Defining Digitalities I: What’s Digital about Digits? Thomas Haigh University of Wisconsin, Milwaukee & Siegen University WORKING PAPER SERIES | NO. 30 | JULY 2023 Collaborative Research Center 1187 Media of Cooperation Working Paper Series Collaborative Research Center 1187 Media of Cooperation Print-ISSN  2567–2509 Online-ISSN  2567–2517 DOI  doi.org/10.25819/ubsi/10259 dspace.ub.uni-siegen.de/handle/ubsi/2452 URN  urn:nbn:de:hbz:467-24526 This  work  is  licensed  under  the  Creative  Commons  Attribution-NonCommercial-No- Derivatives 4.0 International License. This Working Paper Series is edited by the Collaborative Re- search Center Media of Cooperation and serves as a platform  to circulate work in progress or preprints in order to encour- age the exchange of ideas. Please contact the authors if you  have any questions or comments. Copyright remains with the  authors. The Working Papers are accessible online at:  https://www.mediacoop.uni-siegen.de/de/publikationen/ working-papers-media-of-cooperation/ Print copies can be ordered by sending an email to:  workingpaperseries@sfb1187.uni-siegen.de Publication is funded by the Deutsche Forschungsgemein- schaft  (DFG,  German  Research  Foundation)  –  Project-ID  262513311 – SFB 1187. Cover  image:  Image  created by Wikimedia  user  Carsten Ull- rich, used under CC BY-SA 2.5 (https://creativecommons.org/ licenses/by-sa/2.5/) Layout: Mattis Hunting Universität Siegen SFB 1187 Medien der Kooperation Herrengarten 3 57072 Siegen, Germany https://www.mediacoop.uni-siegen.de.sfb1187.uni-siegen.de workingpaperseries@sfb1187.uni-siegen.de Defining Digitalities I: W hat’s Digital about Digits? T homas Haigh University of Wisconsin, Milwaukee & Siegen University Abstract: Modern discourses emphasizes electronic immateriality as the defining feature of digital technology. The idea that digits might be digital when punched onto cards, or even written on a piece of pa- per, is no longer intuitive. Yet by reconstructing the context in which the categories of digital and analog were first distinguished histori- cally in the 1940s, I argue that the concept of digitality is rooted in the mechanical representation of digits in early computers, which con- temporary observers immediately recognized was shared with earlier technologies such as telephone switching systems, punched cards, and calculating devices. Digitality is not a feature of an object itself, but of the way that object is read (whether by human or by machine) as encoding symbols chosen from a finite set. In conclusion, digitality is constituted through reading practices. Keywords: digital; analog; binary; differential analyzer; Bell Labs. I will argue in this working paper that the historical sequenced to represent quantities of any size or to any study of digitality should begin with careful attention degree of accuracy. to digits.1 Digits matter here in two ways. First, our cur- Digital was, in its original context, a quite literal rent discourse of the digital has its historical roots in term confined to machines that represented numbers the categories of digital and analog, which were defined rather than encompassing control systems based on in the 1940s to distinguish between two approaches to discrete encodings such as automatic looms or musical automatic computation. Digital computers were digital boxes. It was not, however, confined to electronic dig- because they carried out their mathematical operations its or immaterial devices. While the categories of digital by encoding and manipulating digits. Second, some and analog were created in response to the emergence of electronic computation they were immediately un- of the crucial affordances of today’s electronic digital derstood as applicable to earlier technologies going media have their roots in the characteristics that dig- all the way back to the abacus. The initial choice of the its exhibit whether manipulated by humans or by ma- term digital and its eventual resurgence as shorthand chines. Digits are discrete set of symbols that can be for our current technological epoch were both some- reliably transcribed from one medium to another and what arbitrary. Yet taking the continuity seriously can be illuminating. The essential affordances of modern digital technologies are built on top of core affordances of digitality shared not just with earlier kinds of digital 1  By this I mean numerical digits, though others have argued machines but with digits themselves. for tracing the idea of digitality back through another layer of metaphor to explore correspondences between the capabilities The literal digitality of machines that represent of digital systems and human fingers. Benjamin Peters, “Digi- digits is distinct from a broader and later sense of digi- tal”, in Digital Keywords: A Vocabulary of Information Society tality as the encoding of sequences of symbols. Digits & Culture, ed. Benjamin Peters (Princeton, NJ: Princeton Uni- versity Press, 2016):93-108. are a subset of the alphanumeric characters manipu- 4    CRC Media of Cooperation Working Paper Series No. 30 JULY 2023 lated automatically by computers from the 1950s on- analogy, of the system being investigated. Kline sug- wards, and those symbols were used in turn to repre- gests that this term slightly predated digital in this con- sent other things such as audio, video, and pictures. text, having been used since the 1930s. Vannevar Bush When the concept of digitality was stretched to include at MIT had investigated the behavior of power grids by these non-numerical capabilities it was originally a building in the laboratory what were essentially scale kind of metaphor, though with time the metaphor has models – each small wire and current proportional to been naturalized to the extent that the connection of digitality and digit is now easy to overlook. the much heavier wires