The book From One to Infinity was recommended by a teacher I respect very much. When I first read the title of the book, I thought it was a math book, so I was worried. I didn't like math since I was a child. Although I do well in every exam, I'm really not interested.

But the teacher said that this book is "a book that affects a generation." After the introduction of China in the late 1970s, many popular science workers were fooled. Such a high-profile evaluation really piqued my appetite, so I crustily skin of head and started reading. Unexpectedly, this is really not a math book, but a popular science book.

This book is magnificent and can be described as a popular science book for general education in natural science. With vivid language, rambling ways and interesting metaphors, this paper introduces some important scientific advances in the first half of the 20th century to readers, including basic mathematics knowledge, Einstein's theory of relativity and four-dimensional space-time structure, and probes into the achievements of human beings in understanding the microscopic world (such as basic particles and genes) and the macroscopic world (such as the solar system and galaxies).

Geogregamov (1904-1968), a Russian-American, studied under niels bohr and Rutherford at Copenhagen University and Cambridge University. His two teachers are both famous. Bohr is the father of atomic structure theory and won the Nobel Prize in physics. Rutherford was the father of nuclear physics and won the Nobel Prize in chemistry.

It is said that a good teacher makes a good teacher. He himself is famous for advocating the theory that the universe originated from the Big Bang. He is an outstanding popular science writer and has officially published 25 books. Among them, From One to Infinity is his most famous masterpiece, and he won the Kalinga Science Award of UNESCO.

I can't help admiring the author. The writing technique of this book is so special that it is completely different from the boring and difficult to understand of general popular science books. It basically takes interesting stories as the introduction and main material, crushes all the most useful and important theoretical knowledge of mathematics, physics and biology, and adds humorous language to cook a series of "delicious dishes", which makes people happily complete an interesting journey of natural science achievements with laughter. This narrative method makes the originally dry scientific knowledge interesting and easy to read.

Structurally, this book can be divided into four parts. The first part is "number" in mathematics; The second part includes four-dimensional space, Einstein's theory of relativity and so on. The third part is the micro-world: particles that make up matter and cells and genes that make up life; The fourth part is the composition of the universe, solar system, galaxies, stars and planets.

Below, I will focus on three points and take you to appreciate this book.

1, on "number" in mathematics

At the beginning of the book, I told a story. Two nobles decided to play a counting game, and whoever said the largest number would win. "Very well," said a nobleman. "You go first!" The other racked his brains for a few minutes and finally said the biggest number he thought of: "three". Now it's the first turn to think. After thinking hard for a quarter of an hour, he abstained and said, "You won!" " "

As soon as I finished reading this story, I immediately thought of Laozi's "Tao gives birth to one, life gives birth to two, and life gives birth to three." Is it a coincidence? Or is there another meaning? This humorous but thought-provoking writing style is really worth learning. Isn't everything infinite? There is no end. It's really wonderful!

When talking about natural numbers and artificial numbers, the author talked about imaginary numbers. However, he didn't pile up the concepts and let you think for yourself. Instead, he suggested, "Now, let's do some advanced arithmetic. Two two get four, three three see nine, four forty-six, five five twenty-five, so the square root of four is two, the square root of nine is three, the square root of sixteen is four and the square root of twenty-five is five. But what is the square root of a negative number? "

Negative numbers also have square roots? I have to say that this is really a great invention of mathematicians. Generally speaking, the square root of a negative number is meaningless. However, the Italian mathematician Caldan invented the concept of "imaginary number" in16th century, and wrote the square root of-1 as I. The geometric interpretation of imaginary number is: a number multiplied by I is geometrically equivalent to rotating 90 counterclockwise. This unusual rotation led to the introduction of the concept of space into mathematics, and three-dimensional space was discovered. Later, combined with time, a four-dimensional space followed the four-dimensional geometric law and developed Einstein's theory of relativity.

Seeing this, I can't help but wonder. Imaginary number is really a wonderful invention, which shows that don't say impossible, there is no impossible, only unexpected. When human's innovative thinking is developed, it can often lead to another cave.

2. About four-dimensional space and Einstein's theory of relativity.

Because the above is extended from imaginary number to multidimensional space. The author simply took us to the physical space and began to explore the unusual nature of space.

From this, I was inspired that quantum mechanics, whether it is four-dimensional or five-dimensional, or even the current fantasy, is unimaginable to us, because we are limited by living in a three-dimensional space, and we only observe this space from the inside, but we can't jump out of the limitation and observe it from the outside.

In the book, the author also quoted a story about gloves. Gloves of the left hand should not be worn on the right hand (the palm and the back of the hand will change) to show that the left hand is tied to the right hand. But if you look at it from the outside like you look at all kinds of surfaces, you can change left and right when the space is distorted, just like Mobius ring. If the three-dimensional space can be properly distorted, people who travel around the universe can come back with their hearts in their right chest. Glove manufacturers only need to make a one-size-fits-all product, put half of it in a spaceship and circle the universe, and when they come back, this half can be used on the other hand. Think about it, four-dimensional space is not so mysterious.

