Big data: the end of the scientific method?

For it is not the abundance of knowledge, but the interior feeling and taste of things, which is accustomed to satisfy the desire of the soul. (Saint Ignatius of Loyola). We argue that the boldest claims of big data (BD) are in need of revision and toning-down, in view of a few basic lessons learned from the science of complex systems. We point out that, once the most extravagant claims of BD are properly discarded, a synergistic merging of BD with big theory offers considerable potential to spawn a new scientific paradigm capable of overcoming some of the major barriers confronted by the modern scientific method originating with Galileo. These obstacles are due to the presence of nonlinearity, non-locality and hyperdimensions which one encounters frequently in multi-scale modelling of complex systems. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.