Mariam Mirzakhani, an Iranian mathematician who died on 20 17, was the first woman to win the Fields Prize, the highest prize in mathematics. She described learning mathematics as "like a person lost in the jungle, trying to find a way out with everything he has learned".
Although she lived only 40 years old, she should be said to be a lucky dog. She went deeper than most people in the "math jungle" and finally won the math championship.
More and more evidence shows that human beings seem to be the lucky ones in nature and the only animals that can cross the "mathematical jungle". But where does this ability come from? Why did it develop? What is the purpose of development? ..... To answer these questions, it not only involves some hot topics in neuroscience, but also forces us to rethink "What is mathematics?" "Is mathematics a discovery or an invention?" Questions about the nature of mathematics.
Dealing with the world through "modeling"
Nature is a complex, changeable and dangerous place. The change of habitat, the attack of predators and the lack of food ... the survival of organisms depends on their ability to perceive the surrounding environment. But do bison measure the number and size of lions in order to make a fight/flight decision? Or starlings always keep a proper distance from their neighbors in the air in order to keep formation; Or the sheep feed along the lush route ... According to Carl Feliston, a neuroscientist at the University of London, all these activities mean doing math.
"Because mathematics is simple, thrifty and symmetrical, if you regard it as a language, it will be better than other ways to describe the world. Almost all life, from dolphins to slime molds, can understand the world mathematically to serve their own survival, "he said.
Aren't there many "model" competitions now? For a complex process, establish a relatively simple mathematical model, and then input parameters to see the running results under different conditions. What Fei liston actually means, then, is that any form of life needs to "model" its living environment in order to play a role.
Fei liston's viewpoint can be traced back to1970s, when cybernetics put forward a principle: in order to provide effective control, robots must first establish a mathematical model of their interaction with the environment before taking corresponding actions. Since then, almost all artificial intelligence research has followed this principle. Today, human beings can make such great achievements in the field of artificial intelligence, thanks to this principle.
Since robots interact with the outside world through "modeling", it is reasonable to speculate that creatures also interact with the outside world through "modeling" to some extent.
For example. When the bison notices the lion approaching, it will instinctively mobilize a decision-making mechanism called "flight/fight", and decide whether to escape or fight according to its own estimation of the size, distance and strength of the lion. Functionally, this decision-making mechanism can be regarded as a mathematical model, in which parameters such as lion size, distance and self-strength are input, and the result of "flight" or "battle" is output. Any parameter change may lead to different output results.
Cultivate an accurate sense of numbers to correct the sense deviation.
Since it is a mathematical model, of course, it is impossible to simplify reality. Especially for life, when danger approaches, quick action is the main thing, and accurate retreat is secondary. For example, the "flight/fight" model mentioned above, it is almost the same to consider those three factors. As for the factors such as "the color of the lion" and "will it rain in the sky", it can be ignored. If too many factors are considered, decision-making will slow down and affect the speed of action.
It is the way we handle the world that determines the unsatisfactory deviation of our senses.
Take Weber-Fechner Law, which reflects the relationship between psychological quantity and physical quantity, as an example. This law says: our ability to distinguish the differences between the two senses decreases with the increase of sensory intensity. For example, you can easily distinguish 1kg from 2kg with a portable weight, but it is not so easy to distinguish 2 1kg from 22kg. The same is true of the ability to distinguish brightness, volume, etc.
We are proud that although human beings have the same sensory biases as other animals, they have developed the ability to identify and correct them. Most obviously, we invented numbers: this is a sign system, which allows us to immediately judge that the gap between (2 1 and 22) and (1 and 2) is the same.
Compared with the school, we can't say who invented the school. The school must have been decentralized at first, but later it developed into one. At first, a teacher may take one student, and later a teacher may take several students. When there are more and more students, there will be more and more important teachers, and it is not realistic to attend classes, so it may be necessary to divide subjects, which will gradually develop into a school.