and larger currents of the real power network. He followed this up with something more flexible and more abstract: the differential ana- lyzer. Each of its six spinning disks represented one Historical Origins of Digital and Analog term in a differential equation. The disks were mounted on shafts, which span While digitality has recently been equated with imma- more rapidly as quantities they represented increased. teriality, the antonym of digital is not physical but ana- The wheels sat vertically on top of the disks. Like the log. As Ronald Kline has explained in his careful and ex- stylus of a record player they could be moved closer or haustively researched paper on the topic, the terms were further from the middle of the disk. The closer they got introduced during the second world war as automatic to the outer edge of a disk they more rapidly they ro- computer projects began to proliferate.2 Kline’s earliest tated. Motion of a wheel was mechanically amplified to identified use of the words to distinguish between two control the motion of the next disk. Adjustments, in- classes of computer occurred in 1942, in a document by cluding the positioning of wheels and the use of gears George Stibitz of AT&T’s Bell Labs. During the war he to add together the motion of two shafts, changed the worked with the National Defense Research Committee, relationships between the six terms.4 a group chartered to bring scientific expertise to assist Specific parts of the integrator were thus analo- in the nation’s struggle. Stibitz introduced the juxta- gous to specific parts of the system being modelled. position of analog and digital in a memo commenting The integrator as a whole became an embodiment of on a set of proposals for the design of a computer able the mathematical equation, an analogy with the entire to direct anti-aircraft guns. That was a mathematical system being modelled. Allegory might have been a bet- problem: the gun had to fire not at the plane’s current ter word than analogy for this complex correspondence. position but at the place it would be when the shell’s arc In an allegory, such as George Orwell’s Animal Farm or intersected with its own future course. This required the a biblical parable, each part of the story corresponds rapid solution of differential equations.3 with something specific in the larger world. The rela- Stibitz is best remembered as the creator, between tionships between the different objects in the story are 1937 and 1946, of a series of computers that used elec- the same as those between the analogous features of the tromechanical relays to represent numbers. These world. If the rotation of one disk in the differential ana- took the approach he designated as digital. Their relays lyzer represents the height of a shell, another its veloc- switched automatically between two possible positions. ity, and a third its acceleration then the relationships A cluster of relays represented a number using the bi- between those disks should, when the device is prop- nary number system. Addition, multiplication, and erly adjusted, be very close to the relationships of those other mathematical operations took place automati- real-world quantities. There were no digits involved cally as electrical impulses moved through wires but –operators controlled the speed of one or more of the the arithmetic involved followed the same basic rules disks by tracing input curves using devices coupled to that a school child might have carried out using a pencil the motion of wheels. At the far end of the machine, a and paper (adjusted, of course, for the differences be- mechanical arm sketched the shape of the result. Differ- tween binary and decimal – add 1 to 1 to get 0 carry 1, ential analyzes were the most advanced automatic com- rather than add 1 to 9 to get 0 carry 1). The machines puters of the 1930s. Comparable principles were used in were digital because their mechanisms encoded digits the gun director design chosen for the NRDC project, and and manipulated them to reach their solutions. had already been applied for comparable systems used The other class of machines were called analog for fire control on naval vessels. because their internal structure provided a model, or Analog computers were sold and developed into the 1970s. They used a range of media to represent changes in the quantities being computer. In some fluid dripped 2  Ronald R Kline, “Inventing an Analog Past and a Digital between tanks, in others variations in electrical cur- Future”, in Exploring the Early Digital, ed. Thomas Haigh (Cham, Switzerland: Springer, 2019):19-39. 3  David A Mindell, Between Human and Machine: Feedback, 4  Larry Owens, “Vannevar Bush and the Differential Analyzer: Control, and Computing Before Cybernetics (Baltimore: Johns The Text and Context of an Early Computer,” Technology and Hopkins University Press, 2002), ch. 9 & 11 provides an account Culture 27, no. 1 (January 1986):63-95. Vannevar Bush, “The of the NRDC’s work in this area that foregrounds the role of Differential Analyzer. A New Machine for Solving Differential Stibbitz and Shannon and follows the legacy of this project into Equations,” Journal of the Franklin Institute 212, no. 4 (October Stibbiz’s general purpose relay computing projects. 