2+2=5

2+2=5

The Poetics of Dyscalculia, or the Word and the Number in the Blind Spot of Digital Humanities

Author
Susanne Strätling
Keywords
digital humanities, dissidence, miscalculation, word-number relations, arithmetic, logometric, antinomic speech, literature and mathematics
Abstract
Historically and systematically, the word and the number are closely related in many ways. The number often represents the stable, rational and literally calculable super-sign, while the word is associated with impermanence and indeterminacy. When the digital humanities convert texts into tables, they assume that more reliable and well-founded statements about literature can be made on the basis of numbers. But this conviction overlooks the fact that literature itself has written an extensive history of miscalculation. Indeed, literature counters the rampant numerical compulsion with an alternative – number dissidence. Using the example of the unequal equation 2+2=5, the article reconstructs this poetics of miscalculation.

Introduction

В арифметике главное – сохранить холодную голову,
горячее сердце и добрые, добрые руки – вот скажем,
ту берешь единицу, успокаиваешь, успокаиваешь ее,
и она расслабляется, засыпает и незаметно для себя
вдруг начинает двоиться, троиться и там и –
4, и 5, и 6, и 7, и 8, и 9, и 41, и 73, 158, 11929, 103005, 12.350.410,
и 743.190.00, и даже совсем 666.000.666.000 и так далее.

Arithmetic is all about keeping your head cool,
your heart warm and your hands very, very kind –
say, you take the number one, you calm it down,
there, there, and it relaxes, falls asleep and, without noticing,
multiplies by two, by three and so on, and so on – 4, and 5,
and 6, and 7, and 8, and 9, and 41, and 73, 158, 11929,
103005, 12,350,410, and 743,190.00 and even 666,000,666,000, and so on.

(Dmitrii Prigov 2001: 127)

In a short parody of Viktor Shklovskii’s sentimental montage literature written by Aleksandr Arkhangelskii Roman Jakobson makes a small appearance, confessing to his “friend Vitia”: «Если бы я не был филологом, я был бы кассиром.» (Arkhangel’skii 1988): “If I were not a philologist, I would be a cashier.” This succinct dictum characterises the business of structuralism quite aptly. Philologists such as Jakobson played no small role in the elevation of accounting to a method of textual and linguistic analysis by treating words as values. Arkhangel’skii’s parody is more than a pseudo-biographical anecdote about one of the founding fathers of structuralism, however. It points to an evolution of philology, from a study of language to a study of numbers, that had begun before structuralism and which has reached new heights in the current digital humanities boom.

Against the background of this far-reaching disciplinary transformation, the present essay rethinks the translatability of words into numbers and the calculability of words as numbers in the context of the long philological and philosophical tradition of miscalculation. However, the radical embrace of mathematical errors in literature aims at something more than bluntly discrediting numerical dogmatism. Much more, the resistance to mathematical regularity is directed toward word work and the foundations of poetics. This article discusses three aspects of the poetic engagement with dyscalculia: 1) literature as an expression of the antinomic, 2) narration as production of alternative orders, and 3) writing as an act of materializing abstract signs.

The Word and the Number: Double Coding and Numerical Compulsion

The relationship between verbal and numerical symbol systems is as close as it is historically and systematically diverse. Numbers are not only abstract mathematical objects. In making meaning, the number shares with the word its function as a “discursive medium” (Mersch 2003: 16). As a concrete act, counting is historically very closely linked with the acts of naming and deciphering. Linguistically, this nexus is reflected, for example, in the numerus as a fundamental category of grammar. It has also left etymological traces: in German, for instance, the word Zahl (number) derives from the *ur-German talo = number, speech; in Russian, chitat' (reading) and schitat' (counting, calculating) differ only in a single sound.

Heuristically simplified, we can distinguish between two modes of word-number relations:

1) One is rooted in the double coding of symbols as letters and numerals. This double coding is reflected in the earliest examples of language magic and in the origin myths of several writing systems. When Plato, for example, criticises the institute of writing in Phaedrus, he refers to the myth of Theuth, whom the Egyptians considered the inventor of numbers and calculus as well as of letters and writing. The dual use of symbols as mathematical and linguistic signs also essentially determines the multifunctionality of some alphabets, most famously the Greek, which also coded musical notes along with numbers and letters (Schubart 2004: 1119-1146).

Numerical-phonographic notations are exceedingly efficient since they enable simultaneous calculation and writing without changing systems. However, they pose a considerable hermeneutical challenge: dual writing codes tend to be so complex as to require special reading techniques. Sign systems in which linguistic and numerical values overlap do not only raise questions of number-based hermeneutics as practised in gematria or arithmetical exegesis (Krochmalnik 2019). Rather, they reveal the fundamental problem of the calculability of language – to which modernity has reacted with mathematically inspired formal languages and with the fusion of cybernetics and linguistics. This problem of linguistic calculus leads to the second mode of word-number relations:

2) Rather than proceeding from the double identity of signs, this mode insists on an irrevocable structural difference between words and numbers. At the same time, it seeks to subject language to calculation. In this paradigm, words are not read as numbers, and numbers are not noted down with letters. Instead, words are counted and computed. Here, both letters and words are the objects rather than the means of calculation. Hermeneutical questions recede into the background, replaced by statistics or logometrics in the broadest sense. This second type of word-number relations includes complex arithmetical operations of the poetic ars combinatoria as well as the language algorithms of modern automatic poetry and, last but not least, the quantitative research methods of empirical literary studies. These methods are based on the presumption that symbolic and technical practices are mutually interrelated, a condition that has become particularly evident since computers have become a crucial means of writing.

