political pundit, because it was all just BS before him.
As a trained philosopher, I also appreciated Sumpter's attempt to talk about the moral implications of the use of these formulas. Knowledge of them is often concentrated in the hands of few Big Tech companies which hold a lot of power. However, Sumpter turns to AJ Ayer, a logical positivist, for help. Ayer is a natural ally for hard-nosed analytical types, but the logical conclusion of his view is that we can't really talk about politics or morality. Sumpter appeals to our moral intuitions. But what if my moral intuitions are racist and sexist? Even if discussion of politics and morality is not verifiable in the same manner as science (which I don't think--you can set up moral axioms and see if behavior agrees or not with them, in the same analytical approach as math; and you can formulate hypotheses about what individuals or states should do in certain situations and then see if you're right, in the experimental approach of science), it doesn't mean we can't talk about them. Clearly moral and political statements have some meaning or humans wouldn't make them.
But the broader question is whether or not analytical training can help with the kind of critical thinking that is desperately needed today. I'm sympathetic to Sumpter's view that a STEM training is the way to go about this. After all, isn't stating your assumptions, proposing theories in an ego-less manner, and then verifying and revising them what critical thinking is about? However, it's not my experience that STEM education develops critical thinking. It's about rote memorization that is tested through well-defined problems. Sumpter argues that everyone should learn the 10 principles, in the same way people have argued that everyone should learn to code. Possibly, but I think a diversity of perspectives trained in critical thinking around different types of problems would be more useful.
In any case, the ten formulas are:
1. The obligatory Bayes chapter - New information should be judged in terms of how it fits in with old information.
2. Logistic Regression - 1 / ( 1 + aX^b) - I was surprised it wasn't linear regression, but the discussion of online betting was interesting.
3. Confidence intervals - h * n +/- 1.96 * o * n ^ 0.5 - It's very helpful to understand that a signal-to-noise ratio depends on the square root of the number of samples. So to find smaller and smaller amounts of signal (such as 1-3%), you need large samples (> 10,000).
4. The Markov Assumption - P(St+1|St)=P(St+1|St,St-1,St-2...S1) - Modeling is about eliminating variables that don't matter. Many problems can be modeled without considering the past and by focusing on a few parameters. I've often heard people talk about Markov assumptions, and I knew that it had something to do with each link in a chain being able to ignore previous links, but this chapter helped to clarify what this means.
5. Gaussian Elimination - A * p = p - Graphs are represented as matrixes and we find stationary transformations through elimination.
6. Feedback - dX = hdt + f(X)dt + o * e - Similar to the confidence interval, we have a signal and we have noise, but now we have feedback effects over time. This is what many market analysts before 2008 missed.
7. Correlation - (too complex to write) - The reason why many old algorithms (like YouTube's) weren't useful is they grouped people together and recommended things based on correlations with what other people liked. But just because I like art films and foreign language films doesn't mean that when you show a french speaker more advertisements for American art house films that they'll watch them.
8. Rewards and Decay - Qt+1 = (1-a)Qt + aRt - This formula will converge at infinity of the average reward. Change over time is modeled as a simple decay or reinforcement parameter.
9. Gradient Descent - -d(y-yx)^2/dx - Tuning models involves going in the direction that minimizes error the most.
10. If/then thinking - See discussion above about analytical and critical thinking
November 13, 2025
Bordeaux diversion was the extra 30mins needed to finally tick one off after a long tough patch of half-reads.
Equations & context were mostly a good read and well laid out, but felt like the book could have been 60% of the size for improved quality, dragged at times.
Equations & context were mostly a good read and well laid out, but felt like the book could have been 60% of the size for improved quality, dragged at times.
December 29, 2022
I have greatly enjoyed the book, even though I have to say I needed to spend some longer time on some chapters, go back and forth, go further to notes check the details.
The book refers to the equations of mathematics that model and try to quantify uncertainity.
The books starts with classical results of probability theory and ends with the latest AI achievements which the reader can see it is a culmination of all the previous works started hundreads of years ago.
I particularly enjoyed the examples, I would say this is the strongest point of the book.
Instead of giving the classical examples of a die roll, Sumpter chose to explain the equations through everyday examples that would most of us make feel excited about:
betting strategies, how Instagram suggestions work, how the feeling over an objects' price is formed or how to measure the accuracy of medical tests/studies.
The book refers to the equations of mathematics that model and try to quantify uncertainity.
The books starts with classical results of probability theory and ends with the latest AI achievements which the reader can see it is a culmination of all the previous works started hundreads of years ago.
I particularly enjoyed the examples, I would say this is the strongest point of the book.
Instead of giving the classical examples of a die roll, Sumpter chose to explain the equations through everyday examples that would most of us make feel excited about:
betting strategies, how Instagram suggestions work, how the feeling over an objects' price is formed or how to measure the accuracy of medical tests/studies.
September 22, 2022
Divide-By-Zero-Error
This was a fairly interesting numbers and maths book.
Not the best I've read, but it had some okay bits.
I think it could have been much shorter, as a lot of it was verbose. But still interesting enough.
3.7/5
This was a fairly interesting numbers and maths book.
Not the best I've read, but it had some okay bits.
I think it could have been much shorter, as a lot of it was verbose. But still interesting enough.
3.7/5
October 29, 2021
Excellent mental models and thorough explanations of important equations. Terrible conclusions.
April 24, 2022
My book rating equation gives this interesting book 3.66667 stars, which I am rounding up to 4.
March 13, 2022
Este foi, provavelmente, o melhor livro que li este ano até agora.
A forma como o autor explica as diferentes equações e a sua utilização na vida real é bastante interessante e fácil de compreender.
Recomendo a todos os que têm curiosidade e querem aprender mais sobre a influência da matemática no dia a dia.
A forma como o autor explica as diferentes equações e a sua utilização na vida real é bastante interessante e fácil de compreender.
Recomendo a todos os que têm curiosidade e querem aprender mais sobre a influência da matemática no dia a dia.
December 7, 2023
Good stuff
New way of telling old stories
New way of telling old stories
June 14, 2024
divida o mundo em três categorias: dados, modelos e absurdos.
O método usado para escolher os melhores parâmetros é chamado de regressão logística.
Se um resultado é importante para você, considere a possibilidade de que ele seja atingido e também a de que não seja.
Pensar probabilisticamente é ser realista em relação aos ganhos e perdas esperados. Nas corridas de cavalos e no futebol, os azarões tendem a ser superestimados por jogadores inexperientes, mas na vida real tendemos a ser excessivamente prudentes. A aversão ao risco faz parte da natureza humana. Não se esqueça de que o ganho de encontrar um trabalho que você realmente aprecie ou um parceiro ou parceira que você ame de verdade é inestimável. Isso significa que você deve estar disposto a correr grandes riscos para atingir seus objetivos.
