The human sleep-cycle has been divided into discrete sleep stages that can be recognized in electroencephalographic (EEG) and other bio-signals by trained specialists or machine learning systems. It is however unclear whether these human-defined stages can be re-discovered with unsupervised methods of data analysis, using only a minimal amount of generic pre-processing. Based on EEG data, recorded overnight from sleeping human subjects, we investigate the degree of clustering of the sleep stages using the General Discrimination Value as a quantitative measure of class separability. Virtually no clustering is found in the raw data, even after transforming the EEG signals of each 30-s epoch from the time domain into the more informative frequency domain. However, a Principal Component Analysis (PCA) of these epoch-wise frequency spectra reveals that the sleep stages separate significantly better in the low-dimensional sub-space of certain PCA components. In particular the componentC1(t) can serve as a robust, continuous ‘master variable’ that encodes the depth of sleep and therefore correlates strongly with the ‘hypnogram’, a common plot of the discrete sleep stages over time. Moreover,C1(t) shows persistent trends during extended time periods where the sleep stage is constant, suggesting that sleep may be better understood as a continuum. These intriguing properties ofC1(t) are not only relevant for understanding brain dynamics during sleep, but might also be exploited in low-cost single-channel sleep tracking devices for private and clinical use.