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ABSTRACT

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F19UR1N9 7H3 73X7Numerals and their relationship with the letters

océane juvintypographic designesaig estienne 2016

ABSTRACT

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Foreword

SpeCifiCiT ieS of NumeR AlS

Numerals and the idea of numberf igures as alphabet of numberfrom recording a quantity to writingOrigins of graphic shapes

fiGuR eS T HRouGH T He T eX T

Latin script's letters v Hindu-Arabic figuresFigures inside the textResistance of numbersCoexistence of both systems

T He poW eRof NumBeR S

The mystery of numbersHow numerals colonize lettersNumbers as thet absolute truth

Conclusion

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foRewoRd

In a contemporary Latin font we can find various forms, mainly capital letters, lowercase letters, punc-tuation 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 alphanume-ric 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 nume-rals : 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. What is the speci-ficity 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 sys-tem (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 impor-tant role in our societies. They are, as Georges Ifrah

02.Merriam-webster defines a nu-mber as what is represented by numerals, and the symbols repre-senting a number. The word figure stands for “a symbol that repre-sents a number” and “a value that

is expressed in numbers”.

01.or digits or numerals.

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 univer-selle des chiffres, « Introduction »

(p. 3-8), Seghers, Paris, 1982.

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wrote it, our “mediums of dreams, fantasies, meta-physical 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 ?

I. SpeCifiCiT ieS

of

NumeR AlS

04.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 dessan-ti in Marc-Alain ouaknin, mystère des chiffres, Assouline eds, Paris,

2004.

Notches sticks from Aborig-inal Australians, Palaeolithic era. Numerical aide-mémoires

used from prehistory.

➀ NuMeR Al S ANd T He IdeA

of NuMBeR

a. figures as the alphabet of number What we generally know of a number (apart from its complex mathe-matical definition) are the notions of ordinality and cardinality. An ordinal number is used to show a position whereas a cardinal number shows quan-tity and depends on its relations with other num-bers. According to Clarisse Herrenschmidt, coun-ting 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 per-ception is not immediate.

We can meet stones and trees,but three stones and two trees ? Never.To see them, we need some operation.05

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 nume-rical 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

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Economic clay tablet from Sumer, count of goats and sheep. F i red c lay, 7,8 cm x  7,8 cm x  2,4 cm,

2 342 B.C.

Hollow, ovoid clay tablet, Mesopotamia, 15th B.C.. Cuneiform inscription on it counts 48 animals. We found 48 pebbles inside that may established a commer-cial 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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06.It means “little stones”

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 repre-sented by the whole stick. The relief allows the user to feel, through touch, the presence of each repre-sented 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 accoun-ting tablets. Their evolution can illustrate the passage from orality to writing. They begin with calculi, 06 that are little sphere-shaped, cylinder-shaped or cone-shaped clay objects found 3,000 years before Christ. Those easy-to-handle objects were used to repre-sent 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 res-ponsible for the setting of writing.

➁ oRIGINS of GR APHIC SHAPeS

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 trans-formed 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 coun-tries. 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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Hindu-Arabic figures from Co-dex Vigilanus, 976, Spain.

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

interesting in the abacus is that Hindu-Arabic nume-rals 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, partici-pates 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 inven-tion of printing between the 14th and 16th centuries.

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Development of the nume-ral 8, from a diagram from Georges Ifrah, Histoire univer-selle des chiffres, Seghers, Paris,

1982.We can read on it the com-plexity of figures' shape his-

tory.

*Contemporary uses in India

**Contemporary character in Arabic language

***Contemporary ‘8’ figure

1000 10th–13th c. 12th–13th c.1st–2nd c.

500

9th c.

*

**

***

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II. fiGuR eS

T HRouGH

T He T eX T

08.« les grandes inscriptions ro-maines sont impéria les e t conçues pour en imposer », « l’écriture est un outil de dom-ination et de gouvernement » Claude Mediavilla, Histoire de la calligraphie, Albin Michel, Paris,

2006.

07.see Georges Ifrah, Histoire uni-verselle des chiffres, Seghers, Pa-

ris, 1982.

09.Gerrit Noordzij, letterletter, Hart-ley & Marks Inc., Vancouver, 2001

(p.90).

