e^x and e^ix

When x -> infinity, e^x -> infinity, but in contrast e^ix is always bounded to the unit circle according to Euler's formula. This clever trick is said to be an important step that finally led to the discovery of Fourier series.

Rank Correlation Coefficients

To measure the correlation between two rankings rather than two random variables, we can consider using the following non-parametric correlation coefficients.
Spearman's ρ
Kendall's τ

Hellinger metric

Hellinger metric is the square-root of Jensen–Shannon divergence, a symmetric version of Kullback-Leibler divergence. It looks a good choice when measuring the dissimilarity between two distributions (e.g., two multinomial distributions corresponding to a pair of documents), because it is known to be a legitimate distance metric.