These two modes of word-number relations differ in their subject areas as well as in their methodological approaches. And yet both address the same question. Can linguistic signs be formally operationalised in the same manner as numeric signs? This question is tied to a common suspicion: the word is traditionally seen as unreliable, indefinite, and unpredictable; the number as orderly, certain, and rational (Mersch 2003: 24). This mistrust of the word, on the one hand, and faith in numbers, on the other, underwent historical fluctuations, but stabilised by the eighteenth century, at the latest. The cult of numbers gained ground during the Enlightenment, as the period’s glottogenetic speculations make clear. Theories of language origin mostly envision verbal language as a mere phase in the development of an ideal language of numbers. Thus, Étienne Bonnot de Condillac postulates in his Essai sur l'origine des connaissances humaines / Essay on the Origin of Human Knowledge:

L’arithmétique fournit un exemple bien sensible de la nécessité des signes. Si, après avoir donné un nom à l’unité, nous n’en imaginions pas successivement pour toutes les idées que nous formons par la multiplication de cette première, il nous serait impossible de faire aucun progrès dans la connaissance des nombres. Nous ne discernons différentes collections que parce que nous avons des chiffres qui sont eux-mêmes fort distincts. Ôtons ces chiffres, ôtons tous les lignes en usage, et nous nous apercevrons qu’il nous est impossible d’en conserver les idées. (1746: 95)

Arithmetic provides a very clear example of the necessity of signs. It would be impossible to make any progress in the knowledge of numbers if, after giving a name to the concept of unity, we did not successively keep unity in mind for all the ideas we form by the multiplication of this first one. We discern different collections only because we have digits that are themselves very distinct. Take away these digits, abolish the use of signs, and we will discover that it is impossible to preserve the ideas. (translation from French by Hans Aarsleff, 2001: 78)

Condillac argues in two steps. Firstly, it is the number that substantiates the idea of language as a differential sign system. Secondly, it is the number that enables language to be conceptualised. If sign systems are to perform epistemic operations and not merely communicative ones, names must become numbers. Signification, cognition, and calculation all coincide here.

Condillac’s reflections on the philosophy of language amounts to an apotheosis of calculus: whatever is conceivable and imaginable can also be comprehended in numbers. This identification of knowledge and ciphers gains more and more ground, and has hardly ever been proposed as apodictically as in Kelvin’s: “When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind” (1883).

This conviction is accepted not only by the so-called hard sciences. It has serious consequences for all areas of research, not least those that study the word. These consequences also pertain to the literary arts, which find themselves increasingly exposed to the pressure of numerical thinking when they claim to offer a way of exploring new, unsecured knowledge. In his 1913 essay “Der mathematische Mensch” / “The Mathematical Human”, Robert Musil declared philology to be an activity as useless as collecting stamps or ties and recommended „daß man nach je zwei hintereinander gelesenen deutschen Romanen ein Integral auflösen muß, um abzumagern“ (Musil 1978: 1007): “to solve an integral after reading two German novels in succession in order to lose some weight”, the novels being “as fat as pugs”.

However, the medicine of mathematics does not heal the ailments of literature. In the technophile avant-gardes of the 20th century, mathematics reaches right into verbal art. Here, the formula becomes an ideal type of poetic speech. In the Manifesto tecnico della letteratura futurista / Technical Manifesto of Futurist Literature (1912), Tommaso Marinetti suggests using mathematical signs instead of cumbersome adjective-noun constructions because they “riassumendo tutte le spiegazioni, senza riempitivi, ed evitando la mania pericolosa di perder tempo in tutti i cantucci della frase”: “draw together all explanations without fillers, avoid the dangerous mania of wasting time all over the sentence” (translation from Italian).

In his 1916 “Pis’mo dvum iapontsam” / “A Letter to Two Japanese”, Velimir Khlebnikov envisages the language of the future in similarly efficient terms:

Язык Чисел Венка Азийских юношей. Мы можем обозначить числом каждое действие, каждый образ и, заставляя показываться число на стекле светильника, говорить таким образом. Для составления такого словаря для всей Азии (образы и предания всей Азии) полезно личное общение членов Собора Отроков будущего. Особенно удобен язык чисел для радиотелеграмм. Числоречи. Ум освободится от бессмысленной растраты своих сил в повседневных речах. (1986: 605)

The Number Language of the Circle of Asian Youths. We can designate a number for each action and each image, and we speak by making numbers appear on the glass of a lamp. To compile such a vocabulary for all Asia (images and traditions from all Asia), personal communication would be useful between members of the Council of the Future Youths. The language of numbers is especially convenient for radio telegrams. Numberspeak. The mind will be freed from the senseless waste of its power in everyday speech.

While Khlebnikov's numerical language is clearly inspired by radio telegraphy, avant-garde literature also abounds with words being subjugated to numbers beyond modern media technology. In the first part of the (unfinished) poem “Piatyi Internatsional” / “The Fifth International” (1922), Maiakovskii proclaims:

Я
поэзии
одну разрешаю форму:
краткость,
точность математических формул. (1978: 224)

I
permit
only one form of poetry:
the brevity,
the precision of mathematical formulas.

