Figuring the Text - Abstract

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ABSTRACT

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F19UR1N9 7H3 73X7 Numerals and their relationship with the letters

ABSTRACT

ocĂŠane juvin typographic design esaig estienne 2016

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Foreword

specifici t ies of numerals Numerals and the idea of number figures as alphabet of number from recording a quantity to writing Origins of graphic shapes

FIGUR ES T HROUGH T HE T E X T Latin script's letters v Hindu-Arabic figures Figures inside the text Resistance of numbers Coexistence of both systems

T HE POW ER OF NUMBER S The mystery of numbers How numerals colonize letters Numbers as thet absolute truth Conclusion

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01. or digits or numerals.

02.

Merriam-Webster defines a number as what is represented by numerals, and the symbols representing a number. The word figure stands for “a symbol that represents a number” and “a value that is expressed in numbers”.

f or e wor d

In a contemporary Latin font we can find various forms, mainly capital letters, lowercase letters, punctuation and other symbols, as well as signs called f igures 01, available in different aspects (oldstyle, lining, tabular, proportionals, inferiors, superiors, fractions). Figures were added to the alphanumeric code we use every day, however they seem to be particular and complex objects. 02 ▪ First, these signs are linked with the concept of number. In the West, numbers are written with the ten Arabic numerals : 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. What is the specificity of these signs ? What role do number play in the emergence of writing ? ▪ Numerals, as foreign and heterogeneous symbols, have created a place for themselves in the established typographic system (oldstyle, lining, proportional, tabular, superior, inferior, fractions) and in text areas. Because of their complexity, relations between letters and numerals seem to be a rich area of research. What are the ways of inserting figures inside the text ? What are their interactions throughout the history of type ? What is at stake in these interactions ? ▪ Numbers and numerals seem to have played an increasingly important role in our societies. They are, as Georges Ifrah

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03. « supports de rêves, de fantasmes, de spéculations métaphysiques, des matériaux de littératures, les sondes de l’avenir incertain, outil de prédiction » Georges Ifrah, Histoire universelle des chiffres, « Introduction » (p. 3-8), Seghers, Paris, 1982.

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wrote it, our “mediums of dreams, fantasies, metaphysical speculations, literature materials, sensors of an uncertain future, forecasting and prophesying tools”. 03 What do they actually bring to humanity by comparison with letters ? Why are they so common and used today ?

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specifici t ies

of

numerals

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Clarisse Herrenschmidt, Les Trois Écritures. Langue, nombre, code, Éditions Gallimard, Paris, 2007 (p. III).

05. « Nous rencontrons des cailloux et des arbres, mais trois cailloux et deux arbres? Jamais. Pour les voir, il faut quelque opération.»

Quote from Jean-Toussaint Dessanti in Marc-Alain Ouaknin, Mystère des chiffres, Assouline Eds, Paris, 2004.

dea an d th e i u m e ra l s r ➀ n o f n u mb e

a. figures as the alphabet of number What we generally know of a number (apart from its complex mathematical definition) are the notions of ordinality and cardinality. An ordinal number is used to show a position whereas a cardinal number shows quantity and depends on its relations with other numbers. According to Clarisse Herrenschmidt, counting seems to be an important role of the number as well. 04 ▪ The following sentence of Jean-Toussaint Dessanti illustrates the fact that with numbers perception is not immediate.

We can meet stones and trees, but three stones and two trees ? Never.

05 To see them, we need some operation.

A process of abstraction is needed. But as Georges Ifrah notes, man seems to have been capable of memorizing various quantities, before knowing the arithmetical and abstract meaning of number, which is apparent from the earliest writing marks. b. from recording a quantity to writing The oldest numerical inscriptions are estimated to date back to the first civilizations of the Palaeolithic (circa 30,000 years B.C.) and are found on wood sticks (that can be

Notches sticks from Aboriginal Australians, Palaeolithic era. Numerical aide-mémoires used from prehistory.

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Economic clay tablet from S u m e r, c o u n t o f g o a t s a n d s h e e p . F i r e d c l a y, 7,8 cm x 7,8 cm x 2,4 cm, 2 342 B.C.