O segredo de apostar com sucesso não é fazer previsões com absoluta certeza, mas descobrir pequenas diferenças na forma como você vê o mundo e na forma como outras pessoas o veem.
Às vezes tendemos a concentrar todos os nossos esforços em uma “Grande Ideia”, mas, de acordo com a equação do jogador, o segredo consiste em criar diferentes variantes de uma ideia.
os melhores funcionários têm uma coisa em comum: a capacidade de absorver e utilizar novas informações, ajustando rapidamente suas estimativas à nova realidade.
O teorema de Bayes pode ser usado para avaliar corretamente a importância de novas informações e manter a calma quando todos à sua volta estão em pânico.
O primeiro passo para uma abordagem matemática do mundo é reconhecer a forma como usamos os modelos.
Somos o produto de todos os nossos atos, não o resultado de um ou dois erros. Aplique a você mesmo o perdão racional que Bayes nos ensina a aplicar aos outros.
David Hume havia afirmado que “nenhum testemunho é suficiente para provar que um milagre aconteceu, a menos que para desmentir o testemunho seja preciso admitir um milagre ainda maior”.
o pensamento lógico podia revelar verdades do mundo que não estavam ao alcance de nossa experiência cotidiana.
Nenhuma hipótese é 100% verdadeira, mas, à medida que os resultados experimentais se acumulam, algumas se tornam mais plausíveis do que outras.
Os experimentalistas colhem dados (D), e os teóricos formulam hipóteses ou modelos (M) a respeito dos dados. A equação de Bayes é usada para unir os dois componentes.
A geração do século XXI tem acesso a ideias e informações importantes que estariam além da compreensão dos jovens das décadas de 1970, 1980 ou mesmo 1990.
Sempre que vários fatores aleatórios se combinam para produzir um resultado final, o resultado é a distribuição normal, o que significa que a Equação 3 pode ser usada a fim de estabelecer um intervalo de confiança para qualquer atividade que envolva repetir o mesmo tipo de ação ou fazer o mesmo tipo de observação um grande número de vezes.
É fácil subestimar o número de observações necessárias para descobrir pequenas margens nos mercados.
A única forma de compreender o papel da discriminação em uma sociedade é fazer um grande número de observações e calcular um intervalo de confiança.
As estatísticas mostram que o que experimentamos individualmente muitas vezes não reflete o mundo como um todo. Depende de cada um de nós avaliar se nossas vidas são estatisticamente corretas e, caso não sejam, tomar alguma providência.
Em termos de neurose, extroversão, franqueza, alegria, tristeza, raiva e muitos outros traços de personalidade, a diferença entre homens e mulheres é muito pequena. Em um estudo mais recente, Hyde descobriu que as diferenças de gênero também são pequenas em termos de habilidade matemática, expressão oral, diligência, sensibilidade a recompensas, agressividade verbal, comunicabilidade, atitudes em relação à masturbação e a relacionamentos extraconjugais, liderança, autoestima e autoconceito acadêmico. As maiores diferenças entre os sexos estão no interesse pelas coisas em comparação com o interesse pelas pessoas, na agressividade física, no uso da pornografia e nas atitudes em relação ao sexo casual.
Como vou saber se alguém está me contando alguma coisa útil?
A divisão do mundo em modelos, dados e nonsense nos obriga a ser honestos a respeito das premissas que usamos para chegar às conclusões. Ela nos faz encarar com mais seriedade tanto as nossas opiniões como as alheias.
O melhor indicador do sucesso de um arremesso não é o número de acertos do jogador nos últimos cinco arremessos, é a posição dele e dos outros jogadores na quadra e o seu talento individual.
Medir a influência das pessoas se reduz a uma operação de álgebra matricial que um computador executa de forma mecânica e imparcial.
Uma vez que você aceite a inevitabilidade matemática de não ser popular, sua relação com as redes sociais deve melhorar.
A popularidade nas redes sociais é gerada por uma realimentação positiva na qual pessoas que já são populares buscam e conseguem novos seguidores. É uma ilusão estatística gerada pelo paradoxo da amizade.
um crente pode afirmar que Deus é um mistério que transcende o conhecimento humano, que a crença é um ato de fé ou que Deus é um objeto de intuição mística.
não podemos é usar a matemática para provar que certos valores são intrinsecamente bons ou virtuosos.
Em geral, a informação de que dispomos é a popularidade do produto, mas o que nos realmente interessa é a qualidade.
os mercados são uma combinação de sinal, ruído e feedbacks; os modelos mostram que as crises são inevitáveis e permitem que eles tenham uma boa ideia da sua gravidade.
O maior problema das pessoas que não entendem de matemática é que elas acreditam literalmente nos resultados dos modelos.
Não acredite que você é capaz de prever o que vai acontecer na sua vida. Em vez disso, tome decisões que façam sentido para você, nas quais você acredite firmemente (para isso, naturalmente, você pode usar a equação do avaliador). Em seguida, use os três termos da equação do mercado para se preparar mentalmente para um futuro incerto. Não se esqueça do termo do ruído: vai ter de enfrentar muitos altos e baixos que estão fora do seu controle. Não se esqueça do termo social: não se empolgue demais com seus sucessos nem desanime quando a manada não compartilhar das suas ideias. E não se esqueça do termo do sinal: o verdadeiro valor do seu investimento está presente, mas que nem sempre você possa vê-lo.
o conceito da raça não faz sentido do ponto de vista científico. A origem geográfica dos nossos ancestrais simplesmente não explica as diferenças genéticas.
Como as bombas nucleares, os algoritmos não escolhem as vítimas.
a estereotipagem é uma consequência inevitável da necessidade de organizar uma grande quantidade de dados.
Os animais precisam de apenas duas coisas para sobreviver: comida e abrigo. E para se reproduzirem precisam de mais uma coisa: um parceiro. Porém, para conseguirem esses três requisitos básicos necessitam de algo ainda mais fundamental: informação.
Uma das razões pelas quais somos atraídos pelos jogos de computador é o modo como eles medem nossas conquistas. A vida real é confusa.
O problema não está na variedade de opções, mas na indecisão do nosso cérebro entre usufruir e explorar. Queremos estar seguros de que não perdemos nenhuma oportunidade.
Como dizem os antigos, quando você está no alto da montanha, deve apreciar a vista. A matemática confirma este dito popular.
O modo como dados e modelos são combinados e o nonsense é excluído proporciona à matemática uma honestidade essencial que a coloca acima de muitas outras formas de pensar.
