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رياضيات الحياة والموت
الرياضيات هي قصّة العالم من حولنا، ومن شأن الحكمة
التي تشتمل عليها أن تشكّل الفرق بين النجاح والكارثة.
نحن نمارس الرياضيات طوال الوقت، من الطريقة التي نتواصل بها مع بعضنا البعض إلى الطريقة التي نسافر بها، ومن كيفيّة عملنا إلى كيفية استرخائنا. وكثير منّا يدركون ذلك. لكنّ قلّة منّا يقدّرون حقاً القوّة الكاملة للرياضيات، إلى أيّ مدى يتجاوز تأثيرها كلّ مكتب وكلّ منزل، ليشمل قاعات المحاكم وأجنحة المستشفيات؟
في كتابه «رياضيّات الحياة والموت» المذهل وغير العادي يستكشف عالم الرياضيات كِيت ييتس القصص الحقيقية لأحداث غيّرت الحياة وأدّى فيها تطبيق الرياضيات – أو سوء تطبيقها – دوراً حاسماً: مرضى أصيبوا بالعجز بسبب جينات معبئة ورجال أعمال أفلسوا نتيجة خوارزميات خاطئة؛ ضحايا أبرياء لأخطاء العدالة وضحايا غير مقصودين لمواطن خلل في البرمجيات. كما نتعرف إلى قصص مستثمرين خسروا ثروات وأهالٍ خسروا أطفالاً، وكل ذلك نتيجة سوء الفهم الرياضي.
وعلى طول طريق القراءة في هذا الكتاب، يُسلّحنا ييتس بقواعد وأدوات رياضية بسيطة من شأنها أن تساعدنا في اتّخاذ قرارات أفضل في مجتمعنا الكمّي على نحو متزايد. وسوف نكتشف معاً لماذا يُعتبر من المنطقي دائماً التشكيك في إحصائية ما، ومن الحيوي غالباً طلب رأي ثانٍ، ومن المفيد أحياناً الالتزام بقاعدة الـ 37%. لقد حان الوقت لنقبض مجدّداً على زمام السلطة، لأنّ الرياضيّات في بعض الأحيان هي بالفعل مسألة حياة أو موت.
كِيت ييتس هو محاضر أوّل في قسم العلوم الرياضية ومدير مشارك في مركز البيولوجيا الرياضية بجامعة باث. حصل على درجة الدكتوراه في الرياضيات من جامعة أكسفورد في عام 2011.
يوضح بحثه أنّه بالإمكان استخدام الرياضيات لوصف جميع أنواع الظواهر الواقعية: من تكوين الأجنّة إلى حشود الجراد، ومن مرض النوم إلى نمط قشرة البيض. وهو مهتم بشكل خاص بالدور الذي تؤدّيه العشوائية في علم الأحياء. تمّت تغطية أبحاثه في البيولوجيا الرياضية من قبل هيئة الإذاعة البريطانية بي بي سي، والغارديان، والتلغراف، والديلي ميل، وآر تي إي، وساينتيفيك أميركان، ورويترز وغيرها..
إلى جانب منصبه الأكاديمي، يعَدّ كِيت ييتس مؤلفاً ومراسلاً علمياً. ورياضيات الحياة والموت هو أوّل كتاب يصدر له.
التي تشتمل عليها أن تشكّل الفرق بين النجاح والكارثة.
نحن نمارس الرياضيات طوال الوقت، من الطريقة التي نتواصل بها مع بعضنا البعض إلى الطريقة التي نسافر بها، ومن كيفيّة عملنا إلى كيفية استرخائنا. وكثير منّا يدركون ذلك. لكنّ قلّة منّا يقدّرون حقاً القوّة الكاملة للرياضيات، إلى أيّ مدى يتجاوز تأثيرها كلّ مكتب وكلّ منزل، ليشمل قاعات المحاكم وأجنحة المستشفيات؟
في كتابه «رياضيّات الحياة والموت» المذهل وغير العادي يستكشف عالم الرياضيات كِيت ييتس القصص الحقيقية لأحداث غيّرت الحياة وأدّى فيها تطبيق الرياضيات – أو سوء تطبيقها – دوراً حاسماً: مرضى أصيبوا بالعجز بسبب جينات معبئة ورجال أعمال أفلسوا نتيجة خوارزميات خاطئة؛ ضحايا أبرياء لأخطاء العدالة وضحايا غير مقصودين لمواطن خلل في البرمجيات. كما نتعرف إلى قصص مستثمرين خسروا ثروات وأهالٍ خسروا أطفالاً، وكل ذلك نتيجة سوء الفهم الرياضي.
وعلى طول طريق القراءة في هذا الكتاب، يُسلّحنا ييتس بقواعد وأدوات رياضية بسيطة من شأنها أن تساعدنا في اتّخاذ قرارات أفضل في مجتمعنا الكمّي على نحو متزايد. وسوف نكتشف معاً لماذا يُعتبر من المنطقي دائماً التشكيك في إحصائية ما، ومن الحيوي غالباً طلب رأي ثانٍ، ومن المفيد أحياناً الالتزام بقاعدة الـ 37%. لقد حان الوقت لنقبض مجدّداً على زمام السلطة، لأنّ الرياضيّات في بعض الأحيان هي بالفعل مسألة حياة أو موت.
كِيت ييتس هو محاضر أوّل في قسم العلوم الرياضية ومدير مشارك في مركز البيولوجيا الرياضية بجامعة باث. حصل على درجة الدكتوراه في الرياضيات من جامعة أكسفورد في عام 2011.
يوضح بحثه أنّه بالإمكان استخدام الرياضيات لوصف جميع أنواع الظواهر الواقعية: من تكوين الأجنّة إلى حشود الجراد، ومن مرض النوم إلى نمط قشرة البيض. وهو مهتم بشكل خاص بالدور الذي تؤدّيه العشوائية في علم الأحياء. تمّت تغطية أبحاثه في البيولوجيا الرياضية من قبل هيئة الإذاعة البريطانية بي بي سي، والغارديان، والتلغراف، والديلي ميل، وآر تي إي، وساينتيفيك أميركان، ورويترز وغيرها..
إلى جانب منصبه الأكاديمي، يعَدّ كِيت ييتس مؤلفاً ومراسلاً علمياً. ورياضيات الحياة والموت هو أوّل كتاب يصدر له.
342 pages, Paperback
First published September 5, 2019
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September 20, 2019
My problem with books on mathematics is never remembering the formulas, even from one chapter to the next. OK, and being bored with them is a factor too. Kit Yates solved these problems by not using any formulas, or even much math in his delightful (when not frightening) The Math of Life and Death. His secret is really simple: he tells stories. The result is always engaging, often infuriating and sometimes horrifying. We defy the math at our peril.
Using examples from the news, such as epidemics or murder investigations, Yates shows what underlies the events – the basic numbers that anyone can see do or do not add up.
The whole strength of The Math of Life and Death is the power of true events. Yates recognizes their value, and provides the background facts that fit with numbers that prove a point. In the hot new service of gene sequencing, he shows clearly how our assumption about identifying people by DNA samples can go wrong – badly – enough to incarcerate the wrong person. In his own case, 23andMe gave him a death sentence through a wrong interpretation of his genes. He proved it (to his great relief) with other such services and went back to show just how the numbers can lead analysis astray. Sloppy math is hard to prove, but can ruin lives.
He shows that something as unmathematical as algae needs an understanding of math. An algal bloom doubles in size every day, until it covers a lake - in 30 days. If you see the lake is half covered, how long do you think it will take for it to be covered completely? Most would calculate numerous days, based on when the algae first appeared and had reached the halfway point, but the correct answer is one more day. Mistakes like this lead planes to crash, which Yates also shows in painful detail.
Doctors are forever misinterpreting test results, giving patients false death sentences or false reassurances. Yates gives the example of breast cancer tests, by which doctors seem to predict nine out of every two cases of breast cancer in women. The numbers are pretty stark. With false positives from tests, 981 women out of a random 10,000 will be told that they have breast cancer. But of those, only 90 will actually have it. Ninety out of ten thousand (ie. nine per thousand) is not the pandemic plague that should cause panicked fear in women, but that’s how doctors present it when they are surveyed. Given multiple choice questions, doctors fare far worse than if they had chosen random answers. They are prejudiced in the false direction. They have the facts and the numbers wrong. The result is needless surgery, needless chemotherapy, and much pointless suffering.
There is a horrifying chapter on legal ignorance as well. So-called expert witnesses bamboozle judges, juries and opposing lawyers with mumbo-jumbo that no one challenges, because they don’t understand what was said. They just pick out a major conclusion from what they heard, and accept it as true and significant. The result is wrongful convictions. In the major case cited, a young mother went to prison for murdering her first two children, because an expert incorrectly claimed the chances of two children from the same family dying from Sudden Infant Death Syndrome (SIDS) was one in 73 million. (He made up the number himself.) That’s all the jury needed to know. It didn’t matter that the expert was wrong about the odds, or even that the children didn’t really die of SIDS. The number was so overwhelming, the decision was easy to make: she had to be guilty as charged. In upholding the conviction, the appeals court said no one would be fooled by such a wild claim.
