The talk will be devoted to the comparison between the Kolmogorov complexity and Weil height, foreseen by Yu.I. Manin. Both objects
are functions defined on the enumerable "constructive" (to be defined) sets up an additive constant defined intuitively by the amount of
information needed to specify an element of the set. In the first half of the talk the complexity and the height will be defined on the base of
minimal background, and the standard examples will be given.
In the second half the similarities and distinctions between complexity and height will be discussed. In particular, they can not coincide since
one of them is algorithmically calculable and the other is not. Then both will be applied to arithmetic geometry and dessins d'enfants theory.