An arguably even more radical subordination of literature to mathematical systems takes place in the work of the constructivist and ergonomist Aleksei Gastev. In his last lyrical cycle, “Pachka orderov” / “A Batch of Decrees” (1921), he demands a poetry in the decimal system:

Фразы по десятеричной системе.
Котельное предприятие речей.
Уничтожить словесность.
(Gastev 1971: 219)

Sentences according to the decimal system.
A steam boiler factory of speeches.
Destroying literature.

When the decimal place value system determines the poetic word sequence, literature’s right to exist is at stake. If it is to be spared destruction, it must be transformed. In the numerical ordering of speech, word factories also demand the reformatting of verses into precise data. In a 1928 essay on the organization of literary production, Gastev (1966: 204) explicates this as «превращение литературного произведения в таблицу, в чертеж, в карточку»: “the transformation of the literary work into a table, a plan, a map”.

This is not to say that poetics had not considered tables, lists, sketches, plans, curves, and maps before. Still, the complete transformation of literature into a diagram seemsnovel. Rhythm analysis, apt to calculate poetic metres, is particularly open to this paradigm shift. «[Б]удем прислушиваться к голосу чисел»: Andrei Belyi's (2014: 27) attempts to decipher the principle of poetic rhythm “by listening to the voice of the numbers” are exemplary here (fig.1). One might well argue that the diagrams and textual networks of quantitative literary studies derive from this avant-garde tendency. The distant reading methods of today’s literary labs realise the avant-garde dream of calculable literature, recently rediscovered under the label “digital formalism” or “data-driven formalism” (Fischer/Akimova/Orekhov 2019).

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Belyi 2014: Curve diagram of Alexander Pushkin's poem “The Bronze Horseman” (Mednyi vsadnik)

Fragmentary as they are, these examples, from the language origin theories of the Enlightenment to the speech factories of the avant-garde and the literary laboratories of the present day, document a constantly growing pressure to regulate words with numbers or even to substitute them. Numbers are granted the status of precision tools that can be used on words as normative or corrective instruments.

Undoubtedly, poetics can subvert this standardization. One need only consider the strong anagrammatic tradition, with its numerical aleatorics, or the rhizomatic effects of the numerical contrainte. They combine statistics and contingency in a way that appears to suspend the established logic of numbers. On closer inspection, however, these projects are deeply involved in numerical determinism, despite all their ludism. This is clearly illustrated by two examples that are as prominent as they are historically incongruous: Georg Philipp Harsdörffer's Deliciae physico-mathematicae / Physico-Mathematical Delights (1636) and Raymond Queneau's book object Cent mille millards de poèmes / Hundred Thousand Billion Poems (1961). One of the mathematical games suggested by Harsdörffer involves a language machine that generates new words by turning five rings with prefixes, initial and rhyming letters, middle letters, end letters, and suffixes (fig. 2). Leibniz estimated the resulting number of possible combinations at over 97 million (most of them nonsense, to be sure). As for Queneau, his follow-up project to Harsdörffer's endeavour works not on the level of words, but on that of verses, cutting up ten sonnets into single lines, which can be recombined at will into 1410 new poems (fig. 3).

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Harsdörffer 1651: “This little page must be cut out / and divided into five rings / and affixed / to five equal-sized pieces of paper / so that each ring can be rotated separately / when this happens / one must paste this fivefold page back in.” (translation from German)
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Queneau 1961

Even though both projects refer to vastly different contexts – the baroque idea of universal grammar and the experimental poetics of Oulipo – Harsdörffer’s word rings and Queneau’s verse strips share a basic assumption: the sense of numbers lies in not making sense. In both projects, the austere economies of numerical text controlling topple over into a fantastic profusion of linguistic potentiality. Still, their compositional patterns are based in computation. They obey programs which, proceeding from numbers, explore the quantitative delimitation and the qualitative determination of the word.

2+2

But if one wishes neither to let the number dominate the word nor to follow the aleatoric trend into the sphere of nonsensically large numbers one must move beyond these logics of rationality. “Moving beyond” does not mean ignoring numbers completely or declaring the word to be a priori unpredictable. Rather, it means looking beyond the dominant quantitative discourses on literature – even when texts turn into Big Data with 97 million or even a thousand billion elements – to make room for alternative calculation processes in the texts. These processes show how words and numbers can enter relationships outside the limits of calculation and control; they demonstrate how a degree of dyscalculia can be deliberately accepted to open up spaces for speaking. Here, the number does not limit the word but helps dissolve its boundaries.

Miscalculations, “false” in the conventional sense, have a crucial cognitive value. Failing mathematically, they paradoxically succeed epistemically, as can be seen from the (non-)equation “2+2=5”. “2+2” is not an arbitrary example but the archetype of a basic arithmetic operation, a precedent for philosophical proofs of truth and reality, virtually a mathematical natural law: “Nam sive vigilem, sive dormiam, duo & tria simul juncta sunt quinque, quadratumque non plura habet latera quam quatuor; nec fieri posse videtur ut tam perspicuae veritates in suspicionem falsitatis incurrant” remarks René Descartes in Meditationes de prima philosophia (2014: 12): “For no matter if I sleep or am awake, two and three always make five [...] and it seems impossible that such obvious truths could be suspected of being false” (translation from Latin).1 Arithmetic theorems are independent of experience: this is precisely what led Immanuel Kant (1974: 56) to define them as synthetic judgements a priori in his Kritik der reinen Vernunft / Critique of Pure Reason.2 As such, they cannot be wrong and are valid without exception and under all circumstances. Where the arithmetic laws of 2+2 apply axiomatically, one is standing on solid ground; where they become invalid, the world turns upside down.

