  In 1908, Minkowski put forward the idea that invariance under what we call
today the Lorentz group, $GL(1,3, {\bf R})$, would be more meaningful in a
four-dimensional space-time continuum. This suggestion implies that space and
time are intertwined entities so that, kinematic and dynamical quantities can
be expressed as vectors, or more generally by tensors, in the four-dimensional
space-time. Minkowski also showed how causality should be structured in the
four-dimensional vector space. The mathematical formulation proposed by
Minkowski made its generalization to curved spaces quite natural, leaving the
doors to the General Theory of Relativity and many other developments ajar.
  Nevertheless, it is remarkable that this deceptively simple formulation
eluded many researchers of space and time, and goes against our every day
experience and perception, according to which space and time are distinct
entities. In this contribution, we discuss these contradictory views, analyze
how they are seen in contemporary physics and comment on the challenges that
space-time explorers face.
