Is the Mismatch Negativity a symmetrical measure of change?: mathematico-philosophical and experimental investigations aimed at mapping psychotopologies

Abstract

The event-related potential known as the Mismatch Negtivity (MMN) is a psychophysical measure of discriminable change. It is most simply evoked through experiments in the oddball paradigm, in which two stimuli are presented in random alternation, one more happening more frequently, thereby called the standard, and another more rarely, thereby called the deviant. The MMN is the waveform computed as the subtraction of the response to the standard from the response to the deviant. The literature characterizes the MMN as a waveform whose peak amplitude increases and peak latency decreases with decrements in the probability of presentation of deviant and with the difference between standard and deviant stimuli. This characterization of the MMN is in its essence incomplete, as it does not determine how to measure the difference between standard and deviant stimuli, and many metric spaces can be used for the domain of physical stimuli. The literature commonly assumes that the MMN is a symmetrical measure of change and that reversing roles of standard and deviant for the physical stimuli employed in the experiments will not affect the MMN. Differences observed between the MMNs obtained in the pair of experiments determined by the swapping of roles have been explained by differences in other event-related potentials being recorded in the experiments. This work shows that the MMN symmetry assumption is ill-defined, lacking in mathematical rigour, and proposes an experimental framework for cleanly investigating whether the MMN behaves as a symmetrical measure of change under a given metric for the space of physical stimuli. Furthermore, experimental results for the frequency MMN, under the metric absolute value of difference, in Hertz, between the fundamental frequency of three-harmonics complex tones, are presented, and it is shown that, in this metric space for physical stimuli, the MMN is an asymmetrical measure of change. If it is assumed, a priori, that the MMN is a symmetrical measure of change, then searching for metric spaces for physical stimuli, under which the MMN behaves as such, can be used as a tool for mapping the psychotopology of processing that sort of stimuli.