All kinds of forecasts and prognoses have become an important part of our life. Above all this concerns the safety of such complex systems as nuclear power stations, modem aircraft and ships, and so forth. Early warning about natural calamities, be it earthquakes or twisters, is likewise of much importance. The latest achievements of nonlinear dynamics, of the theories of risk control and self-organizing criticality have given us a handy tool for the development of the prognostication science. But on the other hand, we have obtained added proof of the temporal limitations of prognosis as well. This range of problems is studied at the M. V. Keldysh Institute of Applied Mathematics (RAS). Its two leading researchers-Deputy Director Georgi Malinetsky, Dr. Sc. (Phys. & Math.), and Sergei Kurdyumov, Corresponding Member of the Russian Academy of Sciences (RAS)-have this to say on the subject. Up until the 1960s only two classes of processes were believed to be in existence. The first one comprised dynamic systems in which their future condition was rigorously determined by their past, i.e. it was quite predictable. Once you have a sufficient body of data on their past, you can look far into their future too, as it was argued by the French astronomer, mathematician and physicist Pierre Laplace (1749-1827), honorary member of the St. Petersburg Academy of Sciences. Or, in modem parlance, once you have good computers and an adequate database, you can predict anything... As to the other class of processes, their future did not depend on their past. Only later, in the 1970s, did we realize there was yet another, third class of processes described in formal terms by dynamic systems. A very important class of processes which can be predicted but for a relatively short time ahead; next comes the hard statistics. A simple pendulum demonstrating dynamic randomness is a graphic example. But first, let's look into its design. Two rigidly interconnected rods are pivoted at a d ... Читать далее