  By numerical simulations in {\it real time} we provide evidence in favour of
sphaleron like transitions in the hot, symmetric phase of the electroweak
theory. Earlier performed observations of a change in the Chern-Simons number
are supplemented with a measurement of the lowest eigenvalues of the
three-dimensional staggered fermion Dirac operator and observations of the
spatial extension of energy lumps associated with the transition. The
observations corroborate on the interpretation of the change in Chern-Simons
numbers as representing continuum physics, not lattice artifacts. By combining
the various observations it is possible to follow in considerable detail the
time-history of thermal fluctuations of the classical gauge-field
configurations responsible for the change in the Chern-Simons number.
