We present an unsupervised deep learning method for text line segmentation that is inspired by the relative variance between text lines and spaces among text lines. Handwritten text line segmentation is important for the efficiency of further processing. A common method is to train a deep learning network for embedding the document image into an image of blob lines that are tracing the text lines. Previous methods learned such embedding in a supervised manner, requiring the annotation of many document images. This paper presents an unsupervised embedding of document image patches without a need for annotations. The number of foreground pixels over the text lines is relatively different from the number of foreground pixels over the spaces among text lines. Generating similar and different pairs relying on this principle definitely leads to outliers. However, as the results show, the outliers do not harm the convergence and the network learns to discriminate the text lines from the spaces between text lines. Remarkably, with a challenging Arabic handwritten text line segmentation dataset, VML-AHTE, we achieved superior performance over the supervised methods. Additionally, the proposed method was evaluated on the ICDAR 2017 and ICFHR 2010 handwritten text line segmentation datasets.