Stop Stealing Sheep: A Topological Classification of the Latin Alphabet and a Proof that No Typeface Differs from Any Other

You have a favourite font. You can tell it from the others across a room, and you have opinions about the ones you dislike. We prove, with regret, that this feeling has no mathematical content. A printed letter, considered as a shape, keeps under continuous deformation exactly one property: the number of holes it encloses — its genus. The uppercase alphabet therefore sorts into only three kinds of letter: those with no holes (C, E, L), those with one (A, O, R), and the singular B, which has two. Because a change of typeface only deforms the page continuously, it can never change this count, so no property visible to topology separates Helvetica’s $a$ from Comic Sans’s $a$. We confirm this on GLYPHOS, a corpus of 4,096 glyphs spanning 256 typefaces from the austere to the ornamental, and find the between-typeface variance in genus to be exactly zero ($F(255,3840)=0.00$, $p=1.000$). Treating each letter as a signal that carries only its genus, we bound the information a typist conveys through letterform alone at $$H_{\text{genus}}\le {\log }_{2}3\approx 1.585\text{ bits per letter},$$ of which measured English prose uses only $0.93$. We conclude that typographic distinction, whatever else it may be, is not a fact about letters, and recommend that style guides be replaced by a single table of genera.