  Traditional clustering identifies groups of objects that share certain
qualities. Tangles do the converse: they identify groups of qualities that
often occur together. They can thereby identify and discover 'types': of
behaviour, views, abilities, dispositions. The mathematical theory of tangles
has its origins in the connectivity theory of graphs, which it has transformed
over the past 30 years. It has recently been axiomatized in a way that makes
its two deepest results applicable to a much wider range of contexts. This
expository paper indicates some contexts where this difference of approach is
particularly striking. But these are merely examples of such contexts: in
principle, it can apply to much of the quantitative social sciences. Our aim
here is twofold: to indicate just enough of the theory of tangles to show how
this can work in the various different contexts, and to give plenty of
different examples illustrating this.