This is the same principle that guides media claims, and why so few trust the media any more. Shopping for statistics and angles, reporters hone in on some startling number, and taking it out of context, draw conclusions that it doesn’t merit, or maybe worse, just leaving it there to fester in the imagination of people with no other facts to weigh. Absent those facts, the population divides into believers and non-believers, ever more extreme in their positions. It is no wonder that a Boris Johnson can lie about the massive amounts of cash sent to the European Union, and even when the lie is pointed out, it continues to be the foundation for leaving the union. The result has been utter chaos in a farcical government. So while it’s critical to have the numbers behind the claims, few do. Worse, fewer can master them, and a select group will manipulate them to their own advantage.
Yates also tackles algorithms, epidemics, and antivaxxers. The antivaxxers rely on a single, tiny, invalid and misinterpreted study by a (since) defrocked doctor, where he claimed to show that vaccinations cause autism. They don’t, as Yates relates clearly and concisely. Nonetheless, the news traveled from Britain the USA, where it has become gospel to millions who have no need of the facts. They accept the headline as all they need to know. The result is a resurgence of diseases long thought banished, with thousands suffering needlessly. Perversely, parents even mail licked lollipops to each other, so more children can be infected. They believe the false headline, and are ignorant of the death and disfiguration rates from these so-called rites of passage diseases. It is craziness squared, because the numbers were cooked and won out over the facts.
The Math of Life and Death is an endlessly diverting, pleasing, engaging and horrifying look at how lives are affected by the math. It is math in very human terms, and Yates excels at making it plain. And you don’t even have to do the math to see it.
David Wineberg
Using examples from the news, such as epidemics or murder investigations, Yates shows what underlies the events – the basic numbers that anyone can see do or do not add up.
The whole strength of The Math of Life and Death is the power of true events. Yates recognizes their value, and provides the background facts that fit with numbers that prove a point. In the hot new service of gene sequencing, he shows clearly how our assumption about identifying people by DNA samples can go wrong – badly – enough to incarcerate the wrong person. In his own case, 23andMe gave him a death sentence through a wrong interpretation of his genes. He proved it (to his great relief) with other such services and went back to show just how the numbers can lead analysis astray. Sloppy math is hard to prove, but can ruin lives.
He shows that something as unmathematical as algae needs an understanding of math. An algal bloom doubles in size every day, until it covers a lake - in 30 days. If you see the lake is half covered, how long do you think it will take for it to be covered completely? Most would calculate numerous days, based on when the algae first appeared and had reached the halfway point, but the correct answer is one more day. Mistakes like this lead planes to crash, which Yates also shows in painful detail.
Doctors are forever misinterpreting test results, giving patients false death sentences or false reassurances. Yates gives the example of breast cancer tests, by which doctors seem to predict nine out of every two cases of breast cancer in women. The numbers are pretty stark. With false positives from tests, 981 women out of a random 10,000 will be told that they have breast cancer. But of those, only 90 will actually have it. Ninety out of ten thousand (ie. nine per thousand) is not the pandemic plague that should cause panicked fear in women, but that’s how doctors present it when they are surveyed. Given multiple choice questions, doctors fare far worse than if they had chosen random answers. They are prejudiced in the false direction. They have the facts and the numbers wrong. The result is needless surgery, needless chemotherapy, and much pointless suffering.
There is a horrifying chapter on legal ignorance as well. So-called expert witnesses bamboozle judges, juries and opposing lawyers with mumbo-jumbo that no one challenges, because they don’t understand what was said. They just pick out a major conclusion from what they heard, and accept it as true and significant. The result is wrongful convictions. In the major case cited, a young mother went to prison for murdering her first two children, because an expert incorrectly claimed the chances of two children from the same family dying from Sudden Infant Death Syndrome (SIDS) was one in 73 million. (He made up the number himself.) That’s all the jury needed to know. It didn’t matter that the expert was wrong about the odds, or even that the children didn’t really die of SIDS. The number was so overwhelming, the decision was easy to make: she had to be guilty as charged. In upholding the conviction, the appeals court said no one would be fooled by such a wild claim.
This is the same principle that guides media claims, and why so few trust the media any more. Shopping for statistics and angles, reporters hone in on some startling number, and taking it out of context, draw conclusions that it doesn’t merit, or maybe worse, just leaving it there to fester in the imagination of people with no other facts to weigh. Absent those facts, the population divides into believers and non-believers, ever more extreme in their positions. It is no wonder that a Boris Johnson can lie about the massive amounts of cash sent to the European Union, and even when the lie is pointed out, it continues to be the foundation for leaving the union. The result has been utter chaos in a farcical government. So while it’s critical to have the numbers behind the claims, few do. Worse, fewer can master them, and a select group will manipulate them to their own advantage.
Yates also tackles algorithms, epidemics, and antivaxxers. The antivaxxers rely on a single, tiny, invalid and misinterpreted study by a (since) defrocked doctor, where he claimed to show that vaccinations cause autism. They don’t, as Yates relates clearly and concisely. Nonetheless, the news traveled from Britain the USA, where it has become gospel to millions who have no need of the facts. They accept the headline as all they need to know. The result is a resurgence of diseases long thought banished, with thousands suffering needlessly. Perversely, parents even mail licked lollipops to each other, so more children can be infected. They believe the false headline, and are ignorant of the death and disfiguration rates from these so-called rites of passage diseases. It is craziness squared, because the numbers were cooked and won out over the facts.
The Math of Life and Death is an endlessly diverting, pleasing, engaging and horrifying look at how lives are affected by the math. It is math in very human terms, and Yates excels at making it plain. And you don’t even have to do the math to see it.
David Wineberg
April 11, 2020
This is a fantastic book on Mathematics but is a little bit more advanced for novices. It covers a lot of topics all of which amaze one when the maths behind them is revealed. Of particular interest is the last chapter which deals with the modeling of pandemics (this book was written before covid-19 became a thing). Highly recommended by me FWIW.
August 19, 2021
Nepodceňujte dôležitosť matematiky, aby sa vám potom nestalo ako sa stalo minule mne, keď idúcky z vlaku nepozerala som sa pod nohy, bohorovne presvedčená, že presunom z miesta bydliska A, kde rastie v priemere asi tak tisíc stromov na jedného obyvateľa do miesta bydliska B, kde rastie v priemere asi tak jeden strom na tisíc obyvateľov, znížila sa pravdepodobnosť zakopnutia o nejaký po***aný koreň, bodaj by ho čert spral, na jedna k miliónu (lebo však tisíc krát tisíc rovná sa milión), ale potom súc so zlomeným palcom nútená tráviť hodiny čakaním na preplnenej pohotovosti, znovu a znovu som si to prepočítavala v hlave, tisíc krát tisíc, však to sa nedá pomýliť, hovorila som si, až kým som si zhrozene neuvedomila, že, ja krava, som do rovnice zabudli zarátať tú najdôležitejšiu premennú, a to mieru mojej ochoty pravidelne vyberať z účtu peniaze určené na veci ako je poriadna obuv a míňať ich na knižky o obrích krvilačných mimozemských pavúkoch, chystajúcich sa na inváziu Zeme, ktorí keby ale videli tie formy života bujnejúce na verejných toaletách ružinovskej pohotovosti, nielenže by od základov prehodnotili svoju zahraničnú politiku, ale už nikdy by nevyšli z domu bez biolotu, sava, svätenej vody a kapsuly strychnínu v dutom zube.
Fakt. Nepodceňujte dôležitosť matematiky.
----------
O čom kniha naozaj je, píšem tu:
https://kultura.sme.sk/c/22703878/aj-...
Fakt. Nepodceňujte dôležitosť matematiky.
----------
O čom kniha naozaj je, píšem tu:
https://kultura.sme.sk/c/22703878/aj-...
February 17, 2020
I was never very good at math growing up in China where I never fully understood why I needed to do the proof of equations in math classes. Now as a professional, I am doing a job which forces me to work in math a lot. Slowly seeing the magic of math everywhere from pharmaceutical to industrial production, from sales to oil and gas, and see the value math brings, I started to appreciate it a lot.
This will be a book I want to send as a gift to my kids and my nephews to get them see the power of math in everyday life from when they are little. I want them to understand that math is a powerful tool when you use it wisely, it produces society with great impact. If you didn’t use it right, it could blind people and lead to huge loses and unfairness or cost lives.
-----------------below are just some notes I made for myself---------------
There are seven chapters in the book:
1. Thinking Exponentially
Uncover the connection between exponential behavior with everyday phenomena: eating snacks, bacteria growth, deposit in bank, credit card late payment, Pyramid scheme , nuclear reaction, ice bucket challenge ,and population explosion. This has made the point very clear that the rule of exponential growth can be seen everywhere in life
2. How math makes medicine manageable
Lots of the medical tests are imprecise (e.g.23andMe and the BMI, breast cancer test), sometimes the high false positive will make people question the cost-benefit balance of the test/screening programs. Knowing these shake the unquestioning attitude towards the accuracy of health test for us, even extremely accurate test can be hugely imprecise.
This chapter really reminded me of the broad-brushed percentile record the doctors gave to me and my husband when we were doing ultra sound test during pregnancy (ecological fallacy) and reminded me the time when I have my baby did x ray suggested by a dentist, which now I think might have done her more harm than discovering any true problem.
3. Mathematics in the law
This is probably the saddest chapter in the book with Sally Clark’s story told through the chapter. The author discussed several problem with the case ‘guilty until innocent’, the wrongly calculated ’73 million to one’ probability, the ‘independence mistake’ and the ‘ecological fallacy’, ‘the prosecutor’s fallacy, ‘blinded by math’.
