Mathematics studies the laws of things and summarizes them. Think about it, how wonderful it is when everything in the whole universe can be expressed in a few simple formulas. This is the so-called life two, two gives birth to three, and three gives birth to everything. Similarly, many common sense and intuition in life are often wrong, and mathematics is the tool to take you out of the fog.
This paper gives a famous example, which is also a common example of survivor's deviation. During World War II, the U.S. military hoped to upgrade the plane's thick armor. Because it is necessary to ensure that the quality of the aircraft is not too heavy, it can only be thickened in a certain part. So they counted the situation that the plane was hit, and found that there were the most craters on the wing and the least craters on the engine. They came to the conclusion that the wings are more likely to be shot, and they are going to thicken the wings. However, a math Wald told them that they should thicken the engine part. The reason for the statistical results is that they counted all the lucky fighters, and many fighters that hit the engine part have crashed, which led to the statistical deviation. It can be seen that rational mathematics can often point out the truth and help us make correct decisions.
The first chapter of this book introduces linearity. The relationship between things in real life is often nonlinear. Such as the Laffer curve mentioned in the first section. The so-called Laffer curve is the graph of the relationship between tax rate and national tax proposed by Laffer. Similar to a quadratic curve, there is a maximum in the middle and both ends are 0. In fact, this relationship is relatively intuitive. When the tax rate is 0 and the national tax revenue is 0, it is 100, and all the money earned by ordinary people is turned over, which naturally loses the motivation to work, so the total tax revenue is still 0. Its significance lies in that the relationship between tax rate and tax revenue is nonlinear, and it is not that raising tax rate can increase the total tax revenue. Therefore, when Reagan was in office, he also drastically reduced taxes based on this view. Of course, whether the effect is good or not, the relationship between the two will certainly not be as simple as a quadratic curve. Although it can be determined that both ends are 0, it cannot express the change in the middle. In my opinion, for taxes with many influencing factors, it cannot be simply expressed by the relationship between tax rate and it. It cannot be said that raising the tax rate or lowering the tax rate will inevitably increase the total tax revenue. I don't know much about sociology and economics, but I think it is necessary to integrate many kinds of knowledge, such as probability, chaos, game and human nature, which can not be solved by several formulas. If a reliable theory can be derived, it is a prediction machine, just like the prediction theory in the galactic empire. This is also the guiding theory of economic prosperity and social development. But this theory is still too unrealistic at present.