Physics and Economics
In 2004-2005, I worked with an Iranian economist at Necessity and Chance, LLC. He spoke English as a second language.
Correcting grammar and spelling was only part of the task. Because the economist’s paper had to convey complex physical concepts to professional economists not formally trained in physics, it was vital that its language be as clear as possible.
An excerpt from the finished paper follows.
…These physical underpinnings are central to understanding GBM’s weaknesses. The following survey begins with Brownian Motion’s namesake.
Robert Brown (1827), looking through a microscope, provided the first detailed account of the irregular and incessant zigzag motion of pollen suspended in water. Brown noted that suspended pollen particles execute random movements, but for nearly eighty years, physicists were still baffled, unable to explain the motion’s physical origin.
Part of the difficulty, of course, concerned the complexity of the motion itself. Several features seemed common to all observations: (1) The observed trajectory of the pollen, while continuous, was extremely jagged. (2) The motion never ceased. (3) The pollen particles seemed to move independently of one another. (4) The size of a pollen grain affected its motion: e.g., smaller pollen moved more rapidly. (5) The ambient temperature affected the motion: e.g., higher temperature corresponded to more rapid movements. (6) The motion was modulated by hydrodynamic characteristics of the fluid.
Since a detailed description of each particle was impossible, a probabilistic approach, with corresponding levels of idealization and abstraction, was deemed appropriate. It was left to Einstein (1905) to derive a quantitative description. In order to appreciate some of the subtleties associated with modeling physical Brownian motion, let us briefly consider his approach…