Roman inscriptional capitals on the base of Trajan’s Col-

umn, c. 113 B.C.

➀ l AT IN SCR IP T 'S l eT T eRS

v HINdu-A R ABIC fIGuR eS

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 stone were identif ied to these signs ? Claude 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 conceptas the english expression ‘ninety-two’, and in this respect

our numerical system is a perfect and universalideographic system. 09

Therefore we can postulate that numerals and let-

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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 cal-cule, 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.

11.fonts.com, “oldstyle figures”.

ters are two types of signs designed for two different practices. Vilém Flusser notices two different ges-tures : 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 wri-ter and the reader to think in a particular way.

➁ fIGuReS INSIde THe TexT

Oldstyle figures correspond to the form of numerals as they appeared inside manuscripts from the 12th century. It is with printing that they were forma-lized into this shape, first fixed by Humanistic wri-ting. They “approximate[d] lowercase letter forms by having an x-height, and varying ascenders and des-cenders”. 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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Specimen of François Guyot, circa 1565, in the style of Ga-

ramond.

Lining and Oldstyle numer-als in Adobe Garamond p ro

Regular.

12.Vilém flusser, Does Writing have a future ?, "letters of the alphabet" (p. 23-35), transl. from the German by Roth, Nancy Ann (Die Schrift. Hat Schreiben Zukunft ?, 1987), university of Minnesota Press,

Minneapolis, 2011.

tion. ▪ Then many other figures appeared, corres-ponding to each style of type. They gradually became part and parcel of type design.

➂ ReSISTANCe of NuMBeRS

According to Vilém Flusser, “the assault on numbers by letters concerns a violation of numerical by literal thought”. 12 According to him letters erase particulari-ties of numbers. Indeed, when we use a word proces-sing program, letters are ordered along lines. To show this, Gerrit Noordzij composes a numerals serial in two different ways. The numerals in the matrix have the greatest “magnitude”. It is probably caused by habits of reading, as we are used to decompose a number written with numerals. Moreover, as Vilém Flusser remarks, in a scientific text we are faced with

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1234567890X1234567890x

TUGboat, Volume 34 (2013), No. 2 177

Figure 14: Politanus, Opera, printed by AldusManutius, 1498. Munich Digitization Center andDigital Library. http://daten.digitale-sammlungen.

de/0005/bsb00050563/images/index.html?fip=193.

174.98.30&id=00050563&seite=903

Figure 15: Error page of Hypnerotomachia Poliphili(author unknown) printed by Aldus Manutius,Venice, 1499. Rochester Institute of Technology,Cary Collection.

seems less likely, because Griffo, or whoever cut thenumerals, should have been able to cut a zero as wellas the other numerals.

1499. A year later, Aldus did use a zero properlyaligned with other numerals cut at a very smallsize, on the “errata” page of the HypnerotomachiaPoliphili printed in 1499 (Figure 15).

The Hypnerotomachia is composed in a large(approximately 15 point) humanist roman typefacecut by Griffo. The lowercase is based on the earlierroman, but the capitals are new. Numerals in themain body of the book are roman numerals, but inthe “erratta” page at the end, small Arabic numerals(approximately 60% of the x-height of the text face)are interposed. These numerals have the ring-shapedzero design that became standard for roman faces inthe 16th century. See “20” in line 1 and “10” in line 2.

These examples suggest that Italian Renaissancereaders of humanist manuscripts and printed bookswould have been unlikely to confuse zero with capitalOh; confusion could have occurred between zero andlowercase oh. In most instances, however, numer-als and letters occurred in different contexts, whichwould have lessened the chances of confusion. Wherethey did co-occur, numeral zero and lowercase ohwere differentiated by different size and/or differentductus, at least in type, where the more circularform and lack of thick-thin shading in the zero dis-tinguished it from the humanist oh, which did havethick-thin shading.

Later, in the 16th century and especially inFrance, Arabic numerals gradually became more of-ten used with roman typefaces. A type specimen

Figure 16: Type specimen of Francois Guyot, circa1565. Type Specimen Facsimiles, ed. John Dreyfus.Bowes & Bowes and Putnam, London. 1963. Originaldocument in Folger Library, Washington, D.C. Notenumero-typographical error of ‘6’ substituted forrotationally symmetrical ‘9’.

