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, our oldest known writing system, was developed by the Sumeriansaround 5500 years ago. In pre-Sargonian Lagash [1], the alphabet is thoughtto have consisted of 468 letters, each letter constructed by the relation andorientation of the indentation. The complexity that arises from having onething change in position (relative and absolute) and orientation, similar to ourzeros and ones show that the binary digits are not the only example of minisculesymbol sets used to construct threads of language.Upon inspection, perhaps the first quality of the alphabet that springs to mindis its beauty. That particular quality of alphabets has been consistent throughout history. The subset of the Hebrew alphabet included in the Typst1 mathsymbol set is {ℵ,ℶ,ℸ,ℷ,ש}. Figure 2 shows the Greek letters, and Figure 3 a16th century incarnation of the Latinn alphabet in black letter. Black letter waswidespread and its ornate, gothic style has been replaced by sans-serif. Andyet, black letter was always unreadadble? So why did it become wide spread?Perhaps asemic in nature. Illegebility was a prerequsite of the proser of thepowerful—the church. Even the bible is readable these days—altough very fewdo take the timee make it part Genisis [2]. The King James Bible is published inTimes New Roman [3].1typst.appFigure 1: The Sumerian word ama-ar-gi written in classical Sumeriancuneiform. Meaning “refer to release from obligations, debt, slavery, taxation,or punishment”, the word is the earliest known reference to the concept offreedom.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 Black LetterThough 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) ofmathematics is not the number, but rather the matrix. Thought of as such,the number becomes more akin to the typographical, triangle-like atomic ofCuneiform. Psychoanalytically, it has been argued that a given personality ismerely a mix of archetypes; a linear combination.STEREOTYPESThe mechanical embryology of the Latin letters are still with us today. Letterswere stereotypes, by pressing metal implements into the right shape, and usingit to replicate the given symbol at will. Given the ordered nature of quantity,one could argue a typographical mapping between number and size is apt.PROTOTYPESWhat 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 of Figure 5?Figure 5: Esch of 𝑣ENDOTYPESFENOTYPESPerhaps the most modern masterpiece is the Taliban’s much improved versionof the Afghan flag.GENOTYPESThe fundamental unit in information theory is the symbol. Three famous setsof symbols are the Latin alphabet, the four nucleotides of DNA {𝐴,𝐶,𝑇,𝐺},and the binary alphabet {0,1}. Any countable alphabet can be encoded withanother. The nucleotides could be encoded as {01,011,0111,01111}. Theinvention of the written language was a major milestone in human history,akin to the domestication of wolves into dogs, the invention of the needle, andthe mastery of fire. The ubiquity of the symbol is what splits the past into thehistoric and prehistoric. There are many attributes of the symbo It has beensaid that in our information-theoretic age, the bit has replaced the atom as themost fundamental unit of wealth [4]. If any phenomenon befits the name grandremplacement, it is this. The mid 20-th century saw information formally defined as ln(1𝑝𝑥𝑖), where 𝑥𝑖 is a symbol from an alphabet 𝑋={𝑥0,𝑥1,…,𝑥𝑛−1}[5], each occurring with probability 𝑃={𝑝0,𝑝1,…,𝑝𝑛−1}. Consider an unfaircoin where 𝑋={H,T} and 𝑃={1,0} (i.e., we know it will always land onheads). In that case, using our formula for information we get ln(11)=0. Wegain no (0) information wathcing the coin flip heads, as we already knew thatheads would be the outcome. In the fair-coin-case we have ln(10.5)≈0.693,both the 𝐻 and 𝑇 case. Defined as such, the more unlikely or suprising a givenevent is, the higher its information content. Alphabets of arbitrary countablesizes, can be encoded with a two-digit alphabet. In the case of DNA, we have𝑋={𝐴,𝐶,𝑇,𝐺}, which could be encoded as 𝑋′={00,01,10,11} or 𝑋′={01,011,0111,01111}The notion of information as an exact, measurable quantity was given to usby C. E. Shannon [5] with his seminal 1948 paper A Mathematical Theoryof Communication. With it, he establishes information theory as a science,introducing three towering theorems on which our modern world is (arguably)built: 1) The Data Compression Theorem, proving that for a given source thatproduces symbols from an alphabet 𝜉={𝑠0,𝑠1,…,𝑠𝑛−1} with probabilities{𝑝0,𝑝1,…,𝑝𝑛−1}, there exists an optimal coding scheme that can compressmessages to an average length approaching the source entropy; 2) The ChannelCoding