  We discuss briefly the very interesting concept of Brownian distance
covariance developed by Sz\'{e}kely and Rizzo [Ann. Appl. Statist. (2009), to
appear] and describe two possible extensions. The first extension is for high
dimensional data that can be coerced into a Hilbert space, including certain
high throughput screening and functional data settings. The second extension
involves very simple modifications that may yield increased power in some
settings. We commend Sz\'{e}kely and Rizzo for their very interesting work and
recognize that this general idea has potential to have a large impact on the
way in which statisticians evaluate dependency in data. [arXiv:1010.0297]
