Measurement techniques that probe the second-order susceptibility, such as second-harmonic and sum-frequency generation, are recognized for their ability to study environments with broken centrosymmetry. As a result, they serve as reporters of molecules at surfaces because the second-order susceptibility is often zero in the adjacent bulk media. Although the signals measured in such experiments carry unique information about the interfacial environment, the challenge is to disentangle properties related to the electronic structure as they are wrapped up in the orientation distribution. Over the past 30 years, this challenge has been turned into an opportunity, as many studies have sought to learn about the arrangement of molecules at surfaces. Here we demonstrate that the flipped case is possible, where fundamental properties of the interfacial environment can be extracted in a manner that is completely independent of, and therefore oblivious to, the orientation distribution. Using p-cyanophenol adsorbed at the air-water interface as an example, we illustrate that the cyano group polarizability varies less along the direction of the C-N bond when at the surface than when the same molecules are in the bulk aqueous phase.