Literary reflexes of this mathematical logic are scattered widely. A particularly receptive genre is the dystopian novel, in which the intertwining of apocalyptic crises and arithmetic catastrophes shows a keen sense for the mathematical foundation of modernity. As George Orwell’s 1984, probably the most popular translation of maths into literature, puts it: “Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.” (1984: 226)

“2+2=4” holds a promise that, even in times of doublespeak, the logic of numbers remains unambiguous. When this rule is broken and even equations lose their equilibrium, what can be trusted? The formula “2+2=5” so blatantly contradicts both Descartes’s somnambulistic certainty and Kant’s hard criteria that formal logic treats it as a numerical incarnation of the unprovable. “2+2=5” breaks more than just the rules of arithmetic. It also questions the evidence principles of objectively valid truth. This is precisely why Orwell uses this (non)equation to express dogmatic compulsion and injustice in 1984 (originally published in 1949, presently cited in an edition from the title year):

“How can I help seeing what is in front of my eyes? Two and two are four.”

“Sometimes, Winston. Sometimes they are five.” (1984: 375)

One can have very different reasons to make a 4 into a 5. In 1984, it is, of course, the will of the party. An inspiration for Orwell’s ideological indoctrination through numbers was probably the arithmetic rhetoric of Soviet propaganda. To cite a particularly vivid example: this poster from 1931 propagandises the fulfilment of the Soviet Union’s first 5-year plan, launched in October 1928, in only four years (fig. 4). Here, the visual language and the logic of numbers suggest that if the “workers’ enthusiasm” is added as a variable, 2+2 can indeed add up to 5. Thus, the poster visualises the first goals set by Stalinism by declaring the laws of arithmetic invalid. A different calculation applies here, one that cannot be grasped with the rules of classical mathematics.

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Propaganda poster for the fulfilment of the first five-year plan in four years. Design: Iakov M. Guminer (1931)

Orwell clairvoyantly reveals the manipulative, coercive character of this calculation, which masquerades as enthusiasm but is in practice slavery. But he is overlooking a no less important aspect: the dogmatic pressure of arithmetic is inherent in the very claim to an unchangeable, unquestionable validity of 2+2=4. The quiet horror of this numerical regime was most saliently expressed in another dystopian scenario: Evgenii Zamiatin’s My / We (1920). Its narrator, D-503, enjoys a sonnet entitled “Schast’e”/ “Happiness”:

Вечно влюбленные дважды два,
Вечно слитые в страстном четыре,
Самые жаркие любовники в мире
Неотрывающиеся дважды два…
(Zamiatin 1973: 59f)

Eternally loving two times two,
eternally fused as a passionate four.
No one has loved with such passion before,
with such abandon as they do…

However, this sonnet about the “eternal happiness of multiplication tables” leads D-503 to a heretical thought. The heresy lies not in the use of multiplication tables to disprove God’s existence, but in a fascination with miscalculation. What if the math no longer adds up, if two no longer pair up to produce four?

И нет счастливее цифр, живущих по стройным вечным законам таблицы умножения. Ни колебаний, ни заблуждений. Истина – одна, и истинный путь – один; и эта истина – дважды два, и этот истинный путь – четыре. И разве не абсурдом было бы, если бы эти счастливо, идеально перемноженные двойки – стали думать о какой-то свободе, т.е. ясно – об ошибке? (Zamiatin 1973: 60)

No number is happier than the numbers that live by the well-ordered eternal laws of the multiplication table. No hesitations, no delusions. There is one truth and one true way; and this truth is two times two, and the true way is four. Wouldn’t it be absurd if these happily, ideally multiplied twos started thinking about some kind of freedom – that is , about an error?

As Orwell diagnoses perceptively, miscalculations can, as a symptom of arbitrariness and terror, point to the errosion of the binding foundations of life and knowledge. But, as Zamiatin suggests, they can, as a deliberate deviation from the numerical norm, possess a considerable subversive and emancipatory potential. Such miscalculations might be errors, but they suggest the freedom to deviate. Here, “2+2=5” is not a plea for totalitarian arithmetic à la russe,, but rather a formula of intellectual dissidence, a (non)equation of an oppositional discourse that seeks alternatives to the dominant order, its knowledge and its dogmas. Three aspects of such dissident thinking seem to be particularly relevant for literary studies: the connection between arithmetic and linguistic deviation; the possibility of rethinking narrative patterns arithmetically; and finally, literary vividness and conceivability in the numerical context.

Arithmetic and Deviation

The prototype of arithmetic dissidence was arguably created by Fedor Dostoevskii in his Zapiski iz podpolia / Notes from the Underground (1864). This short novel, written at a time when Dostoevskii had ruined himself with gambling debts, obsessively revolves around the concept of reason; indeed, it is nothing less than a literary critique of pure reason. Just like its philosophical counterpart, this critique is carried out in the field of arithmetic. While Kant used the equation 7+5=12 to prove the existence of synthetic judgments, Dostoevskii cites the formula 2x2=4 as proof of the general inability to know and judge:

а ведь ведь дважды дважды два четыре есть уже не жизнь, господа, а начало смерти. По крайней мере человек всегда как-то боялся этого дважды два четыре, а я и теперь боюсь. Положим, человек только и делает, что отыскивает эти дважды два океаны четыре, океаны переплывет, океаны переплывет, жизнью жертвует в этом отыскивании [...] Дважды два четыре – ведь это, по моему мнению, только нахальство-с. Дважды два четыре смотрит фертом, стоит поперек вашей дороги руки плюется в боки и плюется. Я согласен, что дважды два четыре – превосходная вещь; но если уже все хвалить, то и дважды два пять – премилая иногда вещица. (Dostoevskii 2016: 400f)

but two times two is four, that is no longer life, gentlemen, but the beginning of death. At least people had always feared this two times two is four, and I fear it now, too. Sure, people keep seeking this two times two is four, swimming through oceans, sacrificing their lives in this search [...] Two times two is four, that’s downright impudent, says I. Two times two is four is standing in the middle of your path, arms akimbo and spitting. Sure, two times two is four is an excellent thing; but if I go about praising things, then two times two is five can be really nice sometimes.

