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Mathematical notes on a brief history of mankind
From a biological point of view, we humans belong to the species Homo sapiens. Now we feel that we are unique and exist on this earth, but millions of years ago, we were still in the middle of the food chain and lived in this dangerous land with our companions.

About 2.5 million years ago, ancient humans began to evolve and multiply in East Africa. After another 500,000 years, some of these ancient humans left their homes and began a long migration. They have traveled all over North Africa, Europe and Asia. In order to survive in areas with different climates such as cold, hot, wet and dry, different characteristics have evolved, so human beings have developed different species. Humans in Europe and West Asia became Neanderthals, Homo erectus in East Asia, Solo people living in Jawa Island, Indonesia, and a group of dwarfs, flores people, also living in the island of loris, Indonesia. In the book, the author puts forward his own point of view: from the whole history, the existence of various races in the past was actually the norm, and now there is only one kind of people on the earth, which is an anomaly.

Ancient humans struggled to survive in primitive environment. In order to get food, they follow closely behind large carnivores and pick up food scraps. They learned to break bones with sharp stones and feed on bone marrow, which was the most common use of early stone tools. Due to the strengthening of thinking, their brains began to get bigger, and the bigger brains needed to consume more energy, which made ancient humans pay two prices: first, they had to spend more time looking for food, and second, their muscles degenerated and shrank.

Ancient humans continued to strive to find a breakthrough in survival. They started walking upright. "Stand up" can see farther, which is conducive to better finding enemies and prey. At the same time, their hands can be independent and perform more delicate movements, such as throwing stones and signaling. The more things that hands can do, the stronger human beings become, so people pay more attention to the development of nervous system until they can make and use complex tools. At the same time, the brain becomes bigger, which makes it difficult for women to have children, so the natural selection mechanism allows humans to have children earlier, so it takes longer and more energy for humans to raise children. The hard living conditions of ancient people forced them to rely on more people to raise their children, thus forming families and tribes, and then evolved into races with strong social relations.

After these long evolutions, until 654.38 million+years ago, mankind finally stood at the top of the food chain. Then, man learned to control fire, which made his position in the food chain more unbreakable. They cook food with fire. The cooked food is healthier, and at the same time, it shortens the time for eating, so that human beings can do more things, which shortens human intestines and begins to develop their brains. In addition, fire can also help people resist the attack of wild animals. In ancient times, when the law of the jungle prevailed, they were no longer at a disadvantage.

Tens of thousands of years ago, races such as Denisova and Neanderthals gradually disappeared in the long river of time, leaving Homo sapiens as the last species of mankind. So how did these humans disappear? There are two theories in the scientific community: the first is the "hybrid breeding theory", which talks about love at first sight, two of a kind and the blending of different races; It is believed that Homo sapiens migrated from Africa to all parts of the world and interbred with other races, forming today's human beings. Another completely opposite view, called "substitution theory", holds that the two sides are incompatible with each other, dislike each other, and even genocide may occur. In recent decades, substitution theory has become common sense in this field. This theory is not only more reliable in archaeological evidence but also more correct in politics.