4. Debunking media statistics
This is the chapter that I relates to the most.
The author has describes cases where media manipulate data. One example is Lancôme’ad for its anti-aging line pseudoscience. There are also cases where the media fudging the headline to make their story stands out (or create fake news). The author suggests that “ultimately, the degree to which we believe the stats we come across should depend on how complete a picture the artist paints for us. If it is a richly detailed realist landscape with context a trusted source clear expositions and chains of reasoning then we should be confident in the veracity of the numbers. If however it is a dubiously inferred claim supported by a minimalist single statistic on an otherwise empty canvas we should think hard about whether we believe this truth.”
As a practitioner, I also know how easy it is to manipulate result or present it to bias people’s’ view. It always benefit one party or another to put a spin on a particular finding to suggest correlation, to promote argument or advance someone’s agenda. We need to be really careful o being too readily to be convinced. Let’s be skeptical and ask for more explanation before start to draw any conclusion.
Not only media, consulting service sometimes also have slants on stories when it comes to interpreting numbers or reporting facts. They may even call it the art for science. So again knowing that “Statistics can be cherry picked to present a particular angle on a story”. The author has done a great job ‘help to demystify the tricks traps and expose mathematical manipulations employed. Rather than perceiving them as indisputable facts.
There are also some practical tricks we can use to get free drinks/food from bets. Like how many people do you need in a group to find one pair who share the same birthday, which I find very interesting.
5. Number system
6. Optimization algorithm
In this chapter, the author described one of the 7 millennium prize problem: N vs NP hard.
‘It is often easier to verify a correct solution to a problem than it is to produce the solution in the first place. The P vs NP challenge asks whether every problem they can be checked efficiently by a computer can also be solved efficiently. For example once a jigsaw is complete it is easy to check that it has been done correctly. More rigorous definition of what efficiency means are expressed mathematically in terms of how quickly the algorithm works as the problem gets more complicated -when more pieces are added to the puzzle. The set of problems that can be solved quickly is called P(polynomial time). A bigger group of problems that can be checked quickly but not necessarily solved quickly is known as NP(Nondeterministic Polynomial time)
One of the NP question is ‘Travel salesman problem and vehicle routing’.
• ‘The yes-no decision version of the traveling salesman problem is known as NP- complete. A powerful theorem tells us that if we ever come up with a practical algorithm that solves one NP complete problem, then we would be able to transmute this algorithm to solve any other NO problem, proving that P equals NP. Since almost all internet cryptography relies on the difficulty of solving certain NP, proving P equals NP could be distorts for our online security.’
• ‘Ironically, some of the most astounding scientific discoveries have relied enormously on the creative thinking of highly trained and dedicated individuals. If P equals to NP, then computers would be able to find formal proofs of any mathematical theorem that is provable. Many of the greatest intellectual achievements of humankind might be reproduced and superseded by the work of a robot. At its heat P versus NP is the battle to discover whether human creativity can be automated.’
Other problems described here are:
• Dijkstra’s algorithm— finds the shortest path in polynomial time.
• Optimal stopping (Hiring problem the 37 percent rule (only works 37 % of the time but better than 10 %)
• I like the argument the author made on how the algorithm can be biased and we need to be aware: ‘Even the genuinely pragmatic algorithm have hard coded biases they influence the direction in which the spotlight is shone on the global stage.
We place trust in supposedly impartial algorithms because we are wary of obvious human inconsistencies and inclinations. But although computers may implant algorithm in an objective manner following a predefined set of rules, the rules themselves are written by humans. These programmed might hard code their bias consciences or unconscious directly into the algorithm itself, obfuscating their prejudice by translating them into computer code.’ Several examples are provided here include Amazon automated pricing strategy, and Navinder Sarao algorithm to spoof the market in 2010.
7. Mathematical epidemiology
This chapter is about how math is used in controlling and understanding epidemics. There are also some interesting points that ‘the SIR model illustrates the importance of not coming in to work when unwell. If everyone with an infectious disease followed this practice, we would all benefit. This is the author’s argument for the harm of presentism and he used Chipotle’s case where their stuff who felt under the weather but still kept coming which ended up infect hundreds of people as example.
Other story in this chapter also includes offering HPV vaccination to homosexuals to be cost effective.
This will be a book I want to send as a gift to my kids and my nephews to get them see the power of math in everyday life from when they are little. I want them to understand that math is a powerful tool when you use it wisely, it produces society with great impact. If you didn’t use it right, it could blind people and lead to huge loses and unfairness or cost lives.
-----------------below are just some notes I made for myself---------------
There are seven chapters in the book:
1. Thinking Exponentially
Uncover the connection between exponential behavior with everyday phenomena: eating snacks, bacteria growth, deposit in bank, credit card late payment, Pyramid scheme , nuclear reaction, ice bucket challenge ,and population explosion. This has made the point very clear that the rule of exponential growth can be seen everywhere in life
2. How math makes medicine manageable
Lots of the medical tests are imprecise (e.g.23andMe and the BMI, breast cancer test), sometimes the high false positive will make people question the cost-benefit balance of the test/screening programs. Knowing these shake the unquestioning attitude towards the accuracy of health test for us, even extremely accurate test can be hugely imprecise.
This chapter really reminded me of the broad-brushed percentile record the doctors gave to me and my husband when we were doing ultra sound test during pregnancy (ecological fallacy) and reminded me the time when I have my baby did x ray suggested by a dentist, which now I think might have done her more harm than discovering any true problem.
3. Mathematics in the law
This is probably the saddest chapter in the book with Sally Clark’s story told through the chapter. The author discussed several problem with the case ‘guilty until innocent’, the wrongly calculated ’73 million to one’ probability, the ‘independence mistake’ and the ‘ecological fallacy’, ‘the prosecutor’s fallacy, ‘blinded by math’.
4. Debunking media statistics
This is the chapter that I relates to the most.
The author has describes cases where media manipulate data. One example is Lancôme’ad for its anti-aging line pseudoscience. There are also cases where the media fudging the headline to make their story stands out (or create fake news). The author suggests that “ultimately, the degree to which we believe the stats we come across should depend on how complete a picture the artist paints for us. If it is a richly detailed realist landscape with context a trusted source clear expositions and chains of reasoning then we should be confident in the veracity of the numbers. If however it is a dubiously inferred claim supported by a minimalist single statistic on an otherwise empty canvas we should think hard about whether we believe this truth.”
As a practitioner, I also know how easy it is to manipulate result or present it to bias people’s’ view. It always benefit one party or another to put a spin on a particular finding to suggest correlation, to promote argument or advance someone’s agenda. We need to be really careful o being too readily to be convinced. Let’s be skeptical and ask for more explanation before start to draw any conclusion.
Not only media, consulting service sometimes also have slants on stories when it comes to interpreting numbers or reporting facts. They may even call it the art for science. So again knowing that “Statistics can be cherry picked to present a particular angle on a story”. The author has done a great job ‘help to demystify the tricks traps and expose mathematical manipulations employed. Rather than perceiving them as indisputable facts.
There are also some practical tricks we can use to get free drinks/food from bets. Like how many people do you need in a group to find one pair who share the same birthday, which I find very interesting.
5. Number system
6. Optimization algorithm
In this chapter, the author described one of the 7 millennium prize problem: N vs NP hard.
‘It is often easier to verify a correct solution to a problem than it is to produce the solution in the first place. The P vs NP challenge asks whether every problem they can be checked efficiently by a computer can also be solved efficiently. For example once a jigsaw is complete it is easy to check that it has been done correctly. More rigorous definition of what efficiency means are expressed mathematically in terms of how quickly the algorithm works as the problem gets more complicated -when more pieces are added to the puzzle. The set of problems that can be solved quickly is called P(polynomial time). A bigger group of problems that can be checked quickly but not necessarily solved quickly is known as NP(Nondeterministic Polynomial time)
One of the NP question is ‘Travel salesman problem and vehicle routing’.
• ‘The yes-no decision version of the traveling salesman problem is known as NP- complete. A powerful theorem tells us that if we ever come up with a practical algorithm that solves one NP complete problem, then we would be able to transmute this algorithm to solve any other NO problem, proving that P equals NP. Since almost all internet cryptography relies on the difficulty of solving certain NP, proving P equals NP could be distorts for our online security.’
• ‘Ironically, some of the most astounding scientific discoveries have relied enormously on the creative thinking of highly trained and dedicated individuals. If P equals to NP, then computers would be able to find formal proofs of any mathematical theorem that is provable. Many of the greatest intellectual achievements of humankind might be reproduced and superseded by the work of a robot. At its heat P versus NP is the battle to discover whether human creativity can be automated.’
Other problems described here are:
• Dijkstra’s algorithm— finds the shortest path in polynomial time.
• Optimal stopping (Hiring problem the 37 percent rule (only works 37 % of the time but better than 10 %)
• I like the argument the author made on how the algorithm can be biased and we need to be aware: ‘Even the genuinely pragmatic algorithm have hard coded biases they influence the direction in which the spotlight is shone on the global stage.
