Abstract Reconstructing ancestral characters and traits along a phylogenetic tree is central to evolutionary biology. It is the key to understanding morphology changes among species, inferring ancestral biochemical properties of life, and recovering migration routes in phylogeography. The goal is twofold: to reconstruct the character state at the tree root (e.g. the region of origin of some species), and to understand the process of state changes along the tree (e.g. species flow between countries). Although each goal can be achieved with high accuracy individually, we use mathematics and simulations to demonstrate that it is generally impossible to accurately estimate both the root state and the rates of state changes along the tree branches from the observed data at the tips of the tree. This inherent ‘Darwinian uncertainty principle’ concerning the simultaneous estimation of ‘pattern’ and ‘process’ governs ancestral reconstructions in biology. Increasing the number of tips improves the joint estimation accuracy for certain tree shapes that arise in evolutionary models, however, for other trees shapes it does not.