In this satirical scene, fear and wit intertwine to form a numerical grotesque. Comically presenting the absurd notion of embodied formulaic language, it articulates the awareness of a crisis looming in the rampant mathematisation of human experience. In the most basic multiplication process manifests itself for Dostoevsky as a horror scenario: the total logarithmisation of life. In a mathematically rationalised society

Все поступки человеческие, само собою, будут расчислены тогда по этим законам, математически, вроде таблицы логарифмов, до 108 000, и занесены в календарь. […] Тогда-то, – это всё вы говорите, – настанут новые экономические отношения, совсем уж готовые и тоже вычисленные с математическою точностью, так что в один миг исчезнут исчезнут всевозможные вопросы, собственно потому, что на получатся них получатся всевозможные ответы. […]Конечно, никак гарантировать (нельзя уж я теперь говорю), что тогда не будет, например, ужасно скучно (потому что что ж и делать-то, когда все будет расчислено по табличке), зато все будет чрезвычайно благоразумно. (Dostoevskii 2016: 391)

all human actions will, of course, be mathematically calculated in something like a logarithmic table, up to 108,000, and entered into a calendar. […] Then – that’s you saying that – new economic conditions will arise, all ready and prepared and calculated with mathematical accuracy, so that, with one blow, all questions will disappear, because they will receive their comprehensive answers. […] However, there is no guarantee (and this is me speaking now) that it won't be, for instance, terribly boring (because what can you do when everything has already been calculated in tables) while so very, very rational.

Passages like these suggest reading Notes from the Underground as a manifesto of cultural pessimism directed against the mutual reinforcement of mathematisation and existential alienation. Dostoevskii’s fear of formulae would thus be a symptom of what Edmund Husserl (2012: 6) called the arithmetic conditioning of „bloße Tatsachenmenschen“ (“merely factual people”) in the second half of the 19th century. The function of the number is only partially considered in this diagnosis. Similarly, Aldous Huxley’s (2000: 400) objection that Dostoevsky’s madman is forced to a “violent and bloody conclusion”3 in his confrontation with arithmetical realities, ignores numerical poetics. What is at stake here is above all a conflict between the word and the number, which is of crucial importance for Dostoevsky's poetics of multi-voiced speech.

It was Mikhail Bakhtin (2002) who coined the concepts of polyphony, dialogism and heteroglossia to describe Dostoevskii’s writing. Bakhtin calls the word a battle field pointing out that polyphony does not imply harmony. Dostoevsky’s words are not quite his own; they contain an irreconcilable dispute between voices, a din of contrapuntal speeches and polemic attitudes. This constant self-objection includes the alien – the Other – in every word. One might say that the polyphonic dialogue, in its outspoken regard for heteroglossia and discursive non-identity, practices negative dialectics.

What does this non-identity mean for numbers and the mathematical ideal of consistency? On the battle field of dialogical controversy, the number represents maximum monologicity. It limits the open resonance of speech, reduces ambiguous noise and minimises the risk of unplanned collisions. But it is precisely the principles of correctness and regularity that Dostoevsky draws into the conflict between voices, creating a carnivalesque parody of “numerical correctness”. When 2 and 2 no longer unquestionably and add neatly to 4 but result in shady sums, arithmetic is caught in the turbulent zone of polyphonic contradictions. When numbers argue, rebel, and get in the way, they enter the scene of dialogue.

Against this background, it becomes clear that Dostoevsky’s engagement with the philosophical arithmetic of judgement is primarily a debate about the power of speech. Moreover, we can see the function of numbers in this power dynamic. Dialogicity is not only an antinomic form of speech, it is also an antinomic form of calculation – dyscalculia – as illustrated by the formula 2x2=5. Dostoevskii’s oft-evoked and much quoted polyphonic poetics is thus an arithmetic of the polyphonic number.

Poetics of the Arithmetic Arrangement

«Жила-была четвероногая ворона. Собственно говоря, у нее было пять ног, но об этом говорить не стоит.» / “Once upon a time, there was a four-legged crow. Actually, it had five legs, but it's best not to mention that”, Kharms (1997: 162) writes in his notebook on February 15, 1938. These lines are followed by a brief sketch of how the crow goes to buy coffee. What kind of text is this? An unexecuted narrative nucleus? An experimental fairy tale? An early example of what is now called microfiction or nanonarrative? According to structuralist narratology and introductory courses in literary studies ever since, every narrative needs to violate some norms, to break some rules, to cross some boundaries. If this does not happen, if no difference is experienced, there can be no event. And where there is no event, there is nothing to tell.

