In our information-theoretic age, the bit has replaced the atom as the mostfundamental unit of wealth [1]. If any phenomenon befits the name GreatReplacement, it is this. The notion of information as an exact, measurablequantity was given to us by C. E. Shannon [2] with his seminal 1948 paperA Mathematical Theory of Communication. With it, he establishes informationtheory as a science, introducing three towering theorems on which our modernworld is (arguably) built: 1) The Data Compression Theorem, proving that fora given source that produces symbols from an alphabet 𝜉={𝑠0,𝑠1,…,𝑠𝑛−1}with probabilities {𝑝0,𝑝1,…,𝑝𝑛−1}, there exists an optimal coding scheme thatcan compress messages to an average length approaching the source entropy;2) The Channel Coding Theorem, proving that reliable communication overnoisy channels is possible, at the rate of mutual information between the twoendpoints; and 3) The Rate-Distortion Theorem, describing the minimum bit raterequired to achieve a given level of distortion when compressing beyond theentropy. Information theory, as such, is about the transmission of symbols. Thetransmission 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 failure ofthe body to transmit its own DNA undistorted forward in time to itself. Mortalityis an information-theoretic phenomenon with an information theoretic solution[3].Figure 1: The Alphabet in FrakturThe importance of the symbol is reflected in that has ubiquitously been drawnwith typographical masterpieces like Fraktur (seen in Figure 1), 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 [4]‘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 [5]. In the case of Fraktur,ubiquity has been controversial. Now it has been demoted to denote more exoticmathmatical concepts like Lie algebras 𝔤, prime ideals 𝔭, and maximal ideals 𝔪.But, Fraktur was the de facto font of the Third Reich, and Germanic territoriesat large before that. Etymologically, the word “Fraktur” comes from the Latinfrāctūra (“a fracture”), built from frāctus (“to fracture”). The typeface has its origin in the 16th century. The Holy Roman Emperor Maximilian I commissionedHieronymus Andreae to create a new typeface for Albrecht Dürer’s woodcutprint Triumphal Arch¹. 195 separate wood blocks were cut, and used to imprint36 large paper sheets for a final composite measuring 295 × 357 centimetres,making it one of the largest and most complex prints of that kind 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 known to have disliked the font,publicly denouncing it in a 1934 speech to the Reichstag: Your alleged Gothicinternalization 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. Yetit took almost a decade to abolish the script, with the intervening years seeingRoman characters (of which Fraktur is not) scolded as being under “Jewishinfluence”, urging their use to be replaced by Fraktur, the true “German script”.Even with the immense power afforded the Führer with his position as such,it took him almost a decade to abolish the font, when Matrin Bormann, in a1941 Schrifterlass declared Fraktur to not be “Gothic” but rather Schwabacher“Jewish letters” (controversy). The final demise of Fraktura as the font of theThird Riech was motivated not only by Hitler’s warped sense of typographicalbeauty—if that had been enough, it had like been abolished around the aforegiven 1934 quote—but also practical matters. In the German occupied terriotries,people stuggled to read Fraktur, having not been trained to do so during theirschooling. Further, stereotypes (type of printing plate developed in the late 18thcentury and widely used in letterpress, newspaper, and other high-speed pressruns) supporting the font for the pressing of Joseph Goebbels’ propaganda werefew and far between in these newly invaded countries. In its stead Antiqua, atype face much easilyer discernable 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 idea ofdenoting these by blackboard bold letters is ingenious—draw two diagonal lines,N→ℕ, and the studious mind readily understands that this symbol denotessomething more profound. Popularized in the 1960s during the typewriter era,this shorthand for conceptual difference was particularly apt for the page: strikethe 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, the neucliotides 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 prefix sub?Again, words is the enemy of clarity of thought (see /terminology). As an exampleof a subsymbolic deep learning see /miiii, the trained model therein implementsan algorithm similar to Eq. 1, the modular addition algorithm reverse engineeredby N. Nanda, L. Chan, T. Lieberum, J. Smith, and J. Steinhardt [6].𝑥0→sin(𝑤𝑥0),cos(𝑤𝑥0)𝑥1→sin(𝑤𝑥1),cos(𝑤𝑥1)(1)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 2. To quote Anders Søgaard, there is no directing mapping from Figure 2to the mathematical notation in Eq. 1.Figure 2: The embedding layer of the MIIII modelThe success of sub-symbolic AI, has only further increased the importance ofLiebniz’s array, the way in which data has most often be represented. Now,programs, too, are increasingly represented as such. And yet, the way in whicharrays are turned to ink is a an frequent abomination, compared to the care withwhich symbols are.Figure 3: Taliban's much improved Afghan flag¹https://www.metmuseum.org/art/collection/search/388475References[1]A. McAfee, More from Less: The Surprising Story of How We Learned toProsper Using Fewer Resources–And What Happens Next. New York: Scribner,2019.[2]C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948, doi: 10.1002/j.1538-7305.1948.tb01338.x.[3]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.[4]D. Knuth, “Computer Modern.” 1992.[5]T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed.Hoboken, N.J: Wiley-Interscience, 2006.[6]N. Nanda, L. Chan, T. Lieberum, J. Smith, and J. Steinhardt, “Progress Measures for Grokking via Mechanistic Interpretability,” no. arXiv:2301.05217.arXiv, Oct. 2023.