Numbers, Mathematics And Human Evolution

Zheng Lei / Wen

Human civilization develops with language, characters and numbers. Before the birth of language, expressions and actions used to be means of communication, and numbers may come from the need to count. Even though ancient humans did not need to communicate with people, they also needed to count. Therefore, as early as 37000 years ago, we found the marks carved on wooden sticks and stone slabs to count. From counting to numbers, then to carry system, algebra, geometry, until modern mathematics, this is another main line of human brain development. Many people are afraid of mathematics, which is not surprising, because many people do not need to master the knowledge system developed in tens of thousands of years, and there are not many mathematical concepts and methods to meet the basic daily needs of human beings. If you want to have a general understanding of the system of mathematics, it is recommended to read the pamphlet of the history of minimalist mathematics. Its biggest feature is that each chapter is only 3-5 pages. It is also provided with a large number of color pictures and historical knowledge. It is vivid and interesting, and can basically meet the needs of ordinary readers to understand the general situation of mathematics. After reading this little book, if there is any interest, I recommend another more comprehensive and professional "brief history of Mathematics: the disappearance of certainty" written by Morris Klein, an expert in the history of mathematics.

It may be difficult for us to remember the difficulties in learning arithmetic as a child. But in childhood, people already have the concept of quantity. Then adults will teach children to use five fingers to understand the items corresponding to 1-5. The number is actually abstract. From the specific number of items to the number 1-5 that can be used independently for all items, it is a cognitive leap. Then the child learned to count 6-10, just can count with two hands. This will lay a good foundation for learning decimal system, and then learn two digit addition, subtraction, and multiplication table. Today's early childhood education is very developed, and decades ago, only in grade two or three of primary school can learn these simple arithmetic knowledge. This process is just that modern people inherit what the ancients invented a long time ago. The area with the fastest development of mathematics is also the area with the earliest origin of human civilization. In the Lianghe area, Sumerians began to use the hex system in 4000 BC. The most ingenious thing is that they only used seven symbols. Up to now, people can't find a reference in their daily life. The only thing they know is that Babylon was already the most developed area of agriculture and commerce. In its vicinity, ancient Greece, ancient Egypt, as well as India, where ancient humans migrated to India earlier, there appeared superb mathematical masters, such as Pythagoras, Thales, huarazimu, Brahmagupta, etc. The Arabic numbers are also from India. The Cubans and Egyptians have known for a long time how they could solve the quadratic equation once.

It took tens of thousands of years for the concrete objects to be transformed into abstract numbers, and it took nearly a thousand years to reach the stage of abstract algebraic operations represented by letters. The Arabian mathematician, astronomer, and geographer, alkhwarizimi, invented the term transfer and merger of the same kind. On this basis, he wrote a book now called algebra. What's interesting is that the mathematician's name has been translated into various languages and written in English as algorithm, which we often call "algorithm". Algebra (algebra) in Spanish added a suffix ISTA, which stands for occupation, to become algebrista, which means "bonesetter", which is similar to transference. The author explains a mathematical method with very simple words and a few strokes. For example, Fourier analysis is said to be the process of decomposing any complex waveform into various sine waves. As long as you have learned some elementary mathematics, you can understand it.

The cognition of space obviously belongs to the category of mathematical development. It is easy to understand from one dimension to three dimension. In fact, human beings live in four-dimensional space. Human beings can perceive time and the change of things with time, which is called four-dimensional cognition. Space with dimension n greater than 4 can only rely on reasoning. People understand high dimensional space by means of space reduction. For example, at a given time, you can get a three-dimensional object, you can cut it, observe the profile, this is two-dimensional, you can also use a ruler to draw a line on this surface, get a one-dimensional image, this process has undergone three dimensional reduction. The problem of solid geometry can be solved by reducing dimension into plane geometry.

Randomness is another profound mathematical concept, which needs to learn permutation and combination knowledge first, which is also the most error prone part of mathematics examination. The law of large numbers and the central limit theorem of probability theory are very abstract, but the author simply gives a result that we all know by tossing coins: the more times of throwing, the more times the positive and negative sides appear, the closer to half. For a population with finite variance, the larger the number of samples you randomly select, the more similar the distribution of samples to the symmetrical bell curve, and the closer the average value calculated by the sample to the population mean. The experience given by the author is that the number of samples should not be less than 30. This little knowledge is very useful. If you want to know the average value of a certain index of a large number of items, you only need to randomly select no less than 30 samples to measure, draw the distribution curve, and calculate the average value. You can basically master this situation. Mathematics is difficult, but everyone should know some basic knowledge.