by [Sergei KURDYUMOV], RAS Corresponding Member, Head of Department, RAS Institute of Applied Mathematics named after M. V. Keldysh In 2004 one of the Moscow publishing houses brought out a book called Asymptotic Mathematics and Synergetics. Its authors - Prof. Igor Andrianov, Dr. Sc. (Phys. & Math.), Rem Barantsev, Dr. Sc. (Phys. & Math.), and Leonid Manevich, Dr. Sc. (Tech.) made an attempt to describe in a popular form the essentials of these new branches of knowledge. Biographers studying the legacy of Albert Einstein, Nobel Prizewinner for 1921 and Honorary Foreign Member of the USSR Academy of Sciences since 1926, quote him as saying that sciences are divided into physics and stamp collection. If so, what did the outstanding scholar and philosopher have in mind emphasizing that particular discipline? And one can also recall the words of Galileo Galilei (1564 - 1642), one of the founding fathers of natural sciences. He said that-be it white or red, bitter or sweet, sounding or silent, with pleasant or unpleasant smell - all these are mere "names" for different impacts upon our sensory organs. He said he would never expect from external objects anything else than data on their size, shape, numbers and more or less rapid movements in order to explain the origin of sensations of taste, smell and sounds. He said that if people had no ears, tongues and noses they would have been left with only shapes, numbers and movements which, taken outside of a living being, are nothing but empty names of definitions. In other words, the key principle of idealization suggested by the great Italian scholar for physics-imaginative building of notions about objects, processes and phenomena which do not exist in reality, but have prototypes (such as "point", "absolutely solid, hard body"). This makes it possible to formulate laws, build abstract models of real events. Using this approach Galilei studied movements of bodies. He pointed out that in order to examine this pro ... Читать далее