1931):447-488. Thomas Haigh  5 Figure 1: Bush’s paper describing the differential analyzer used this schematic notation to describe the relationship between each of the six shafts and the corresponding term in a mathematic equation describing the motion of a falling body. The diagram also speci- fies the relationships between shafts, implemented mechanically with devices such as integrators and gear boxes.5 rent replaced the changes of rotational speed used in of Pennsylvania’s 1946 summer school for people in- the differential analyzer. But the many kinds of analog terested in building electronic computers5.6 computer shared two crucial features. Firstly, as with By the end of the 1940s, however, the language of the differential analyzer each quantity used in the com- digital vs. analog was generally accepted by those dis- putation was represented by a different part of the ma- cussing automatic computers. Consistent use of digital chine, and the relationships between these components by John von Neumann in his 1945 First Draft of a Re- were proportional (i.e. analogous) to those between the port on the EDVAC, the first description of the archi- things being computed. Second, variations were con- tecture of modern computers, must have helped.7 The tinuous. In practice there were limits to precision. An concept of digitality was also applied, retroactively, operator might not trace a curve perfectly, for example. to older computing devices. A 1949 article in Scient But in theory any variation, however slight, in the input ific American on “Mathematical Machines” surveyed should lead to a corresponding variation in the output. the latest digital computers like ENIAC and IBM’s SSEC, As Kline showed, while the need to distinguish be- tween these two fundamentally different approaches to 5  Bush, “The Differential Analyzer. A New Machine for Solving computing was widely accepted during the mid-1940s Differential Equations”, p. 457. the specific pairing of analog vs. digital was only one 6  George Stibitz, “Introduction to the Course on Electronic of many used to accomplish this – even among scien- Digital Computers”, in The Moore School Lectures: Theory and Techniques for Design of Electronic Digital Computers, ed. tists connected to the NRDC. One pairing was between Martin Campbell-Kelly and Michael R Williams (Cambridge, computers that measured and those that counted. Digi- MA: MIT Press, 1985):3-16. As Ron Kline has observed, the tal systems were sometimes called pulse or impulse word “digital” occurs only in the title of the lecture, but not in its actual text. Kline, “Inventing an Analog Past and a Digital computers, because many of them encoded numbers Future”. Given that the lecture was titled after the course as a as electrical pulses. Others, drawing on mathematical whole, to serve as an introduction, it seems likely that it re- flected the preferred terminology of organizers of the course categories, described them as continuous-variable (or (primarily Carl C. Chambers of the Moore School) rather than simply continuous) and discrete-variable (or simply dis- of Stibitz himself who was a last-minute substitute for the crete) machines. Stibitz himself used these alternative speaker originally scheduled to give the lecture. forms when giving a lecture at as part of the University 7  John von Neumann, “First Draft of a Report on the EDVAC,” IEEE Annals of the History of Computing 15, no. 4 (October 1993):27-75. 6    CRC Media of Cooperation Working Paper Series No. 30 JULY 2023 Figure 2: The output table, on which a pencil moved by the differential analyzer would draw a curve representing the solution to the problem traced on the input table.8 but went much further back in history. “The first arti- is the human hand, from which, of course, we have our ficial digital computing device,” claimed science writer decimal system. Corresponding to such primitive indica- Harry M. Davis, “was the abacus, a manually operated tors of a numerical unit as a finger, a pebble, or a stylus mechanical memory of great antiquity.” IBM punched scratch, the new automatic computers represent digits by cards, mechanical adding machines, teletypes, tape- such methods as: A round hole in a strip of tape. A square controlled relay computers, and Charles Babbage’s hole in a piece of cardboard. A current in an electromag- unfinished difference engine were also invoked as ex- net. An armature attached to the magnet. A closed pair amples of digital technology.98 While the presence of of electrical contacts. A pulse of current in an electrical teletypes on the list suggests that Davis was already transmission line. An electronic tube in which current is inching towards a concept of digitality that included permitted to flow from filament to plate. A magnetized encodings of text as well as numbers, the other ex- area on a steel or alloyed wire. A magnetized area on a amples were all literally digital in the sense that they coated tape. A darkened area on a strip of photographic encoded and manipulated numerical digits. film. A charged area on the face of a cathode-ray tube. A Davis understood that these numbers could be rep- moving ripple in a tank of mercury. resented in many different media, some easily readable by humans (indeed, joined to the human body) and oth- Although digital and binary are today often conflated, ers invisible to our unaided senses. He explained “The Davis was well aware of that decimal is no less digital Digital Idea” as follows: than binary. Both are number systems that use digits, and both can be encoded in many different media, in- The digital computer is distinguished by the fact that it cluding digital electronics. Witness his advocacy for does not measure: it counts. It never responds to a greater the abacus as the original digital computer, and his ex- or lesser degree; at every stage of its action, it is an ‘all or tensive comparison of the use of decimal, binary coded nothing’ device operating with discrete signals that ei- decimal, and pure decimal number systems for elec- ther exist or do not exist. The simplest digital computer tronic computers. 8  Ibid., p. 454. 