  When pulling a probe particle in a many-particle system with fixed velocity,
the probe's effective friction, defined as average pulling force over its
velocity, $\gamma_{eff}:=\langle F_{ex}\rangle/u$, first keeps constant (linear
response), then decreases (thinning) and finally increases (thickening). We
propose a three-time-scales picture (TTSP) to unify thinning and thickening
behaviour. The points of the TTSP are that there are three distinct time scales
of bath particles: diffusion, damping, and single probe-bath (P-B) collision;
the dominating time scales, which are controlled by the pulling velocity,
determine the behaviour of the probe's friction. We confirm the TTSP by
Langevin dynamics simulation. Microscopically, we find that for computing the
effective friction, Maxwellian distribution of bath particles' velocities works
in low Reynolds number (Re) but fails in high Re. It can be understood based on
the microscopic mechanism of thickening obtained in the $T=0$ limit. Based on
the TTSP, we explain different thinning and thickening observations in some
earlier literature.
