  A human is a thing that moves in space. Like all things that move in space,
we can in principle use differential equations to describe their motion as a
set of functions that maps time to position (and velocity, acceleration, and so
on). With inanimate objects, we can reliably predict their trajectories by
using differential equations that account for up to the second-order time
derivative of their position, as is commonly done in analytical mechanics. With
animate objects, though, and with humans, in particular, we do not know the
cardinality of the set of equations that define their trajectory. We may be
tempted to think, for example, that by reason of their complexity in cognition
or behaviour as compared to, say, a rock, then the motion of humans requires a
more complex description than the one generally used to describe the motion of
physical systems. In this paper, we examine a real-world dataset on human
mobility and consider the information that is added by each (computed, but
denoised) additional time derivative, and find the maximum order of derivatives
of the position that, for that particular dataset, cannot be expressed as a
linear transformation of the previous. In this manner, we identify the
dimensionality of a minimal model that correctly describes the observed
trajectories. We find that every higher-order derivative after the acceleration
is linearly dependent upon one of the previous time-derivatives. This measure
is robust against noise and the choice for differentiation techniques that we
use to compute the time-derivatives numerically as a function of the measured
position. This result imposes empirical constraints on the possible sets of
differential equations that can be used to describe the kinematics of a moving
human.