Theorem, proving that reliable communication over noisy channels ispossible, at the rate of mutual information between the two endpoints; and3) The Rate-Distortion Theorem, describing the minimum bit rate requiredto achieve a given level of distortion when compressing beyond the entropy.Information theory, as such, is about the transmission of symbols. The transmission of symbols, however, is about much more than one might think.Indeed, the symbol too reigns supreme in the context of even deoxyribonucleicacid (DNA), a source with the alphabet {𝐴,𝐶,𝑇,𝐺}. Senescence is the failureof the body to transmit its own DNA undistorted forward in time to itself.Mortality is thus an information-theoretic phenomenon, and as such, if any, itwill have an information theoretic solution [6].The importance of the symbol is reflected in that has ubiquitously been drawnwith typographical masterpieces like Fraktur (seen in Figure 3), the double-struck letters, used to denote fundamental number sets like the naturals ℕ, thereals ℝ and the complex ℂ, peppering the pages of any modern scientific text,D. Knuth [7]‘s font Computer Modern (with which this page is rendered), and,more recently, Fira Code (with which this page is typed). Indeed, the first, andperhaps only take away the average reader of Shannon’s paper will notice, is thebeautifyl way in which it is typed. This too is true for [2]. In the case of Fraktur,ubiquity has been controversial. Now it has been demoted to denote moreexotic mathmatical concepts like Lie algebras 𝔤, prime ideals 𝔭, and maximalideals 𝔪. But, Fraktur was the de facto font of the Third Reich, and Germanicterritories at large before that. Etymologically, the word “Fraktur” comesfrom the Latin frāctūra (“a fracture”), built from frāctus (“to fracture”). Thetypeface has its origin in the 16th century. The Holy Roman Emperor Maximilian I commissioned Hieronymus Andreae to create a new typeface for AlbrechtDürer’s woodcut print Triumphal Arch2. 195 separate wood blocks were cut,and used to imprint 36 large paper sheets for a final composite measuring 295× 357 centimetres, making it one of the largest and most complex prints of thatkind ever produced—a masterpiece befitting the creation of its own typeface.By the 20th century, Fraktur had become the German typeface (ubiquity).However, Adolf Hitler, who was otherwise well-versed in aesthetics, is knownto have disliked the font, publicly denouncing it in a 1934 speech to theReichstag: Your alleged Gothic internalization does not fit well in this age ofsteel and iron, glass and concrete […]. On this particular dimension, Hitler wasso out of step with his compatriots. Yet it took almost a decade to abolish thescript, with the intervening years seeing Roman characters (of which Fraktur is2https://www.metmuseum.org/art/collection/search/388475not) scolded as being under “Jewish influence”, urging their use to be replacedby Fraktur, the true “German script”. Even with the immense power affordedthe Führer with his position as such, it took him almost a decade to abolishthe font, when Matrin Bormann, in a 1941 Schrifterlass declared Fraktur tonot be “Gothic” but rather Schwabacher “Jewish letters” (controversy). Thefinal demise of Fraktura as the font of the Third Riech was motivated not onlyby Hitler’s warped sense of typographical beauty—if that had been enough, ithad like been abolished around the afore given 1934 quote—but also practicalmatters. In the German occupied terriotries, people stuggled to read Fraktur,having not been trained to do so during their schooling. Further, stereotypes(type of printing plate developed in the late 18th century and widely used inletterpress, newspaper, and other high-speed press runs) supporting the fontfor the pressing of Joseph Goebbels’ propaganda were few and far between inthese newly invaded countries. In its stead Antiqua, a type face much easilyerdiscernable by the subject of the extended Third Reich, would be used.In the case of the double-struck letters, for those who have had to explain tostudents that mathematics is not the mere study of numbers (1,2,3,…) butrather the sets thereof (ℤ={0,1,−1,2,−2,…})—or sets in general—the ideaof denoting these by blackboard bold letters is ingenious—draw two diagonallines, N→ℕ, and the studious mind readily understands that this symboldenotes something more profound. Popularized in the 1960s during the typewriter era, this shorthand for conceptual difference was particularly apt for thepage: strike the letter key twice, and voilà…However, in artifcial intelligence, there is a long standing debate betweensuymbolic and sub-symbolic approaches to solving intelligence. With the