We place trust in supposedly impartial algorithms because we are wary of obvious human inconsistencies and inclinations. But although computers may implant algorithm in an objective manner following a predefined set of rules, the rules themselves are written by humans. These programmed might hard code their bias consciences or unconscious directly into the algorithm itself, obfuscating their prejudice by translating them into computer code.’ Several examples are provided here include Amazon automated pricing strategy, and Navinder Sarao algorithm to spoof the market in 2010.
7. Mathematical epidemiology
This chapter is about how math is used in controlling and understanding epidemics. There are also some interesting points that ‘the SIR model illustrates the importance of not coming in to work when unwell. If everyone with an infectious disease followed this practice, we would all benefit. This is the author’s argument for the harm of presentism and he used Chipotle’s case where their stuff who felt under the weather but still kept coming which ended up infect hundreds of people as example.
Other story in this chapter also includes offering HPV vaccination to homosexuals to be cost effective.
This entire review has been hidden because of spoilers.
February 20, 2022
In many respects this is quite an odd book, I suppose the title could be misleading, perhaps sell the book as a listicle type of thing...
Instead the Maths of Life and Death is effectively 7(at least) lessons in maths which are essentially useful to know. The book isn't needlessly dense, nor too superficial. The goal is essentially to provide an understandable summary of a mathematical concept and how its relevant, what we do with that info is ultimately up to us.
I confess there were a few moments where I got a bit overwhelmed with numbers, but really only a couple of times when explaining the statistics of medical tests and rare statistical events. Fortunately 100% understanding of numbers is not needed to understand the concepts as long as you can take Yates' word for it.
The topics covered are:
Exponential growth (and decline) - unfortunately an important topic in modern pandemic times
Sensitivity and Specificity of medical tests - again an important topic!
Laws of mathematics - thankfully nothing to do with disease, this was actually an interesting diversion into the maths often used in legal settings and how they can me misleading
Don't believe the truth - media statistics - in my opinion this chapter could almost be a must read for everyone. Yates explains how statistics can be used and misused publicly, and of most interest without outright misinformation or lying.
Evolution of Number systems - probably more of a general interest one, Yates explains how we came about having base 10 for (most) of our systems, what some alternatives have been and the issues that can arise.
Relentless Optimization - a super interesting dive into algorhythms an important and probably only going to be more important topic.
Containing disease - OK back to the pandemic. Sarcasm aside this chapter is really relevant and useful for understanding public health policies around lock-downs, mitigations and vaccines.
Overall while the maths makes the subjects automatically quite technical Yates does an awesome job making the writing interesting and accessible. I know I praise most non-fiction but this one is highly recommended.
Instead the Maths of Life and Death is effectively 7(at least) lessons in maths which are essentially useful to know. The book isn't needlessly dense, nor too superficial. The goal is essentially to provide an understandable summary of a mathematical concept and how its relevant, what we do with that info is ultimately up to us.
I confess there were a few moments where I got a bit overwhelmed with numbers, but really only a couple of times when explaining the statistics of medical tests and rare statistical events. Fortunately 100% understanding of numbers is not needed to understand the concepts as long as you can take Yates' word for it.
The topics covered are:
Exponential growth (and decline) - unfortunately an important topic in modern pandemic times
Sensitivity and Specificity of medical tests - again an important topic!
Laws of mathematics - thankfully nothing to do with disease, this was actually an interesting diversion into the maths often used in legal settings and how they can me misleading
Don't believe the truth - media statistics - in my opinion this chapter could almost be a must read for everyone. Yates explains how statistics can be used and misused publicly, and of most interest without outright misinformation or lying.
Evolution of Number systems - probably more of a general interest one, Yates explains how we came about having base 10 for (most) of our systems, what some alternatives have been and the issues that can arise.
Relentless Optimization - a super interesting dive into algorhythms an important and probably only going to be more important topic.
Containing disease - OK back to the pandemic. Sarcasm aside this chapter is really relevant and useful for understanding public health policies around lock-downs, mitigations and vaccines.
Overall while the maths makes the subjects automatically quite technical Yates does an awesome job making the writing interesting and accessible. I know I praise most non-fiction but this one is highly recommended.
October 7, 2025
(2.5)
I keep forgetting what is touted by the mainstream is already known by the much more well read.
There wasn’t much I hadn’t already learned in other venues, but the book did have some engaging, interesting anecdotes.
A few notes
“if our species is to survive the threat of extinction presented by overpopulation”
Overpopulation is not a problem.. the population is shrinking everywhere but Africa and that area is now set to decline by about 2050.
Survival through failure to reproduce is becoming quite real.
Earlier the author takes a Trump supporter, Sebastian Gorka a bit to task bc Gorka claimed that a British terror bombing was performed on the anniversary of an earlier bombing. Besides the math, the author makes the claim that by linking these two events, Gorka is trying to give the false impression that Islamic jihadists are far more organized. However, Gorka doesn’t make that claim. This only becomes of note bc later the author trundles out Gorka for saying this
“The biggest problem we have is not mass shootings, they are the anomaly. You do not make legislation out of outliers. Our big issue is black African gun crime against black Africans… black young men are murdering each other by the bushel. Assuming Gorka was referring to African Americans”
The author then briefly hand waves the info away by trying to spastically link the number of officers to black crime. He then ends the chapter without actively using any numbers to discredit the truth: black men 15-45 make up 3% of the population but commit approx 50% of all murders…for some reason the author doesn’t like that math…hmmm
“Covid-19 is indeed zoonotic, originating in bats and potentially passing through livestock or wild animals before jumping species again to infect the first human being in the Chinese city of Wuhan”
This is an ebook so he could fix this paragraph. Covid 19 originated in a lab in Wuhan.
“COVID-19 pandemic, once outbreaks are in full swing, it is often impractical to develop and test an effective vaccine within a short time frame.”
Well, kudos to Trump and warp speed then for getting this done.
I keep forgetting what is touted by the mainstream is already known by the much more well read.
There wasn’t much I hadn’t already learned in other venues, but the book did have some engaging, interesting anecdotes.
A few notes
“if our species is to survive the threat of extinction presented by overpopulation”
Overpopulation is not a problem.. the population is shrinking everywhere but Africa and that area is now set to decline by about 2050.
Survival through failure to reproduce is becoming quite real.
Earlier the author takes a Trump supporter, Sebastian Gorka a bit to task bc Gorka claimed that a British terror bombing was performed on the anniversary of an earlier bombing. Besides the math, the author makes the claim that by linking these two events, Gorka is trying to give the false impression that Islamic jihadists are far more organized. However, Gorka doesn’t make that claim. This only becomes of note bc later the author trundles out Gorka for saying this
“The biggest problem we have is not mass shootings, they are the anomaly. You do not make legislation out of outliers. Our big issue is black African gun crime against black Africans… black young men are murdering each other by the bushel. Assuming Gorka was referring to African Americans”
The author then briefly hand waves the info away by trying to spastically link the number of officers to black crime. He then ends the chapter without actively using any numbers to discredit the truth: black men 15-45 make up 3% of the population but commit approx 50% of all murders…for some reason the author doesn’t like that math…hmmm
“Covid-19 is indeed zoonotic, originating in bats and potentially passing through livestock or wild animals before jumping species again to infect the first human being in the Chinese city of Wuhan”
This is an ebook so he could fix this paragraph. Covid 19 originated in a lab in Wuhan.
“COVID-19 pandemic, once outbreaks are in full swing, it is often impractical to develop and test an effective vaccine within a short time frame.”
Well, kudos to Trump and warp speed then for getting this done.
November 16, 2020
3.5/5
This is mostly a distilled-down version of Kahenman's Thinking, Fast and Slow, with somewhat more friendly writing and some better, more "personal" story-writing. There's a few newer bits, but if I was told that this was a summary of Thinking, I wouldn't have been surprised.
A few additional stories and background gives it a few points, but the lack of new information keeps me from bumping it to 4 stars.
It's also pretty low on anything new math-wise for me. I'm sure Yates knows his stuff, but he's very careful, too careful, not to include anything particularly difficult, which also means that nothing particularly interesting ever gets shown. I suppose this depends on the reader, so take that with a grain of salt.
So, it's pretty good, assuming you don't intend to read Thinking and assuming you have a limited math background, but are curious about how things work anyway
This is mostly a distilled-down version of Kahenman's Thinking, Fast and Slow, with somewhat more friendly writing and some better, more "personal" story-writing. There's a few newer bits, but if I was told that this was a summary of Thinking, I wouldn't have been surprised.
A few additional stories and background gives it a few points, but the lack of new information keeps me from bumping it to 4 stars.
It's also pretty low on anything new math-wise for me. I'm sure Yates knows his stuff, but he's very careful, too careful, not to include anything particularly difficult, which also means that nothing particularly interesting ever gets shown. I suppose this depends on the reader, so take that with a grain of salt.
So, it's pretty good, assuming you don't intend to read Thinking and assuming you have a limited math background, but are curious about how things work anyway
October 31, 2023
Mathematical literacy, is as important as other more common meanings we attribute to the word literacy. Without the ability to understand numbers and their meaning we cannot make sense of the world around us. We can be led to believe what is not true in news headlines and advertisements that use figures in ways that make them seem supportive of their argument or product. In worse cases, mathematical illiteracy has caused many a healthy person agonising over the results of a medical test there was no reason to worry about, and led to information misinterpretation that was used to convict innocent people in court.
Although I do not share the (obviously biased) opinion of the author that “maths is (almost) everything” and the excessive importance he attributes to mathematical modelling, I loved this book. It is packed with useful information and written in a very clear and engaging way.
