In formal language theory, an alphabet is a non-empty set of symbols, oftendenoted 𝜉={𝑠1,𝑠2,…} or in the continuous case {𝑠𝑖:𝑖∈ℝ}. The family ofalphabets include the Latin letters {𝐴,𝐵,…,𝑍}, the binary digits {0,1}, andthe genetic nucleotides {𝐴,𝐶,𝑇,𝐺}. Sequences of symbols from an alphabetare known as strings—be they books, genomes, or binary data. Seen in Figure 1,Cuneiform, the oldest surviving writing system, was developed by the Summarians around 5500 years ago. In pre-Sargonian Lagash, the alphabet is thought tohave consisted of 468 symbols. Upon inspection, perhaps the first quality of thealphabet that springs to mind is its beauty. That particular quality of alphabetshas been consistent throughout history. The subset of the Hebrew alphabetincluded in the Typst¹ math symbol set is {ℵ,ℶ,ℸ,ℷ,ש}. Figure 2 shows theGreek letters, and Figure 3 a 16th century incarnation of the Latin.Figure 1: The Sumerian word ama-ar-gi written in classical Sumerian cuneiform.Meaning “refer to release from obligations, debt, slavery, taxation, or punishment”, the word is the earliest known reference to the concept of freedom.𝛼 𝛽 𝛾 𝛿 𝜀 𝜁 𝜂 𝜃 𝜄 𝜅 𝜆 𝜇 𝜈 𝜉 𝜊 𝜋 𝜌 𝜎 𝜏 𝜐 𝜑 𝜒 𝜓 𝜔Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ ΩFigure 2: The Greek Alphabet𝔞 𝔟 𝔠 𝔡 𝔢 𝔣 𝔤 𝔥 𝔦 𝔧 𝔨 𝔩 𝔪 𝔫 𝔬 𝔭 𝔮 𝔯 𝔰 𝔱 𝔲 𝔳 𝔵 𝔶 𝔷𝔄 𝔅 ℭ 𝔇 𝔈 𝔉 𝔊 ℌ ℑ 𝔍 𝔎 𝔏 𝔐 𝔑 𝔒 𝔓 𝔔 ℜ 𝔖 𝔗 𝔘 𝔙 𝔛 𝔜 ℨFigure 3: The Latin Alphabet in FrakturThough recent events might have changed the connotations we have of theRussian Cyrillic alphabet, Figure 4 shows its undeniable beauty.а б в г д е ё ж з и й к л м н о п р с т у ф х ц ч ш щ ъ ы ь э ю яА Б В Г Д Е Ё Ж З И Й К Л М Н О П Р С Т У Ф Х Ц Ч Ш Щ Ъ Ы Ь Э Ю ЯFigure 4: The Russian Cyrillic AlphabetArchetypesLinear algebra teaches us that the most fundamental unit (or symbol) of mathematics is not the number, but rather the matrix. Thought of as such, the numberbecomes more akin to the typographical, triangle like atomics of Cuneiform.Psychoanalytically, is has been argued that a given personality is a mere mix ofarchetypes, a linear combination, if you will.StereotypesThe mechnical embrology of the Latin letters are still with us today. Letters weresteretypes, by pressing metal implements into the right shape, and using it toreplicate the represented symbol at will. Given ordered nature of quantity, onecould argue a typographical mapping between number and size is apt.PrototypesIndeed, what representation of the vector 𝑣=[1.0,0.8,0.6,0.5,0.1,0.0,0.1]communicates its nature best? The affore written numerical representation ofFigure 5?a ą b c ć d e ę f g h i j k l ł m n ń o ó p r s ś t u w y z ź żA Ą B C Ć D E Ę F G H I J K L Ł M N Ń O Ó P R S Ś T U W Y Z Ź ŻFigure 5: Esch of 𝑣EndotypesFenotypesPerhaps the most modern masterpiece is the Taliban’s much improved versionof the Afghan flag.GenotypesReferences¹typst.app