deeplearning revolution, this debate has largely been settled with subsymbolism asthe winning paradigm. But what is subsymbolism? If the atoms of DNA, theneucliotides denoted by the afforementioned alphabet {𝐴,𝐶,𝑇,𝐺}, are symbolic, what atoms might that atoms of deep learning be so as to merits the prefixsub? Again, words is the enemy of clarity of thought (see /terminology). As anexample of a subsymbolic deep learning see /miiii, the trained model thereinimplements an algorithm similar to Eq. 1, the modular addition algorithmreverse engineered by𝑥0→sin(𝑤𝑥0),cos(𝑤𝑥0)(1.1)𝑥1→sin(𝑤𝑥1),cos(𝑤𝑥1)(1.2)For those nont mathematically inclindes, Eq. 1 might seem inscruitable, butcomparing that to the weights of the trained model directly, focusing only onthe first two lines, of the equation, visualized as deep learning weights, we haveFigure 6. To quote Anders Søgaard, there is no directing mapping from Figure 6to the mathematical notation in Eq. 1.rtestFigure 6: The embedding layer of the MIIII modelBODY PARAGRAPHSARCHETYPESPerhaps the most compelling quality of typographical masterpieces like Fraktur(seen in Figure 3) and the double-struck letters lies not within the symbolsthemselves, but in the world around them: in their ubiquity. Indeed, thedouble-struck letters (known also as blackboard bold) denoting fundamentalnumber sets like the naturals ℕ, the reals ℝ, and the complex ℂ, pepper thepages of countless scientific texts.In the case of Fraktur ubiquity has, however, at times been controversial. NowFraktur has been demoted to denote more exotic mathematical concepts likeLie algebras 𝔤, prime ideals 𝔭, and maximal ideals 𝔪.A more recent example of a topdown easthetic decree, is the Taliban’s 2022 newAfghan flag, seen in . One can but imagine the Fürer would approved of thechange, having had pro Arab bias, declaring Mohammed Amin al-Husseini, anhonerary aryan.Modern masterpieces like Computer Modern [7] (the font rendering this page)and Fira Code [8] (the font used to write it) exemplify the care in letterform design dominating academic literature and software development environmentsalike.A glance through the research labs of even the most prolific institutions,however, will show the aesthetically astute that bad taste is abundant, inspiteof Fira Code populating the monitors, and Computer Modern dominating thepage. This stands in stark contrast to the aesthetics of artists like Thor TaoHansen3 and Svend Sømod, whose fascination with constructs like order andentropy falls precisely within the realm of the Niels Bohr Institute (to keep thereferences Scandinavian). Inspecting the pages of the papers these labs produceshows Knuth’s typeface, which might as well have been shaped by Tao himself.The meaning of the pages, though beyond Tao’s grasp, is imbued with thatsame beauty.Soceity in the thrawls of even the strangets, and morally repugnant ideas, tendto operate with typographic diginity into oblivion.Why this ubiquity?One cannot but imagine aestheticians of the third rich be in anything but in aweof the aeshtics of the Wahabi Jihadistst [9].3https://thortaohansen.comThe care with which the atoms of literacy have been constructued throughouthistory is rivaled only by the ubiquoity of these typgraphical masterpieces:Fraktur, double-struk, Computer Modern, and more recently, Fira Code, blahblah.STEREOTYPESBut these symbols were not, a mere guarantee of beauty on the levels that low.Fraktur, in particular, was construced for stereotyping. Something somethingwith the kaiser, wood cut, etc. Taliban. Hitler again?Figure 7: The Hebrew AlphabetFigure 8: The Hebrew AlphabetTYPESThat are many types. Types are sets. Rasmus møgelberg. Types types blah blah,category theory, Nutoriously abstract blah blah. The MATRIX. Liebniz. Array.FENOTYPESLook at this. And this. And the brain. Wow.GENOTYPESIntroducing esch.It has been argued [4] that in the 20th century, the bit replaced the atom as themost fundamental unit of wealth. Throughout human history, it is asserted,societal prosperiy and the pillaging of the natural resources of the earth hasbeen as inseperable as day and light.The increase in societal prosperity, for the first time in human history, decoupled from an increase in the use of natural resources.Throughout letters and natural philosophy, certain typographical masterpieces have achieved universal adoption. The ubiquity, for example, of thedouble-struck letters—used to denote number sets like the real ℝ, the naturalℕ, and the complex ℂ—is irrefutable. And indeed, in computer science, thede facto font supreme is Donald Knuth’s computer modern (with which thepresent page is rendered). However, just as the bit has replaced the