T$_{z}$ ), it provides excellent agreement with the experimental data. Our observations provide clear evidence of the anisotropic nature of the dipole-dipole interactions through the observed anisotropy in the apparent rethermalization. From the agreement of the data with the model, we conclude that the rethermalization behavior is actually dominated by the anisotropic nature of the inelastic collisions. What then can we conclude about elastic collisions? The best fit value for the elastic collision cross section is finite and increases with increasing d . This is consistent with the prediction that the elastic collision rate for polar molecules will scale as d 4 [26], and, furthermore, the fit values agree with the prediction of cross sections on the order of σ$_{el}$ = 7 · 10 − $^{8}$cm$^{2}$/ (s Debye $^{4}$) [26]. How- ever, the presence of inelastic loss and the resulting anisotropic heating make it difficult to accurately extract a measured value of the elastic cross section for a more precise comparison with theory. The results presented here demonstrate that modest applied electric fields can dramati- cally alter the interactions of fermionic polar molecules in the quantum regime. For future efforts aimed at studying many-body phenomena in dipolar molecular quantum systems it will be necessary to protect the gas from strong inelastic loss and heating [11, 12, 27]. In particular, the demonstration here of strong spatial anisotropy for inelastic collisions of polar molecules suggests that going to a two-dimensional trapped gas will be a promising route to realizing a long-lived quantum gas of polar molecules with dipole-dipole interactions. This could be achieved, for example, with polar molecules confined in an array of 2D pancakes in a 1D optical lattice trap [11, 12]. Interestingly, even when short-range inelastic loss processes are suppressed, the attractive part of the long-range dipole-dipole interaction could still give rise to correlations between neighboring 2D pancakes in the 1D lattice trap [28, 29]. For the fit to a quantum threshold model [14] in Fig. 1 B, we write the inelastic loss rate coefficient, β = K$_{0}$T$_{z}$ + 2 K$_{1}$T$_{x}$ , as the sum of two terms corresponding to m$_{L}$ = 0 and m$_{L}$ = ± 1 scattering, respectively, and we assume T$_{z}$ = T$_{x}$ = T . The d -dependent coefficients, K$_{0}$ and K$_{1}$ are obtained using A. Methods K$_{0}$$_{,}$$_{1}$ = γ 3 π ℏ 2 √ 2 µ $^{3}$V 3 / 2 0 , 1 k$_{B}$, (2) 11