at the phase velocity; since phase is not causal, the phase velocity of a wave packet can be faster than light. Causal notions are important in general relativity to the extent that the existence of an arrow of time demands that the universe's semi-Riemannian manifold be orientable, so that "future" and "past" are globally definable quantities. Engineering A causal system is a system with output and internal states that depends only on the current and previous input values. A system that has some dependence on input values from the future (in addition to possible past or current input values) is termed an acausal system, and a system that depends solely on future input values is an anticausal system. Acausal filters, for example, can only exist as postprocessing filters, because these filters can extract future values from a memory buffer or a file. Biology, medicine and epidemiology Austin Bradford Hill built upon the work of Hume and Popper and suggested in his paper "The Environment and Disease: Association or Causation?" that aspects of an association such as strength, consistency, specificity, and temporality be considered in attempting to distinguish causal from noncausal associations in the epidemiological situation. (See Bradford-Hill criteria.) He did not note however, that temporality is the only necessary criterion among those aspects. Directed acyclic graphs (DAGs) are increasingly used in epidemiology to help enlighten causal thinking. Psychology Psychologists take an empirical approach to causality, investigating how people and non-human animals detect or infer causation from sensory information, prior experience and innate knowledge. Attribution: Attribution theory is the theory concerning how people explain individual occurrences of causation. Attribution can be external (assigning causality to an outside agent or force—claiming that some outside thing motivated the event) or internal (assigning causality to factors within the person—taking personal responsibility or accountability for one's actions and claiming that the person was directly responsible for the event). Taking causation one step further, the type of attribution a person provides influences their future behavior. The intention behind the cause or the effect can be covered by the subject of action. See also accident; blame; intent; and responsibility. Causal powers Whereas David Hume argued that causes are inferred from non-causal observations, Immanuel Kant claimed that people have innate assumptions about causes. Within psychology, Patricia Cheng attempted to reconcile the Humean and Kantian views. According to her power PC theory, people filter observations of events through an