O poder da lógica e da matemática de nos surpreender depende, como sua utilidade, das limitações da nossa razão.
As pessoas não estão em busca de lucro, estão em busca de emoção.
Aqueles que trabalham duro, que aprendem e perseveram são os vencedores.
Comece por pensar em termos de probabilidades, tanto para arriscar para conseguir o que você deseja, como para compreender que está correndo o risco de fracassar. Melhore seu poder de julgamento coletando dados antes de tirar conclusões. Aumente sua confiança, não se convencendo de que tem razão, mas girando a roleta várias vezes. Cada lição que as equações nos ensinam, de revelar o filtro criado pelas redes sociais e compreender como as sociedades nos coloca à beira do ponto crítico, ressalta a importância de ser honesto a respeito do nosso modelo e assegurar que os dados sejam usados como forma de aperfeiçoamento.
O método usado para escolher os melhores parâmetros é chamado de regressão logística.
Se um resultado é importante para você, considere a possibilidade de que ele seja atingido e também a de que não seja.
Pensar probabilisticamente é ser realista em relação aos ganhos e perdas esperados. Nas corridas de cavalos e no futebol, os azarões tendem a ser superestimados por jogadores inexperientes, mas na vida real tendemos a ser excessivamente prudentes. A aversão ao risco faz parte da natureza humana. Não se esqueça de que o ganho de encontrar um trabalho que você realmente aprecie ou um parceiro ou parceira que você ame de verdade é inestimável. Isso significa que você deve estar disposto a correr grandes riscos para atingir seus objetivos.
O segredo de apostar com sucesso não é fazer previsões com absoluta certeza, mas descobrir pequenas diferenças na forma como você vê o mundo e na forma como outras pessoas o veem.
Às vezes tendemos a concentrar todos os nossos esforços em uma “Grande Ideia”, mas, de acordo com a equação do jogador, o segredo consiste em criar diferentes variantes de uma ideia.
os melhores funcionários têm uma coisa em comum: a capacidade de absorver e utilizar novas informações, ajustando rapidamente suas estimativas à nova realidade.
O teorema de Bayes pode ser usado para avaliar corretamente a importância de novas informações e manter a calma quando todos à sua volta estão em pânico.
O primeiro passo para uma abordagem matemática do mundo é reconhecer a forma como usamos os modelos.
Somos o produto de todos os nossos atos, não o resultado de um ou dois erros. Aplique a você mesmo o perdão racional que Bayes nos ensina a aplicar aos outros.
David Hume havia afirmado que “nenhum testemunho é suficiente para provar que um milagre aconteceu, a menos que para desmentir o testemunho seja preciso admitir um milagre ainda maior”.
o pensamento lógico podia revelar verdades do mundo que não estavam ao alcance de nossa experiência cotidiana.
Nenhuma hipótese é 100% verdadeira, mas, à medida que os resultados experimentais se acumulam, algumas se tornam mais plausíveis do que outras.
Os experimentalistas colhem dados (D), e os teóricos formulam hipóteses ou modelos (M) a respeito dos dados. A equação de Bayes é usada para unir os dois componentes.
A geração do século XXI tem acesso a ideias e informações importantes que estariam além da compreensão dos jovens das décadas de 1970, 1980 ou mesmo 1990.
Sempre que vários fatores aleatórios se combinam para produzir um resultado final, o resultado é a distribuição normal, o que significa que a Equação 3 pode ser usada a fim de estabelecer um intervalo de confiança para qualquer atividade que envolva repetir o mesmo tipo de ação ou fazer o mesmo tipo de observação um grande número de vezes.
É fácil subestimar o número de observações necessárias para descobrir pequenas margens nos mercados.
A única forma de compreender o papel da discriminação em uma sociedade é fazer um grande número de observações e calcular um intervalo de confiança.
As estatísticas mostram que o que experimentamos individualmente muitas vezes não reflete o mundo como um todo. Depende de cada um de nós avaliar se nossas vidas são estatisticamente corretas e, caso não sejam, tomar alguma providência.
Em termos de neurose, extroversão, franqueza, alegria, tristeza, raiva e muitos outros traços de personalidade, a diferença entre homens e mulheres é muito pequena. Em um estudo mais recente, Hyde descobriu que as diferenças de gênero também são pequenas em termos de habilidade matemática, expressão oral, diligência, sensibilidade a recompensas, agressividade verbal, comunicabilidade, atitudes em relação à masturbação e a relacionamentos extraconjugais, liderança, autoestima e autoconceito acadêmico. As maiores diferenças entre os sexos estão no interesse pelas coisas em comparação com o interesse pelas pessoas, na agressividade física, no uso da pornografia e nas atitudes em relação ao sexo casual.
Como vou saber se alguém está me contando alguma coisa útil?
A divisão do mundo em modelos, dados e nonsense nos obriga a ser honestos a respeito das premissas que usamos para chegar às conclusões. Ela nos faz encarar com mais seriedade tanto as nossas opiniões como as alheias.
O melhor indicador do sucesso de um arremesso não é o número de acertos do jogador nos últimos cinco arremessos, é a posição dele e dos outros jogadores na quadra e o seu talento individual.
Medir a influência das pessoas se reduz a uma operação de álgebra matricial que um computador executa de forma mecânica e imparcial.
Uma vez que você aceite a inevitabilidade matemática de não ser popular, sua relação com as redes sociais deve melhorar.
A popularidade nas redes sociais é gerada por uma realimentação positiva na qual pessoas que já são populares buscam e conseguem novos seguidores. É uma ilusão estatística gerada pelo paradoxo da amizade.
um crente pode afirmar que Deus é um mistério que transcende o conhecimento humano, que a crença é um ato de fé ou que Deus é um objeto de intuição mística.
não podemos é usar a matemática para provar que certos valores são intrinsecamente bons ou virtuosos.
Em geral, a informação de que dispomos é a popularidade do produto, mas o que nos realmente interessa é a qualidade.
os mercados são uma combinação de sinal, ruído e feedbacks; os modelos mostram que as crises são inevitáveis e permitem que eles tenham uma boa ideia da sua gravidade.
O maior problema das pessoas que não entendem de matemática é que elas acreditam literalmente nos resultados dos modelos.