Kharms opens with a deviation. A four-legged crow. Moreover, as it turns out in the following sentence, this four is not made up by 2+2 but by 2+3. A five-legged crow, then. The zoological strangeness here certainly qualifies as an event, indeed arguably as a sensation. Kharms, however, does not use it as the starting point for eventful narration. He declares the difference null and void, ending just where a narrative might begin eventually.

This short text belongs to a series of prose miniatures in which Kharms dispels objects, subjects, and spaces. Using the motifs and rhetoric of withdrawal, these texts arguably pursue a negative narratology. As they progress, no plot unfolds. Instead, the act of narration is handled regressively or explicitly allowed to fail. Rather than creating worlds, Kharms’s miniatures annihilate them. For this reason they have been described as “apophatic literature”, which strives towards zero reference (Hansen-Löve 1994). But perhaps this kind of narrative could be more precisely characterized by modifying Bartleby’s maxim: “I would prefer not to tell.”

In this sense, the crow miniature is a micromanifesto of anti-narrative prose. – and it is such by virtue of being a numerical. Indeed, counting and recounting are as closely related as recounting is to happening. Narration is catalogical in its origin; it names and enumerates (Wedell 2011: 13). This long known nexus of narrative and numbers is still productive today (just consider the extensive literature of lists). After all, counting and recounting are speech acts that respond to the same question: “What counts?” (Ibid.)

Counting is a core process for establishing connections between word, the word order. One could say: while poetic speech is measured in metres, prose speech is counted in numbers. Its connectivity at this level is determined by rules of series. Kharms recorded the following in his notebook in the summer of 1932 during his exile to Kursk, a few years before the crow story:

Вот числа. Мы не знаем, что это такое, но мы видим, что по некоторым своим свойствам они и и вполне определенном порядке. И даже многие из нас в, что числа есть только выражение этого порядка, бессмысленно располагаться этого порядка существование числа – бессмысленно. (1993: 119)

Take numbers. We don’t know what they are, but we see that they can be strung together in a strict and clearly defined order according to some of their characteristics. Indeed, many of us even think that numbers are only an expression of this order and that beyond this order the existence of numbers makes no sense.

It is precisely beyond this order that Kharms’s numeric prose positions itself. Research has focused above all on the idea of infinity (of cisfinitum) and Kharms’s fascination with zero (Niederbudde 2003; Jampol'skij 1998: 287-313). But there is still more to it: this prose attempts to envision numbers and the act of counting – and thus also narrating – outside the limits of a regulated system with a clear logic of connection: «Числа не связаны порядком. Каждое число не предполагает себя в окружении других чисел.» (Kharms 2014) / “Numbers are not connected by any arrangement. No number can be assumed to be in the environment of other numbers.” (Kharms 1992c: 131)

This postulate repositions counting and recounting in relation to each other. The number no longer presupposes a structural model, and counting no longer means an ordered sequence of fixed operative steps. Rather, it generates impulses for structural disconnection. Kharms thus approaches a concept of numbers close to that of formal calculation. Counting conceived as calculus means manipulating mathematical symbols without regard to anything they might represent. The very efficiency of calculus lies in its complete indifference to the properties of the things being counted. This is what Krämer (1991: 1) has called the “operative use of symbols”. It is also what Poincaré had in mind when he said, “mathématique est l'art de donner le même nom à des choses différentes”: “mathematics is the art of giving different things the same name”.

Kharms radicalises this arbitrariness by detaching numbers not only from objects but also from each other. His prose and the characters in it arise against the background of this disjunctive concept. If the number can be preceded or followed by anything whatsoever, then the narrative is no longer determined semantically or formally. The four-legged crow with five legs marks this point of radical narrative contingency. Here, word and number become unavailable, not to be caught up or bound by numerical or narrative means.

The Aesthetics of Arithmetic Visualility

The word and the number are both highly abstract media. What words say is by no means coextensive with what they claim to figuratively show. The concreteness of numbers lies not in the representation of the objects counted; rather, numbers themselves are visible and thus manageable entities. According to Krämer (1991: 3), „dem neuzeitlichen Zahlbegriff […] gilt als Zahl, was als Referenzgegenstand eines arithmetischen Symbols, mit dem regelgerecht verfahren werden kann, interpretierbar ist“ / “the modern numerical concept […] defines a number as that which that can be interpreted as the reference object of an arithmetic symbol that can be used in a rule-based fashion”. Since the introduction of the Indian numerical system and the zero, arithmetic has been – as media philosophy has repeatedly pointed out – a writing technique. Rather than moving the beads on an abacus, we are now dealing with „regelgeleitete Formen und Umformen von Zeichenreihen“ (ibid. 1991: 198) / “rule-guided forming and reshaping of series of signs” on paper. Though numbers can be verbalised, you can only write a formal numerical language, not speak it. This makes calculus a “paper tool” in Ursula Klein’s sense (2002), a tool that combines graphic visuality and manipulability.

It is this combination that renders the number so productive for writing projects in the visual arts. In the 1970s, for instance, Kabakov designed a series of concept albums that could be described as an artistic typology of homo sovieticus. Each revolves around an allegorical figure exemplifying some desirable socialist energy. One of the albums is dedicated to Gorskii, doing maths. Gorskii is working on a kind of mathesis universalis of real existing socialism proceeding from the spirit of arithmetic. Obsessively counting things and creating sequences, he keeps discovering that certain things cannot be integrated, fall out of the sequence. Again and again, he is forced to add up anew and form another sequence to arrive at the total numerical index of the Soviet cosmos (fig. 5).