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Hollow, ovoid clay tablet, Mesopotamia , 15th B.C..

Cuneiform inscription on it counts 48 animals. We found 48 pebbles inside that may established a commercial transaction (in Denise Schmandt-Besserat, Les plus Anciens Précurseurs de l’écriture).

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Calculi from Qalaat Djarmo.

Objects of fired clay, from 1 cm to 1,5 cm high, second half of 7th millennium.

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It means “little stones”

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called notches sticks or numerical bones when they are on bones). They are among proto-writing and were used to memorize quantity. Here is how it works : each notch figures one object from a set that is represented by the whole stick. The relief allows the user to feel, through touch, the presence of each represented object. No need to know numbers. Therefore a means to represent a quantity and memorize it was required long before writing and it could have impulsed it as well. ▪ Indeed writing appeared in Sumer in the 4th millennium before Christ on accounting tablets. Their evolution can illustrate the passage from orality to writing. They begin with calculi , 06 that are little sphere-shaped, cylinder-shaped or coneshaped clay objects found 3,000 years before Christ.

Those easy-to-handle objects were used to represent the number of animals in a herd for example. To establish contracts, they were enclosed inside a clay ball that was later covered with signs that expressed its contents and then flattened to become a simple numeral tablet. Therefore, writing made invisible objects visible and numerical signs are probably responsible for the setting of writing. shap e s o f graphic ➁ Origins Arabic figures are not really from Arabia. Before

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arriving in the Middle East, numerals were invented in India, with Brahmi writing. First, ten numerals appeared between the 6th century and the middle of the 10th century. The real invention was that each figure to the left of another represented ten times more than the one on the right. Thus, every number can be represented with the use of a few symbols, and there is one unique way to write each number.

This principle was disseminated all over the world for its efficiency. The first ones to adopt it, however, were the Arabs. ▪ Nagâri numerals were transformed in the Middle East into two different scripts.

First, eastern Arabs drew Hindi numeral during the 9th century. Their form is still used in Arabic countries. Later on, the forms of Ghubar numerals were materialized by western Arabs. The latter were later imported across Europe. ▪ The system of Roman numerals which was used in Europe was replaced

by Hindu-Arabic numerals from the 10th century onwards. The abacus (calculation board) is at the core of the European history of numerals. Indeed it was there that the first signs that looked like Hindu-Arabic figures appeared. At this time, the various shapes they took were called apices of Boethius. They were written for the first time inside the Codex Vigilanus, a Spanish arithmetic treaty, published in 976. What is

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interesting in the abacus is that Hindu-Arabic numerals were first appropriated through manipulation and orality without any written inscriptions. Then, European calculators gave up the abacus in favour of written calculations. The book from the well-known mathematician Fibonacci, Liber Abaci in 1202, participates widely to the diffusion of numeral forms, which took a roughly stable cursive writing in the 13th and 14th centuries. They became official with the invention of printing between the 14th and 16th centuries.

Hindu-Arabic figures from Codex Vigilanus, 976, Spain.

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Represention of numbers on Gerbert’s abacus thanks to apices. In Georges Ifrah, Histoire universelle des chiffres, op. cit.

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** 500

9th c.

1st–2nd c.

1000

Development of the numeral 8, from a diagram from Georges Ifrah, Histoire universelle des chiffres, Seghers, Paris, 1982.

We can read on it the complexity of figures' shape history.

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10th–13th c.

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12th–13th c. * Contemporary uses in India ** Contemporary character in Arabic language *** Contemporary ‘8’ figure

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07. see Georges Ifrah, Histoire universelle des chiffres, Seghers, Paris, 1982.

08. « les grandes inscriptions romaines sont impériales et conçues pour en imposer », « l’écriture est un outil de domination et de gouvernement » Claude Mediavilla, Histoire de la calligraphie, Albin Michel, Paris, 2006.

