Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (a cause) contributes to the production of another event, process, state, or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause.In general, a process has many causes, which are also said to be …

The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another …

The Discworld is the fictional setting for all of Terry Pratchett's Discworld fantasy novels. It consists of a large disc (complete with edge-of-the-world drop-off and consequent waterfall) resting on the backs of four huge elephants which are in turn standing on the back of an enormous turtle, named Great A'Tuin (similar to Chukwa or Akupara from Hindu mythology) as …

Historical usage By Aristotle. Aristotelian logic identifies a categorical proposition as a sentence which affirms or denies a predicate of a subject, optionally with the help of a copula.An Aristotelian proposition may take the form of "All men are mortal" or "Socrates is a man." In the first example, the subject is "men", predicate is "mortal" and copula is "are", while in the second example ...

Synchronicity (German: Synchronizität) is a concept first introduced by analytical psychologist Carl G. Jung "to describe circumstances that appear meaningfully related yet lack a causal connection." In contemporary research, synchronicity experiences refer to one's subjective experience that coincidences between events in one's mind and the outside world may be …

Retrocausality, or backwards causation, is a concept of cause and effect in which an effect precedes its cause in time and so a later event affects an earlier one. In quantum physics, the distinction between cause and effect is not made at the most fundamental level and so time-symmetric systems can be viewed as causal or retrocausal. [page needed] Philosophical …

In biology. Ultimate causation explains traits in terms of evolutionary forces acting on them.; Example: female animals often display preferences among male display traits, such as song. An ultimate explanation based on sexual selection states that females who display preferences have more vigorous or more attractive male offspring.. Proximate causation explains biological …

The Kramers–Kronig relations are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane.The relations are often used to compute the real part from the imaginary part (or vice versa) of response functions in physical systems, because for stable systems, causality implies the condition of analyticity, …

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus.Any manifold can be described by a collection of charts ().One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of …

T-symmetry and causality. The requirement of time-reversal symmetry, in general, is difficult to reconcile with the principle of causality. Maxwell's equations and the equations for electromagnetic waves have, in general, two possible solutions: a retarded (delayed) solution and an advanced one. Accordingly, any charged particle generates waves, say at time = and point …