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Kabakov: sheets from the album “Matematicheskii Gorskii” / “The Mathematical Gorsky” (ca. 1972)
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Kabakov: sheets from the album “Matematicheskii Gorskii” / “The Mathematical Gorsky” (ca. 1972)

Kabakov describes the subject of this infinite reordering as a struggle with consistent systematic signification through sequencing:

О том, что все в жизни включено в „ряд“, все находится в каком-то ряду; о невключенности в „ряд“, „чуждости“, о выпадении из ряда и попадании в новый, уже другой ряд. (Kabakov 1999: 100)

It’s about how everything is part of a “sequence”, everything is in a certain order; it’s about not being included in this “sequence”, about “otherness”, about falling out of the sequence and into a new, different one.

“The Mathematical Gorskii” with his compulsive serialization and sequentialization seems like a close relative of the narrator and enumerator Kharms. Using the medium of the image in addition to text, he, too, creates and disintegrates sequences, testing numerical ordering systems that never prove stable enough to guarantee coherence in form or content.

Literature has repeatedly explored this tension between the representation of things, on the one hand, and the graphic visual quality of numbers, on the other, in developing numerological concepts of imagination or recording figures that transcend mathematical models. A particularly intricate experiment in this area was carried out by the cubo-futurist Khlebnikov. His small but complex œuvre revolves around a kind of theory of everything. While Kharms isolates numbers from each other, for Khlebnikov, numbers glue things together. To draw another comparison: while Dostoevsky conjures up the horror scenario of living imprisoned in a logarithmic table, Khlebnikov draws so-called Doski sud'by / Tables of Destiny: tables that correlate the dates of historical events and biographies. The lives of Christ and Marx are correlated by Klebnikov (1972b: 338), as are the dates of historical battles (Fig. 7).

31 марта 1871 года – начало Парижской Коммуны. Через 768⋅22 – 16 июля 1917 года – вооруженное выступление рабочих в Петрограде.
29. мая 1871 года – разрушение Вандомской колонны как знак отречения от власти над другими народами. Через 1053⋅16 – 16 июля 1917 – вооруженное выступление в Петрограде.
7 марта 1848 года – восстание в Париже. Через 1053⋅20 – 2 ноября 1905 – Красный Петроград.
29. апреля 1848 года – манифестация безработных с требованием права на труд. Через 1053⋅8 – 10 апреля 1871 года – провозглашение Парижской Коммуны.

(Khlebnikov 2018: 205)

March 31, 1871 – beginning of the Paris Commune. 768⋅22 later – on July 16, 1917 – armed uprising of the workers in Petrograd.
May 29, 1871 – destruction of the column in Place Vendôme as a sign of the renunciation of power over other peoples. 1053⋅16 later – on July 16, 1917 – armed uprising in Petrograd.
March 7, 1848 – uprising in Paris. 1053⋅20 later – November 3, 1905 – Red Petrograd.
April 29, 1848 – demonstration of the unemployed demanding work. 1053⋅8 later – April 10, 1871 – Proclamation of the Paris Commune.

This numerical network of closely interwoven events and data is almost impossible to escape and can be extrapolated to predict future events. Systematically, the numbers here primarily refer to years, dates and days. They are signifiers of time. Medially, however, they have a different function, converting texts into other visual formats, shifting the nexus from word/number to image/number. This concerns the epistemic pseudo-evidence of the table claiming to represent the big data of world history as a unified formula. And this also concerns the iconic quality of the number itself.

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Khlebnikov: "Zhizn stoletii pri svete 3n” / “The Life of the Centuries in the Light of 3n” (Doski sud'by / Tables of Destiny, 1920-22)

As can already be seen in the Doski sud’by, Khlebnikov (2006) cultivates a special preference for exponentiation, calling it «действие наиболее скупого расходования чернил»: an “operation that most economically uses ink” (fig. 6). The economy, he argues, lies in abbreviating long multiplication chains. Apart from these economic advantages, however, he seems particularly attracted to the visual form of this calculation method:

33+3 + 33+2 + 33+1 = 1053
Это уравнение очень красиво, если ее написать цепями нисходящих степеней троек. Закономерно уходящие показатели своими головками кивают на ковыль, как верхушки трав и волнуются ржаными полями чисел, какой-то рожью троек.

33+3 + 33+2 + 33+1 = 1053
This equation is very beautiful if you write it in a series of decreasing powers of three. The decreasing exponents nod their heads toward the feather grass, themselves like blades of grass, [like] undulating rye fields of numbers, rye fields of threes.

What enables this aesthetic perspective on numbers? Niederbudde (2006: 284) points out that the notation of exponentiation – with a number at the base and the exponent above – inserts a vertical axis into a horizontal sequence of numbers. This axis renders numbers particularly visible, or rather – it renders them visible as numbers in the first place. „Chlebnikov begreift Rechnen also vor allem als visuelle Kunst“, writes Niederbudde (2002): “Khlebnikov thus interprets arithmetic primarily as a visual art”. This expansion of the number appears to contain something else, too: calculation is used here as a paper tool in Ursula Klein’s sense.

