Background

These are some of my interests outside of economics:

• Applied Mathematics
  • Pattern Formation in Animal Coats
  • Engineering Analysis of Biological Structures
    • D'Arcy Thompson's Proposition That All Creatures Can Jump the Same Heighth
    • The Dynamics of Belt Drives
• Pure Mathematics
  • Bezout's Theorem
• Physics
  • Optics
  • Lasers
    Coherence of Stimulated Emission
  • Magnetism
    • Diamagnetism
  • Solid State Physics
    • Brillouin Zones
• Nonlinear partial differential equations
  Perturbation Analysis
• Solitary solutions to the Regularized Long Wave Equation.
  These are of interest because they are wave phenomena which behave like particles. In contrast to the soliton solutions to equations such as the Korteweg-deVries equation which re-emergence from collisions unchanged the collision of solitary solutions may create secondary solitary solutions and/or radiation-like sinusoidal solutions.
  
• The creation of a convolution algebra to handle nonlinear terms of differential equations.
  Laplace and Fourier transforms provide convenient ways for converting the problem of solving a differential equation to one of solving an algebraic equation. The transform of the convolution of two functions is equal to the product of the transforms of the two functions. The relationship also works the other way; i.e,, the transform of the product of two functions is the convolution of the transforms of the two functions. Usually this does not help in the solution to the original problem. The Polish mathematician Miczynski has develop a convolution algebra that works in a limited number of cases in solving differential equations.
  
• Differential Geometry.
  It is said with justification that mathematics is the queen of sciences. Within mathematics differential geometry is a field of special beauty because it combines geometry, analysis and algebraic structures. I am particularly interested in the differential forms approach to differential geometry.
  
• Algebraic Topology, Homology and Cohomology
  These are related to the previous topic but separate subject on their own. Homology and cohomology provide a method of characterizing the shape and structure of an object.
  
• Spherical Trigonometry
  
• Art, particularly that art which lends itself to representation by computer graphics, such as Mondrian and Lichtenstein.
• People and cultures in unexpected places.
  For examples,
  • Vikings in Greenland and Vinland. Vikings have long held a fascination for me. The Vikings were interesting to me in large part because they showed up in so many unusual place at such an early time such as on the Caspian Sea and in Baghdad. After years of interest in this topic that I realized that it was just a special case of this more general interest.
  • The Phoenicians exploring the coast of western Africa I find similarly interesting.
  • Likewise I was fascinated that around 300 A.D. the Roman Emperor Marcus Aurelius had 5000 Sarmatian warriors transported from the area of the Black Sea to what is now northern England. The Romans also transported people from what is now Morroco to the Canary Islands.
  • A Duke of Courland in what is now Latvia tried to establish a colony in west Africa in what is now Gambia.
  • The Navahoes and Apaches are descendants of people who migrated from what is now northwestern Canada, the Athabascans or Da Nene people.
  • Germans, with the encouragement of Catherine the Great, established settlements in Siberia.
  • There were several counties in south central Texas that were once largely populated with German immigrants.
  • About half the population of Guayana are descendants of immigrants from India.
  • The Greeks in ancient times had a colony, Bactria, in what is now Afghanistan.
  • In more recent times there was a muslim kingdom called Cham in what is now central Viet Nam.
    
    
  
  
• The role of the Alans and Sarmatians in world history.
  These were nomadic peoples of central Asia speaking languages belonging to the Iranian family. These groups controlled extensive empires in the early part of the first millenium. People from these groups showed up in places as far apart as China on the east to Portugal and Scotland on the west. A remnant of the Alans survived in the Caucausus Mountains and are known as the Ostetes. Some of the most important legends and myths of medieval Europe, such as the Holy Grail, may be traced to the Alans. The Sarmatians may have been the source of the Arthurian stories. A modern footnote on the Alans is that Joseph Stalin was half Alan from his mother's side. On his father's side he is usually considered to have been Georgian, but he may actually have been the illegitimate son of the famous Russian explorer Przhevalsky. But that is another story.
  
  
• Ankhnaton, the radical pharaoh of ancient Egypt.
  Ankhnaton formulated monotheism in ancient Egypt and was overthrown when he sanctioned the destruction of the temples and priesthoods for the traditional religion. Sigmund Freud argues in Moses and Monotheism that most of the Hebrews who fled Egypt were followers of Ankhnaton's monotheism and that Judaism owes much to the monotheism of Ankhnaton. The Egyptian archeologist Oman argues that the person history knows as Moses was, in fact, Akhnaton.
  
  
• Symmetry and group theory applied to science and art.
  Group theory is a fascinating subject in its own right, but it becomes doubly fascinating in its applications. The applications in physics which I am particularly interested in are in particle physics, quantum mechanics, field theory and solid state physics. The latter includes crystallography as well as the analysis of models and computational methods. Group theory has some small applications in musics, art and architecture. Overt symmetry is often beautiful but a beauty that arises from a hidden or at least nonobvious symmetry is sublime.
  
  
• Category theory.
  Category theory is a unification of many branches of mathematics. What looks at first sight to be "abstract nonsense" turns out to have concrete applications. What is beautiful is to find theorems in various branches of mathematics that are all merely instances of one theorem in category theory.
  
  
• Optics and photography.
  I have had a general interest in photography and started studying optics to help me understand photography better. But the more I study optics the more interesting I find it to be in its own right and now my interest in photography seems to be an adjunct to my interest in optics.
  
  
• Linguistics in all of its various aspects.
  I find linguistic theory along with computer language theory interesting, challenging and important. I also like to know the meaning of foreign words that I come across in ordinary life such as store signs in Spanish or in Vietnamese. I have had a lot of fun with discovering the literal meaning of place names in China. When traveling in California I make it a practice to take along a Spanish dictionary to find the meaning of names of geographic features and places. There are certain languages I try to learn more about: Mandarin, Spanish, Portuguese, Dutch and Afrikaans. I also want to learn more about Friesian because of its relationship to Old English. Likewise I find Lowland Scottish interesting because of its relationship to English. There are certain computer languages I have learned and am trying to remain proficient in or at least not forget completely: Pascal, C, Lisp, Prolog and Gofer. There are others I want to learn but just have not gotten around to doing so such as C++, ML, Forth and CGI.
  
  
• 3D modeling including Visual Reality Modeling Language VRML
  This ultimately will be of value in teaching economics. Instructors have a difficult time drawing three dimensional graphs and students consequently have a difficult time understanding the relationships involved. VRML will create such diagrams that students can not only see but they can exam by turning them around and tranversing them.
  
  
• Culture as God.
  Long ago it occured to me that "culture" in an anthropological sense had most if not all the attributes of God. Amongst the people who belong to a particular culture it is omnipresent and omniscient. In some ways a culture is like a language (language is in fact a crucial part of a culture) in that just as all speakers of a language know when some utterance is grammatically correct so all members of a culture know whether a particular action is right or wrong. They may not always do right but they know whether what they do is right or wrong. This is a topic that I would like to devote more time and energy to and will do so some day.
  
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