Geometric models are used for modelling meaning in various semantic-space models. They are seductive in their simplicity and their imaginative qualities, and for that reason, their metaphorical power risks leading our intuitions astray: human intuition works well in a three-dimensional world but is overwhelmed by higher dimensionalities. This note is intended to warn about some practical pitfalls of using high-dimensional geometric representation as a knowledge representation and a memory model—challenges that can be met by informed design of the representation and its application.