Não acredite que você é capaz de prever o que vai acontecer na sua vida. Em vez disso, tome decisões que façam sentido para você, nas quais você acredite firmemente (para isso, naturalmente, você pode usar a equação do avaliador). Em seguida, use os três termos da equação do mercado para se preparar mentalmente para um futuro incerto. Não se esqueça do termo do ruído: vai ter de enfrentar muitos altos e baixos que estão fora do seu controle. Não se esqueça do termo social: não se empolgue demais com seus sucessos nem desanime quando a manada não compartilhar das suas ideias. E não se esqueça do termo do sinal: o verdadeiro valor do seu investimento está presente, mas que nem sempre você possa vê-lo.
o conceito da raça não faz sentido do ponto de vista científico. A origem geográfica dos nossos ancestrais simplesmente não explica as diferenças genéticas.
Como as bombas nucleares, os algoritmos não escolhem as vítimas.
a estereotipagem é uma consequência inevitável da necessidade de organizar uma grande quantidade de dados.
Os animais precisam de apenas duas coisas para sobreviver: comida e abrigo. E para se reproduzirem precisam de mais uma coisa: um parceiro. Porém, para conseguirem esses três requisitos básicos necessitam de algo ainda mais fundamental: informação.
Uma das razões pelas quais somos atraídos pelos jogos de computador é o modo como eles medem nossas conquistas. A vida real é confusa.
O problema não está na variedade de opções, mas na indecisão do nosso cérebro entre usufruir e explorar. Queremos estar seguros de que não perdemos nenhuma oportunidade.
Como dizem os antigos, quando você está no alto da montanha, deve apreciar a vista. A matemática confirma este dito popular.
O modo como dados e modelos são combinados e o nonsense é excluído proporciona à matemática uma honestidade essencial que a coloca acima de muitas outras formas de pensar.
O poder da lógica e da matemática de nos surpreender depende, como sua utilidade, das limitações da nossa razão.
As pessoas não estão em busca de lucro, estão em busca de emoção.
Aqueles que trabalham duro, que aprendem e perseveram são os vencedores.
Comece por pensar em termos de probabilidades, tanto para arriscar para conseguir o que você deseja, como para compreender que está correndo o risco de fracassar. Melhore seu poder de julgamento coletando dados antes de tirar conclusões. Aumente sua confiança, não se convencendo de que tem razão, mas girando a roleta várias vezes. Cada lição que as equações nos ensinam, de revelar o filtro criado pelas redes sociais e compreender como as sociedades nos coloca à beira do ponto crítico, ressalta a importância de ser honesto a respeito do nosso modelo e assegurar que os dados sejam usados como forma de aperfeiçoamento.
December 18, 2022
“Each lesson the equations teach us … reiterates the importance of being honest about our (mental) model and ensuring we use data to improve ourselves”.
One of the best books I’ve read for the year 2022.
Written by British mathematicians & also a professor of a Swedish university who signifies the notion that everything in our life which appears hazy, random, and unexpected can be explained by mathematics. There's always formulas & equations for literally everything. From financial decisions to personal decisions, though you might not want people to view you as someone cumulative, it does help with life decisions. Sumpter highlights one fact; if life is so simple & there are apparent shortcuts for achieving all of our life goals, why do so many popular books—i.e., by Sheryl Sandberg, J. Peterson, Mark Manson, etc—presents contradictory viewpoints? Their words of wisdom demonstrate a paradox & proves that everything in life is mathematical; there isn’t any formula that couldn’t give us the answers. Told from the perspective of a secret mathematical society referring to themselves as ‘TEN’, the chapters demonstrate how components of our life that seem arbitrary and trivial are just as subject to the laws of mathematics as things that we are more likely to assume.
Excellent mental models & detailed explanations for each equation. Sumpter did a great job articulating complex ideas and using examples, stories, & anecdotes. My fav are ‘reward equation’ and ‘learning equation’. Not gonna lie, it's such an amazing book (for me)! Content wise & the story line 😙👌🏻 I even discussed & asked my mum (women in maths lol). Sumpter dumb-ed things down for his readers. Though most parts of the books are explained in layman terms, the application part, i.e., ‘how you can use them too’, might not be easy bcs not everyone is adept in mathematics. Also, I would appreciate it if Sumpter tones down on how TEN ‘changes’ everything. The equations work, they’re sacred, we got it ok.
Recommended for anyone who’s curious or wants to learn more about the influence of mathematics in our everyday life.
One of the best books I’ve read for the year 2022.
Written by British mathematicians & also a professor of a Swedish university who signifies the notion that everything in our life which appears hazy, random, and unexpected can be explained by mathematics. There's always formulas & equations for literally everything. From financial decisions to personal decisions, though you might not want people to view you as someone cumulative, it does help with life decisions. Sumpter highlights one fact; if life is so simple & there are apparent shortcuts for achieving all of our life goals, why do so many popular books—i.e., by Sheryl Sandberg, J. Peterson, Mark Manson, etc—presents contradictory viewpoints? Their words of wisdom demonstrate a paradox & proves that everything in life is mathematical; there isn’t any formula that couldn’t give us the answers. Told from the perspective of a secret mathematical society referring to themselves as ‘TEN’, the chapters demonstrate how components of our life that seem arbitrary and trivial are just as subject to the laws of mathematics as things that we are more likely to assume.
Excellent mental models & detailed explanations for each equation. Sumpter did a great job articulating complex ideas and using examples, stories, & anecdotes. My fav are ‘reward equation’ and ‘learning equation’. Not gonna lie, it's such an amazing book (for me)! Content wise & the story line 😙👌🏻 I even discussed & asked my mum (women in maths lol). Sumpter dumb-ed things down for his readers. Though most parts of the books are explained in layman terms, the application part, i.e., ‘how you can use them too’, might not be easy bcs not everyone is adept in mathematics. Also, I would appreciate it if Sumpter tones down on how TEN ‘changes’ everything. The equations work, they’re sacred, we got it ok.
Recommended for anyone who’s curious or wants to learn more about the influence of mathematics in our everyday life.
April 26, 2023
3.49 stars. I strongly recommend it for its clear explanations of the equations, as well as its applications and practical advice.
I'd give it 5 stars, but almost two whole chapters digress into cracker barrel philosophy, repeatedly claiming that most data modelers are logical positivists. If that's true, naive verificationism could be making a major contribution to the "replication crisis" in science by encouraging researchers to double down on their confirmation bias. But as far as I can tell, it's just puffery. Logical positivism made notable contributions to analytic philosophy, but as a school of thought, it started dying in the 1950s and was dead by the 1970s. Asked in 1977 what he saw as its main defects, the author's favorite logical positivist, A.J. Ayers, quipped that "nearly all of it was false." (Well, at least it was falsifiable.) Labeling everything but math and data "non-sense" is a catchy sneer, but it isn't an actual argument.
Then, in the last chapter, the author serves up the least competent discussion of the trolley problem I've seen anywhere, including a clumsy caricature of utilitarianism and a charming belief that his own moral intuitions are universal. By any standards, including his own, the chapter is a mixture of "non-sense" and bad science.