As formal signs, numbers do not denote objects: to enable symbolic operations, the number must detach itself from things. Instead, it draws its meaning solely from the system in which it is used. Khlebnikov proceeds from this zero-reference point of the number, radicalizing it until it gains material concreteness as a thing in itself. However, as a visual thing on the paper surface, the representation of the number takes on a new form. While from a media historical point of view, representing numbers in writing was a prerequisite for their operational emancipation from visible things, in Khlebnikov’s work, this representation becomes a prerequisite for rendering numbers visible as things. The image of threes as grasses is subject not to a mathematical but to an aesthetic potentiation: if formal systems of calculation can no longer point to anything beyond themselves, their graphemes become manipulatable as visual images.

Open End or Numerus Apertus

When El Lissitzky (1967: 122) published his art-theoretical manifesto „K. und Pangeometrie“ / “Art und Pangeometry” in Carl Einstein’s Europa Almanach in 1925, he preceded it with the preamble: „Die Parallelen zwischen K. und Mathematik müssen sehr vorsichtig gezogen werden, denn jede Überschneidung ist für die K. tödlich.“ / “Parallels between art and mathematics must be drawn very carefully because any overlap is deadly for art.” Much like artists, literary scholars have good reasons to distrust numbers, if only because discursive and numerical symbol systems are not readily compatible: words cannot simply be translated into numbers and vice versa. And yet, there are good reasons for literary studies to deal more offensively and openly with numerical issues. The clearest one is that literature itself keeps seeking encounters with the number, particularly when we are considering dissidence and difference – when conflicts erupt in language that are negotiated (but not harmonized) via mathematical concepts.

The (mis)equation “2+2=5” is an attempt to explore these fractions and asymmetries. Its significance lies precisely in the fact that numbers do not represent secured, propositional knowledge here. Rather, they offer an alternative form of thinking and representation. This poses a massive threat to the order of correct calculation. But it also raises the courage necessary to make mistakes and try out the irregular. “2+2=5” insists on the intrinsic non-mathematical logic of literature and, last but not least, takes delight in the incalculable.

On October 18, 1812, Lord Byron (1974: 159) wrote to Annabella Millbanke, his future wife, whom he also called the “Princess of Parallelograms”: “I know that two and two make four – and should be glad to prove it too if I could – though I must say if by any sort of process I could convert two and two into five it would give me much greater pleasure.” One could argue that literature is concerned with exactly these conversions, far beyond the fragment discussed today. For there exists not only a desire to take pleasure in the text – which is, alas, more often proclaimed than practiced in literary studies – but there is yet another pleasure to be (re)discovered: the pleasure of the number. This pleasure can be experienced in artistic dyscalculia: 2+2 sometimes adding up to 5. All it takes is a certain enthusiasm (of the non-Stalinist kind).

Susanne Strätling
FU Berlin
susastra@zedat.fu-berlin.de

Translated by Alexandra Berlina

Notes

1 And further: "Quapropter ex his forsan non male concludemus Physicam, Astronomiam, Medicinam, disciplinasque alias omnes, quae a rerum compositarum consideratione dependent, dubias quidem esse; atqui Arithmeticam, Geometriam, aliasque ejusmodi, quae nonnisi de simplicissimis & maxime generalibus rebus tractant, atque utrum eae sint in rerum naturâ necne, parum curant, aliquid certi atque indubitati continere. Nam sive vigilem, sive dormiam, duo & tria simul juncta sunt quinque, quadratumque non plura habet latera quàm quatuor; nec fieri posse videtur ut tam perspicuae veritates in suspicionem falsitatis incurrant" (Descartes 2014: 12-15): “Therefore it can be rightly concluded from this that physics, astronomy, medicine, and all other sciences which depend on the observation of composite bodies contain space for doubt – but that arithmetic, geometry, and other such which deal only with the simplest and most general objects, caring little whether they exist in reality or not, contain something certain and unquestionable. For no matter if I sleep or wake, two and three always make five, a square never has more than four sides, and it seems impossible that such obvious truths could be suspected of being false.” (translation from Latin)

2 Kant (1974: 56) proves this with the arithmetic theorem 7+5=12.

3 “The hero of Dostoevskii’s Notes from Underground protests against the intolerable tyranny of two and two making four. He prefers that they shall make five, and insists that he has a right to his preference. And no doubt he has a right. But if an express train happens to be passing at a distance of two plus two yards, and he advances four yards and a half under the impression that he will still be eighteen inches on the hither side of destruction, this right of his will not save him from coming to a violent and bloody conclusion.” (Huxley 2000: 400).

Bio

Susanne Strätling is professor of Slavic Languages and Literatures at Freie Universität Berlin (Germany). Previously she taught at LMU Munich and University of Potsdam. Her main fields of research are the mediality of literature, metaphorology, and cheiro-poetics. Recent publications include: Die Hand am Werk. Poetik der Poiesis in der russischen Avantgarde [The Hand at Work. Poetics as Poietics in the Russian Avant-garde] (Paderborn: Fink, 2017); Rukhlivyi prostir [Space in Motion], co-edited with K. Mishchenko (2018); “Energie — ein Begriff der Poetik?” [Energy — A poetic concept?], in Kraft, Intensität, Energie. Zur Dynamik der Künste zwischen Renaissance und Gegenwart, ed. by Frank Fehrenbach et al. (Berlin: de Gruyter, 2017).

The original German version of this article was published in refubium, FU Berlin

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Suggested Citation

Strätling, Susanne. 2020. “2+2=5. The Poetics of Dyscalculia, or the Word and the Number in the Blind Spot of Digital Humanities.” Apparatus. Film, Media and Digital Cultures in Central and Eastern Europe 10. DOI: https://dx.doi.org/10.17892/app.2020.00010.237

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