  In a causal world the direction of the time arrow dictates how past causal
events in a variable $X$ produce future effects in $Y$. $X$ is said to cause an
effect in $Y$, if the predictability (uncertainty) about the future states of
$Y$ increases (decreases) as its own past and the past of $X$ are taken into
consideration. Causality is thus intrinsic dependent on the observation of the
past events of both variables involved, to the prediction (or uncertainty
reduction) of future event of the other variable. We will show that this
{{temporal}} notion of causality leads to another natural spatio-temporal
definition for it, and that can be exploited to detect the arrow of influence
from $X$ to $Y$, either by considering shorter time-series of $X$ and longer
time-series of $Y$ (an approach that explores the time nature of causality) or
lower precision measured time-series in $X$ and higher precision measured
time-series in $Y$ (an approach that explores the spatial nature of causality).
Causality has thus space and time signatures, causing a break of symmetry in
the topology of the probabilistic space, or causing a break of symmetry in the
length of the measured time-series, a consequence of the fact that information
flows from $X$ to $Y$.