Finally, his ongoing metaphor of data modelers as a "secret society" was cute when he introduced it, but it quickly became tedious. It added nothing and misled some reviewers into taking the metaphor literally and deciding he's a crank.
I'd give it 5 stars, but almost two whole chapters digress into cracker barrel philosophy, repeatedly claiming that most data modelers are logical positivists. If that's true, naive verificationism could be making a major contribution to the "replication crisis" in science by encouraging researchers to double down on their confirmation bias. But as far as I can tell, it's just puffery. Logical positivism made notable contributions to analytic philosophy, but as a school of thought, it started dying in the 1950s and was dead by the 1970s. Asked in 1977 what he saw as its main defects, the author's favorite logical positivist, A.J. Ayers, quipped that "nearly all of it was false." (Well, at least it was falsifiable.) Labeling everything but math and data "non-sense" is a catchy sneer, but it isn't an actual argument.
Then, in the last chapter, the author serves up the least competent discussion of the trolley problem I've seen anywhere, including a clumsy caricature of utilitarianism and a charming belief that his own moral intuitions are universal. By any standards, including his own, the chapter is a mixture of "non-sense" and bad science.
Finally, his ongoing metaphor of data modelers as a "secret society" was cute when he introduced it, but it quickly became tedious. It added nothing and misled some reviewers into taking the metaphor literally and deciding he's a crank.
October 16, 2021
Fantastic book about applied mathematics in real life
I’m not sure why previous reviews were so negative. It seems likely previous reviewers were more concerned with political alignment than the actual content.
This is an incredible book. I’ve done the rare thing of also purchasing a copy in hardcover to refer to again and again.
I say this as a practicing data scientist at a Fortune 100 company; this book will, or should, change the way you think about the world. I have a very strong background in mathematics and data science, so none of the concepts were exactly new to me. That said, they were described accurately, and the mind blowing part was the way the author connected the application of these equations into different domains for the purpose of showing the wide variety of problems which can be solved using these ten simple equations.
I would highly encourage everyone to pick up a copy and at least familiarize yourself with the concepts, as these equations are actually changing your world, right now, and you owe it to yourself to understand them. Hopefully you can find a way to apply them to make your life better; I know I certainly will be.
Highly highly recommended!
I’m not sure why previous reviews were so negative. It seems likely previous reviewers were more concerned with political alignment than the actual content.
This is an incredible book. I’ve done the rare thing of also purchasing a copy in hardcover to refer to again and again.
I say this as a practicing data scientist at a Fortune 100 company; this book will, or should, change the way you think about the world. I have a very strong background in mathematics and data science, so none of the concepts were exactly new to me. That said, they were described accurately, and the mind blowing part was the way the author connected the application of these equations into different domains for the purpose of showing the wide variety of problems which can be solved using these ten simple equations.
I would highly encourage everyone to pick up a copy and at least familiarize yourself with the concepts, as these equations are actually changing your world, right now, and you owe it to yourself to understand them. Hopefully you can find a way to apply them to make your life better; I know I certainly will be.
Highly highly recommended!
March 30, 2021
As is usual from David Sumpter, TEN equations is an exceptional and exhaustive read.
There is another review which understably questions why Sumpter opts to expand on the equations through use cases in industries such as gambling, sport, search and social media but the answer is somewhat obvious, is it not? He has real experience of the mechanics in the industries but most of all they’re popular sports or companies well known to all who’ve given themselves an almost unassailable lead by harnessing key mathematical principles for their benefit. They’re provocative through their profiteering as the rest of the world sits in the 99% oblivious to the terms the true game is played on.
David has a wonderful way of adding a human touch to what can be complex academic principles so again like all of his books it’s well worth taking the time out to read them.
There is another review which understably questions why Sumpter opts to expand on the equations through use cases in industries such as gambling, sport, search and social media but the answer is somewhat obvious, is it not? He has real experience of the mechanics in the industries but most of all they’re popular sports or companies well known to all who’ve given themselves an almost unassailable lead by harnessing key mathematical principles for their benefit. They’re provocative through their profiteering as the rest of the world sits in the 99% oblivious to the terms the true game is played on.
David has a wonderful way of adding a human touch to what can be complex academic principles so again like all of his books it’s well worth taking the time out to read them.
Read
January 24, 2023Kinda politically charged and peterson bashing. Not as much math as expected; author tends to ramble in barely relevant threads. Also weak conclusions to points made.
May 13, 2025
Upon reading about the 10 most-important equations, one immediately thinks of Maxwell’s, Einstein’s, Newton’s, and similar equations. The 10 equations discussed in this book are lesser-known, except possibly for Bayes’ rule, discussed in Chapter 1 titled “The Judgement Equation.” They are however quite important in our personal and work-related decision-making and in our interactions with others.
Personal experiences have led the author to believe in TEN, his pretend secret society that has produced the 10 equations which have worked for him. “These equations have shaped my thinking in ways that have helped me find happiness and fulfillment. They have also made me a better person: More balanced in my outlook and better able to understand the actions of others.”
In the rest of this review, I list the chapter titles and briefly describe (in parentheses) my understanding of the equations, along with their significance and applications.
1. The Judgement Equation (Many scary situations, such as turbulence in flight or testing positive for a deadly disease, become less so if you analyze them through the application of Bayes’ rule)
2. The Betting Equation (Logistic regression allows you to cash in on a small informational edge by increasing the probability that you come out on the winning side)
3. The Confidence Equation (Pay attention not just to the expected value but also the variations or uncertainties, as in the specification that the value of x is 4 plus-or-minus 1)
4. The Skill Equation (The performance of a bank teller should be judged by the number of customers s/he can serve per unit time; the fact that the customer queue keeps growing isn’t his/her fault)
5. The Influencer Equation (Random movements or connections can lead to stationary distributions, as in Markov chains, a fact that Google exploited in its PageRank algorithm)
6. The Market Equation (Variations in the value of a stock consist of an overall trend, the signal, and local fluctuations, the noise. Deriving and using the signal allows you to make money from long-term investments)
7. The Advertising Equation (Advertisers categorize people according to correlations among things they like. This sounds like stereotyping, but it works great as an advertising strategy)
8. The Reward Equation (When you watch a series of episodes of a TV show or play a computer game, the decision to continue the activity or to abandon it is based on a running quality or satisfaction score, a value that is updated with each additional step)
9. The Learning Equation (Entertainment and e-commerce sites want to keep your attention for as long as they can. They use learning algorithms to predict what will keep you on the site, so that they can sell you things or feed you ads)
10. The Universal Equation (The ‘if … then … else’ construct is a universal building block for use in algorithms. It helps us find shortest paths in graph, merge two sorted sublists, or synthesize any other desired function)
I read the e-book version of this title, in which the equations, the supposed heart of the book, appeared as tiny images, making them quite difficult to read and understand. In many cases, I had to take screenshots of the pages and enlarge them in order to read the equations and the associated analyses. I hope this problem is fixed in future editions.