Figure 17: Gaillarde by Robert Granjon, 1570. TypeSpecimen Facsimiles II, H.D.L. Vervliet and HarryCarter, ed. John Dreyfus. Bodley Head, London, andUniversity of Toronto Press, Toronto. 1972. Originaldocument in Plantin-Moretus Museum, Antwerp.Original approximately 9 point.

attributed to Francois Guyot (Figure 16), circa 1565,displays complete Arabic numerals for several sizes oftype. As in 15th century Arabic numerals, Guyot’snumerals had ascending and descending forms. Thezero is cut as a small circular ring roughly the sizeof a lowercase oh but without thick-thin shading.Guyot’s types are cut in the style of Garamond, acanonical form in 16th century typography, and maybe the earliest example of Arabic numerals cut foreach size and style of type by the punch-cutter andcast by the typefounder.

A specimen of a small (approximately 9 point)roman, named “Gaillarde”, cut by Robert Granjon,is dated 1570, with the circular ring-form zero (Fig-ure 17). (The cutting is very fine, but the photoreproduction of the printed specimen makes it lookrougher than it is.)

Thus, during the second half of the 16th century,Arabic numerals became incorporated into commonexpectations of what characters a “font” contained—at least capital and lowercase letters, punctuation,

Oh, oh, zero!

Comparison of different am-biguous signs in fonts univers

(up) and oCR-B (down).

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

2013.

“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.

04 . CoexISTeNCe of BoTH SySTeMS

With the development of writing and its uses, at the end of the 20th century, computing mixed increa-singly 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 possibili-ties 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 let-ters often lead to confusion in program writing and

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14.Charles Bigelow, op. cit.

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 recogni-tion, each character had to have more than 7 % diffe-rences from another. ▪ The coexistence of nume-rals 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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III. T He poW eR

of

NumBeR

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

2012. 

15.source : Merriam-webster.

16.Marc-Alain ouaknin, mystère des chiffres, Assouline eds, Paris, 2004.

➀ THe MySTeRy of NuMBeRS

Numbers and their representations open a new pers-pective 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 emp-tiness, 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 intri-cacy of the world. Kabbalah is a mystical Jewish tra-dition 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

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Comparison of various models dated of Renaissance, in Ed-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

epistemology and history of mathematics, 2002).

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 num-bers, numerals allow to move beyond a single and unique meaning, to activate the surface of writing.

➁ How NuMeR AlS Col oNIze leT TeRS

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, sta-bility 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 crea-tion. ▪ 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 accor-ding to many scientists, artists, it corresponds to a

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particulièrement Paul Pichaureau qui a corrigé une première version de cet article comme unecopie de bac (et s'il reste des erreurs, c'est que je les ai introduites depuis !).

Figure 30 — Comparaison de divers modèles de la Renaissance ; d'après [Tuf94, p.113]

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.

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 clas-sical forms (Alexandrine, sonnet...), but also of creati-vity 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 beco-ming dictators in our current world. Indeed they are regarded as authoritarian evidence of the reality. Do numbers constitute the language of the universe ?

➂ NuMBeRS AS THe ABSoluTe TRuTH

Pythagoras, in the 6th century B.C., gave numeric foundations to the knowledge and understanding of the natural world. Indeed we can find specific num-bers, 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 crea-tion of the typographer when he is making fonts and he has to deal with numerical codes and mea-sures. ▪ Algorithms are governing us. With tech-nological 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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What to do in front of all these numerals and how to

read them ?(photograph by John Elk)

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CoNCluSIoN

Numerals are particular objects which interact diffe-rently than letters with their environment. Typography has chosen to combine both, in spite of some incon-gruities, and the Latin script composition system has appropriated numerals and their matrix fonctiun-ning. ▪ 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.

▪ G ood luCk

To ouR fIRST y eA R ST udeN TS !

layout Océane Juvin

TypefacesWork Sans medium, bold from Wei Huang ▪ Antique Regent regu-lar & italic drawn by František Štorm

April 2016

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