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