Godfried T. Toussaint (New York University Abu Dhabi)

Measuring the Complexity of One-Dimensional Visual and Auditory Sequences
Professor Godfried T. Toussaint, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates


A mathematical measure of pattern complexity based on sub-symmetries possessed by the pattern, originally proposed by C. Alexander and S. Carey (1968), and shown by them to correlate highly with empirically derived measures of cognitive complexity in the visual domain, is found to also correlate significantly with empirically derived complexity measures of perception and production of auditory temporal and musical rhythmic patterns. A sub-symmetry in a sequence is a subset of contiguous (connected) elements of the sequence that exhibits mirror symmetry. Not only does the sub-symmetry measure correlate highly with the difficulty of reproducing the rhythms by tapping after listening to them, but the empirical measures exhibit similar behaviour, for both the visual and auditory patterns, as a function of the relative number of sub-symmetries present in the patterns. This simple measure is also compared to the measures of complexity, homogeneity, order, and symmetry proposed subsequently by F. Papentin & M. Krüger (1983) to approximate upper bounds on the Kolmogorov complexity in a computationally feasible manner. To put this work in context, a short partial review of the plethora of complexity measures used in computer science, psychology, linguistics, and music technology will precede the presentation of the new results.

See here for some relevant literature:



Friday, July 25, 2014


11:00 am - 12:00 pm

TASC1 Building, Room No. 9204, Simon Fraser University, Burnaby