0 1 2 3 0.2 0.4 0.6 0 1 2 3 0.2 0.4 0.6 0.5 1.0 0.2 0.4 0.6 0 1 2 3 0.2 0.4 0.6 0 1 2 3 0.2 0.4 0.6 0.5 1.0 0.2 0.4 0.6  Time (s)  Temperature ( µ K) 0 Debye (A) T x T z (B) 0.084 Debye Time (s) (C) 0.158 Debye  Time (s) (D) 0 Debye  Time (s)  Temperature ( µ K) (E) 0.084 Debye  Time (s) (F) 0.158 Debye  Time (s) FI G. 4: Apparent cross-dimensional rethermalization as a function of dipole moment for T$_{z}$ > T$_{x}$ (u pper row, A-C) and T$_{z}$ < T$_{x}$ (lower row, D-F) in the polar molecule gas. The experimental data reveal a striking difference between the results for heating the gas in the vertical direction (A to C) and heating in the horizontal directions (D to F), and thus provide evidence for the strong anisotropic characteristic of dipolar interactions (see text). The electric field is applied along ˆ z . vertical and horizontal directions. In the following, we present measurements of the time evolution of the expansion energy in the two directions for different d . To probe the spa- tial anisotropy of dipolar collisions, we start by adding energy along one direction of the cylindrically symmetric trap using parametric heating. Here, we modulate the power of both optical trapping beams at twice the relevant harmonic trapping frequency for 50 ms (z-direction) or 100 ms (x,y-directions). We then wait 100 ms before quickly increasing the electric field (in less than 1 µ s) to the desired final value and measuring the time dependence of the vertical ( T$_{z}$ ) and horizontal ( T$_{x}$ ) “temperatures” of the cloud. Here, T$_{z}$ and T$_{x}$ simply correspond to the measured expansion energies in the two directions. We note that this type of measurement is commonly used in ultracold atom gas experiments to measure the elastic collision cross section [25]. Figure 4 shows the experimental data for these rethermalization experiments with three values of d and under two initial conditions: T$_{z}$ > T$_{x}$ (upper row, A-C) and T$_{z}$ < T$_{x}$ (lower 9