I particularly liked the last chapter about infectious disease propagation and how vaccination is one of the most effective ways to fight them. Yates tells us about the origins of the no-vax movement, which I did not know. A paper published in the well-respected The Lancet by an author named Wakefield, proposed a link between the MMR vaccine (measles, mumps and rubella) and autism spectrum disorders. This was later proved fraudulent as the author was found to have manipulated data to give the false impression of a link between MMR vaccine to autism while he himself had submitted patents for a rival vaccine. On the back of his ‘findings’, Wakefield launched his own personal anti-MMR campaign, and most of the mainstream media couldn’t resist the bait: indulging the fears of many parents, the story snowballed to an incredible scale. In the 20 years since Wakefield’s original paper, comprehensive studies have repeatedly debunked his conclusions. Sadly, though, Wakefield’s influence lives on, as do so many other lies that once taking roots in the collective mind, are very difficult to remove.
A small sample of Yates’ writing:
Mathematics, at its most fundamental, is pattern. Every time you look at the world you are building your own model of the patterns you observe. If you spot a motif in the fractal branches of a tree, or in the multi-fold symmetry of a snowflake, then you are seeing maths. When you tap your foot to a piece of music, or when your voice reverberates and resonates as you sing in the shower, you are hearing maths. If you bend a shot into the bend of the back of the net or catch a cricket ball on its parabolic trajectory, then you are doing maths. With every new experience, every piece of sensory information, the models you’ve made of your environment are refined, reconfigured and rendered ever more detailed and complex.
I believe this book will appeal to everyone, even people who don’t like maths or think their knowledge of the subject is very limited. Yates does not use a single equation in the whole book and explains everything very clearly, with examples related to everyday life. In a nutshell, as the back-cover puts it so well, “This is a book about how maths can change your life for better or worse”.
Although I do not share the (obviously biased) opinion of the author that “maths is (almost) everything” and the excessive importance he attributes to mathematical modelling, I loved this book. It is packed with useful information and written in a very clear and engaging way.
I particularly liked the last chapter about infectious disease propagation and how vaccination is one of the most effective ways to fight them. Yates tells us about the origins of the no-vax movement, which I did not know. A paper published in the well-respected The Lancet by an author named Wakefield, proposed a link between the MMR vaccine (measles, mumps and rubella) and autism spectrum disorders. This was later proved fraudulent as the author was found to have manipulated data to give the false impression of a link between MMR vaccine to autism while he himself had submitted patents for a rival vaccine. On the back of his ‘findings’, Wakefield launched his own personal anti-MMR campaign, and most of the mainstream media couldn’t resist the bait: indulging the fears of many parents, the story snowballed to an incredible scale. In the 20 years since Wakefield’s original paper, comprehensive studies have repeatedly debunked his conclusions. Sadly, though, Wakefield’s influence lives on, as do so many other lies that once taking roots in the collective mind, are very difficult to remove.
A small sample of Yates’ writing:
Mathematics, at its most fundamental, is pattern. Every time you look at the world you are building your own model of the patterns you observe. If you spot a motif in the fractal branches of a tree, or in the multi-fold symmetry of a snowflake, then you are seeing maths. When you tap your foot to a piece of music, or when your voice reverberates and resonates as you sing in the shower, you are hearing maths. If you bend a shot into the bend of the back of the net or catch a cricket ball on its parabolic trajectory, then you are doing maths. With every new experience, every piece of sensory information, the models you’ve made of your environment are refined, reconfigured and rendered ever more detailed and complex.
I believe this book will appeal to everyone, even people who don’t like maths or think their knowledge of the subject is very limited. Yates does not use a single equation in the whole book and explains everything very clearly, with examples related to everyday life. In a nutshell, as the back-cover puts it so well, “This is a book about how maths can change your life for better or worse”.
December 15, 2020
For most people, the thought of reading a maths book is not even something that they would ever consider. They had been put off maths at school and almost certainly have never done anything other than added a few numbers up or split a bill in a restaurant (when we could go to them). But in this modern world maths is the foundation of our modern society.
Every time you are online, you are using prime numbers to make secure transactions, we use AI in our phones and home to find and recommend music and lots of other things and we mustn’t forget the power that algorithms have over our lives that never seems to diminish. Over the past year, numbers have been a feature of our life as the pandemic has spread like wildfire across the world. We see the charts and graphs rising with the horrific death toll.
How this figure rises is covered in the first of the seven chapters of this book, exponential numbers. In here he looks at real-life examples of numbers that grow in the way from nuclear explosions to bank interest. The second chapter is all about risk as he begins with an email about his DNA after a genetic test with a particular emphasis on calculating medical odds and a lot on false positives and how to understand results.
The phrase, there are lies, damned lies and statistics is so very true. They are banded about a lot on the news by people who frankly have no place in repeating them nor have the first clue as to the statistic being quoted in a lot of instances. Thankfully Yates is her to clear the muddied waters in his Chapter, Don’t Believe The Truth. He starts with the birthday problem, which is how few people do you need in a room before you will find two people with matching birthdays. Discounting twins, the real answer is much less than people expect. He debunks statistics that papers use but explaining that you need context to understand increases in numbers, not just a percentage.
The next chapter talks about errors and how people can make simple errors when converting from one number system to another, i.e. imperial to metric, as well as making mistakes when miscalculating dosages and increasing them by tenfold. Maths ignorance is ripe for errors to be made and they can be life-threatening too. The penultimate chapter is on that modern joy, the algorithm. In here, Yates, explains how they do have their uses, i.e. by working out the best delivery routes and how some books on Amazon are priced in the millions of dollars because of an over-enthusiastic algorithm. The final chapter is all about disease. Cheerful stuff, I know, but maths can be used to model outbreaks and there is the clearest explanation of the R number I have read.
Bearing in mind this was written in 2019 before the coronavirus outbreak this is still quite a prescient book. For those that get break out in a sweat when they read x = 2y, they will be pleased to hear that there are no equations in the book. There is the occasional graph and all the way through there are clear diagrams and explanations as to what is going on and why it is happening in a particular way. It can sometimes be grim, but it is an endlessly fascinating book.
Every time you are online, you are using prime numbers to make secure transactions, we use AI in our phones and home to find and recommend music and lots of other things and we mustn’t forget the power that algorithms have over our lives that never seems to diminish. Over the past year, numbers have been a feature of our life as the pandemic has spread like wildfire across the world. We see the charts and graphs rising with the horrific death toll.
How this figure rises is covered in the first of the seven chapters of this book, exponential numbers. In here he looks at real-life examples of numbers that grow in the way from nuclear explosions to bank interest. The second chapter is all about risk as he begins with an email about his DNA after a genetic test with a particular emphasis on calculating medical odds and a lot on false positives and how to understand results.
The phrase, there are lies, damned lies and statistics is so very true. They are banded about a lot on the news by people who frankly have no place in repeating them nor have the first clue as to the statistic being quoted in a lot of instances. Thankfully Yates is her to clear the muddied waters in his Chapter, Don’t Believe The Truth. He starts with the birthday problem, which is how few people do you need in a room before you will find two people with matching birthdays. Discounting twins, the real answer is much less than people expect. He debunks statistics that papers use but explaining that you need context to understand increases in numbers, not just a percentage.
The next chapter talks about errors and how people can make simple errors when converting from one number system to another, i.e. imperial to metric, as well as making mistakes when miscalculating dosages and increasing them by tenfold. Maths ignorance is ripe for errors to be made and they can be life-threatening too. The penultimate chapter is on that modern joy, the algorithm. In here, Yates, explains how they do have their uses, i.e. by working out the best delivery routes and how some books on Amazon are priced in the millions of dollars because of an over-enthusiastic algorithm. The final chapter is all about disease. Cheerful stuff, I know, but maths can be used to model outbreaks and there is the clearest explanation of the R number I have read.
Bearing in mind this was written in 2019 before the coronavirus outbreak this is still quite a prescient book. For those that get break out in a sweat when they read x = 2y, they will be pleased to hear that there are no equations in the book. There is the occasional graph and all the way through there are clear diagrams and explanations as to what is going on and why it is happening in a particular way. It can sometimes be grim, but it is an endlessly fascinating book.
November 13, 2020
I was that rare English major who enjoyed taking college math. I loved the way derivatives seemed to make sense – for a while, at least – and I loved the feeling of a math problem coming together. I didn’t get to the point with my studies in math where I was doing anything remotely original, but I got to where I felt I could appreciate the way a nimble math mind can clarify something about the world.
I got to the point, that is, where I could begin to appreciate the way math can tell a story.
I’ve been fortunate since then to work at the University of Scranton with people like Jerry and Stacy Muir, Anthony Ferzola, and Jason Graham who’ve shown me in my conversations with them that math can be a tool for understanding the world. Too often, it can seem like a set of problems we have to solve with specific and sometimes arbitrary rules. They show me, instead, that math is just a different language for clarifying – or sometimes extending – the world in front of us.
I mention all of that because, while I think the title of this book overrates its actual subject matter, this is a book that explores a range of the ways that we can tell stories with math.
Kip Yates promises us early that he’ll stay away from equations, a promise he mostly keeps. Instead, he finds example after example to show us how math underlies many of our collective experiences.