atom inthe realm of wealth generation [4], so to has numeracy supercede literacy asthe intelectual blah blah. The most frequent operation in scientific computingis perhaps matrix multiplication. Similarly, ask any chat both what the mostimportant numerical algorithm of the 20th centuy is and it will tell you thediscretete Fourier transform (DFT) or the fast Fourier transform (FFT).Perhaps the most defining characteristic of typographical works like ComputerModern , Fraktur and blackboard bold as seen in Figure 1, is their perfection.Indeed, fonts are frequently perfect, and these perfect objects scatteredthroughout the perfect pages, whose dimensions are such that slicing themvertically so that a square is created leaves a sliver of the exact dimensions ofthe original page. In here lies one of many transcendental numbers, the goldenratio, frequently denoted 𝜑—another emaculate sybol.Perhaps bthe most defining characteristic of typographical works like Computer Modern , Fraktur, and blackboard bold—as seen in Figure 1—is theiralmost comical pursuit of perfection. Indeed, these fonts are meticulouslycrafted to be flawless, like mathematical playthings scattered across pristinelycalculated pages. Speaking of mathematical perfection, these pages are designed with such exquisite proportions that when you slice them vertically tocreate a square, the remaining rectangle maintains the exact proportions ofthe original page—because heaven forbid we use dimensions that don’t containhidden mathematical treasures. Within this obsessively precise ratio lies oneof mathematics’ many transcendental numbers, the golden ratio, frequentlydenoted by 𝜑—yet another immaculate symbol in typography’s relentless questto make everything just so perfectly perfect. One almost wonders if the mathematicians who devised these systems spent a touch too much time ensuringtheir letters were as pristine as their proofs. Not quite right. The tone shouldbe loving of the perfection.Here is the corrected verion:>Perhaps the most defining characteristic of typographical works like ComputerModern , Fraktur, and blackboard bold—as seen in Figure 1—is their perfection.Indeed, these fonts are meticulously crafted to be flawless, like mathematicalplaythings scattered across pristinely calculated pages—pages masterpiecesin themselves with their exquisite proportions that when you slice them vertically to create a square, leaves a rectangular sliver that maintains the exactproportions of the original page. Within this obsessively precise ratio lies oneof mathematics’ many transcendental numbers, the golden ratio, frequentlydenoted by 𝜑—yet another immaculate symbol in typography’s vast arsenal ofbeauty.lease improve this next section to fit better with the rest, and make sure thepoints are clear:> Modern works frequently defile the page and the typographic masterpiecesscattered throughout it with obscenities constructed in the internals ofmatplotlib and concocted by a busy scientific mind who dares not even noticethe sacrilege he is committing. > It is not limited to that—pamphlets makea mockery of the physical world by etching into it visual contraptions thatmust haunt even the most aesthetically illiterate. Notable exceptions are farbetween. One such example is the Taliban’s flag seen in [].Here’s a revised version that better matches the reverent tone while maintaining the contrast:Perhaps the most defining characteristic of typographical works like ComputerModern , Fraktur, and blackboard bold—as seen in Figure 1—is their perfection.Indeed, these fonts are meticulously crafted to be flawless, like mathematicalplaythings scattered across pristinely calculated pages—pages masterpiecesin themselves with their exquisite proportions that when you slice them vertically to create a square, leaves a rectangular sliver that maintains the exactproportions of the original page. Within this obsessively precise ratio lies oneof mathematics’ many transcendental numbers, the golden ratio, frequentlydenoted by 𝜑—yet another immaculate symbol in typography’s vast arsenal ofbeauty.In stark contrast, modern works routinely transgress against these sacredtraditions. Scientific manuscripts, hurriedly assembled, defile their pages withcrude figures hastily constructed in the depths of matplotlib—their authors,consumed by deadlines and data, seemingly oblivious to the typographical sinsthey commit. This degradation extends beyond academia: everyday pamphletsand posters assault our visual sensibilities with garish designs that would makeany typographer weep. Rare exceptions to this pandemic of typographicalmediocrity do exist, such as the elegant simplicity found in the