9  Harry M Davis, “Mathematical Machines,” Scientific American 180, no. 4 (April 1949):28-39. Thomas Haigh  7 Figure 3: An example punched card in the early 24 column format, taken from an 1895 issue of the Railway Gazette. Most of the fields represent two- and three-digit decimal numbers, in a format that could be tallied automatically by tabulating machines. The non- numeric fields were used to sort and filter the cards. Printed labels on the card aided human legibility. Source: Wikimedia. Digitality as a Reading Practice cause there are only ten possible values for each digit and the symbols were chosen to be easily distinguished In the beginning, then, what made digital computers from each other. They can be misread – for example digital was their representation of quantities as digits a badly formed 9 might be mistaken for a 0. But we and their manipulation of these digits by mechaniz- cannot change their value by making them bigger or ing the ordinary processes of arithmetic. They did their smaller as we might do in an analog system of repre- mathematics in the same ways learned by school chil- sentation. (This observation may strike you as trite, but dren. Within each digital computer were mechanisms consider the humble bar chart, in which larger quanti- to encode digits. I term this sense of digital numerical ties are represented by drawing proportionally longer digitality in the sense of numerical mathematics, which bars. Or infographics, in which dollar signs of different relies on the manipulation of digits to provide approxi- sizes might be used to represent amounts of money. mate solutions to equations. Analog representations of that kind are good for vi- Matter itself is neither digital nor analog. What is sualizing quantitative data, but bad for recording it). digital or analog is not an object itself, but the way in Neither can we represent a number part way between which an object is read. Digitality is active: the practice of 1 and 2 by writing down a symbol that looks a bit like examining a part, usually a very small part, of the world a 1 and a bit like a 2. If presented with a squiggle that and classifying it as falling into one of a finite number doesn’t clearly map to a valid representation of any of of valid states. Digitality is enacted by reading practices. the ten digits we would either guess which it was meant As we shall see in the next paper in this series, not all of to represent based on context or reject it as unreadable. the processes now viewed as digital involve actual dig- These characteristics underly the discreteness of digital its. But the process of digital reading takes place literally representations: each digit is constrained to one of ten if we attempt to read a telephone number written on a possible values with no valid intermediate states. piece of paper, or peer myopically at a credit card trying Machines read digitally with sensor mechanism that to type the number it contains into a web browser. These controls part of the action of the machine. On this level number are inarguably and literally digital: strings of there is no distinction between reading programs and digits. Most of the numbers we deal with are written us- data. That is true whether the mechanism in question ing Arabic numerals, which means that they are written directs a loom, increments an accumulator, or trans- out using the digits 0 to 9. mits an encoding of the information just read, thus These are the digits that gave rise to the broader transcribing it from one digital format to another. Some category of digitality. Reading them is made easier be- part of the machine must change from one state to an- 8    CRC Media of Cooperation Working Paper Series No. 30 JULY 2023 Figure 4: A detail from the mechanical difference engine constructed by the London Science Museum according to the design of Charles Babbage. The position of each wheel encoded a single decimal digit; each column encoded a full number. A full rotation of a wheel caused the wheel above it to advance by one place, carrying 1 to the next digit as it reset to zero. Linkages from between wheels allowed the machine to add together the contents of adjacent columns. Humans read the numbers by looking at the markings on the wheels. The leftmost column was connected to a printing mechanism, able to read and transcribe its value once the computation was complete. Image created by Wikimedia user Carsten Ullrich, used under CC BY-SA 2.5 (https://creativecommons.org/licenses/ by-sa/2.5/). other according to the value being read. That part might total the values stored in specific fields from cards that be a circuit that fills with current if a hole is punched met certain criteria. IBM machines produced from 1928 in a certain position on a card, a hammer that strikes a onwards standardized on a larger, 80 column card. string in a player piano when a hole is sensed on a roll Numbers on punched cards could be read by hu- of paper, or a sensor that changes its resistance in re- mans and by machines, though with different prac- sponse to the momentary light fluctuations on a fiber tices. Humans used complicated neural mechanisms optic cable. to interpret light reflected from the cards. Tabulating Here (in figure 3) is an example of a digital repre- machines probed the card with electrical connectors, sentation intended to be readable by both humans and using the values encoded in particular columns to sort machines. Punched cards holding numbers were intro- cards into one pile or another or to increment coun- duced for the 1890 census. The original cards had 45 col- ters. umns and twelve rows. The card could be conceptualized Although Harry Davis insisted that digital reading as containing a single 45-digit decimal number, though involve signals with just two states, existing and not ex- in practice cards usually encoded several distinct data isting, this is not always the case. Many digital systems, fields of a few digits each. Space on the card could be par- for example, distinguish between ten different states titioned to code different data fields. Within each field, representing the ten decimal digits. Sometimes, as with only one hole was