Andres Escala – On the Mathematical Formulation of Empirical Laws


“On the Mathematical Formulation of Empirical Laws

Andres Escala

Universidad de Chile

Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the Π theorem (Vaschy 1892; Buckingham 1914). However, in many areas such as Astronomy, Economics or Biology most fundamental relations do not
satisfy this basic mathematical requirement. In this talk, using the Π theorem we show that it is possible to construct homogeneous equations that describes the star formation rate in galaxies (Astronomy) and the metabolic rates of animals (Biology), in agreement with data in the literature (Utreras, Becerra & Escala 2016; Escala 2018).


Auditorium of Physics Faculty


Thu 23 November 2017