This book was written in 2001 by two Japanese educators, and was released at a time when the Japanese Ministry of Education was implementing a major basic education reform, promoting the banner of "Pleasant Education". The difference is that the former promotes a spirit of truly pleasant education, making the boring and incomprehensible theory of probability very easy to understand, while the latter is concerned that the public will lose interest in writing mathematics, away from true knowledge.
In addition to the features of shallow-deep, combined with everyday examples, the most impressive is that each section contains two pages. This allows people without great motivation to learn to read easily and continuously, as if someone who wants to exercise should start with one squat per day instead of doing twenty or thirty.
The book's content is very clear, and the concepts and announcements are transcribed on only six pages of the notebook. The concepts are listed, with the binomial distribution formula, expectation value, differential, standard deviation, dispersion, Bechev's theorem (also known as Bechev's theorem, this section took three days to understand), correlation, differential coefficients, linear regression, expectation value of multiple random variables, calculation of the difference and the difference, the expectation value and the difference of the binomial distribution, the supergeometric distribution. These words look very professional, in fact, on average each one takes only 5 minutes to understand.
How to calculate the properties and correlations of probabilities and random variables is not important for people who do not intend to work in finance, business analysis, or artificial intelligence, but it is very important to understand the concept of probability, and to have a statistical mindset about probability. VanVie did not even think about the fact that the theory of probability is more important knowledge than the theory of gravity and genetic replication, is the essential common sense of modern citizens, is there such a mindset that directly determines the degree of a person's expansion.
This article on probability in Java is a simple record of the five most simple wisdoms of probability theory.
The first wisdom: randomness. The most basic idea of probability theory is that something happens for no reason, and that's the concept of randomness. We are always in the habit of reducing the occurrence of an event to a variety of causes. Modern cognitive science has found that causality is the basic mechanism of human cognition of the external world, and that losing logic causes the human cognitive system to collapse. This makes it difficult to understand randomness, while there is a deeper philosophical theory behind randomness, called non-continuity.
The second wisdom is that there is always an error. Even in the most rigorous physical experiments, there is no guarantee that there will be no accidental effect at all, but only a method of taking the average value through multiple experiments, using range values to represent the results of the experiments, and trying to minimize the impact of the accidental factors. Even so, the results of the experiments do not represent true values that must be within the specified range, in fact, this range is only a result of the calculation of probabilities, which only shows that the true value is outside the range.
The third wisdom: the gambler's fallacy. This is where we start to learn how to identify the pitfalls. The so-called gambler's fallacy is that when a gambler is gambling, if a certain situation occurs several times, he believes that there is a greater probability that a situation that has not occurred will occur in the future. For example, if he has already hit the jackpot several times when he throws a color ball, he believes that the jackpot should be at stake. This thinking is the habit of the vast majority of people, but also the instinctive thinking of people.
Fourth wisdom: Find laws where there are no rules. The core of probability theory is that independent random events are irregular and unpredictable. We don't need to be overly concerned with random events, and we shouldn't try to find rules in randomness. Lottery analysis has been around for many years, and lottery stores on the streets have a trend map of past prizes, and there are so-called lottery experts on all major websites who predict future lottery moves. From the perspective of people with a probability mindset, predicting lottery moves is still a very funny thing.
第五个智慧：小数定律。数据多的时候规律总是会被找到，而当数据少的时候，规律有时候会自己“跳出来”。随机现象可以看上去很不随机，甚至非常整齐。这个很好理解，两个点连成一条直线，你可以说这两个点就在这条直线上；三个点则必然会有一个三角形；四个点…永远都能有一个自洽的结论，说明几个点构成一个图形，但实际上点在不在图形上，没有相关性，也就是因果关系。小数定律是诺贝尔经济学奖丹尼尔.卡尼曼戏称的，他认为理解小数定律和理解大数定律是相辅相成的。这跟前面的赌徒谬误的意思差不多，在生活中是最容易被忽视而造成可笑错误。比如，你曾经被河南人骗过，又恰好听说自己的一个朋友被河南人骗过，如果你进一步在网上发现有人被河南人骗过，那是否就会得出河南人骗子特别多的结论？（以前我就是这么认为的，无知啊！）可是无论从理论分析，还是从相关实验研究来看，都找不到河南人骗子多的统计数据，说明这只能是一种以讹传讹的认知偏误。很多网络上的经济、政治评论员，经常会从一两个事件就总结出一条博人眼球的规律来，在“开化”人看来，这种行为都是很无知的。
To understand that the random distribution is not the same as the mean distribution, probability and whether a single event occurs without a direct connection, it is necessary to be patient and learn a little knowledge of probability. It does not take much time, perhaps only an hour, we can understand the general concept, and then slowly practice, consolidate and deepen the thinking of probability theory in our lives. This can be very helpful in our lives, and I recently came across such an example. A friend suggested that I pay attention to the distribution of funds, the probability of distribution of funds is less than zero in this wave market last year.
In this era of rapid technological development and information explosion, the exchange rate IQ tax is sometimes unavoidable, and the result is the same as a model of a mobile phone that someone greedily bought cheaply on the side of the road. But now the technology of the pothole is also progressing, like the classification fund with several layers of coats of cabbage harvesting tools, which will surely be endless in the future. This requires us to thoroughly refine some basic disciplines, deserving of the title of a modern citizen.
Translated from the author's book by Liu Pei Yunhan