Chinese academia likes harmony and rarely engages in serious scientific confrontation, so there is a tradition of compatibility and inclusiveness in Peking University, but it is rare for Western scientific critical thinking and schools to compete.Revolutions in the history of science have often benefited from a number of scientific questions that are not afraid to offend others.
The most famous example in history is the birth of quantum mechanical wave equations.In 1924, at the age of 32, Dr. de Broglie of the University of Paris proposed a mathematical formula for the wave-particle duality of electrons, which relates the momentum of particle motion (the product of mass and velocity) to the corresponding particle wavelength.In 1925, the 38-year-old Austrian physicist Schrödinger praised de Broglie's new ideas in a speech in which Debye, a 41-year-old Dutch physicist and chemist known for his harsh criticisms, was a favorite pupil of Sommerfeld, the pioneer of quantum mechanics.Debbie questioned on the spot, you talk about waves, what is the wave equation?Then he left Schrödinger speechless.Schrödinger went home and thought about it. Why didn't he think about it?In fact, de Broglie waves are the solution to the wave equation.As the solution knows, building the equation that the solution can satisfy is a difficult mathematical problem.Soon Schrödinger published the most famous wave equation of quantum mechanics in history.Debye is said to regret that he had only consulted sharply and had missed the greatest discovery of his life.I guess Schrödinger must have been overjoyed because Debye was his god of inspiration in Greek mythology.
As you know, the search for the basic framework of dynamics is the foundation of science.Physics began with Newtonian mechanics by describing the dynamics of physics using differential equations of continuous time.After discovering chaotic evidence from empirical data in 1985, I tried to find fundamental equations for economic dynamics.To my surprise, the basic models of econometrics are discrete-time difference equations for ease of regression analysis of data.If modeling is based directly on empirical observation, what is the starting point of economic dynamics? One of my own contributions to physical mathematics was the introduction in 1987 of the less common "delayed differential equations" in physics, also known as "difference-differential equations," into nonlinear dynamics.It was inspired by Berlin's questioning.Mr. Hauberlin's question, point me in the direction of the breakthrough.
At an international symposium organized for me by Prigozhin in Brussels in the fall of 1985, I reported empirical analysis of the discovery of monetary chaos, with observed fractional dimensions around 1.5.Most of the scholars who attended the meeting congratulated him, and Prigozhin did not find anything wrong.Samuelson, a renowned Nobel Prize-winning economist in mathematics, found nothing wrong with the newsletter but wanted to know if there was more empirical evidence beyond the monetary index to be convincing. Tinbergen, the Dutch econometrician who shared the first Nobel Prize in economics, is a student of Ehrenfest, a renowned Dutch physicist who is one of the few physicists in history to talk to Einstein.In his correspondence with me, Timbergen confessed that he did not understand Prigozhin's thermodynamic achievements had outstripped his teacher's.However, to pass the famous teacher off, but sad Hao Berlin question off.
After listening to my report, Hao Berlin immediately put my army on the spot.He said, "How can you be 1.5?At that time, known mathematical models, ordinary differential equations, such as Lorentz models simplified by hydrodynamics, 2D equations only had limit ring solutions, and 3D or more ordinary differential equations could produce 2 fractional dimensions.However, the introduction of the logic Stee 1 dimensional difference equation in ecological equations can only produce fractional dimensions of a few zero points.How can economic chaos create a few dimensions of one point?At the time, I admitted that I had not thought about it.
After the meeting, I looked through the mathematical manuals and published chaos models of all disciplines and found that only the delayed differential equations (also known as differential-differential equations) of chaotic oscillations published by Canadian theoretical biologists Mackey and Glass in 1977.The reason is that delay differential equations are more complex than ordinary differential equations.One-dimensional univariate delay differential equations can be expanded into infinite-dimensional systems of ordinary differential equations.Previously, physicists only knew that the movement of neurons was a differential-differential model, but it was difficult to solve, so the study of neurons generally only discussed linear equations, and few people studied nonlinear differential equations.Chaos studies are the first to use nonlinear differential equations among physiologists, and economics is the second.
I think of the rules of the game that control similar highways economically, such as the U.S. highway speed limit and upper limit, which must be at least 45 miles per hour and at most 65 miles per hour.But no driver strictly adheres to it.If the police are not present, they will exceed 70-80 miles, and some vehicles will be behind by as much as 45 miles.The police arrived to narrow the range of speed changes a little, but there was a delay in controlling the response.I call this nonlinear motion a soft boundary oscillation.Most known models of physics and biology are hard boundaries or periodic boundaries.
I finally answered Prigokin's request and Hao Berlin's questions in 1987, proposing a theoretical and observational model of economic chaos, which was highly appreciated by the interdisciplinary PhD committee and graduate school dean through a PhD in physics.But the article was difficult to publish because the editor of the review couldn't understand my mathematical model.As one of the world's leading researchers on nonlinear differential equations, my graduate student, Wen Kehong, found only one American mathematician to review.
It was only then that I learned of Hauberlin's question that I "forced" my research into the margins of nonlinear dynamics.There are only one or two people in economics who can understand why we emphasize that dynamics use continuous time, and that differential equations are too simple to describe economic complexity.But no one but my students followed because it was hard to publish.Econometrics' popular differential equation solution matrix iteration is fine, even differential equations do not need to be solved.It can be seen that economic complexity is higher than biological complexity in chaos mathematics, and biological chaos is more complex than ecological chaos.The study of economic complexity has progressed slowly over the past 30 years, with very few open markets in academia.The required mathematical knowledge far exceeds the current knowledge range of economic mathematics in mainstream Western universities, which is the main reason for the methodology.Of course, efficient market theory asserts that financial markets are Brownian movements, and it also brainwashes the economic theory community, and it is worthwhile that economic complexity became a new trend in Western research after the 2008 financial crisis.China also established a national interdisciplinary study group on economic complexity under the Econometric Society in 2015, more than 30 years after Day published its first theoretical article on economic chaos in 1982, and we published a unified theoretical and empirical article.After Hauberlin's work on chaotic mechanisms using symbolic dynamics was published, there were few follow-up studies.Therefore, even Mr. Li Zhengdao said that chaos cannot be eaten as food, but it can be drunk as water, which is to see the great uncertainty of chaos research.
Interestingly, the physics community is still very controversial about chaos research.Mainstream physics, biology, and economics fear chaos as a negative "disorder."The most famous is the meteorologist Lorenz.The so-called "butterfly effect" claimed by Lorenz, if a butterfly's wings could produce hurricanes thousands of kilometers away, there would be no hope for any weather forecast or climate control.This is clearly an overstatement.Because any positive feedback shock consumes more and more energy, once the available energy is exhausted, negative feedback will play a leading role in controlling instability within a certain range and becoming a "strange attractor."Therefore, Prigozhin believes that chaos produces order, which means that nonlinear complex motion and linear motion ratio are higher order.