Recently, it has been discussed that the popular ChatGPT may replace the top 10 professions. Among them, the media worker where the editor works is one of them, and there is a sense of crisis... So I began to test the real strength of ChatGPT, a competitor-let it write An article on the math problem in "Three-Body":
【ChatGPT】
According to the article generated above, ChatGPT made a brief summary of the novel "Three-Body Problem" and listed the related mathematical problems. Such as the three-body problem, chaos theory, statistics, game theory. But it lacks the support of detailed content, and the readability is not ideal.
When asked about some specific content, the content is still relatively empty and even some errors may appear. For example, when asking about the three-body problem, it was said that it was proposed by Euler, but it was actually proposed by Newton in 1687.
In the opinion of the editor, the articles written by ChatGPT can be used as an outline reference, so the editor started content creation and expansion based on this outline:
【Editor】
"The Three-Body Problem" is a long series of science fiction novels created by Chinese writer Liu Cixin. It tells the story of the Three-Body Problem civilization, which is still unable to solve the Three-Body Problem due to its harsh living environment and after experiencing more than a hundred destructions and rebirths. They decide to flee to the outside world. At this time they obtained the coordinates of the earth and decided to invade the earth...
The unsolvable three-body problem in the classical sense
"The Three-Body Problem" runs through many esoteric concepts of physics. It is often said that the end of physics is mathematics, and the goal of physics is to describe all matter and energy in the universe with precise mathematical language. In "The Three-Body Problem", Wei Cheng's calculation of the three-body problem has attracted special attention. In the first part, the three-body game is for gamers to solve the three-body problem. Regarding the three-body problem, it is described in the novel that "the reason why the sun moves irregularly is that there are three suns in our world, and they are doing unpredictable three-body movements under the influence of mutual gravitation. When our When a planet revolves around one of the suns, it is a constant epoch; when the other one or two suns move within a certain distance, its gravitational force will take the planet away from the sun it surrounds, making it in three The erratic movement within the gravitational range of the sun is a chaotic epoch; after an indeterminate period of time, our planet is captured again by a certain sun, temporarily establishing a stable orbit, and the epoch begins again. This is a game of cosmic rugby The athletes are the three suns, and our world is the ball!"
The three-body problem in the real world: the three mass, initial position and initial velocity are all arbitrary celestial bodies that can be regarded as particle points, and the law of motion under the action of mutual gravitation. The simplest example is the motion of the sun, earth, and moon in the solar system. Mathematically, it can be described by a set of differential equations.
Illustration: three-body movement (picture source Wikipedia)
So can this system of differential equations be solved? The classical solution is to find the first integral, energy integral, angular momentum integral, momentum integral, which are all first integrals. It took hundreds of years to find other first integrals of the three-body problem, but Brons proved in 1887 that there is no algebraic first integral of the three-body problem. Later, Poincaré proved that there is no first integral whose resolution depends on mass. The research of mathematicians such as Xia Zhihong has proved that for some masses, there is no form of first integral. This means that in the classical sense, the three-body problem is unsolvable, and an explicit formula cannot be written.
Scientists such as Poincaré have confirmed that there is no general solution that can prove all situations of three-body motion, but there are some very simple but meaningful special solutions. For example, the famous Lagrangian points, also known as translation points, are five special solutions to the restricted three-body problem in celestial mechanics. The five special solutions Euler deduced the first three in 1767, and Lagrange deduced the remaining two in 1772. These five points are written as L1, L2, L3, L4, L5. Three of these points (L1, L2, L3) are unstable and two (L4, L5) are stable. For example, if two celestial bodies orbit, there are five positions in space where a third object (with negligible mass) can be placed so that its relative position to the other two celestial bodies remains unchanged. Ideally, two objects in the same orbit rotate with the same period, and the gravitational force of the two celestial bodies is balanced at the Lagrangian point, making the third object relatively stationary with the first two objects.
Illustration: There are 5 Lagrangian points in the sun-earth system (picture source Wikipedia)
The definitions and positions of the five Lagrange points are as follows:
L1: On the connecting line between the two large celestial bodies M1 and M2, and between them.
L2: On the line connecting two large celestial bodies, and on the side of the smaller celestial body.
L3: On the connecting line between two large celestial bodies, and on the side of the larger celestial body.
L4: On the third vertex of the equilateral triangle with the line connecting the two celestial bodies as the base, and in front of the orbit of the smaller celestial body around the center of mass of the two celestial body system. The reason why this point is stable is that the distances from it to the two objects are equal, and the ratio of its gravitational force to the two objects is just equal to the ratio of the masses of the two objects.
Illustration: The resultant force of the two-day gravity points to the center of mass of the system (picture from Wikipedia)
L5: On the third vertex of the equilateral triangle with the line connecting the two celestial bodies as the base, and behind the orbit of the smaller celestial body around the center of mass of the two celestial body system. L4 and L5 are sometimes called triangular Lagrange points or Troy points.
The three-body problem has important applications in aviation and aerospace: for example, China's lunar probe Chang'e-2 was docked on L2 for a long time. The current space telescope Webb is also permanently parked at L2. The location of L2 is 1.5 million kilometers away from the earth, in the opposite direction from the sun.
