Jordan Allen Berg has made great achievements in mathematics popularization. He has published articles in Wired, The New York Times, Washington post, The Wall Street Journal, The Boston Globe and other media all the year round, which has aroused widespread concern. Bill Gates is also one of his readers.
About this book
This book mainly talks about the charm of mathematics and how to acquire the skills of solving problems in life with mathematical principles. The author thinks that mathematics can help us to better understand the structure and essence of the world, and should be put in the toolbox of every thoughtful person, so as to better solve problems and avoid fallacies and mistakes.
This book abandons complicated technical terms and brings us a zero-based math class, with anecdotes, basic equations and simple charts in the real world.
Core content
Mathematics is one of the most important basic sciences for human beings, and it is also the most useful thinking tool in life. Especially in the current era of big data, we need the power of mathematical thinking.
This book uses mathematical methods to analyze and solve many problems in daily life. You will find that with mathematical tools, we can see things more thoroughly and more interestingly. The author uses entertaining cases and methods to help us re-understand five concepts related to mathematics, namely linearity, reasoning, regression, existence and expectation.
I linearity-a mathematical method for evaluating atrocities
It is not enough to evaluate atrocities mathematically by linear method. In the field of mathematics, there is a principle of testing right and wrong: if we use different methods to calculate and get different conclusions, it means that there is something wrong with our methods.
Comparing the cruelty of tragedy and comparing the quantity are two different things, which are very different in essence. Comparing the size of the quantity, we can always rely on mathematics, but it is cruel, we need brains. Calculating linear regression can be done by computer, but judging whether the result is meaningful depends on human wisdom.
Second, reasoning-Baltimore stockbroker
Baltimore stockbrokers guessed the rise and fall of stocks ten times in a row, which is a scam with hidden probability behind it. When we do mathematical reasoning, we should take this story as a warning: we must be careful in the analysis of big data. There may be more than one root of quadratic equation, and the same observation may produce many theories. It is not the truth that leads us astray, but the omission of some assumptions in reasoning.
Third, return-is the child's height related to parents?
Research shows that the probability of tall parents giving birth to tall children is not 100%. In fact, the height of parents and children is affected by the regression effect. Everything that is affected and random on the vertical axis of time follows this law. As long as the data is large enough, human height or IQ tends to average regression.
Fourth, existence-does public opinion really exist?
The principle of "the minority is subordinate to the majority" is simple and seemingly fair, but only when two viewpoints are involved can the best effect be achieved. As long as there are more than two views, most people's preferences will be contradictory.
It can be said that public opinion does not exist at all. More precisely, public opinion will exist only if most people agree with it. If we act according to logic, we often need to go against the opinions of the majority. For politicians, it is their duty to make rational use of inconsistent public opinion.
Verb (abbreviation of verb) Expectation-What kind of lottery ticket is worth buying?
The purchase value of lottery tickets is different from the winning value. The purchase value is the amount you spend on buying a lottery ticket, while the winning value is the real value of the lottery ticket after the introduction of probability theory. We can express it by expectation. The expected value of lottery tickets is not worth buying only if it is lower than the purchase value. If it is higher than the purchase value, the lottery ticket is worth buying when your purchase amount reaches a certain amount.
Golden sentence:
1. When you hear the so-called experts talk about statistical data again, especially some figures obtained by linear regression method, remember that not all lines are straight lines, and not all data are telling the truth.
Devil Mathematics: The Power of Mathematical Thinking in the Age of Big Data
2. In the face of the analysis of big data, we must be cautious. The same observation can lead to many possible reasons. It is not the truth that leads us astray, but the omission of some assumptions in reasoning.
No matter how high their parents' IQ is, their offspring can't always be smart, and they will inevitably be influenced by "returning to the average" and become a member of ordinary people.
4. The principle of "the minority is subordinate to the majority" is simple and seemingly fair, but the best effect can be achieved only when two viewpoints are involved. As long as there are more than two views, most people's preferences will be contradictory.
Mathematics is not just a boring formula or equation. Mathematical principles can be used to solve many problems in our reality. This is the secret that makes mathematics full of wisdom and fun.
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