Despite the ambiguity of reference-dependent surface potentials, which yield different EEG waveforms for each recording site depending of the chosen reference, the relationship between signals in an EEG topography is fixed. This is a direct consequence of the principle described above (Fig. 1), that is, the relative difference between two recording sites is unaffected by the choice of the recording reference (e.g., Osselton, 1965). For this reason, the difference between any two ERP waveforms in a given EEG montage is exactly the same for a nose, linked-mastoids or average reference, regardless of their uniquely different ERP waveforms at either site (Fig. 3). By extension, this reference-independent relationship of EEG activity recorded at different scalp sites is also true for ERP difference waveforms (i.e., between conditions or groups). However, condition (or group) differences at specific sites are also affected by the choice of reference (cf. column 3 in Fig. 3, showing faces-minus-words ERP difference waveforms as an example). This characteristic relationship between EEG activity at different recording locations (i.e., topography) is both unique (i.e., there is only one difference between any two sites) and reference-free, and it is at the core of the surface Laplacian.2
