  One of the core advantages topological methods for data analysis provide is
that the language of (co)chains can be mapped onto the semantics of the data,
providing a natural avenue for human understanding of the results. Here, we
describe such a semantic structure on Chen's classical iterated integral
cochain model for paths in Euclidean space. Specifically, in the context of
population time series data, we observe that iterated integrals provide a
model-free measure of pairwise influence that can be used for causality
inference. Along the way, we survey recent results and applications, review the
current standard methods for causality inference, and briefly provide our
outlook on generalizations to go beyond time series data.