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Gerrit Noordzij, Letterletter, Hartley & Marks Inc., Vancouver, 2001 (p.90).

e tt e rs script 's l ur es f ➀ Latin rabic ig v H in d u -A

Before using Hindu-Arabic numerals, Europeans had Roman numerals. We can still see them in specific places, for example in books. ▪ Their shapes came first from heathens and were absorbed by the Latin alphabet under the Roman Empire. 07 Was it for its prestige that the Roman square capitals carved in s tone were identif ied to these signs ? Cl aude Mediavilla reminds us that “large Roman inscriptions are imperial and designed to be impressive” and during the Roman Empire “writing is a domination and governance tool”. 08 Hindu-Arabic numerals were finally adopted because they were much easier to use. Numerals are indeed more useful than letters to represent the concept of number.

When written in numerals, numbers are ideographic.

For the reader they might be rather logographic ; German readers will read 92 as ‘zweiundneunzig’ whereas French readers will read ‘quatre-vingt-douze’, but both expressions are addressing the same concept as the English expression ‘ninety-two’, and in this respect our numerical system is a perfect and universal ideographic system. 09 Therefore we can postulate that numerals and let-

Roman inscriptional capitals on the base of Trajan’s Column, c. 113 B.C.

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10. « de gauche à droite, tout au long d’une ligne, un trait ondulé interrompu par endroits. C’[est] un geste linéaire. Quand on calcule, on sélectionne des petits cailloux pris dans un grand tas et on les rassemble en petits tas. C’est un geste ponctuel. » Vilém Flusser, Petite philosophie du design, « Pourquoi, au fond, les machines à écrire font-elles du bruit ? » (p.53-57), transl. from German by Claude Maillard, Circé, Paris, 2002.

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Fonts.com, “Oldstyle Figures”.

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ters are two types of signs designed for two different practices. Vilém Flusser notices two different gestures : in western countries, people write by drawing from left to right, all along a line, a wavy stroke, sometimes disrupted. This is a linear movement. When we calculate, we select little stones taken from a big pile, and then we gather them into small piles.

This is a one-off movement. 10 Numerals designate an arithmetic entity whereas letters designate a linguistic element. Both types of sign belong to a specific system, and involve the writer and the reader to think in a particular way. t e th e t e x u r e s insi d ig f ➁ Oldstyle figures correspond to the form of numerals as they appeared inside manuscripts from the 12th century. It is with printing that they were formalized into this shape, first fixed by Humanistic writing. They “approximate[d] lowercase letter forms by having an x-height, and varying ascenders and descenders”. 11 ▪ François Guyot’s Specimen (c. 1565) seems to be the first example of figures punched and cast for each size and style of typeface. When the numerals were first incorporated to texts, there were not very well inserted in the typographical composi-

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tion. ▪ Then many other figures appeared, corresponding to each style of type. They gradually became part and parcel177of type design.

X1234567890 x 1234567890 Figure 16: Type specimen of Fran¸cois Guyot, circa f n u mb e rs 1565. Type Specimen Facsimiles, ed. John Dreyfus. sistanc e o e R

Bowes & Bowes and Putnam, ➂ London.

1963. Original document in Folger Library, Washington, D.C. According toNote Vilém Flusser, “the assault on numero-typographical error of ‘6’ substituted for rotationally symmetrical ‘9’. by letters concerns a violation of numerical

numbers by literal thought”. 12 According to him letters erase particulari12.

Vilém Flusser, Does Writing have a future ?, "Letters of the alphabet" ties of numbers. Indeed, when we use a word proces(p. 23-35), transl. from the German

by Roth, Nancy Ann (Die Schrift. sing program, letters are ordered along lines. To show Hat Schreiben Zukunft ?, 1987), University of Minnesota Press, this, Gerrit Noordzij composes a numerals serial in Minneapolis, 2011. two different ways. The numerals in the matrix have the greatest “magnitude”. It is probably caused by Granjon, Type Figure 17: Gaillarde by Robert habits of1570. reading, as we are used to decompose a Specimen Facsimiles II, H.D.L. Vervliet and Harry number written Carter, ed. John Dreyfus. Bodley Head, London, and with numerals. Moreover, as Vilém University of Toronto Press, Toronto.