He has a chapter that explores the math of a viral outbreak, whether of a meme or a, well, actual virus. I’ve heard those explanations countless times since our recent pandemic broke out, but I have to hand it to Yates that he renders the math more clearly than any other I have read.
He has some good stories about the history of mathematics and how a ‘technology’ of numbers has helped us. I’ve read elsewhere about the strange invention of the concept of zero. Here, in a way that makes sense and makes me laugh, he talks about how the Romans were limited in their ability to calculate because Roman numerals lacked the nimbler decimal placement that we take for granted. He talks as well about how the base-10 system is not a necessary construct, pointing out that a 12/60 system – one that continues to underlie our measurement of time – took hold in a number of sophisticated systems.
And he does a nice job of critiquing what I might call a rhetoric of numbers. He talks about some of the psychological effect of propagandists using statistics, and he shows how easy it is to manipulate accurate numbers (let alone inaccurate ones) in the different ways they get represented.
I’m not sure the whole of this is all that coherent, but I’m not looking for coherence in a book like this. Instead, I’m looing for an interesting mind to guide me through a way of thinking that I don’t know as fully as I’d like.
Yates delivers in that, and there’s a joy in following him as he pursues his related range of mathematical speculations.
I got to the point, that is, where I could begin to appreciate the way math can tell a story.
I’ve been fortunate since then to work at the University of Scranton with people like Jerry and Stacy Muir, Anthony Ferzola, and Jason Graham who’ve shown me in my conversations with them that math can be a tool for understanding the world. Too often, it can seem like a set of problems we have to solve with specific and sometimes arbitrary rules. They show me, instead, that math is just a different language for clarifying – or sometimes extending – the world in front of us.
I mention all of that because, while I think the title of this book overrates its actual subject matter, this is a book that explores a range of the ways that we can tell stories with math.
Kip Yates promises us early that he’ll stay away from equations, a promise he mostly keeps. Instead, he finds example after example to show us how math underlies many of our collective experiences.
He has a chapter that explores the math of a viral outbreak, whether of a meme or a, well, actual virus. I’ve heard those explanations countless times since our recent pandemic broke out, but I have to hand it to Yates that he renders the math more clearly than any other I have read.
He has some good stories about the history of mathematics and how a ‘technology’ of numbers has helped us. I’ve read elsewhere about the strange invention of the concept of zero. Here, in a way that makes sense and makes me laugh, he talks about how the Romans were limited in their ability to calculate because Roman numerals lacked the nimbler decimal placement that we take for granted. He talks as well about how the base-10 system is not a necessary construct, pointing out that a 12/60 system – one that continues to underlie our measurement of time – took hold in a number of sophisticated systems.
And he does a nice job of critiquing what I might call a rhetoric of numbers. He talks about some of the psychological effect of propagandists using statistics, and he shows how easy it is to manipulate accurate numbers (let alone inaccurate ones) in the different ways they get represented.
I’m not sure the whole of this is all that coherent, but I’m not looking for coherence in a book like this. Instead, I’m looing for an interesting mind to guide me through a way of thinking that I don’t know as fully as I’d like.
Yates delivers in that, and there’s a joy in following him as he pursues his related range of mathematical speculations.
September 30, 2019
No Formulas. Just Numb3rs. In this book about how math shapes our lives, British math professor Yates doesn't take us into the algebra, geometry, and even trigonometry that we all use daily - whether we realize it or not. Instead, he takes an approach similar to the now decade old US television show Numb3rs, starring David Krumholtz and Rob Morrow, wherein he shows applications of higher level mathematics in fields such as epidemiology, medicine, law, journalism, elections, and several others. Yates cites real world examples including unjust convictions and Ebola outbreaks and many others to show how math was used incorrectly and what the math actually showed in that situation, to help the reader begin to get an overall sense of math without getting bogged down in the technical calculations. Truly an excellent book for even the more arithmophobic among us, as it shows the numbers all around us and explains how we can have a better sense of them.
Disclaimers: 1) I LOVED Numb3rs back in the day and would still be watching it if it were still on the air. 2) I have a computer science degree and very nearly got secondary mathematics education and mathematics bachelors degrees at the same time as my CS one - so obviously I'm a bit more attuned to math than others.
Disclaimers: 1) I LOVED Numb3rs back in the day and would still be watching it if it were still on the air. 2) I have a computer science degree and very nearly got secondary mathematics education and mathematics bachelors degrees at the same time as my CS one - so obviously I'm a bit more attuned to math than others.
March 31, 2021
This is an engaging and fascinating journey through the world of mathematics, even if you’re as math-challenged as I am. I may not be a math geek, but I understand how it underpins everything. Reality itself can be described with it.
Mathematics can save us or destroy us. Its application has made our lives easier and better while at the same time its misapplication could ruin or even end us if we’re not careful. The author presents many examples of why we need it as well as the myriad ways it can go catastrophically wrong. I found the last chapter particularly applicable to the current pandemic.
Though this book can feel a little dry at times, I can’t help but forgive the author for that considering the value of this information.
I feel smarter now.
Mathematics can save us or destroy us. Its application has made our lives easier and better while at the same time its misapplication could ruin or even end us if we’re not careful. The author presents many examples of why we need it as well as the myriad ways it can go catastrophically wrong. I found the last chapter particularly applicable to the current pandemic.
Though this book can feel a little dry at times, I can’t help but forgive the author for that considering the value of this information.
I feel smarter now.
April 18, 2021
Nota al margen: Si van a escribir reseñas, no las dejen para después. Escriban de una porque lo leído desafortunadamente se olvida.
El subtítulo de este libro fue realmente lo que me enganchó para comprarlo y para leerlo (Acuérdense que un hobby es comprar libros y otro muy distinto es leerlos) "7 principios matemáticos que dan forma a nuestra existencia. Al principio me imaginé de todo tipo de curiosidades naturales, biológicas y astronómicas sin embargo cuando empecé a leer me encontré más bien con las matemáticas aplicadas a la vida cotidiana.
La medicina, la forma de contar, la publicidad y hasta la justicia. Particularmente amigo lector de mis reseñas le cuento que leí este libro en media pandemia de Covid-19 en el año 2021 y que además de los temas anteriores, en este libro coincidencialmente me encontré las matemáticas de la propagación de un virus.
El libro en términos generales está bien escrito y los ejemplos usados, casi todos ellos historias de la vida real, dan cuenta de un matemático investigador juicioso detrás de la obra. Kit Yates es un biólogo que se introdujo al mudo de las matemáticas y lo que se encontró como resultado fue muy apasionante según cuenta, pero además de gran ayuda para el mundo y la ciencia dado que esta combinación resulta ser bastante potente cuando se aplica a problemáticas reales.
Ustedes saben que mi estilo de reseña busca más comentarle mi opinión y emociones sentidas al leer el libro y no tanto contarle el relato de lo que el libro expone, sin embargo hay cosas curiosas que tengo que decir para antojarlo de leer este libro. Impresionante cómo se equivocan los resultados de los exámenes médicos debido a un tema meramente matemático, ese capítulo es violento de interesante y mi enseñanza es que siempre es mejor una segunda verificación. Por eso los invito a que no se queden sólo con esta reseña y vayan a leer un par más antes de leer el libro. (Aquí t la de mi gran amigo Jorge Zuluaga).
Otro dato curioso que me encantó leerlo y además me obligó a ser mejor ciudadano y evitar problemas con la justicia es el altísimo número de posibilidades que tienes de ser declarado culpable siendo inocente cuándo un fiscal pone como prueba reina de su acusación una estadística sacada de alguna autoridad válida. Ve por tu vida con cuidado y si se mete en problemas con la ley, dígale a su abogado que le de una leída a este libro.
Por último les cuento que yo por decisión personal de bienestar hace 6 años no veo noticias. En el libro entendí cómo justificar matemáticamente que no vale la pena verlas porque están plagadas de errores matemáticos que nos hacen ver la vida más negra de lo que realmente es. Ustedes saben que soy posibilista y que por más mal que esté la vaina, con toda seguridad estamos mejor que en cualquier momento del pasado.
Cierro la reseña diciéndole que si usted cumple con alguno de los atributos a continuación, usted debería leer este libro:
- A usted no le gustan las matemáticas pero le gusta saber cómo funcionan las cosas.
- Usted es curioso y le encantan los datos curiosos.
- A usted le encanta hablar de temas de los que casi nadie sabe.
- A usted le gustan las lecturas que lo ponen moderadamente a pensar sobre lo que está leyendo.
- Usted es o trabaja en publicidad, periodismo, medicina, derecho, ingeniería de sistemas o software.
El subtítulo de este libro fue realmente lo que me enganchó para comprarlo y para leerlo (Acuérdense que un hobby es comprar libros y otro muy distinto es leerlos) "7 principios matemáticos que dan forma a nuestra existencia. Al principio me imaginé de todo tipo de curiosidades naturales, biológicas y astronómicas sin embargo cuando empecé a leer me encontré más bien con las matemáticas aplicadas a la vida cotidiana.
La medicina, la forma de contar, la publicidad y hasta la justicia. Particularmente amigo lector de mis reseñas le cuento que leí este libro en media pandemia de Covid-19 en el año 2021 y que además de los temas anteriores, en este libro coincidencialmente me encontré las matemáticas de la propagación de un virus.
