  It has long been noticed that high dimension data exhibits strange patterns.
This has been variously interpreted as either a "blessing" or a "curse",
causing uncomfortable inconsistencies in the literature. We propose that these
patterns arise from an intrinsically hierarchical generative process. Modeling
the process creates a web of constraints that reconcile many different theories
and results. The model also implies high dimensional data posses an innate
separability that can be exploited for machine learning. We demonstrate how
this permits the open-set learning problem to be defined mathematically,
leading to qualitative and quantitative improvements in performance.
