There is more to globalisation than just world-wide economic interconnectedness. Equally important is that cultures grow together, engage in rapprochements, harmonise global pluralism, find common values in human existence, agree on international laws and share fundamental ethics. It is not important whether women wear a hijab, or indigenous art is copyrighted; but it is important whether the death penalty is invoked for blasphemy, apostasy and homosexuality, or whether an inconvenient journalist exercising free speech can be murdered with impunity by the justice system of a potentate. Many problems span the whole world and cannot be solved by nationalist isolation. Human rights conventions and internationalised laws, agreements and compacts are a step in the right direction. Much more remains to be done. But from where to take the answers? Looking at many cultural expressions and major cultural impulses over the centuries and millennia of homo sapiens' existence - even going back to the Neanderthal - no coherent picture emerges of a trend, a teleological movement towards a set goal, a bright future, a utopia. Interrogating evolution, religion, secularisation, reason, ethics does not suggest an answer. Cultural features relating to sexuality, the ideas of equality, liberty and democracy, just show how varied and often unsatisfactory the pursuit of these ideals has been. The history of approaches to environmental issues, of the food quest, migration and violence neither reveals nor prescribes a future course.Navigating its cultural future humankind is alone. No natural law, religious determinism, or DNA predisposition steers our course. At the moment the values of the modern Western liberal democracy seem to point the way. But this may not last in the shifting maze of global cultural multilateralism.