Abstract

The notion of time has intrigued mankind from the pre-Socratic philosophers of Antiquity till the physicists and philosophers of today. From an all-devouring god-like Titan, it became tamed in modern times, reduced to an abstract, quantifiable and measurable dimension of space-time and even more, subjugated to transformation in relativistic physics. Important mathematical discoveries made in the 18th and 19th centuries have paved the way for time-independent descriptions of the dynamics of mechanical, thermodynamic and energetic systems. We focus in particular on the role of the Hamiltonian, which is the Legendre transformation of the Lagrangian, which has been instrumental for the development of both Quantum Mechanics and Modern Hopfield Networks, among others. More-over, this paper elaborates on the intrinsic time-dependencies encountered in the physical world, from the sub-atomic scale, through the time-dependent propagation of perturbations in DNA and biological cycles, to the characteristic fluctuations in meteorology and global weather systems. Also the role of time-independent modeling in Neural Learning Networks and AI is critically examined.