El libro en términos generales está bien escrito y los ejemplos usados, casi todos ellos historias de la vida real, dan cuenta de un matemático investigador juicioso detrás de la obra. Kit Yates es un biólogo que se introdujo al mudo de las matemáticas y lo que se encontró como resultado fue muy apasionante según cuenta, pero además de gran ayuda para el mundo y la ciencia dado que esta combinación resulta ser bastante potente cuando se aplica a problemáticas reales.
Ustedes saben que mi estilo de reseña busca más comentarle mi opinión y emociones sentidas al leer el libro y no tanto contarle el relato de lo que el libro expone, sin embargo hay cosas curiosas que tengo que decir para antojarlo de leer este libro. Impresionante cómo se equivocan los resultados de los exámenes médicos debido a un tema meramente matemático, ese capítulo es violento de interesante y mi enseñanza es que siempre es mejor una segunda verificación. Por eso los invito a que no se queden sólo con esta reseña y vayan a leer un par más antes de leer el libro. (Aquí t la de mi gran amigo Jorge Zuluaga).
Otro dato curioso que me encantó leerlo y además me obligó a ser mejor ciudadano y evitar problemas con la justicia es el altísimo número de posibilidades que tienes de ser declarado culpable siendo inocente cuándo un fiscal pone como prueba reina de su acusación una estadística sacada de alguna autoridad válida. Ve por tu vida con cuidado y si se mete en problemas con la ley, dígale a su abogado que le de una leída a este libro.
Por último les cuento que yo por decisión personal de bienestar hace 6 años no veo noticias. En el libro entendí cómo justificar matemáticamente que no vale la pena verlas porque están plagadas de errores matemáticos que nos hacen ver la vida más negra de lo que realmente es. Ustedes saben que soy posibilista y que por más mal que esté la vaina, con toda seguridad estamos mejor que en cualquier momento del pasado.
Cierro la reseña diciéndole que si usted cumple con alguno de los atributos a continuación, usted debería leer este libro:
- A usted no le gustan las matemáticas pero le gusta saber cómo funcionan las cosas.
- Usted es curioso y le encantan los datos curiosos.
- A usted le encanta hablar de temas de los que casi nadie sabe.
- A usted le gustan las lecturas que lo ponen moderadamente a pensar sobre lo que está leyendo.
- Usted es o trabaja en publicidad, periodismo, medicina, derecho, ingeniería de sistemas o software.
October 4, 2022
Rating: 9/10
As someone who is not naturally talented in Mathematics, I found this book really entertaining and unique. I loved Yates writing style; he explains everything so simply and vibrantly, using relevant examples to help keep the reader engaged (ex. the Amanda Knox trial, covid19, BLM movement).
Yates shows us how mathematics can be used for betterment or worse, depending on how it's used.
He touches on the use of mathematics in law, business, health/medicine, media, and technology. In each chapter, he gives 1-3 examples of mathematics gone wrong and what should've been done instead.
Yates does a phenomenal job at showcasing to the reader why we shouldn't naively trust numbers; he does this by exploring common errors in mathematics (asking & answering the wrong questions, inputting the wrong variables, illogical calculations, etc).
I'd argue that it's not a book ABOUT mathematics (that is to say, how it came about) but rather HOW mathematics is used in different subject fields. I think there are only a few equations used throughout the whole book. Otherwise, the design and flow of the content were incredibly smooth and easy to follow.
In each chapter, Yates covers the following:
1. Exponents, exponential growth
2. Odds, ratios, and binary testing
3. Probabilities, independent/dependent variables
4. Samples sizes, framing, biases
5. Number systems
6. Algorithms, optimization, P versus NP
7. Proportions, r-naught, exponential growth
One downfall: It's unclear exactly what the different mathematical principles are. After reading the book and going through each chapter, I can somewhat differentiate the principles. But a lot of what's taught is similar and overlaps each other.
The book was written so each chapter covered a different domain and a mathematical principle or two were applied within that domain. I think it should've been the opposite. Each chapter covers a different principle that's applied in 1-2 different domains.
As someone who is not naturally talented in Mathematics, I found this book really entertaining and unique. I loved Yates writing style; he explains everything so simply and vibrantly, using relevant examples to help keep the reader engaged (ex. the Amanda Knox trial, covid19, BLM movement).
Yates shows us how mathematics can be used for betterment or worse, depending on how it's used.
He touches on the use of mathematics in law, business, health/medicine, media, and technology. In each chapter, he gives 1-3 examples of mathematics gone wrong and what should've been done instead.
Yates does a phenomenal job at showcasing to the reader why we shouldn't naively trust numbers; he does this by exploring common errors in mathematics (asking & answering the wrong questions, inputting the wrong variables, illogical calculations, etc).
I'd argue that it's not a book ABOUT mathematics (that is to say, how it came about) but rather HOW mathematics is used in different subject fields. I think there are only a few equations used throughout the whole book. Otherwise, the design and flow of the content were incredibly smooth and easy to follow.
In each chapter, Yates covers the following:
1. Exponents, exponential growth
2. Odds, ratios, and binary testing
3. Probabilities, independent/dependent variables
4. Samples sizes, framing, biases
5. Number systems
6. Algorithms, optimization, P versus NP
7. Proportions, r-naught, exponential growth
One downfall: It's unclear exactly what the different mathematical principles are. After reading the book and going through each chapter, I can somewhat differentiate the principles. But a lot of what's taught is similar and overlaps each other.
The book was written so each chapter covered a different domain and a mathematical principle or two were applied within that domain. I think it should've been the opposite. Each chapter covers a different principle that's applied in 1-2 different domains.
November 27, 2019
"However, approximately 85 percent of automated warnings in ICUs are false alarms."
If you're at all fascinated with numbers, you will love this book. There are no actual formulas in this book, instead what it shows you is how math is a part of every aspect of our lives from medicine to law to sales. This book is full of real-life stories, many you might know from hearing about them in the news and many others that are just as powerful. It breaks down the math behind the stories and shows the examples of how mathematics is an integral part of our lives even if it's not always obvious.
The powerful part of this book is when it highlights all the ways in which mathematics has been used/interpreted incorrectly and caused people's lives to be ruined or altered forever. When a monitor in the ICU is muted because it beeps too much and then it can't beep when in fact it needs to, it can (and does) kill people. When data is interpreted incorrectly (as it often is) it can (and does) cause innocent people to go to jail. These are real-life consequences of mathematical errors that cause people to behave in ways that (inadvertently) harm other people.
This book is full of powerful examples that make you feel both cringe with horror and delighted (I was so excited to find out that the ice bucket challenge had such a positive outcome.) But more often than not, it's a sobering look at the role math plays in our lives and the harm we can do when we misuse it.
I loved reading this book and if numbers are your thing at all, I can't recommend it enough.
thank you to Scribner and netgalley for an early copy in exchange for an honest review.
If you're at all fascinated with numbers, you will love this book. There are no actual formulas in this book, instead what it shows you is how math is a part of every aspect of our lives from medicine to law to sales. This book is full of real-life stories, many you might know from hearing about them in the news and many others that are just as powerful. It breaks down the math behind the stories and shows the examples of how mathematics is an integral part of our lives even if it's not always obvious.
The powerful part of this book is when it highlights all the ways in which mathematics has been used/interpreted incorrectly and caused people's lives to be ruined or altered forever. When a monitor in the ICU is muted because it beeps too much and then it can't beep when in fact it needs to, it can (and does) kill people. When data is interpreted incorrectly (as it often is) it can (and does) cause innocent people to go to jail. These are real-life consequences of mathematical errors that cause people to behave in ways that (inadvertently) harm other people.
This book is full of powerful examples that make you feel both cringe with horror and delighted (I was so excited to find out that the ice bucket challenge had such a positive outcome.) But more often than not, it's a sobering look at the role math plays in our lives and the harm we can do when we misuse it.
I loved reading this book and if numbers are your thing at all, I can't recommend it enough.
thank you to Scribner and netgalley for an early copy in exchange for an honest review.
June 5, 2022
Leftist book. I expected something that only explored facts not opinions about politics and various topics that are controversial, like vaccinations. He explains reasons why we should not use statistics and other data to mislead by twisting data, but uses data to his advantage to prove his point of view. It was rather ironic. I love math and I picked this book for a book club, and it read more like right wing vs left wing, than math of life and death. At the end I wasn't even sure what 7 mathematical principles her was talking about in the sub title.
October 23, 2019
A lot of familiar mathematical ideas, but told engagingly and with plenty of wit. I especially enjoyed the final chapter on epidemiology (although I'd have liked a bit more mathematical detail, even in the form of diagrams rather than equations).
February 5, 2020
I have been a lifelong reader, I love learning and this book was right in my lane, enjoyed the new exposures.
August 14, 2025
Picked up this book with a feeling that I’ll be a bit (whole hella) smarter after reading it. Well… I feel dumber ( I didn’t get dumber, just feel it) because it was a lot of explaining that I wasn’t picking up. To be fair, I wasn’t going back in and attempt to really understand it. I think I got the general idea. But who knew math can have so many effects on non math things? I did find the section about epidemics very interesting, the role mathematics in law useful, and think everyone should read chapter 4: don’t believe the truth, the bunking media statistics because people just believe what they hear on tv (I’m definitely not guilty of that…) w/o the understanding the statistic or asking why it’s being used. Bumping up my star rating after writing this review because maybe I am a bit smarter after reading this book.
