Deterministic systems

Since the Pythagorean attempts to explain the tangible world by means of numerical quantities related to integer numbers, western culture has been characterized by the idea that Nature can be described by mathematics. This idea comes from the explicit or hidden assumption that the world obeys some precise rules. It may appear obvious today, but the systematic application of mathematics to the study of natural phenomena dates from the seventeenth century when Galileo inaugurated modern physics with the publication of his major work Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze (Discourses and Mathematical Demonstrations Concerning Two New Sciences) in 1638. The fundamental step toward the mathematical formalization of reality was taken by Newton and his mechanics, explained in Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), often referred to as the Principia, published in 1687. This was a very important date not only for the philosophy of physics but also for all the other sciences; this great work can be considered to represent the high point of the scientific revolution, in which science as we know it today was born. From the publication of the Principia to the twentieth century, for a large community of scientists the main goal of physics has been the reduction of natural phenomena to mechanical laws. A natural phenomenon was considered really understood only when it was explained in terms of mechanical movements.