The novel "Three-Body Problem" describes that when the three stars are far away, the civilization of the Three-Body Problem enters the long night and extreme cold, and when two or three stars approach, it faces the destruction of civilization. Only when one of the stars is close will it have the comfortable changing of seasons, alternation of day and night, and suitable temperature like the earth. The trajectories of stars in Trisolaris are uncertain and full of variables. A small change in the position of a star, or even a slight change in Trisolaris, may have a huge impact on the future, which cannot be predicted. So the three-body is a chaotic system. Next, we discuss chaos theory.
chaos theory
Origin of Chaos Theory: King Oscar II of Sweden was very interested in science. In 1887, he set up an award to encourage scientists to do research. This problem is the N-body problem, and the three-body problem is a special case when N=3. We now know that there is no solution to the three-body problem, but at that time Poincaré handed in the paper, and later it needed to be published after winning the prize. The editor of the publishing house couldn’t understand something and asked Poincaré. This question is interesting. Poincaré found an error and began to realize the complexity of the three-body problem. The revised article mentioned the phenomenon of chaos for the first time, and gave the concept of chaos "chaos refers to the uncertainty of the long-term behavior of the orbit" . Since the rewritten paper was also very important, the grand prize was still awarded to him. Poincaré's discovery opened the door to chaos theory for us, and he is considered the early pioneer of chaos theory.
(Poincaré)
Chaos theory is a method of both qualitative thinking and quantitative analysis. It is used to explore behaviors that cannot be explained and predicted by a single data relationship in a dynamic system, but must be explained and predicted by an overall and continuous data relationship.
In 1963, the American meteorologist Lorenz formally proposed chaos theory, nonlinear systems have diversity and multi-scale. In chaos theory, very small changes in initial conditions will eventually have a huge impact on future evolution. Lorenz made a vivid metaphor: a butterfly flapping its wings in Brazil will cause a tornado in Texas, the United States. This is the famous butterfly effect .
Illustration: Lawrence Attractor - Theoretical Basis of Butterfly Effect
(picture from Baidu Encyclopedia)
Lorentz was the first to write the mathematical formulation of the physical system of weather, consisting of three differential equations:
By assigning values to the three parameters a, b, and c, the orbit described by this equation can be drawn, as shown in the figure below. This orbit has three characteristics - non-divergence, non-convergence and non-periodic. Therefore, the solution orbit of the Lorentz system will fall into an endless motion starting from many initial value points, and this motion is not periodic, and an orbit curve with complex structure and various states will be drawn.
The meteorological system is a typical chaotic system. It is impossible to make accurate long-term weather forecasts with a time horizon of 2-3 weeks.
Application cases of the chaotic system: In April 1991, Japan launched the lunar probe Hiten. After going to the sky, it was found that the fuel was not enough to reach the designated orbit. Japan asked NASA for help, and Belbruno, a researcher at Caltech's JPL Laboratory, was assigned to assist Japan. He successfully reengineered the orbit and sent Hiten to lunar orbit using the remaining fuel. His key idea is to use limited fuel to send the probe to a chaotic area. Using a small amount of fuel to push the probe will have a particularly large impact on the motion of the probe, and then use a small amount of orbital adjustment to send the probe to the designated area.
The novel "Three-Body Problem" shows the charm and fascination of mathematics, while the Three-Body Problem and Chaos Theory also reflect that although mathematics is abstract, it is ubiquitous.
【Summary】
△ ChatGPT writing:
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The writing speed is amazing: it not only extracts the mathematical theories in the three-body, but also builds a simple framework for the entire article. Its creation process feels more like an intelligent search engine, which presents matching keywords and information in a certain text frame and language logic; (I am still amazed at ChatGPT’s ability to understand and express Chinese)
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The accuracy of the content is uncertain: manual follow-up proofreading is required for the theoretical accuracy of its output;
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Lack of in-depth and relevant expansion of content.
△ Human writing:
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In the early stage of writing an article, a large amount of data retrieval and material collection are required, which takes up a considerable part of the creation time;
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In the process of outputting the article, the editor will continue to dig deep, research and expand the relevant content according to the key points, not only bringing in his own thoughts, emotions, imagination and language style, but also constantly thinking about the logic of the paragraphs and sentences of the article to bring to readers. feel.
After testing, I am glad that ChatGPT has not yet reached the level of replacing the editor, but the boundary of autonomous learning of artificial intelligence in the future is unknown, just like "Three-Body" or the boundary of the universe in the real world. Today, the rapid development of AIGC content creation has brought us many surprises. I believe that in the future, we can rationally use AI to liberate humans from tedious work, to think and create more valuable things: such as the boundary between AI and humans...
About Huayuan Computing
Huayuan Computing Technology (Shanghai) Co., Ltd. ("Huayuan Computing" for short), established in 2002, focuses on algorithm research and innovative applications, focusing on the research, application and development of cognitive intelligence technology. Based on the development of mathematics application and computing technology, the company focuses on cognitive intelligence technology and innovates self-developed underlying algorithms; based on the scenario application of the cognitive intelligence engine platform, it provides AI+ industry solutions for digital governance, intelligent manufacturing, digital cultural tourism, retail finance and other industries Solutions, to achieve comprehensive empowerment, so as to promote the transformation and upgrading of industry intelligence, and make the world smarter.
reference:
https://chat.openai.com/chat
https://swarma.org/?p=39598
https://s.r.sn.cn/Pt6kfs
https://zh.wikipedia.org/wiki/%E6%B7%B7%E6%B2%8C%E7%90%86%E8%AE%BA
https://zh.wikipedia.org/wiki/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E7%82%B9