Taliban’s flag[], where ancient calligraphic traditions still hold sway over modern shortcuts.what are pretentuious words for essays? Like monograph is for book. Here aresome pretentious alternatives for "essay":In letters and natural philosophy, perhaps pervasiveness is the most definingcharacteristic of typographical masterpieces like Fraktur, ‘s Computer Modern,and the double-struck letters—frequently used to denote number sets like thereals ℝ, the integers ℤ, and the complex ℂ. That sentence is a bit hard to follow- the connection between "pervasiveness" and the examples isn’t quite clear.Here’s a suggested revision that maintains the formal tone while being moreprecise:In letters and natural philosophy, typographical masterpieces like Fraktur,‘s Computer Modern, and the double-struck letters are ubiquitous—the latterhaving become the universal language for denoting fundamental number setslike the reals ℝ, the integers ℤ, and the complex numbers ℤ.Alternative version:In letters and natural philosophy, typographical masterpieces like Fraktur (seeFigure 1), ‘s Computer Modern, and the double-struck—also known as blackboard bold—letters (see Figure 2) are ubiquitous—the latter having become theuniversal language for denoting fundamental number sets like the reals ℝ, theintegers ℤ, and the complex ℂ.Stereotypes ahI’ll help clean up the typos and improve the flow while maintaining the scholarly tone. Here’s the corrected version:StereotypesIn the case of Fraktur, ubiquity has at times been controversial. Etymologically,the word "Fraktur" comes from the Latin frāctūra ("a fracture"), built fromfrāctus ("to fracture"). The typeface has its origin in the 16th century. The HolyRoman Emperor Maximilian I commissioned Hieronymus Andreae to create anew typeface for Albrecht Dürer’s woodcut print Triumphal Arch. 195 separatewood blocks were cut and used to imprint 36 large paper sheets for a finalcomposite measuring 295 × 357 centimetres, making it one of the largest andmost complex prints of that kind ever produced—a masterpiece befitting thecreation of a typeface:[Fraktur alphabet displays remain unchanged]By the 20th century, Fraktur had become the de facto German typeface.However, Adolf Hitler—otherwise well versed in aesthetics—is known to havedisliked the font, publicly denouncing it in 1934 in a speech to the Reichstag:Your alleged Gothic internalization does not fit well in this age of steel and iron,glass and concrete […].On this particular dimension, Hitler was so out of step with his compatriots thatit took almost a decade to abolish the script, with the intervening years seeingroman characters (of which Fraktur is not) derided as being under "Jewishinfluence," urging their replacement by Fraktur, the only "German script."Therefore, even with the immense power afforded Hitler as Führer of Germany,it took until 1941 when Martin Bormann, in a Schrifterlass (typeface decree),declared Fraktur to not be "Gothic" but rather Schwabacher "Jewish letters."The final demise of Fraktur as the de facto font of the Third Reich was motivatednot only by Hitler’s warped sense of typographical beauty—if that had beenenough, it would have been abolished earlier—but also by practical matters.In the German-occupied territories, people struggled to read Fraktur, havingnot been trained to do so during their schooling. Furthermore, stereotypes(type of printing plates developed in the late 18th century and widely used inletterpress, newspaper, and other high-speed press runs) supporting the fontfor the printing of Joseph Goebbels’ propaganda were few and far between inthese newly invaded countries. In its stead, Antiqua—a typeface much moreeasily discernible by the subjects of the extended Third Reich—would be used.> In letters and natural philosophy, typographical masterpieces like Fraktur(see Figure 1), ‘s Computer Modern, and the double-struck—also known asblackboard bold—letters (see Figure 2) are ubiquitous—the latter having becomethe universal language for denoting fundamental number sets like the realsbb{𝑅}, the integers bb{𝑍}, and the complex bb{𝐶}. These typographicalgems are all from a time in which literacy reigned supreme, and indeed literacyis still a precondition for success in the modern world. However, just as thebit as replaced that atom, in terms of health generation, so, arguably, hasthe number replaced the letter, in terms of economic utility. Numeracy nowsupercedes litereacy in economic utility. > > Indeed, as it turns out Leibniz’searly 18th century matrix, the object of study of linear algebra, is the substrateon which we would 300 years later breath intelligence into our machines—andagain, the symbol would a central role: > > 1. Assign a number 𝑖 to each symbolof your alphabet 𝐴. > 2. Construct a |𝐴|×ℎ matrix 𝐸, a set of ℎ×ℎ matrices,and a ℎ×|𝐴| matrix. > 3. For every character in a sequence multiply row 𝑖 of𝐸 through the remaining arrays. >4.Interpret interpret the final output as a probability over the alphabet. > 5.Tweak the numercal values of the arrays from step 2, to assign high probabilityto the true next character in your data. > > Given large enough amounts ofdata, and nothing else, artificial intelligence was born: A set of matricies. > >Stereotypes > > In the case of Fraktur, ubiquity has at times been controversial.