punched – akin to a person repre- the punched cards (or with counting on one’s fingers) senting a digit by folding one of ten digits of their hands. ten different values of a decimal digit are represented Tabulating machines were configured accordingly, to with ten different objects, each of which has one of Thomas Haigh  9 two possible states, such as punched or not punched. of digits, each of which was restricted to a predetermined In other cases, there may be one object with ten valid set of possible values (0-9 for decimal, 1 and 0 for bi- states or positions – as with digits written on a piece nary, and so on). It might seem odd to focus here on the of paper. representation of numbers using a finite set of encoded Mechanical adding machines and calculators all symbols as the original hallmark of digitality. As children had to use some mechanism to represent digits. Most learn in school the set of integers is infinite because any did it with cog wheels of one kind or another, rotat- number, however large, can be incremented. We should ing through ten different positions, as seen in figure 4. distinguish here between numbers and digits. Each digit When a wheel advanced from 9 back to 0 it would push has only ten possible values. But two decimal digits to- the wheel next to it to advance by one position, per- gether have one hundred possible values, three have a forming a carry to the next digit place. Rather than be- thousand, and so on to infinity. We can always add more ing an “all or nothing” signal, the wheel had ten stable digits to the sequence. By introducing a decimal point, positions. sequences of digits can be made to approximate fractions to a finite but arbitrary level of accuracy. Analog to Digital Conversion Digits have such a good fit with processes of tally- ing that the difference between analog and digital was sometimes expressed as the difference between mea- suring and counting.10 If we are attempting to count the number of times the word “digital” appears in this text, or the number of marbles in a jar, the result will be a whole number (technically, a positive integer) which can be expressed in digital form with no loss of preci- sion. In mathematical terms, the thing being counted is itself discrete. The digital representation can capture the quantity perfectly. Sometimes we must assign digits to approximately represent the value of something continuous. Imagine we are using a ruler to measure the length of an object, Figure 5: This digital thermometer automates the process of or a traditional thermometer to measure a temperature. digital reading traditionally carried out by a human peering The thermometer itself is analog: as its temperature rises at the gradations marked along the side of a tube containing and falls the fluid within expands and contracts propor- mercury or alcohol. Image created by Wikimedia user Hedwig tionally. To read a thermometer we turn that continuous Storch, used under license CC BY-SA 3.0 (https://creativecom- variation into a number. In both cases we visually com- mons.org/licenses/by-sa/3.0/). pare the length of something continuous to a measuring scale marked out with gradations. We pick the closest marking and record a length as 87mm, an angle as 27 Reading vs. Writing degrees, or a temperature as 39.5 degrees. In doing this we map the analog reality of continuous variance onto Why do I call digitality a way of reading, rather than way whichever number seemed closest. If we have access to of writing? Surely the digits extracted from a mecha- a better instrument, or a magnifying glass, we might be nism, or read from a scrap of paper, had to be written able to specify the result to a higher degree of precision, before they were read. Thus, you might suggest, it is adding digits after the decimal point. But any analog the act of writing a message encoded in a finite set of system has inherent physical limits to its precision. possible symbols, or perhaps the conjunction of writing The processes described above are known as analog and reading, that define digitality. to digital conversions, a task usually undertaken by elec- Yet the digits produced by the process of digital tronic systems that translate continuous variation on an reading were not always encoded by a sender. In fact, input circuit to output pulses that encode digits. Analog many digital reading practices capture information to digital conversion is the process of turning a measure- from nature. Consider, for example, a digital ther- ment into a number. mometer –a widely used modern device that is literally Digital systems approximated the continuous vari- digital in the sense proposed by Stibitz back in 1943. ability of the natural world by encoding a finite sequence It automates the measuring process required to use a conventional thermometer. The thermometer mea- sures the ambient temperature, i.e. the thermal energy 10  In the mid-1940s Norbert Wiener, the founder of cybernetics, preferred the terminology of measurement device/counting de- of molecules in the environment, and outputs a set of vice to analog/digital. digits. This is a form of digital reading. The digital en- 10    CRC Media of Cooperation Working Paper Series No. 30 JULY 2023 coding used is determined by the machinery, but the Representing Numbers with Switches content of message comes from nature. The same is true, on a vastly greater scale, of images As Harry Davis recognized in his 1949 article popular- produced by digital cameras. Each of the many millions izing the concept of digitality, the new idea described of pixels in the sensor array is measuring the intensity many earlier technologies but had been introduced to and color of the light falling on it and converting this to held categorize a proliferation of new ways of encod- a numerical value. ing numbers using electronic and electromechanical One might