The first phenomenon is about exponential amplification. Bartlett, a physicist, said, "The biggest defect of human beings is that they can't understand the exponential function." Functions such as y equal to the x power of 2 are exponential functions. For example, we can fold a piece of paper big enough to be as high as Mount Everest, and we don't have to fold it many times. There are also wheat and cell division on the chessboard. Why can't our brains imagine a similar phenomenon? As the author said, these numbers can climb up, but we just don't know them because of the structure of our minds. The scale of our mind is similar to Zhu's scale (the scale to measure the strength of earthquake). The human eye can see more than 654.38+00000 levels of light with different brightness, but we don't think that the brightest thing is 654.38+00000 times brighter than the darkest thing. The reason is that there are not so many storage locations in the human brain. This physiological structure limits the mathematical ability of human beings. For example, all big numbers are the same to us, and there is not much difference between 1 100 million field and 1 100 million field. There are too many gradations and details that we can't feel. Flowers grow, mountains move and so on. So I think when the mind meets mathematics, it is an incredible and wonderful feeling.
The second phenomenon is about estimating risks. My personal understanding is related to the content of mathematical probability statistics. Statistics are not enough to make risk assessment meaningful. For example, the rising incidence of cancer is frightening. In fact, people live longer and longer, and they can get cancer. Physicist Louis wrote in his book that pedestrians are more likely to be killed by cars every mile than drivers. Can we draw the conclusion that driving is safer than walking? It can be seen that simple numerical comparison is unacceptable to society. The attitude towards risk is developed in the cultural background and is deeply influenced by psychology, ethics and beliefs. For example, according to statistics, if 30 million packs of cigarettes are sold every day, on average, 1600 people will die from smoking. This is equivalent to hiding a pack of explosives in the 18250 pack of cigarettes (if the cigarettes are harmless). We can accept the fate of being boiled to death like a frog, but we can't accept the fate of suddenly exploding like firecrackers. This is the result that the mind cannot accept statistics.
I think there is a place where the mind can never meet mathematics. We accept it with pure reason, but it is so incredible.