数学及其在社会科学中的应用 
送交者: jingchen 2017年08月25日09:45:53 于 [教育学术] 发送悄悄话 
Mathematics and its application tosocial sciences
I like thebeauty and symmetry in Mr. Treynor's equilibrium models so much that I starteddesigning them myself. I worked on models in several areas:
Monetarytheory Businesscycles Optionsand warrants
For 20years, I have been struggling to show people the beauty in these models to passon knowledge I received from Mr. Treynor.
In monetarytheory  the theory of how money is related to economic activity  I amstill struggling. In business cycle theory  the theory of fluctuation in theeconomy  I am still struggling. In options and warrants, though, people seethe beauty.
Black's comments show that he, as well as many others,sensed the close relations among different economic and financial problems. Hiscomments also show that it is not always easy to extend an idea from one fieldto another field, even this might look straight forward with the benefit ofhindsight.
I tried to understand life systemsfrom the thermodynamic laws since I was an undergraduate student. I hope todevelop a mathematical theory of life systems parallel to classical mechanicsas a mathematical theory of general systems. I read about many existingtheories, such as Prigogine's theory. However, these theories do not model lifeprocesses directly. For a long time, I had little idea how to develop such atheory. I only knew that thermodynamic processes are represented by partialdifferential equations. So I stick to the theory of partialdifferential equations, hoping something will turn up some day.
It was after many years before I bumped into the BlackScholes equation.The BlackScholes equation was originated in financial economics. From myperspective, this equation is a mapping from lognormal processes. Lognormalprocesses can be understood as the representation of extracting low entropy tocompensate for dissipation, which is the essence of life processes. I sensedthat the BlackScholes theory could lead me further in developing amathematical theory of living systems.
I started to think about the BlackScholes theory in 1995,when I was teaching mathematics in Hong Kong. In 1997, I joined an investmentbank. There, I learned to associate mathematical theories with investmentdecisions. Abstract symbols become concrete. A year later, I returned toacademia , this time as a finance professor in Singapore. After severalyears, I worked out a theory of economics that provide an analyticalrelation among major factors in economics: such as fixed cost, variable cost,investment horizon, discount rate and uncertainty. It provides a simple andconsistent understanding on broad range of problems in economic and biologicalsystems. More detailed discussion can be found from books and papers written byme and others.
When financial crises or economic downturn occur, they areoften blamed on "unintended consequences" from economicpolicies. But from our theory, we can solve the equations to obtainquantitative results of long term consequences of those policies. It turns outthat the so called unintended consequences are simply long term consequences ofthe economic policies. Currently, economic policies are mainly measured fromtheir short term impacts. We hope that the introduction of a theory on long termimpacts of economic policies will stimulate more active discussion.
Since most prominent economists have a stake in the dominanttheory, they are reluctant to discuss rival theories. But mathematiciansdon't have such concerns. This gives opportunities for mathematicians andother outsiders to make fundamental breakthroughs in economictheories. Neoclassical economics, the current dominant economic theory,was developed around 1870, mainly by Jevons and Walras. Both Jevons and Walraswere trained as a scientist and an engineer, not as an economist.
Mathematics has played a substantial role in deepening ourunderstanding of the world. Calculus, stochastic calculus, Maxwell equations Schrodingerequation, BlackScholes equation are just a few examples. But the applicationsof mathematics in the vast field of social sciences are still largely cosmetic.By actively engaging in the field of social sciences, mathematicians maycrucially impact the future of science and human society. In the process,we can work on more exciting research that are more relevant to the realworld.
References
Systematic discussion about the new economictheory can be found in my two books.
The Physical Foundation of Economics: An AnalyticalThermodynamic Theory, World Scientific, Hackensack,NJ (2005)
The Unity of Science and Economics: A New Foundation ofEconomic Theory, (2016), Springer
James Galbraith's book, TheEnd of Normal: The Great Crisis and the Future of Growth, (2015), Simon & Schuster,discussed many of my ideas in great clarity.
Moreinformation, including all my papers, can be found from my website



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