June 22, 2020
The Maths of Life and Death, written by Kit Yates, who is a senior lecturer in the Department of Mathematical Sciences and co-director of the Centre for Mathematical Biology at the University of Bath, aims to show that ‘maths is for everyone’ and that mathematics is ‘first and foremost, a practical tool to make sense of our complex world.‘ This is a mission that I’m definitely on board with. I’m convinced that maths is the worst taught of all school subjects in England (due to the failure of central government policies to attract and reward good teachers), leaving a lot of people with the idea that maths isn’t for them. It’s frustrating to see people who are otherwise really smart refusing to even engage with an argument if it contains numbers or anything else ‘sciency’. Yates’s book, on the whole, definitely does a good job of explaining some basic mathematical concepts simply and clearly, and showing how they are relevant in the ‘real world’. The book is almost entirely focused on statistics, and the one chapter that strays into the realm of pure mathematics – on algorithms – will probably be less accessible for the average reader. However, having a solid understanding of some basic concepts in statistics is both vital and possible for everyone, and so I think this focus works well.
I have to say that most of the examples used in The Maths of Life and Death were already familiar to me, which is probably the result of my amateur enthusiasm for statistics rather than any undue repetition on Yates’s part, although there is a certain amount of crossover with Ben Goldacre’s Bad Science. Because I’m interested in medicine, I was already familiar with the material on medical statistics covered in chapter two, and with much of the epidemiological information in chapter seven (this, of course, is not Yates’s fault, but because this chapter focuses on controlling global pandemics, it makes for a rather chilling read in the wake of Covid-19). Chapter three, on the law, retells the story of the infamous Sally Clark case, where statistics were used to ‘prove’ that the chances of experiencing two stillbirths in the same family were 1 in 73 million, and so Clark must have murdered her two children; as Yates shows, this figure could only have been arrived at through multiple statistical errors. And I already knew about the ‘birthday problem’ in chapter four, which shows that in any school class it’s more likely than not that two children share the same birthday, although I loved hearing the story of how Yates used this fact to pitch his literary agent, Chris Wellbelove, while they were having drinks in a pub:
I bet him the next round of drinks that I would be able to find two people, in the relatively quiet pub, who shared a birthday. After a quick scan of the room, he readily took me on and indeed offered to buy the next two rounds if I could find such a pair, so unlikely did he think the prospect of a match. Twenty minutes and a lot of baffled looks and superficial explanations later… I had found my pair of birthday-sharers and the drinks were on Chris.
Yates’s prose is clear and straightforward, which is absolutely necessary for a book of this type. Occasionally, when he is trying to write about the bigger implications of statistics, it becomes a bit banal, but this isn’t the case most of the time. I also liked that he explained his calculations both in the text and through the use of diagrams – I found the text easier to follow, but others would probably prefer the diagrams, so this works for everyone. All in all, I’d recommend this book as an accessible and important introduction to understanding the use and abuse of statistics. 3.5 stars.
I would like to thank Quercus for sending me a free copy of this book to review.
I have to say that most of the examples used in The Maths of Life and Death were already familiar to me, which is probably the result of my amateur enthusiasm for statistics rather than any undue repetition on Yates’s part, although there is a certain amount of crossover with Ben Goldacre’s Bad Science. Because I’m interested in medicine, I was already familiar with the material on medical statistics covered in chapter two, and with much of the epidemiological information in chapter seven (this, of course, is not Yates’s fault, but because this chapter focuses on controlling global pandemics, it makes for a rather chilling read in the wake of Covid-19). Chapter three, on the law, retells the story of the infamous Sally Clark case, where statistics were used to ‘prove’ that the chances of experiencing two stillbirths in the same family were 1 in 73 million, and so Clark must have murdered her two children; as Yates shows, this figure could only have been arrived at through multiple statistical errors. And I already knew about the ‘birthday problem’ in chapter four, which shows that in any school class it’s more likely than not that two children share the same birthday, although I loved hearing the story of how Yates used this fact to pitch his literary agent, Chris Wellbelove, while they were having drinks in a pub:
I bet him the next round of drinks that I would be able to find two people, in the relatively quiet pub, who shared a birthday. After a quick scan of the room, he readily took me on and indeed offered to buy the next two rounds if I could find such a pair, so unlikely did he think the prospect of a match. Twenty minutes and a lot of baffled looks and superficial explanations later… I had found my pair of birthday-sharers and the drinks were on Chris.
Yates’s prose is clear and straightforward, which is absolutely necessary for a book of this type. Occasionally, when he is trying to write about the bigger implications of statistics, it becomes a bit banal, but this isn’t the case most of the time. I also liked that he explained his calculations both in the text and through the use of diagrams – I found the text easier to follow, but others would probably prefer the diagrams, so this works for everyone. All in all, I’d recommend this book as an accessible and important introduction to understanding the use and abuse of statistics. 3.5 stars.
I would like to thank Quercus for sending me a free copy of this book to review.
February 17, 2020
As a math nerd, I am always looking for books that provide insight into the use of mathematics in our lives. I skimmed through this book and found some interesting tidbits on disease, exponents, and statistics. The examples and stories include a lot of visuals which helps but there is a lot of detail here (more than I personally needed, since I was reading this book for fun).
October 30, 2020
The best book i had ever read in math after the parrot's theorem novel🖤
April 18, 2023
Knjiga obrađuje temu sveprisutnosti matematike u svakodnevnom životu, od načina na koji se predstavlja efikasnost lekova, odluka koje donose sudovi do savremenih algoritama koji dovode do toga da neka vest postane popularna. Pisana je vrlo jednostavnim i lako razumljivim stilom sa hrpom interesantnih anegdota: Kako proceniti broj puževa u dvorištu; Kako je greška u prebacivanju imperijalnih u metričke jedinice dovela do katastrofalne štete od 125 miliona $; Koja matematička greška je doprinela porazu Američke akcije u Zalivu svinja; Koja je bila uloga statistike u čuvenoj aferi Drajfus...
June 19, 2023
While I didn’t major in math nor am I a mathematician, per se…. I was maybe one course shy of a math minor in college and utilize math and statistical concepts regularly in my career.
With that said, while the author says this is NOT a book about math for mathematicians, it moves quickly and I was engaged and at times had to slow down or back up to catch what he was saying.
The author addresses subjects such as misleading statistics, making projections, imperial versus metric systems, etc.
I found it a delightful listen.
With that said, while the author says this is NOT a book about math for mathematicians, it moves quickly and I was engaged and at times had to slow down or back up to catch what he was saying.
The author addresses subjects such as misleading statistics, making projections, imperial versus metric systems, etc.
I found it a delightful listen.
August 6, 2021
Libro que con ejemplos cotidianos nos demuestra que a veces los números también pueden equivocarse en una pequeña parte y las consecuencias pueden ser tremendas. Estos siete capítulos te harán ver las matemáticas desde otra perspectivas y leerás un montón de curiosidades que te dejarán con la boca abierta.
March 9, 2024
I won’t pretend that I fully understood all of the math described in this book but I did find the discussions about how math can be used, and misused, fascinating. One of the math classes I remember taking in college (oh so long ago) was How to Lie with Statistics. Concepts from that class, which I enjoyed, and Probability, which I didn’t (mainly because the instructor was ancient, monotone, and boring), were prevalent in this book. There were also some surprising topics in which math played a role, such as the Bay of Pigs Crisis. Even if you’re not a math lover it would be interesting to read through this to see just how much math impacts our daily lives for the good and the bad.
February 28, 2025
Books about math written in plain English are among my favorite micro-genres.
Yates delves into many real-world scenarios and dips our toes into some more advanced topics, as a treat.
Well-written and easy to read, and especially delightful when you're reminded of its Britishness with each use of "maths."
Thanks Julie!
Yates delves into many real-world scenarios and dips our toes into some more advanced topics, as a treat.
Well-written and easy to read, and especially delightful when you're reminded of its Britishness with each use of "maths."
Thanks Julie!
October 1, 2021
I enjoyed this though a fair bit was a repeat of things I know, there was some new info and it was throughly entertaining.
November 28, 2020
I thoroughly enjoyed this book partly because it is a well-written explanation of why math is important which included real-world examples and partly because the author is British and he uses the word "maths" which seems significantly cooler than the American "math." This book is a great way to support the importance of studying math and why it's important to understand how to think mathematically. I am not a "math person" meaning I don't see numbers and doing mental math isn't just tricky, it's painful for me, but I can understand the beauty of math and the importance of learning to think and problem solve. Kit Yates demonstrates the dangers of failing to grasp mathematical reasoning in real-world situations raging from medical to legal circumstances. I would recommend this for math teachers as a way to explain math to some of the students who, like me, felt like math wasn't relevant for them.
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December 7, 2020Understandable as it may be, our trust in math is easy to turn into over trust. This can lead to problems. At least according to Kit Yates. There's always more room for error when we don't leave any. Errors on both sides of it too, the human who gives the input and the human who interprets it, the human who writes the code and the human who approves it. While code and math itself seems more or less infallible, it is perfectly happy to be Calvin in the bathtub. We need to understand that. But not trusting data is a difficult thing to manage. Where do you draw the line? If you don't have an advanced degree in it, how do you decide who you can trust? That comes down to human choices. Often, it's evaluating the person doing the math. Even something that seems as objective as code or STEM really has its credibility built up by the people who perform it.
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