From boiling lead and black art: An essay on the history of mathematical typography

Math fonts from six different type systems, courtesy Chalkdust I’ve always felt like constructing printed math was much more of an art form than regular typesetting. Someone typesetting mathematics is less a “typist” and more an artist attempting to render abstract data on a two-dimensional surface. Mathematical symbols are themselves a language, but they are fundamentally a visual representation of human-conceived knowledge—knowledge that would be too inefficient to convey through verbal explanations. This brings the typesetting of mathematics closer to a form of data visualization than regular printed text. No matter how hard it’s ever been to create printed text, creating printed math has always been even harder. In pre-digital times, equation-laden texts were known as “penalty copy” because of the significant additional time and expense it took to set math notation for printing presses. Even when modern word processors like Microsoft Word include equation editors, they tend to be difficult to use and often produce unpleasing results. While LaTeX and similar variants produce the highest quality digital math type, these frameworks also have much more of a learning barrier than general word processing. But these modern quibbles are much more the fault of hedonic adaption than any of the tools available to us today. We have it vastly easier than any previous stage of civilization, and I think it’s critically important for those of us that write math to have at least a basic awareness of the history of mathematical typesetting. For me, knowing this history has had several practical benefits. It’s made me more grateful for the writing tools I have today—tools that I can use to simplify and improve the presentation of quantitative concepts to other actuaries. It’s also motivated me to continue to strive for elegance in the presentation of math—something I feel like my profession has largely neglected in the Microsoft Office era of the last twenty years. Most importantly, it’s reminded me just how much of an art the presentation of all language has always been. Because pre-Internet printing required so many steps, so many different people, so much physical craftsmanship, and so much waiting, there were more artistic layers between the author’s original thoughts and the final arrangement of letters and figures on pages. More thinking occurred throughout the entire process. To fully appreciate mathematical typography, we have to first appreciate the general history of typography, which is also a history of human civilization. No other art form has impacted our lives more than type. The first two Internets While the full history of printing dates back many more centuries, few would disagree that Johannes Gutenberg’s 15th-century printing press was the big bang moment for literacy. It was just as much of an Internet-like moment as the invention of the telegraph or the Internet itself. Before Gutenberg, reading was the realm of elites and scholars. After Gutenberg, book production exploded, and reading became exponentially more practical to the masses. Literacy rates soared. Reformations happened. The Gutenberg Printing Press I would argue that the invention of the printing press was on par with the evolutionary “invention” of human language itself. In The Origins of Political Order, Francis Fukuyama explains that spoken language catalyzed the separation of humans from lower forms of primates: The development of language not only permits the short-term coordination of action but also opens up the possibility of abstraction and theory, critical cognitive faculties that are unique to human beings. Words can refer to concrete objects as well as to abstract classes of objects (dogs, trees) and to abstractions that refer to invisible forces (Zeus, gravity). Language also permits practical survival advantages for families and social groups: By not stepping on the snake or eating the root that killed your cousin last week, you avoid being subject to the same fate, and you can quickly communicate that rule to your offspring. Oral communication became not only a survival skill, but a tool of incredible influence. Rhetoric and the art of persuasion were highly valued in Greek and Roman societies. If spoken language was the first human “Internet,” mass printing was the next key milestone in the democratization of human knowledge. Mass production of printed material amplified the human voice by incalculable orders of magnitude beyond oral communication. Like all inventors, Johannes Gutenberg didn’t really make anything new so much as he combined existing materials and technologies in new ways. Gutenberg didn’t invent printing. He didn’t invent the press. He didn’t even invent movable type, which typically involves arranging (typesetting) casts of individual letters that can be brushed or dipped in ink and pressed to a page. Metal movable type arranged by hand Gutenberg’s key innovation was really in the typecasting process. Before Gutenberg’s time, creating letters out of metal, wood, and even ceramic was extremely time consuming and difficult to do in large quantities. Gutenberg revolutionized hot metal typesetting by coming up with an alloy mostly made of lead that could be melted and poured into a letter mold called a matrix. He also had to invent an ink that would stick to lead. His lead alloy and matrix concepts are really the reasons the name Gutenberg became synonymous with printing. In fact, the lead mixture he devised was so effective, it continued to be used well into the 20th century, and most typecasting devices created after his time continued using a similar matrix case to mold type. From a workflow perspective, Gutenberg’s innovation was to separate typecasting from typesetting. With more pieces of type available, simply adding more people to the process allowed for more typesetting. With more typeset pages available, printing presses could generate more pages per hour. And more pages, of course, meant more books. But let’s not kid ourselves. Even post-Gutenberg, typesetting a single book was still an extremely tedious process. Gutenberg’s first masterpiece, the Gutenberg Bible (c. 1450s), was—and still is—considered a remarkable piece of art. It required nearly 300 pieces of individual type. Every upper and lower case instance of every letter and every symbol required its own piece of lead. Not only did each character have to be set individually by hand, justification required manual word spacing line by line. The Gutenberg Bible Even though Gutenberg’s innovations allowed books to be printed faster than ever before, it was an excruciating process by today’s one-click standard. But it was within those moments spent arranging characters and lines that the so called “black art” of book printing flourished. Typesetting even a basic text was an intimate, human process. A better way to cast hot lead The art of hand-setting type would be passed down from generation to generation for over 400 years until the Industrial Revolution began replacing human hands with machines in all aspects of life. The most famous of the late 19th century technologies to refine typesetting were Monotype and Linotype, both invented in America. The Monotype System was invented by American-born Tolbert Lanston, and Linotype was invented by German immigrant Ottmar Mergenthaler. Both men improved on the system Gutenberg devised centuries earlier, but each added their own take on the art of shaping hot lead into type. Because Linotype machines could produce entire fused lines of justified lead type at a time, they became extremely popular for most books, newspapers, and magazines. Just imagine the look on people’s faces when they were told they could stack entire lines of metal type rather than having to arrange each letter individually first! Four lines of Linotype, courtesy Deep Wood Press The Monotype System produced individual pieces of type. It could not produce the same lines per hour as Linotype, but it maintained the art and flexibility of setting individual pieces of type. Monotype also took a more mathematical approach to typesetting: In many ways the key innovation in the Monotype System was not the mechanical device, ingenious as it was. To allow the casting of fully justified lines of type, Tolbert Lanston chose not to follow the path of Ottmar Merganthaler, who used tapered spacebands to create word spacing. He instead devised a unit system that assigned each character a value, from five to eighteen, that corresponded to its width. A lower case “i”, or a period would be five units, an uppercase “W” would be eighteen. This allowed the development of the calculating mechanism in the keyboard, which is central to the sophistication of Monotype set matter. (Letterpress Commons) And so it was fitting that Monotype, while slower than Linotype, offered more sophistication and ended up a favorite for mathematical texts and publications containing non-standard characters and symbols. The Monotype System is an exquisite piece of engineering, and in many ways represents a perfection of Gutenberg’s original workflow using Industrial Age technology. It’s also a fantastic example of early “programming” since it made use of hole-punched paper tape to instruct the operations of a machine—an innovation that many people associate with the rise of computing in the mid-20th century, but was in use as early as 1725. Like Gutenberg, Lanston sought to refine the workflow of typesetting by dividing it into specialized sub-steps. The Monotype System consisted of two machines: a giant keyboard and type caster. The keyboard had distinct keys for different cases of letters, numbers, and common symbols. The keyboard operator’s job was essentially to type character-by-character and make decisions about where to end lines. Once a line was ended, the machine would calculate the word spacing required to justify the line and punch holes into the paper tape. The