Personal experiences have led the author to believe in TEN, his pretend secret society that has produced the 10 equations which have worked for him. “These equations have shaped my thinking in ways that have helped me find happiness and fulfillment. They have also made me a better person: More balanced in my outlook and better able to understand the actions of others.”
In the rest of this review, I list the chapter titles and briefly describe (in parentheses) my understanding of the equations, along with their significance and applications.
1. The Judgement Equation (Many scary situations, such as turbulence in flight or testing positive for a deadly disease, become less so if you analyze them through the application of Bayes’ rule)
2. The Betting Equation (Logistic regression allows you to cash in on a small informational edge by increasing the probability that you come out on the winning side)
3. The Confidence Equation (Pay attention not just to the expected value but also the variations or uncertainties, as in the specification that the value of x is 4 plus-or-minus 1)
4. The Skill Equation (The performance of a bank teller should be judged by the number of customers s/he can serve per unit time; the fact that the customer queue keeps growing isn’t his/her fault)
5. The Influencer Equation (Random movements or connections can lead to stationary distributions, as in Markov chains, a fact that Google exploited in its PageRank algorithm)
6. The Market Equation (Variations in the value of a stock consist of an overall trend, the signal, and local fluctuations, the noise. Deriving and using the signal allows you to make money from long-term investments)
7. The Advertising Equation (Advertisers categorize people according to correlations among things they like. This sounds like stereotyping, but it works great as an advertising strategy)
8. The Reward Equation (When you watch a series of episodes of a TV show or play a computer game, the decision to continue the activity or to abandon it is based on a running quality or satisfaction score, a value that is updated with each additional step)
9. The Learning Equation (Entertainment and e-commerce sites want to keep your attention for as long as they can. They use learning algorithms to predict what will keep you on the site, so that they can sell you things or feed you ads)
10. The Universal Equation (The ‘if … then … else’ construct is a universal building block for use in algorithms. It helps us find shortest paths in graph, merge two sorted sublists, or synthesize any other desired function)
I read the e-book version of this title, in which the equations, the supposed heart of the book, appeared as tiny images, making them quite difficult to read and understand. In many cases, I had to take screenshots of the pages and enlarge them in order to read the equations and the associated analyses. I hope this problem is fixed in future editions.
November 14, 2023
This book is an excellent complement to Hello World: Being Human in the Age of Algorithms as it helps expand readers' perspective on key mathematical ideas that underlie data science. The author also discusses abundant cases of how each of these data science ideas is applied in human enterprises - the good, the bad and the ugly.
The author is quite gifted in providing layman explanation on how each of these math ideas works. I have read so many popular science books in the past that discussed about the utility of correlation but these books never explained how correlation was derived which hindered my appreciation of this concept. This book is the first that clearly brings me to understand how correlation is formulated and I'm thankful for the author's convincing writing communication talent.
Compared to The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World, this book contains less technical details on how each math idea works but the author compensates for this lack with his layman-termed descriptive examples on how it works and I find it as revealing in educating readers to the knowledge. But it is the human-side narratives of how these math ideas are applied in real world cases that make this book more enlightening for any one interested in understanding the real impact of data science to our contemporary lives. The author shares many of his personal and professional experiences relevant to the matters being discussed which shows how extensive his insights in data science is.
Readers who are keen in understanding important ideas and their practical applications that are pivotal to AI's role in our lives will immensely appreciate this informative book.
For more book that will also complement his one (and is also mentioned by the author, I recommend Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy.
The author is quite gifted in providing layman explanation on how each of these math ideas works. I have read so many popular science books in the past that discussed about the utility of correlation but these books never explained how correlation was derived which hindered my appreciation of this concept. This book is the first that clearly brings me to understand how correlation is formulated and I'm thankful for the author's convincing writing communication talent.
Compared to The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World, this book contains less technical details on how each math idea works but the author compensates for this lack with his layman-termed descriptive examples on how it works and I find it as revealing in educating readers to the knowledge. But it is the human-side narratives of how these math ideas are applied in real world cases that make this book more enlightening for any one interested in understanding the real impact of data science to our contemporary lives. The author shares many of his personal and professional experiences relevant to the matters being discussed which shows how extensive his insights in data science is.
Readers who are keen in understanding important ideas and their practical applications that are pivotal to AI's role in our lives will immensely appreciate this informative book.
For more book that will also complement his one (and is also mentioned by the author, I recommend Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy.
Read
May 6, 2025É um livro interessante e informativo que explica como as equações matemáticas podem ser aplicadas em diferentes aspectos da vida cotidiana.
1. No capítulo sobre a equação do jogador, aprendi que a força é a energia transferida, e a aceleração é a taxa de transferência. Isso ajuda a entender como a força atua em diferentes situações e como ela pode ser medida e controlada.
2. No capítulo sobre a equação do avaliador, aprendi que quando se trata de probabilidade, o tamanho conta. Isso destaca o fato de que conforme a amostra se torna maior, a probabilidade de obter resultados precisos também aumenta.
3. No capítulo sobre a equação da confiança aprendi que a melhor rota é a mais curta, mas não sempre é a mais rápida. Isso lembra que há vezes em que a rota menos direta pode levar a melhores resultados, mesmo que seja mais longa.
4. No capítulo sobre a equação do desempenho aprendi que a difusão é a força motriz da natureza que molda todas as formas de vida e ela pode ser observada em diferentes contextos.
5. No capítulo sobre a equação do influenciador, aprendi que a energia não é criada nem destruída, ela simplesmente muda de forma. Isso nos lembra que a energia é uma entidade constante e que ela pode ser vista em diferentes formas em nosso mundo.
6. No capítulo sobre a equação do mercado, aprendi que os planetas se movem em curvas, e não em linhas retas. Isso nos lembra que a natureza não é perfeita e que, às vezes, pode apresentar padrões inesperados e complexos.
7. No capítulo sobre a equação do anunciante aprendi que a resistência elétrica é uma medida da dificuldade de fluxo de corrente elétrica através de um material. Isso ajuda a entender como a resistência elétrica afeta nossas vidas e como ela pode ser controlada.
