Can we, should we create a Museum of the contemporary world ? A selection of objects would not be capable of embrassing modernity and would only poorly illustrate it. How are we to show abstraction, artifice, complexity ? How to deal with the present ? The paper suggests a double possibility, providing present-day topics and innovation are separated. Multi-media would deal with present-day topics, together with permanent carefully selected projections. Innovation, shown through a more static material, would address the question of the future man, already present, trying to escape his own limits, including body limits, through both miniaturisation and gigantism.