  We suggest an unified presentation to teach fundamental constants to graduate
students, by introducing four lower limits to observed phenomena. The reduced
Planck constant $\hbar$ is the lowest classically definable action. The inverse
of invariant speed, $s$, is the lowest observable slowness. The Planck time,
$t_{\rm P}$, is the lowest observable time scale. The Boltzmann constant, $k$,
determines the lowest coherent degree of freedom; we recall a Einstein
criterion on the fluctuations of small thermal systems and show that it has
far-reaching implications, such as demonstrating the relations between critical
exponents. Each of these four fundamental limits enters in an inequality, which
marks a horizon of the universe we can perceive. This compact presentation can
resolve some difficulties encountered when trying to defining the epistemologic
status of these constants, and emphasizes their useful role in shaping our
intuitive vision of the universe.
