  With the relentless rise of computer power, there is a widespread expectation
that computers can solve the most pressing problems of science, and even more
besides. We explore the limits of computational modelling and conclude that, in
the domains of science and engineering that are relatively simple and firmly
grounded in theory, these methods are indeed powerful. Even so, the
availability of code, data and documentation, along with a range of techniques
for validation, verification and uncertainty quantification, are essential for
building trust in computer generated findings. When it comes to complex systems
in domains of science that are less firmly grounded in theory, notably biology
and medicine, to say nothing of the social sciences and humanities, computers
can create the illusion of objectivity, not least because the rise of big data
and machine learning pose new challenges to reproducibility, while lacking true
explanatory power. We also discuss important aspects of the natural world which
cannot be solved by digital means. In the long-term, renewed emphasis on
analogue methods will be necessary to temper the excessive faith currently
placed in digital computation.
