How do we compose a common world? Not so long ago, the project that wished to see modernization spread all over the world came across unexpected opposition from the world itself. Should we give up, deny the problem, or grit our teeth and hope for a miracle? Alternatively we could inquire into what this modern project means so as to find how it can start again on a new footing. Such an inquiry becomes possible if we accept that there is a huge gap between the Moderns' experience and the accounts they give of it. The aim, both ambitious and modest, will be to propose an alternative for the term 'modernize', one which is compatible with the expression 'ecologize' and which we sum up with the term 'composition'. Learning how to compose the common world is what is at stake.