8. No capítulo sobre a equação da recompensa aprendi que a energia que é gasta aqui é libertada ali. Isso nos lembra que nada é perdido no universo e que a energia pode ser transformada de uma forma para outra.
9. No capítulo sobre a equação do aprendizado, aprendi que a atração gravitacional entre dois corpos é proporcional ao produto das suas massas e inversamente proporcional ao quadrado da distância entre eles.
10. No capítulo sobre a equação universal aprendi que as equações são a base de tudo o que fazemos. Elas são a linguagem que as nossas mentes entendem.
1. No capítulo sobre a equação do jogador, aprendi que a força é a energia transferida, e a aceleração é a taxa de transferência. Isso ajuda a entender como a força atua em diferentes situações e como ela pode ser medida e controlada.
2. No capítulo sobre a equação do avaliador, aprendi que quando se trata de probabilidade, o tamanho conta. Isso destaca o fato de que conforme a amostra se torna maior, a probabilidade de obter resultados precisos também aumenta.
3. No capítulo sobre a equação da confiança aprendi que a melhor rota é a mais curta, mas não sempre é a mais rápida. Isso lembra que há vezes em que a rota menos direta pode levar a melhores resultados, mesmo que seja mais longa.
4. No capítulo sobre a equação do desempenho aprendi que a difusão é a força motriz da natureza que molda todas as formas de vida e ela pode ser observada em diferentes contextos.
5. No capítulo sobre a equação do influenciador, aprendi que a energia não é criada nem destruída, ela simplesmente muda de forma. Isso nos lembra que a energia é uma entidade constante e que ela pode ser vista em diferentes formas em nosso mundo.
6. No capítulo sobre a equação do mercado, aprendi que os planetas se movem em curvas, e não em linhas retas. Isso nos lembra que a natureza não é perfeita e que, às vezes, pode apresentar padrões inesperados e complexos.
7. No capítulo sobre a equação do anunciante aprendi que a resistência elétrica é uma medida da dificuldade de fluxo de corrente elétrica através de um material. Isso ajuda a entender como a resistência elétrica afeta nossas vidas e como ela pode ser controlada.
8. No capítulo sobre a equação da recompensa aprendi que a energia que é gasta aqui é libertada ali. Isso nos lembra que nada é perdido no universo e que a energia pode ser transformada de uma forma para outra.
9. No capítulo sobre a equação do aprendizado, aprendi que a atração gravitacional entre dois corpos é proporcional ao produto das suas massas e inversamente proporcional ao quadrado da distância entre eles.
10. No capítulo sobre a equação universal aprendi que as equações são a base de tudo o que fazemos. Elas são a linguagem que as nossas mentes entendem.
January 16, 2023
Sumpter has Bill Nye applied math energy. His central gimmick—a secret society of people who know math—is a bit much. He's most interesting when connecting equations and philosophy, but he likes logical positivism more than his hero Ayers did, and his ultimate appeal to ethical intuitionism is unsatisfying. Still very interesting in places, and I'm generally with him.
I like the core idea of trying to distill a lot of understanding into a few core concepts. I think Sumpter's book highlights both the promise and challenge of attempting this.
Here are the names Sumpter uses for his equations (and more conventional names):
1. The Judgment Equation (Bayes' theorem)
2. The Betting Equation (Logistic regression)
3. The Confidence Equation (Normal confidence intervals)
4. The Skill Equation (Markov property; memorylessness)
5. The Influencer Equation (Stationary distribution; PageRank)
6. The Market Equation (A sort of autoregressive differential model?)
7. The Advertising Equation (Correlation coefficient)
8. The Reward Equation (Exponential moving average; Q-learning)
9. The Learning Equation (Derivative of quadratic loss; gradient descent)
10. The Universal Equation (If-then; trying to get from "is" to "ought")
With the exception of #6, I was reasonably familiar with all of these. My failure to feel connected to the literature (or even what a common name might be) for #6 makes me feel that this book might not be the best way to encounter these ideas for the first time.
I like the core idea of trying to distill a lot of understanding into a few core concepts. I think Sumpter's book highlights both the promise and challenge of attempting this.
Here are the names Sumpter uses for his equations (and more conventional names):
1. The Judgment Equation (Bayes' theorem)
2. The Betting Equation (Logistic regression)
3. The Confidence Equation (Normal confidence intervals)
4. The Skill Equation (Markov property; memorylessness)
5. The Influencer Equation (Stationary distribution; PageRank)
6. The Market Equation (A sort of autoregressive differential model?)
7. The Advertising Equation (Correlation coefficient)
8. The Reward Equation (Exponential moving average; Q-learning)
9. The Learning Equation (Derivative of quadratic loss; gradient descent)
10. The Universal Equation (If-then; trying to get from "is" to "ought")
With the exception of #6, I was reasonably familiar with all of these. My failure to feel connected to the literature (or even what a common name might be) for #6 makes me feel that this book might not be the best way to encounter these ideas for the first time.
April 30, 2022
A popular-maths book is always delightful for me. While this one might seem a bit too basic if you are someone with any kind of mathsy background, it is still worth your time (and it is not that long in the end, so you won't waste much of it in any case).
Yes, you have heard a lot of this already - least of all you know about the existence of variances and standard deviations, you know how simple the Bayes' rule is and how powerful it gets and you might even be aware how Netflix knows what to recommend to you. However, as with an academic talk that is too general, you'll end up happy about hearing about things you already understand and you might very well still end up with a new perspective on things you've been aware of...
..and to get off my snobby high horse, if you don't happen to have the right kind of maths background and you are also a beginning nerd, this book is a very nice intro to some of the aspects of maths that run the current world.
Finally, for an added bonus, it is always nice to end with a surprise, specifically read in an actual published book about a spare-time project of your former colleague he was telling you as he was creating it. Good on you, Adam!
Yes, you have heard a lot of this already - least of all you know about the existence of variances and standard deviations, you know how simple the Bayes' rule is and how powerful it gets and you might even be aware how Netflix knows what to recommend to you. However, as with an academic talk that is too general, you'll end up happy about hearing about things you already understand and you might very well still end up with a new perspective on things you've been aware of...
..and to get off my snobby high horse, if you don't happen to have the right kind of maths background and you are also a beginning nerd, this book is a very nice intro to some of the aspects of maths that run the current world.
Finally, for an added bonus, it is always nice to end with a surprise, specifically read in an actual published book about a spare-time project of your former colleague he was telling you as he was creating it. Good on you, Adam!
October 27, 2024
The book irritates me. Sumpter crafts this hyperbole narrative of an illuminati-style group "TEN" that, utilizing ten equations, has come to govern the world over the last century, with him chiefly amongst "them". I find it so reductive and presumptuous that I found it difficult getting through. He's also very preachy, commenting on religion, climate change, Jordan Peterson, or high-frequency trading , when judging by what he's writing, he seems as equally uninformed as the bankers he is judging in the book for being uninformed.