attempt to distinguish between digital methods. The engineering techniques used to build sensors of this kind, each measuring a single value, and electronic digital computers have several historical ori- the act of reading which involves looking at a sequence gin points. One is in electronic circuits used to tally, a of coded symbols. But sampling values from a sensor technique pioneered in the 1920s and 1930s by physicist at regular intervals, as the analog to digital converters Charles E. Wynn-Williams for use in nuclear physics in- used in digital audio recorders do, will produce a time strumentation. sequence of values. Another origin point, and the one I shall focus on Nature includes at least one example of a more here, is in switching. Automatic telephone exchanges, complex digital code with no human author. Historians introduced for local calls in the early twentieth century, of science have written about the use of information received decimal digits as sequences of pulses gener- theory by researchers investigating DNA in the 1950s. ated as telephone dials rotated themselves back to their The very phrase “genetic code” makes assumptions resting positions. The exchange equipment read these tied to information theory and digital communica- pulses digitally, tallying them by advancing its switch- tion. Attempts were made, without much success, to ing equipment to its next position each time a pulse was use analysis of this kind to make predictions about how received. The next digit dialed on the handset, repre- genetic information was stored and, once the role of sented as another sequence of pulses, controlled the DNA was clear, how base sequences coded for particular next switch. amino acids. US telephone numbers used three digits to code Suddenly chemical sequences without a human au- which exchange within a city the call should be directed, thor were being treated as a medium, holding a digital and thus told the local exchange of the caller which ca- message. The title of Lilly Kay’s book Who Wrote the Book ble to switch the connection onto. Once this connection of Life captures her objection to this: researchers viewed was made, the last four digits set the switches in the themselves as reading a text but were in fact construct- destination exchange to complete the electric connec- ing one, bring ideas from information theory that hin- tion from the caller’s telephone line to the telephone dered more than they helped.11 Her point is an interesting line whose number had been dialed.12 Automatic dialing one, but subsequent developments in gene sequencing of calls between cities, which added an additional three and manipulation suggest that the digital information optional digits for long distance connections, automat- perspective on the genome eventually became a source ically took a few decades more to become widely estab- of leverage. The six billion nucleotides contained in a lished because of the complexity of the task. Switching genome can be read and transcribed into a data file that equipment was bulky. AT&T spread local exchanges fits comfortably inside a modern smartphone. While the throughout the neighborhoods served, and built central connection between that data and human life is not fully exchanges for major cities in large, windowless build- understood, it can nevertheless be searched for informa- ings. tional markers signaling traits and disease tendencies. The relay, a switch that turned on and off under Thus digitality always involves a practice of reading electrical control, was invented for telegraphy. Hence that maps a continuous range of possible states in the the name: relays were first used to boost and repeat physical world, such as the almost infinite range of ac- signals on long distance lines. But they could also be tual temperatures, onto one of a finite number of possi- used to switch telephone calls. In 1937, Claude Shan- ble states. In some cases, such as reading numbers from non was part way through a master’s degree in engi- a punched card, the effect of this process is intended to neering at MIT when he was hired for a summer in- be the recovery of information deliberately written to ternship by Bell Labs. His exposure to its network of the medium. But in other cases, such as a digital ther- switching circuits, the most complex in the world, mometer or digital audio recording, the information provided him with the subject for his thesis. Shan- captured by the digital reading practice was not delib- non had already experienced analog computing, as an erately encoded by an author. 12  The same system had been used with human operators, with the destination exchange specified by name and only the last four digits given numerically. To help in switching between the two methods, which coexisted for decades, letters were printed on the dial and exchange numbers were chosen to cor- 11  Lily E Kay, Who Wrote the Book of Life: A History of the respond with the names of the exchanges to make them easier Genetic Code (Stanford: Stanford University Press, 2000). to remember. Thomas Haigh  11 operator of a differential analyzer, but he conceptual- a high or low voltage, to allow other circuits to read its ized the switching circuits he encountered at Bell Labs content. The information stored in it will persist un- in terms of logic rather than numbers. In switching til a pulse is received on its reset line, which primes it circuits, wires either carried electrical pulses or they to store the value provided at that instant on its input didn’t. Relays opened or closed. It would be five years line. Early digital electronics used two vacuum tubes until Stibitz, also of Bell Labs, would introduce the to produce a flip-flop; later systems used two transis- terminology of digital and analog. Shannon drew not tors. Each flip-flop was the equivalent of a single relay on