Not so long ago, the project that would have seen modernization spread over the whole planet came up against unexpected opposition from the planet 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 has meant so as to find out how it can be begun again ‘on a new footing. Such an inquiry becomes possible if we accept that there is a huge disjunction between what the Moderns experience and the accounts they give of that experience. Via our website, we propose to continue the inquiry that was begun with the hard-copy “interim report” published as a book with Découverte. First, by adding to the work the documentation it was lacking (notes, glossary, references, visual material and articles). Then, in a second step, by offering a useful digital environment that will turn readers into co-researchers. And finally, as a third step, by republishing the collective results of both digital transactions and diplomatic negociations. Chosen mediators will there invite a certain number of commentators and co-researchers to face-to-face meetings organised around the most thorny questions the inquiry has thrown up, those where the opposition between values and the accounts given of them is the most serious. The aim, both ambitious and modest, will be to propose an alternative for the term “modernize”, one that is compatible with the expression “ecologize” and which we sum up with the term “composition”. Learning how to compose the common world, this is what is at stake.