> Etymologically, the word "Fraktur" comes from the Latin frāctūra ("a fracture"), built from frāctus ("to fracture"). The typeface has its origin in the 16thcentury. The Holy Roman Emperor Maximilian I commissioned HieronymusAndreae to create a new typeface for Albrecht Dürer’s woodcut print TriumphalArch. 195 separate wood blocks were cut and used to imprint 36 large papersheets for a final composite measuring 295 × 357 centimetres, making it one ofthe largest and most complex prints of that kind ever produced—a masterpiecebefitting the creation of a typeface:> By the 20th century, Fraktur had become the de facto German typeface.However, Adolf Hitler—otherwise well versed in aesthetics (he is known tohave enjoyed the illustration of Figure 2, which is inarguably beautiful)—isknown to have disliked the font, publicly denouncing it in 1934 in a speech tothe Reichstag: Your alleged Gothic internalization does not fit well in this ageof steel and iron, glass and concrete […]. > > On this particular dimension,Hitler was so out of step with his compatriots that it took almost a decadeto abolish the script, with the intervening years seeing roman characters (ofwhich Fraktur is not) derided as being under "Jewish influence," urging theirreplacement by Fraktur, the only "true German script." Therefore, even withthe immense power afforded Hitler as Führer of Germany, it took until 1941when Martin Bormann, in a Schrifterlass (typeface decree), declared Frakturto not be "Gothic" but rather Schwabacher "Jewish letters." > > The finaldemise of Fraktur as the de facto font of the Third Reich was motivated notonly by Hitler’s warped sense of typographical beauty—if that had been enough,Fraktur would have been abolished earlier—but also by practical matters. Inthe German-occupied territories, people struggled to read Fraktur, havingnot been trained to do so during their schooling. Furthermore, stereotypes(type of printing plates developed in the late 18th century and widely used inletterpress, newspaper, and other high-speed press runs) supporting the fontfor the printing of Joseph Goebbels’ propaganda were few and far between inthese newly invaded countries. In its stead, Antiqua—a typeface much moreeasily discernible by the subjects of the extended Third Reich—would be used.> > archetypes > > The history of double-struck letters, too, is marred bypracticality, though in much less perverse ways. 1950s saw ample use of bothblackboard and typewriters, as well as the need to differentiate between concepts of fundamentally different natures (i.e., the set of all natural numbersand the number of steps in a particular procedure), of which the same letterwould naturally lend itself to use. Typewriters archived this by striking twice,and blackboard scribles by adding a strategic extra line to the given symbol.> > > mathbb{C} = {a + b i space|space a, b in mathbb{R}, i^2= −1} > >> > mathbb{A;B;C;D;E;F;G;H;I;J;K;L;M;N;O;P;Q;R;S;T;U;V;W;X;Y;Z} > > >Figure 2: The definition of the complex numbers (top) and the alphabet indouble-struck / blackboard bold letters (bottom) > > Like Computer Modern by ,Fraktur, and double-strike look flawless, like perfect typographical playthingsscattered across pristinely calculated pages—pages masterpieces in themselveswith their exquisite proportions that when you slice them vertically to createa square, leaves a rectangular sliver that maintains the exact proportions ofthe original page. Within this obsessively precise ratio lies one of mathematics’many transcendental numbers, the golden ratio, frequently denoted by 𝜑—yetanother immaculate symbol in typography’s vast arsenal of beauty. > > Rareexceptions to this pandemic of typographical mediocrity do exist, such as theelegant simplicity found in the Taliban’s flag, seen in all its glory in Figure2, where calligraphic mastery yet holds sway. > > ![](/public/figs/esch/esch/Flag_of_the_Taliban.svg) > > The official Afghan flag, as of the Taliban’s 2022takeover > > Numeracy is to the 21st century what litteracy has been to