  I present an intuitive answer to an often asked question: why is the
integrated difference K-U between the kinetic and potential energy the quantity
to be minimized in Hamilton's principle?
  Using elementary arguments, I map the problem of finding the path of a moving
particle connecting two points to that of finding the minimum potential energy
of a static string. The mapping implies that the configuration of a
non--stretchable string of variable tension corresponds to the spatial path
dictated by the Principle of Least Action; that of a stretchable string in
space-time is the one dictated by Hamilton's principle. This correspondence
provides the answer to the question above: while a downward force curves the
trajectory of a particle in the (x,t) plane downward, an upward force of the
same magnitude stretches the string to the same configuration x(t).