We have a ready-made observation coordinate to establish the thinking space, and this coordinate is time. Once time is added to the three-dimensional coordinates of space, it is equivalent to entering space to observe people's activities outside. When both space and time extend from one to infinity, human beings break through their own limitations. Just like the story about comparing two infinite hotels, the four-dimensional distance between two events seems to be no longer an incredible thing, and it is easy to measure.

So, can time and space change each other? With the infinity of mathematics and time, this problem becomes simple. That is to say, when watching an event from a moving object, as long as the time axis on the spatio-temporal map rotates by an angle according to the speed of the event, it can be transformed into each other under the condition that the spatial axis is unchanged.

For example, imagine a person eating on a moving train. The waiter thinks he is drinking aperitif and eating sweets in the same place, but for two people standing on the side of the road and looking in, one sees him drinking aperitif and the other sees him eating sweets. The two times are several miles apart. This is the four-dimensional geometry of space-time transformation.

3. About the micro-world

The author said in the book that there are 92 kinds of chemical elements in nature, which are combined in different proportions to form an endless variety of complex chemicals. In ancient Greece, people knew that matter could not be divided indefinitely, and there was always an indivisible basic unit. In Greek, "atom" means "inseparable". Scientific exploration is endless, and atoms have been proved to be separable, including nucleons, electrons, neutrinos, neutrons and so on.

To digress, this book was written in the 1950s and 1960s after all. Now it seems that the further development of science has once again proved the infinity of all things, and quantum has appeared. The discussion about the composition of matter is not as thorough as the author imagined.

The endless exploration of truth is precisely the charm of science.

Anyway, when it comes to particles, how do we understand nuclear fission and atomic fission?

Different kinds of nuclei are composed of different numbers of hydrogen nuclei, which are represented by positively charged protons and uncharged neutrons respectively. In the nucleus, there are two opposite forces, one is to suppress the surface tension of each nucleus, and the other is to split the repulsive force of each charged part in the nucleus. If repulsion prevails, the nucleus may split, break into two or more pieces and fly away at high speed. This process is called "atomic fission". Element 47 of the periodic table is silver, until the element of silver is mainly surface tension, and the heavy element in the second half is mainly repulsion. Therefore, elements heavier than silver are theoretically unstable. Once bombarded strongly enough from the outside, it will split into two or more pieces and release huge internal nuclear energy.

When it comes to physics, we can't help but talk about the law of disorder.

For example, if you pour a glass of water and observe it carefully, what you see is only a clear and uniform liquid, and you can't see any signs of internal movement. But in fact, seemingly calm water, molecules are moving violently. The random motion of water molecules or molecules of all other substances is called thermal motion, also known as Brownian motion. Thermal motion, like molecular dancing, follows three laws: conservation of energy; Heat can be spontaneously transferred from high-temperature objects to low-temperature objects, but it is impossible to spontaneously transfer from low temperature to high temperature; Absolute zero is out of reach. Absolute zero, that is, all molecules are at rest.

The microscopic world of matter is so colorful. So, as a living body, what about its microscopic world?

In the book, the author tells us the cells and genes that make up life.

All living things, its whole development process and mature characteristics, are almost determined by genes in cells. Gene is the smallest unit of living matter, which has all the characteristics of life, and is also related to molecules (such as protein) that obey general chemical laws. Genes are stable and can pass on the properties of matter for thousands of generations without change. The number of atoms that make up a gene is relatively small and well designed, because different attributes and changes in atomic distribution can produce different organs.

4. About the universe

Finally, let's look up from the microscopic world and see the vast universe.

For example, the following question: What is "cosmic expansion"?

The expansion of the universe means that all galaxies are leaving the Milky Way. In other words, all galaxies are separating from each other. For example, if a balloon full of dots is blown into the balloon, ants staying at one point will think that all other points are "running away".

The process of the expansion of the universe is as follows: first, the universe is in its infancy, and the universe is squeezed into a sphere with a radius eight times that of the sun, but this dense state will not exist for a long time. Then it expands rapidly in just 2 seconds, and the density of the universe reaches millions of times that of water. After a few hours, the original continuous gas will split into a single gas ball and form a star. Finally, it continues to expand, and the stars separate to form various nebula systems, which are now galaxies, and are now retreating to the depths of the universe.

Of course, the content of this book itself is much richer than the points I listed. I just picked a leaf and a grass to let you feel it. If you want to appreciate the breadth and interest of this book, I suggest you read the original.

Finally, I want to say that after reading this book, I think science is really interesting, and mathematics doesn't make me feel so disgusting.

Look, a book has changed my attitude towards mathematics. Therefore, it is necessary to read books that you don't want to read.

(End of this article)

I have devoted my life to reading classic books, writing heavy words and living a profound life. I'm Du Doudou, thank you for your attention.

About the author: Du Doudou, who has been engaged in IT for more than 20 years, has studied English, computer, aesthetics and psychology. Debuted in his early years, and later worked for many world-renowned IT foreign companies. Now he works in a research institute. Bookworm is the code word of free-time code. He is also a signing author of several platforms, a member partner, a 10,000-volume good book studio and the founder of a 10,000-volume good book reading club.