previouscenturies. How does one visuallize the array, the mathematical resepticle ofdata, and the atom of modern scientfic computing, inclduing that of artificalintelligence. Chizzled with light in stone like materials that now posses theintelligence it initially took to create them. Like a fire that has learned to lightit self (cormac mccarthy style please). In contrast to the archtycal beautfy ofFraktur, Computer Modern, double-strike, we present Esch, our attempt ofcreating a framework worthy of neighbouring the typgraphical masterpiecesso often defaced by matplotlib. In the following we will present its form, andafter that we will present its code. > > Esch (verb): To pretend to have M. C.Escher as an intern and have him make plots for your scientific programming,but really it is just a piece of software. > > 1. "This baffoon sure knows how toesch—paper accepted." > 2. "Thank God I can esch. Esch is all you need." > 3."This ‘researcher’ thinks to esch is enough to hide bad work. Not so. > 4. "Toesch or not to esch that is the question." > > In stark contrast, modern worksroutinely transgress against these sacred traditions. Scientific manuscripts,hurriedly assembled, defile their pages with crude figures hastily constructedin the depths of matplotlib—their authors, consumed by deadlines and data,seemingly oblivious to the typographical sins they commit. This degradationextends beyond academia: everyday pamphlets and posters assault our visualsensibilities with garish designs that would make any typographer weep. > > Atvirian we love colors, as can be seen throughout our website. Indeed, we cherish the color space so much, that colors should stand alone, uninterupted byother dimensions of vartiaion like form, and size. > > It is into this typgraphicalvoid that esch (v) brings 1) an immediate system, 2) a set of guiding principles,and 3) a few haphazard drafts and examples to get the ball rolling. > > ![](/public/figs/esch/temp.svg) Correct and fix this tonally (make it consistent),and fill out missing sections.In letters and natural philosophy, typographical masterpieces like Fraktur (seeFigure 1), ‘s Computer Modern, and the double-struck—also known as blackboard bold—letters (see Figure 2) are ubiquitous—the latter having become theuniversal language for denoting fundamental number sets like the reals bb{𝑅},the integers bb{𝑍}, and the complex numbers bb{𝐶}. These typographicalgems hail from a time when literacy reigned supreme, and indeed, literacy isstill a precondition for success in the modern world. However, just as the bit hasreplaced the atom in terms of wealth generation, so, arguably, has the numberreplaced the letter in terms of economic utility. Numeracy now supersedesliteracy in economic importance.Indeed, as it turns out, the mathematical concepts explored by Leibniz in theearly 18th century laid the groundwork for linear algebra, and these conceptswould, 300 years later, become the substrate on which we would breathe intelligence into our machines. And once again, the symbol would play a centralrole:Given large amounts of data and nothing else, artificial intelligence was born:a set of matrices.—StereotypesIn the case of Fraktur, ubiquity has at times been controversial. Etymologically,the word "Fraktur" comes from the Latin frāctūra ("a fracture"), built fromfrāctus ("to fracture"). The typeface has its origin in the 16th century. The HolyRoman Emperor Maximilian I commissioned Hieronymus Andreae to create anew typeface for Albrecht Dürer’s woodcut print Triumphal Arch. 195 separatewoodblocks were cut and used to imprint 36 large paper sheets for a finalcomposite measuring 295 × 357 centimeters, making it one of the largest andmost complex prints of that kind ever produced—a masterpiece befitting thecreation of a typeface:Figure 1: The alphabet in FrakturBy the 20th century, Fraktur had become the de facto German typeface.However, Adolf Hitler—otherwise well-versed in aesthetics—is known to havedisliked the font, publicly denouncing it in 1934 in a speech to the Reichstag:"Your alleged Gothic internalization does not fit well in this age of steel andiron, glass and concrete […]."On this particular matter, Hitler was so out of step with his compatriots thatit took almost a decade to abolish the script. In the intervening years, Romancharacters (which Fraktur is not) were derided as being under "Jewish influence," urging their replacement by Fraktur, the only "true German script."Therefore, even with the immense power afforded Hitler as Führer of Germany,it was not until 1941 that Martin Bormann, in a Schrifterlass (typeface decree),declared Fraktur to be not "Gothic" but rather Schwabacher "Jewish