1972.

Original in a scientific text we are faced with Flusser remarks, document in Plantin-Moretus Museum, Antwerp.

Original approximately 9 point.Specimen of François Guyot,

circa 1565, in the style of Garamond.

attributed to Fran¸cois Guyot (Figure 16), circa 1565, displays complete Arabic numerals for several sizes of type. As in 15th century Arabic numerals, Guyot’s numerals had ascending and descending forms. The zero II is cut as a small circular ring roughly the size of a lowercase oh but without thick-thin shading.

Guyot’s types are cut in the style of Garamond, a canonical form in 16th century typography, and may

Lining and Oldstyle numerals in A dobe G a ram ond P r o Regular.

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“islands of numbers” that stand out from the text.

Due to their various origins, figures are not structured in the same way letters are. New tricks were needed to combine their drawing with that of letters.

e C o e x ist e nc

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Charles Bigelow, « Oh, oh, zero ! », in TUGboat, Vol. 34, n°2, www. tug.org/tugboat/contents.html, 2013.

y st e ms o f b o th s

0 4 .

With the development of writing and its uses, at the end of the 20th century, computing mixed increasingly numerals and letters of the alphabet and they therefore became interdependent. In his article, Charles Bigelow introduces a new need for their differentiation, especially between the letter ‘o’ or ‘O’ and the ‘zero’. 13 Indeed, with the emergence of monospaced fonts for typewriters, the possibilities of misunderstanding increased and there were no longer ways to know which was what according to the context because numerals freed themselves from lists and tables to integrate computer texts. The ambiguities that may exist between numerals and letters often lead to confusion in program writing and Comparison of different ambiguous signs in fonts Univers (up) and OCR-B (down).

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Charles Bigelow, op. cit.

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have to be carefully considered.

In most digital monospaced sans-serif fonts strict modernist design purity is subordinated to legibility. 14 Standards of legibility appeared as DIN 1451 in 1931 and some characteristics were added, subtracted or modified to some letters and numerals. They became standard forms. In the font OCR-B designed by Adrian Frutiger in 1968 and developed for optical recognition, each character had to have more than 7 % differences from another. ▪ The coexistence of numerals and letters revealed new issues in font design.

Moreover, numbers appeared to be more suited to our technological and scientific world. What makes numerals powerful ?

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15. source : Merriam-Webster.

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Marc-Alain Ouaknin, Mystère des chiffres, Assouline Eds, Paris, 2004.

➀ th Numbers and their representations open a new perspective in alphabetical writing. Numbers can be used not only to count, but also to reveal a new truth, a new reality. How wonderful tools ! ▪ First, the vocabulary tells us that early on, numerals were associated with secret. Indeed the word cipher which designates a “message in code” also means “zero”, 15 ever since the Middle Ages. Actually cipher comes from the medieval word cifra, which came itself from the Arabic sifr, meaning vacuum. When the signs from the Hindu-Arabic system arrived in Europe, it was such an upheaval for European calculators that they were first secretly disseminated. The figure ‘zero’ was especially considered as devilish for it signified emptiness, which could not exist in a society where God was thought to be everywhere. ▪ The Hebrews or the Greeks used characters for both words and numbers too. These characters allowed them to give dual-meaning to words that would reveal the intricacy of the world. Kabbalah is a mystical Jewish tradition that uses Hebrew characters to explain the meaning of life. For Marc-Alain Ouaknin, it is “the art of making numbers meaningful”. 16 Kabbalah does not consist in just translating names and words, it is an

Table of 27 Hebrew letters with their names and their numeric values. We read them from right to left. In Josy Eisenberg and Adin Steinsaltz, L’Alphabet sacré, Fayard, Paris, 2012.

