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The word "complexity" is most often used as a meta--linguistic expressionreferring to certain intuitive characteristics of a natural system and/or itsscientific description. These characteristics may include: sheer amount of datathat must be taken into account; visible "chaotic" character of these dataand/or space distribution/time evolution of a system etc.  This talk is centered around the precise mathematical notion of "Kolmogorovcomplexity", originated in the early theoretical computer science and measuringthe degree to which an available information can be compressed.  In the first part, I will argue that a characteristic feature of basicscientific theories, from Ptolemy's epicycles to the Standard Model ofelementary particles, is their splitting into two very distinct parts: the partof relatively small Kolmogorov complexity ("laws", "basic equations", "periodictable", "natural selection, genotypes, mutations") and another part, ofindefinitely large Kolmogorov complexity ("initial and boundary conditions","phenotypes", "populations"). The data constituting this latter part areobtained by planned observations, focussed experiments, and afterwardscollected in growing databases (formerly known as "books", "tables","encyclopaedias" etc).  In this discussion Kolomogorov complexity plays a role of the centralmetaphor.  The second part and Appendix 1 are dedicated to more precise definitions andexamples of complexity.

Kolmogorov complexity as a hidden factor of scientific discourse: from Newton's law to data mining