Statistical procedures must be used to usefully describe a system consisting of a large number of particles. A classic example is gases. A liter of any gas in ambient conditions -for example, the air on a spring day- contains a whopping 20,000 trillion molecules : wanting to describe it by studying the behavior of each one of them is practically impossible. To achieve this, statistical methods are used to obtain relationships between the properties of individual molecules, such as energy and speed, with the properties of the gas as a whole, that is, its pressure, temperature…
The study of the behavior of gases, carried out by the German physicist and mathematician Ludwig Boltzmann in 1877, laid the foundation for a branch of physics called statistical physics . Without it today it would be impossible to understand such disparate things as the internal structure of stars or superconductors .
Statistical physics has many applications but the most spectacular is its use in economics . Hearing it, one may wonder what relationship there may be between the behavior of the gas in a butane cylinder and the evolution of interest rates. It is possible that we can see it clearly if we analyze the movement that any molecule makes in the air. That molecule is subject to such a number of influences, mainly collisions with other molecules in the air, that it is impossible to predict the direction in which it is going to travel. This is Brownian motion , discovered early in the last century by the Scottish clergyman and botanist Robert Brown, and it is the best example of erratic motion.
At the end of the 1820s, a French botanist published an article describing the behavior of pollen grains suspended in water. The pollen moved constantly through the water without following a defined path. It was an erratic movement, impossible to predict , and it became more noticeable as the temperature of the water increased.
Perhaps out of boredom or because he thought it would be interesting to test such observations, Brown, with the well-known dedication of monks, began a systematic study of the random motion of pollen grains in water in the same year he was appointed Conservative Botanist. from the British Museum, 1827. Brown corroborated the Frenchman’s observations and, to his surprise, also discovered such syncopated movement in pollen from the Museum , which had been stored in a dry environment for more than twenty years. With this, he demonstrated that it could not be the product of the metabolic activity of living organisms: under these conditions, pollen It was nothing more than a sad memory of what it was.
So he decided to see if the same thing happened with other types of particles of the same size – about five thousandths of a millimeter – but of a decidedly inorganic nature: earth, pulverized road rocks, glass dust and even tiny bits of the famous Sphinx of Gizah . In all of them, Brown found the same type of unpredictable behavior, which clearly indicated that this movement was something that had nothing to do with biology. So what was it about?
The work of this English clergyman was so good that his name was linked for life to this phenomenon. Such a curious waste of time did not attract the attention of any of the brains that had laid the foundations of thermodynamics and the kinetic theory of gases, Kelvin, Clausius, Maxwell or Boltzmann, which proves that nature always surprises, even the more prepared minds. For the next fifty years, Brownian motion remained stored in the drawer of singular unknowns in science.
Despite everything, there were some attempts at explanation. All of them vain, easily refuted with simple experiments. Some proposed that it was the light used to illuminate the preparation in the microscope that caused it, which increased the temperature of the water and caused the appearance of convection currents. However, experiments showed that neither the color nor the intensity of light influenced the movement . Others invoked the electrical forces that could appear between particles in suspension, forgetting Brown’s observations with isolated particles and others in which the water was replaced by other liquids with completely different electrical properties and in which, however, it continued to be produced. the mysterious movement
In the last quarter of the 19th century, the consensus had spread among those very few scientists who were concerned about Brownian motion that the cause was the constant bombardment to which the dust particle was subjected by the molecules that make up the water. Molecular motion – or at least its effects – was finally visible to the human eye.
The stock market is also subject to a very high number of influences, all of them unpredictable, which makes it impossible to predict its future evolution. Can a relationship be established between the two disciplines? Yes. In 1900 the French mathematician Bachelier discovered that stock market fluctuations could be described using the equations of Brownian motion . In particular, he proposed a formula for setting the price of an option based on the idea that such fluctuations followed the same process as a molecule moving in any gas.
This work was forgotten until the 1970s, when scientists Black and Scholes introduced the methods of statistical physics to describe financial activities such as options trading . Since then we have witnessed a renewed interest in this curious relationship. Until then, it depended on the ‘smell’ and subjective analysis of the economist; objective tools are now available to study them.
Isn’t it fascinating to discover that the study of the behavior of a gas is used to assess the risks that a bank faces in the world market?
References:
Sinha , S. , Chatterjee , A. , Chakraborti , A. and Chakraborti , BK ( 2010 ) Econophysics: An Introduction , Wiley-VCH