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opening on an other possible reality, through numeric values hidden behind letters. ▪ The magic square is an interesting figure known from Antiquity that plays with numbers, numerals and letters. It is assigned magic powers. It is a steady microcosm that ensures protection because the sums of numerals on each of its lines and columns and even sometimes diagonals are equal. In this particular form, governed by numbers, numerals allow to move beyond a single and unique meaning, to activate the surface of writing. z e l e tt e rs l s c o l o ni ra e m u n How ➁ Ever since the Renaissance, numerals have become part of letters’ structure and identity. Indeed, in the 16th century, engravers, printmakers and artists tried to explain the forms of letters with numbers, and to rationalize them and give them objectivity, stability and superiority. Moreover, starting in the 18th century types have been indentified by a numeral that indicates the character size. Today, with digital type design, numerals are at the core of letter creation. ▪ In the same way as letters, the pages’ text areas have been idealized by numbers ever since the Renaissance, with the use of geometry. The Golden ratio is supposed to give them harmony and according to many scientists, artists, it corresponds to a

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Comparison of various models epistemology and history of dated of Renaissance, in Edmathematics, 2002). ward Tufte, Visual Explanations – Images and Quantities, Evidence and Narrative, Graphic Press, Cheshire, 1997 (in Jacques André, De Pacioli à Truchet : trois siècles de géoétrie pour les caractères, 13th colloquium Inter-IREM of

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universal aesthetic pleasure. Like everywhere else, numerals order our circulation inside the book thanks to page and chapter numbering. ▪ Moreover, in literature, numbers are instruments of rules in classical forms (Alexandrine, sonnet...), but also of creativity and they often provide opportunities to play. The members of the Oulipo (which stands for “workshop of potential literature” in French) used them to create new poem structures, or introduce potentiality, as in the case of Raymond Queneau’s Cent mille milliards de poèmes. Numerals are a new language that offers new possibilities of writing. ▪ But numbers are becoming dictators in our current world. Indeed they are regarded as authoritarian evidence of the reality. Do numbers constitute the language of the universe ? u t e tr u th th e abs o l as rs e mb Nu ➂

17. « [Peut-être le monde n’est-il calculable] que parce que nous l’avons bricolé pour aller avec nos calculs. » Vilém Flusser, Petite philosophie du design, « Pourquoi, au fond, les machines à écrire font-elles du bruit ? » (p.53-57), transl. from the German by Claude Maillard, Circé, Paris, 2002.

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Pythagoras, in the 6th century B.C., gave numeric foundations to the knowledge and understanding of the natural world. Indeed we can find specific numbers, such as the Golden ratio or Pi, everywhere in nature. The world appears to be calculable, but “it may only be because we have adjusted it to fit our calculations”. 17 Whether numbers come before or after nature, they are tools with which we try to understand reality in order to modify it. ▪ Today

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computers are necessary. It deals with data being transformed into numbers, whose basic units are bits (for BInary digiTs). In computing, all characters are now encoded in numbers. For example in ASCII code, ‘A’ is ‘65’. Computing conditions the creation of the typographer when he is making fonts and he has to deal with numerical codes and measures. ▪ Algorithms are governing us. With technological evolution, we let computers manage a lot of complex data about us and our world. Numerals dehumanize us, they are used to identify us and replace us. The mass of permanently collected data increases the use of numerals to describe and modify the world. Numerals have become a basic unit of information.

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C O N C LU S IO

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Numerals are particular objects which interact differently than letters with their environment. Typography has chosen to combine both, in spite of some incongruities, and the Latin script composition system has appropriated numerals and their matrix fonctiunning. ▪ Today numerals are omnipresent, and we can easily say that they rule the world. Indeed, our world is conceived as numerous data, and the rise of big data is a sign of intensified quantification. ▪ Numerals, under cover of rationality, objectivity, transparency, accuracy, have become instruments of manipulation. They seem to be self-sufficient, and are used as authoritative arguments. It is therefore especially important today to understand and analyse them, and manipulating their forms may be a way to enlighten people about them.

What to do in front of all these numerals and how to read them ? (photograph by John Elk)

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k G o od Luc ! st u d e nts ar e y ▪ irst f r u o t o

Layout Océane Juvin Typefaces Work Sans medium, bold from Wei Huang ▪ Antique Regent regular & italic drawn by František Štorm April 2016

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