  In a recent thermodynamic analysis of the harmonic oscillator and using an
interpolation procedure, Boyer has shown that the existence of a zero-point
energy leads to the Planck spectrum. Here we avoid the interpolation by adding
a statistical argument to arrive at Planck's law as an inescapable result of
the presence of the zero-point energy. No explicit quantum argument is
introduced along the derivations. We disclose the connection of our results
with the original analysis of Planck and Einstein, which led to the notion of
the quantized radiation field. We then inquire into the discrete or continuous
behaviour of the energy and pinpoint the discontinuities. Finally, to open the
door to the description of the zero-point fluctuations, we briefly discuss the
statistical (in contrast to the purely thermodynamic) description of the
oscillator, which accounts for both thermal and temperature-independent
contributions to the energy dispersion.
