On the motivation and foundation of Natural Time Analysis: Useful remarks

Abstract: Since its introduction in 2001, natural time analysis has been applied to diverse fields with remarkable results. Its validity has not been doubted by any publication to date. Here, we indicate that frequently asked questions on the motivation and the foundation of natural time analysis are directly answered if one takes into account the following two key points that we have considered as widely accepted when natural time analysis was proposed: First, the aspects on the energy of a system forwarded by Max Planck in his Treatise on Thermodynamics. Second, the theorem on the characteristic functions of probability distributions which Gauss called Ein Sch\"ones Theorem der Wahrscheinlichkeitsrechnung (beautiful theorem of probability calculus). The case of the time series of earthquakes and of the precursory Seismic Electric Signals are discussed as typical examples.