Natural laws and human prediction

Interrelations between dynamical and statistical laws in physics, on the one hand, and between classical and quantum mechanics, on the other hand, are discussed within the philosophy of separating the natural from the human, as a very specific part of Nature, and with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies of chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of motion, continuity of both phase space and the motion spectrum, and the time reversibility but nonrecurrency of statistical evolution, within the general picture of chaos as a specific case of dynamical behavior. Analysis of the apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of quantum chaos as a new generic dynamical phenomenon is outlined together with a few other examples of such chaos: linear (classical) waves, the (many-dimensional) harmonic oscillator, the (completely integrable) Toda lattice, and the digital computer. I conclude with discussion of the two fundamental physical problems: quantum measurement (psi-collapse), and the causality principle, which both appear to be related to the phenomenon of dynamical chaos.