What is the Geometry of a Surface

substitution or k-alphabetic substitution, with k known, and if the text if vfc text. Texts written in many natural languages, with certain exceptions, tend to be vfc texts. Near-exceptions are German (and, presumably, other germanic languages) in which the vfc character is somewhat diminished by the frequency of consonant-consonant digrams, and Spanish (and, presumably, other romance languages) in which certain vowel-vowel pairs are frequent. Despite these deviations from the vfc rule, the second singular vectors classify correctly most of the letters which occur with a frequency high enough to be statistically significant. A computer program which uses the SVD as the starting point in an automated, heuristic approach to solving cryptograms is described by Schatz [7].