Abstract We introduce a framework for qualitative reasoning about directions in high-dimensional spaces, called EER, where our main motivation is to develop a form of commonsense reasoning about semantic spaces. The proposed framework is, however, more general; we show how qualitative spatial reasoning about points with several existing calculi can be reduced to the realisability problem for EER (or REER for short), including LR and calculi for reasoning about betweenness, collinearity and parallelism. Finally, we propose an efficient but incomplete inference method, and show its effectiveness for reasoning with EER as well as reasoning with some of the aforementioned calculi.