numerical mathematics but on mathematical logic, switch. specifically Boolean algebra. He equated switches that In a sense, analog to digital conversion occurs all were turned on with logical statements that were true, the time inside digital computers. Within computers and switches that were turned off with logical state- and other digital electronic devices, most digital read- ments that were false. The circuits used to intercon- ing maps sensor data onto a set of just two valid states, nect those switches corresponded to the basic logical typically corresponding to the binary digits 1 and 0 or to operators: AND, NOT, and OR. Shannon argued that true and false. Consider, for example, computer elec- switching circuits could be converted into logical ex- tronics. When data is being moved around insider a pressions. Once expressed algebraically the circuits computer, voltage levels on a given data or address line could be manipulated to transform them into the sim- rise and fall millions of times every second. We talk of plest possible representations, which could in turn be computers being stuffed with 1s and 0s, but those states mapped back onto circuit diagrams, ensuring that the are actually represented by high and low voltages. Tra- simplest and most efficient designs would be used. The ditionally a 5-volt power supply is used. Ideally the vocabulary later used to talk about digital electron- power supply would give a constant output of exactly ics: digital logic, logic gates, truth tables, and so on is 5 volts, and logic gates would switch instantly from 5 rooted in this equivalence of digital circuits and logi- volts to 0 volts. In practice though, power supplies fluc- cal propositions. Shannon also equated true with 1 and tuate and give only approximate voltages and compo- zero with false, providing numerical interpretations of nents do not switch instantly or conduct perfectly. So the switches which he showed, in one of his examples, the manufacturer of a chip might guarantee that it will could be used to create a binary adder.13 treat inputs between 5 volts and 2 volts as high, and all Shannon’s thesis has been called the most conse- inputs of between 0.8 volts and 0 volts. This is called quential master’s degree thesis in history, though his- thresholding. The continuous variation of the actual torians have argued against the assumption that this voltage compressed into just two valid states. one document can explain a revolution in engineering Because electronic systems so often rely on read- practice. For one thing, Shannon was not the first or ing methods with only two valid values it is common only person attempting to combine logic and circuit de- to conflate digital and binary. This is not true, even for sign. For another, his method took considerable refine- electronics. One could, for example, use voltages from ment over many years before it was used for practical 0V to 9V to encode the digits 0 to 9, rounding off to the purposes by ordinary engineers.14 nearest volt. A value of 2.2V would be rounded to 2, of Relay switches of the kind used in some 1930s tele- 4.9V to 5, and so on. But the circuitry required to do this phone exchanges and many early digital computers rely would be far more complex, and far more likely to be on a metal strip to move physically from one position to read incorrectly. In practice, digital electronic comput- another, and thus could switch at most a few hundred ers have relied almost entirely on two-value encodings, times a second. That was more than enough to keep up whether or not they use binary arithmetic. Even com- with the speed of a telephone dial, but it put a severe puters built using ternary (base 3) rather than binary cap on the maximum speed of a digital computer. The logic and arithmetic still relied on two-value hardware Harvard Mark 1 computer, built by IBM and installed in in their memory units and logic circuits. This meant 1944, took three seconds to carry out a multiplication. that each trit (ternary digit) was encoded inefficiently Electronic circuits could switch much faster than as two bits.15 relays. One of the crucial building blocks of digital elec- Each flip-flop stored a single bit, but the circuits tronics is the flip-flop circuit, also known as the latch. were joined together to store larger numbers. For ex- This is the electronic equivalent to a relay switch. The ample, eight flip flops could store an 8-bit binary num- circuit has two stable states, meaning that it stores a ber, which since the 1960s has been known as a byte. single bit of information. Its output line carries either This simplifies the design of computer logic – binary adding and multiplying circuits are trivial in compari- son to their decimal equivalents, though using binary 13  Jimmy Soni and Rob Goodman, A Mind at Play: How Claude Shannon Invented the Information Age (New York, NY: Simon & Schuster, 2017)@ch. 4. 14  Maarten Bullynck, “Switching the Engineer’s Mindset to Boolean: Applying Shannon’s Algebra to Control Circuits and Digital Computing (1938-1958)”, in Exploring the Early Digital, 15  Francis Hunger, SETUN: An Inquiry into the Soviet Tenary ed. Thomas Haigh (Cham, Switzerland: Springer, 2019):87-99. Computer (Leipzig, Germany: Institut für Buchkunst Leipzig). 