Theoretical models of higher cognitive function predict that cortical activity will exhibit families of spatial-temporal patterns of activity whose individual members are related to each other by specific symmetry transformations. In the trion model, it is suggested that these inherent symmetries play a vital role in how we think and reason. We have developed a method of analysis (SYMMETRIC analysis), which detects families of patterns in EEG data, and characterizes the symmetry relationships between members of those pattern families. Using this analysis, significant symmetry families have been found in EEG and single unit spike train data. If symmetry is a crucial aspect of brain function, it is possible that different pathologies are associated with specific types of symmetry relationships in brain activity that could be detected in EEG data by a SYMMETRIC analysis.