The article examines the possibilities of applying Alain Badiou's approach to complex-unstable processes. The French philosopher considers the ontology and phenomenology of an event as the mathematics of sets. The similarity of Badiou's views with the description of politics is shown, as well as the possibility of applying the concept of political progress to the sequence of events and assessing their moral value. Badiou proceeds from a situation that does not represent unity, changes according to internal laws, is infinite in content. Before the situation becomes unstable, these properties allow us to apply modern methods of processing and scaling big data. By its composition, the situation has a set of non-political elements that objectively characterize stationary processes, and a growing "wandering" variety of political facts that subjectively reflect reality. This situation is called a pre-political situation, in which there is a "duality". When the duality becomes apparent, Badiou's approach should be applied, in which a special count procedure is carried out. This procedure involves choosing an external "generic" set and forcing into the situation. A well-constructed generic set has elements that are suitable in practice for ordering "chaotic" political elements in the overall structure of the set. As a result, an event is declared. The new situation consists of modified elements of the previous situation and generic elements. It can be completely or partially structured, so again it is possible to apply the big data methodology. Forcing an event is seen as a fragment of policy. According to Badiou, revolutionary events correspond to truth and birth procedures. For less singular events, it is necessary to search for and clarify the " right direction" to the truth, which can be clarified through the concept of political progress. The big data methodology and Badiou's approach, supplemented by the research of Denquin, Ranciere, and Domanov, can describe a wide range of phenomena.