12    CRC Media of Cooperation Working Paper Series No. 30 JULY 2023 does create extra work to convert output into decimal Conclusion form for the benefit of humans. But the same bimodal circuits and switches could The modern discourse of digitality has departed quite also be used to represent decimal numbers. ENIAC, the dramatically from a direct connection with the literal first programmable electronic computer, was entirely representation of digits. Some so-called digital formats, decimal.16 It grouped together ten flip-flops to repre- such as those for audio and video, do involve the con- sent a single decimal digit, in an assembly known as a version of analog inputs to encoded numbers but this is “ring counter.” Only one of the ten flip-flops was ac- rarely what people have in mind when they talk about tive at a time. Each input pulse to the counter advanced the digital or about digital cultures. its position by one, for example from 3 to 4. This de- In fact, the concept of digitization, while literally sign was conceptually straight forward – the electronic extremely appropriate, has rarely been invoked by peo- equivalent of a cog with ten possible positions or a card ple discussing processes of quantification as used, for punched in one of ten holes. But using hardware capa- example, by governments to describe their populations. ble of storing ten bits to store just one decimal digit was Neither would a digital historian be liable to risk confu- inefficient. Other early computers that used decimal, sion with a quantitative historian (particularly as the lat- rather than binary, arithmetic packed their digits more ter are virtually extinct, while the former have recently effectively, storing each decimal digit in just four bits proliferated). by coding digits with combinations of active flip-flops. Yet it is important to emphasize the early and en- As Davis noted in his 1949 article, this method was far during connection of digitality with digits. Digits are more efficient, allowing IBM’s SSEC to represent each digital, whether counted on figures, written on paper, decimal number using less than half the number of encoded on a punch card or represented by minute elec- tubes requirement by ENIAC. IBM continued to use dec- trical fluctuations. By the 1950s, however, the concept imal number representations in its computers intended of digitality was broadening to include systems of rep- for business use well into the 1960s, and its competitors resentation based on sequences of symbols of any kind, Univac and Burroughs also released decimal machines. not just on encoded digits. As I will explore in two fur- ther working papers, coauthored with Sebastian Gieß- mann, this reflected both the evolution of computer technology toward non-numerical applications and the conceptual influence of Claude Shannon’s mathemati- cal treatment of communication. 16  Or at least ENIAC used only the decimal number system and made no use of the binary number system. One can distinguish here between two senses of the word binary. The most general is to describe a choice with only two valid values. For example, the traditional but now disparaged idea of gender. The most common is to describe the base 2 numbering system. Almost all digital electronic logic is binary in the former sense because it is based around components that signal to each other using two valid states. Those signals may or may not represent numbers coded in binary. In talking about digital computers, however, the conventional way of classifying them is according to the numbers coded by these dyadic pulses. Some computers per- formed their arithmetic on decimal numbers, some on octal numbers, some on binary numbers, and some on hexadecimal numbers. Thomas Haigh  13 References Bullynck, Maarten. “Switching the Engineer’s Mindset to Bool- ean: Applying Shannon’s Algebra to Control Circuits and Digital Computing (1938-1958).” In Exploring the Early Digital, edited by Thomas Haigh, 87-99. Cham, Switzerland: Springer, 2019. Bush, Vannevar. “The Differential Analyzer. A New Machine for Solving Differential Equations.” Journal of the Franklin Institute 212, no. 4 (October 1931): 447-488. Davis, Harry M. “Mathematical Machines.” Scientific American 180, no. 4 (April 1949): 28-39. Hunger, Francis. SETUN: An Inquiry into the Soviet Tenary Computer. Leipzig, Germany: Institut für Buchkunst Leipzig. Kay, Lily E. Who Wrote the Book of Life: A History of the Genetic Code. Stanford: Stanford University Press, 2000. Kline, Ronald R. “Inventing an Analog Past and a Digital Future.” In Exploring the Early Digital, edited by Thomas Haigh, 19-39. Cham, Switzerland: Springer, 2019. Mindell, David A. Between Human and Machine: Feedback, Control, and Computing Before Cybernetics. Baltimore: Johns Hopkins Univer- sity Press, 2002. Owens, Larry. “Vannevar Bush and the Differential Analyzer: The Text and Context of an Early Computer.” Technology and Culture 27, no. 1 (January 1986): 63-95. Peters, Benjamin. “Digital.” In Digital Keywords: A Vocabulary of In- formation Society & Culture, edited by Benjamin Peters, 93-108. Princeton, NJ: Princeton University Press, 2016. Soni, Jimmy, and Rob Goodman. A Mind at Play: How Claude Shan- non Invented the Information Age. New York, NY: Simon & Schuster, 2017. Stibitz, George. “Introduction to the Course on Electronic Digital Computers.” In The Moore School Lectures: Theory and Techniques for Design of Electronic Digital Computers, edited by Martin Camp- bell-Kelly and Michael R Williams, 3-16. Cambridge, MA: MIT Press, 1985. von Neumann, John. “First Draft of a Report on the EDVAC.” IEEE Annals of the History of Computing 15, no. 4 (October 1993): 27-75. 14    CRC Media of Cooperation Working Paper Series No. 30 JULY 2023 Author Thomas Haigh is a Professor of History and Computer Science at the University of Wisconsin—Milwaukee and visiting Comenius Professor at Siegen University. He is the primary author of A New History of Modern Computing (MIT, 2021) and ENIAC in Action (MIT, 2016) and the editor of Histories of Computing (Harvard 2011) and Exploring the Early Digital (Springer, 2019). Learn more at www.tomandmaria.com/tom. The author would like to thank Ron Kline for the detailed feedback he made on a draft of this paper, and to acknowl- edge a debt to Erhard Schüttpelz, Sebastian Giessmann, and the participants in our workshop series on digitality for the many conversations that have shaped the ideas within.