ABSTRACT
In spite of its ‘improper’ origin from games of chance, probability theory is used in modern science because a large number of real-world phenomena seem to defy any attempt at deterministic description. Many of these phenomena, moreover, evolve in space and time. Examples are not hard to nd: the height of waves in a rough sea, the noise from a jet engine, the electrical noise of an electronic component or, in the eld of vibrations, the vibrations of an aeroplane ying in a patch of atmospheric turbulence, the vibrations of a car travelling on a rough road or the response of a building to earthquake and wind loads. Without doubt, the question as to whether these phenomena are intrinsically deterministic and, because of their complexity, we are simply incapable of a deterministic description is legitimate, but the fact remains that we cannot predict exactly what will happen at a future instant of time, no matter how many observations we make. Since, however, under repeated observations these phenomena generally do show patterns and regularities that t into a probabilistic description, we choose a different (and more pragmatic) approach: we simply leave open the question about their intrinsic nature and tackle the problem by dening them as random and by consequently adopting a probabilistic treatment.