It all feels misplaced in a book about maths.
It's sad, because I appreciate the quest of trying to highlight the most impactful equations, that's why I picked up the book. I fondly remember taking stats and especially algorithms classes in Uni and marveling at how a new elegant solution could suddenly crack a previously unimaginable problem, and have a huge impact. He does have some interesting paragraphs, I thought the influencer chapter was illuminating, and I also enjoyed his chapter on Bayes, but it's just wrapped up in so much bullshit that I wouldn't recommend it to anyone.
He gushes about Taleb in the book, but I'm sure he'd be disappointed about a book that makes such sweeping claims when in reality, there is just way too much noise.
It all feels misplaced in a book about maths.
It's sad, because I appreciate the quest of trying to highlight the most impactful equations, that's why I picked up the book. I fondly remember taking stats and especially algorithms classes in Uni and marveling at how a new elegant solution could suddenly crack a previously unimaginable problem, and have a huge impact. He does have some interesting paragraphs, I thought the influencer chapter was illuminating, and I also enjoyed his chapter on Bayes, but it's just wrapped up in so much bullshit that I wouldn't recommend it to anyone.
He gushes about Taleb in the book, but I'm sure he'd be disappointed about a book that makes such sweeping claims when in reality, there is just way too much noise.
January 3, 2023
I'm not sure what I expected when I picked up this book, but a framing of scientific and mathematical achievement as an Illuminati-style secret society wasn't it. Bit of a strange choice but I don't think it took away from the book too much. What did take away from it is its uncertainty; I feel like at times it didn't know whether it wanted to be a self-help book or a math book, and it often felt caught in an uncomfortable middle.
Regardless it was a pretty good dive into some important mathematical concepts. I don't like the "ten equations" framing - most chapters were more about an idea than an equation, with unnecessary importance placed on the equations themselves - but that's easy to look past.
I very much liked that Sumpter didn't make any effort to keep the book "apolitical". His personal views aside, he takes time to debunk some very popular figures on the basis that their arguments go against math and science. If you agree with those arguments and don't want to hear that they're wrong, you may complain that this book is "too political". But in that case, you're missing the entire point.
Regardless it was a pretty good dive into some important mathematical concepts. I don't like the "ten equations" framing - most chapters were more about an idea than an equation, with unnecessary importance placed on the equations themselves - but that's easy to look past.
I very much liked that Sumpter didn't make any effort to keep the book "apolitical". His personal views aside, he takes time to debunk some very popular figures on the basis that their arguments go against math and science. If you agree with those arguments and don't want to hear that they're wrong, you may complain that this book is "too political". But in that case, you're missing the entire point.
December 28, 2021
Sumpter does a great job explaining how the 10 equations rule our lives, and can be used for great purposes in our daily life. However he seems to suggest that some semidefinite form of logical positivism is a valid way of seeing the world, by separating "models, data, nonsense," and further posits that we can do better today than moral codes such as the Ten Commandments. Of course we can. Ethics, morality, and the extant question of how we should live is still too dominant and powerful to relegate it over to the limited methodologies of TEN. The "universal truth" of algorithms and great theorems of pure mathematics do not tell us anything about how to live, and Sumpter admits this. I think any attempt to replace tradition, moral codes, and history with mathematics is elitist, subsuming and frankly, arrogant. Despite these small inconsistencies, the author does arrive at the conclusion that moral intuition does indeed have its place, and occupies a quite crucial one, namely that we use them to define what problems we should solve.
January 18, 2023
As someone who has never taken to math, I found this book eye-opening.
David presents mathematical equations and concepts in a fun way that makes it accessible to the lay person.
Although the book is littered with numerous formulas and calculations which went over my head, he carefully explains their basis for logical/algorithmic thinking.
David links this to answering questions such as:
- Should you quit your job (or your relationship) and try something else?
- Is the plane you are on about to crash?
- How much effort should you put into becoming more popular?
- How many episodes of a Netflix series should you watch before trying something else?
- Is X a bitch?
And other life-changing dilemmas. :)
I found the response to Jordan Peterson and the analysis of the Cambridge Analytica scandal particularly insightful.
Also, it provided food for thought on how applied math can inform/support moral decision-making.
I hope the author will consider providing a summary at the end of each chapter on how to apply the equations in the next edition.
David presents mathematical equations and concepts in a fun way that makes it accessible to the lay person.
Although the book is littered with numerous formulas and calculations which went over my head, he carefully explains their basis for logical/algorithmic thinking.
David links this to answering questions such as:
- Should you quit your job (or your relationship) and try something else?
- Is the plane you are on about to crash?
- How much effort should you put into becoming more popular?
- How many episodes of a Netflix series should you watch before trying something else?
- Is X a bitch?
And other life-changing dilemmas. :)
I found the response to Jordan Peterson and the analysis of the Cambridge Analytica scandal particularly insightful.
Also, it provided food for thought on how applied math can inform/support moral decision-making.
I hope the author will consider providing a summary at the end of each chapter on how to apply the equations in the next edition.
September 28, 2021
Hard to follow on audiobook, but Sumpter explains this in the audiobook, so good for him.
I appreciate he separates his politics to certain sections, but I'm confused. Sumpter acknowledges his politics could be labeled "woke" and explains why he believes what he does. I appreciate this, good. Then he makes certain claims and then doesn't use the "equations to rule the world" to defend them. Like, this is the perfect chance to show the math of anti-racism, and he only does one time, I think. The times he doesn't stand out as feeling unfinished, like I'm waiting on a paragraph that isn't coming. Maybe this was a decision to keep the topic of the book focused on "not-politics", but then why bring up politics at all?
Overall, a great book, explanations of important equations for social media algorithms, AI, online betting, etc.
**I received this book from NetGalley in exchange of an honest review.
I appreciate he separates his politics to certain sections, but I'm confused. Sumpter acknowledges his politics could be labeled "woke" and explains why he believes what he does. I appreciate this, good. Then he makes certain claims and then doesn't use the "equations to rule the world" to defend them. Like, this is the perfect chance to show the math of anti-racism, and he only does one time, I think. The times he doesn't stand out as feeling unfinished, like I'm waiting on a paragraph that isn't coming. Maybe this was a decision to keep the topic of the book focused on "not-politics", but then why bring up politics at all?
Overall, a great book, explanations of important equations for social media algorithms, AI, online betting, etc.
**I received this book from NetGalley in exchange of an honest review.
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