letters."The final demise of Fraktur as the de facto font of the Third Reich was motivatednot only by Hitler’s sense of typographical aesthetics—had that been enoughFraktur would have been abolished earlier—but also by practical matters. Inthe German-occupied territories, people struggled to read Fraktur, having notbeen trained to do so during their schooling. Furthermore, stereotypes (a typeof printing plate developed in the late 18th century and widely used in letterpress, newspaper, and other high-speed press runs) supporting the font for theprinting of Joseph Goebbels’s propaganda were scarce in these newly invadedcountries. In its stead, Antiqua—a typeface much more easily discernible by thesubjects of the extended Third Reich—was adopted.—ArchetypesThe history of double-struck letters, too, is shaped by practicality, though inmuch less contentious ways. The 1950s saw ample use of both blackboards andtypewriters, as well as the need to differentiate between concepts of fundamentally different natures—for instance, using the same letter to denote both a setof natural numbers and a variable in a procedure. Typewriters achieved thisdifferentiation by overstriking characters, while blackboard scribbles addeda strategic extra line to the given symbol, giving birth to blackboard boldnotation. mathbb{C} = {a + b i mid a, b in mathbb{R}, i^2= −1} mathbb{A;B;C;D;E;F;G;H;I;J;K;L;M;N;O;P;Q;R;S;T;U;V;W;X;Y;Z} Figure 2: The definition of the complex numbers (top) and the alphabet indouble-struck / blackboard bold letters (bottom)Like Computer Modern by , Fraktur, and double-struck letters, these fontslook flawless—perfect typographical playthings scattered across pristinely calculated pages. Pages that are masterpieces in themselves, with their exquisiteproportions, such that when you slice them vertically to create a square, theyleave a rectangular sliver maintaining the exact proportions of the originalpage. Within this obsessively precise ratio lies one of mathematics’ many transcendental numbers, the golden ratio, frequently denoted by 𝜑—yet anotherimmaculate symbol in typography’s vast arsenal of beauty.Rare exceptions to the pandemic of typographical mediocrity do exist, such asthe elegant simplicity found in the Taliban’s flag, seen in all its glory in Figure3, where calligraphic mastery still holds sway.![The official Afghan flag, as of the Taliban’s 2022 takeover](/public/figs/esch/esch/Flag_of_the_Taliban.svg)Figure 3: The official Afghan flag as of the Taliban’s 2022 takeover1."This buffoon sure knows how to esch—paper accepted."2."Thank God I can esch. Esch is all you need."3."This ‘researcher’ thinks to esch is enough to hide bad work. Not so."4."To esch or not to esch, that is the question."In stark contrast, modern works routinely transgress against these sacredtraditions. Scientific manuscripts, hurriedly assembled, defile their pages withcrude figures hastily constructed in the depths of matplotlib—their authors,consumed by deadlines and data, seemingly oblivious to the typographical sinsthey commit. This degradation extends beyond academia: everyday pamphletsand posters assault our visual sensibilities with garish designs that would makeany typographer weep.At Virian, we love colors, as can be seen throughout our website. Indeed, wecherish the color space so much that colors should stand alone, uninterruptedby other dimensions of variation like form and size.![An example of Esch-generated visuals](/public/figs/esch/temp.svg)Figure 4: An example of Esch-generated visualsREFERENCES[1]T. Anne et al., “Harnessing Language for Coordination: A Framework andBenchmark for LLM-Driven Multi-Agent Control,” IEEE Transactions onGames, pp. 1–25, 2025, doi: 10.1109/TG.2025.3564042.[2]T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed.Hoboken, N.J: Wiley-Interscience, 2006.[3]D. G. T. Barrett, F. Hill, A. Santoro, A. S. Morcos, and T. Lillicrap, “Measuring Abstract Reasoning in Neural Networks,” 2018.[4]A. McAfee, More from Less: The Surprising Story of How We Learnedto Prosper Using Fewer Resources–And What Happens Next. New York:Scribner, 2019.[5]C. E. Shannon, “A Mathematical Theory of Communication,” Bell SystemTechnical Journal, vol. 27, no. 3, pp. 379–423, 1948, doi: 10.1002/j.1538-7305.1948.tb01338.x.[6]M. N. Bin-Jumah et al., “Genes and Longevity of Lifespan,” InternationalJournal of Molecular Sciences, vol. 23, no. 3, p. 1499, Jan. 2022, doi:10.3390/ijms23031499.[7]D. Knuth, “Computer Modern.” 1992.[8]N. Prokopov, “Tonsky/FiraCode.” Dec. 2024.[9]?. Hirszowicz, The Third Reich and the Arab East, no. v.13. in RoutledgeLibrary Editions: History of the Middle East. Florence: Taylor and Francis,2016.