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Simion Stoilow Institute of Mathematics

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1 Simion Stoilow Institute of Mathematics
A HIDDEN LITERATURE Solomon Marcus Simion Stoilow Institute of Mathematics Romanian Academy

2 Two Lines of Cultural Evolution

3 One can distinguish, in the last three thousand years of the cultural history of mankind, two lines of development: One of them, trying to organize the human knowledge and creativity in disciplines, looking desperately for their identity, each of them aiming to become a world in itself. The other line of development made as its main object of inquiry the need of different aspects of nature and culture to be together, to interact, to develop their metabolism, in absence of which you cannot understand them in their real nature.

4 To Get Order, We Have to Pay a Price

5 The need to introduce some order in human knowledge and creativity, when their complexity was increasing, lead to the segmentation in disciplines. But this is obtained at the expense of the nature of things, because reality, life phenomena and processes either ignore disciplines or go across them. In order to bridge this gap, an alternative line of development directed its focus towards transgression of the disciplinary borders.

6 The Great Failure

7 As a matter of fact, these two lines of evolution are complementary.
They need each other. But it happened that their synergetic capacity was not enough strong and the former line of development obtained the victory at the expense of the latter, in the way cultural institutions and systems of education were conceived. The second line remained rather hidden and now we try to recuperate, to bridge this gap. The literature is one of the victims of this situation. To the need to develop a therapy of this illness, we devote our work

8 A Quasi General Agreement

9 There is a quasi general agreement about the legitimacy and the high interest to read the Bible as literature or to read Plato’s Dialogues as literature or to consider Herodotus’ Histories a literary work. We believe that this capacity of literature to be solidary with / inseparable from other types of human creativity and to interact with them is just its strong point.

10 The topic we are considering is of a high complexity
The problem begins to become more difficult and controversial as soon as we refer to the possible literature hidden in works belonging to ► exact sciences, ► natural sciences, ► information sciences, ► engineering sciences, ► economics, ► some other social sciences. or to In this respect, some preliminary clarifications are necessary, because we have to face a lot of prejudices. The topic we are considering is of a high complexity

11 Daughters of the Ancient Myths

12 In the Greek tradition of the Western World,
Literature and Mathematics beginning with Homer beginning with Thales and Pythagoras are both daughters of the ancient myths, from which they inherited some of their basic features

13 Need of a Presence Accounting for an Absence

14 We refer first to the symbolic function, essential in myths, in poetry and in mathematics.
More generally, sign processes of all kinds, ● iconic, ● indexical or ● symbolic, are essential.

15 Need of a Fictional Universe

16 are the starting fictional characters in Euclid’s Elements
Then, all these fields need to place their action into a fictional universe. Points and Lines as things having no part as things having no thickness are the starting fictional characters in Euclid’s Elements Equally fictional are the characters of the tragedies of Sophocles. In both cases, a fictional scenario is developed. The fiction is the price to be paid in order to get some rigor, be it logical or artistic.

17 The Holographic Capacity

18 Myths, poetry and mathematics need a holographic capacity, i. e
Myths, poetry and mathematics need a holographic capacity, i.e., a capacity of some local, individual aspects to account for the global, the collective ones; of some instantaneous aspects, to account for the eternity. In all myths, irrespective the traditions to which they belong, anthropos and cosmos are in interaction, the former is accounting, in some respects, for the latter.

19 In poetry as well as in mathematics, the finite, the individual, are accounting for the infinity, the global, the total. The beginning of To See a World… by William Blake is a magnific illustration of this principle: To see a World in a Grain of Sand And Heaven in a Wild Flower, Hold Infinity in the palm of your hand And Eternity in an hour.

20 In mathematics, a lot of theorems account for the possibility of the finite to account for the infinity or for the small finite to account for the large finite. The so-called analytic functions are completely determined in the whole complex plane by their behaviour in the neighbourhood of a point.

21 Transgressing Classical Logic

22 Myths, literature and mathematics need to transgress the logic governed by the principles of identity, non-contradiction and excluded middle, i.e., the logic of our sensorial, empirical, intuitive perception of the world, and to replace it by a logic in conflict with this perception. During the 20-th century, a lot of so-called non-classical logics were introduced and this fact is strongly connected with another one: the paradox, considered at the beginning of the 20-th century a pathological, marginal phenomenon, became, with the evolution of logic, physics, biology, computer science and many other fields, a normal, central phenomenon, just as it is in ancient myths and in modern visual arts, music and literature.

23 A Special Kind of Temporality

24 We know now that there is a strong parallelism between myths, quantum physics and art, each of them having a tendency towards a temporality that could be the cancellation of the past-present-future distinction, to be replaced by a continuum present; and the same type of temporality seems to prevail in the perception of a new born baby.

25 Metaphor at Home in Mathematics

26 Metaphor is another thing which is essential in myths, in literature and in mathematics.
If for metaphor in myths and in literature things are very clear, an explanation is necessary for metaphor in mathematics. We have in view the cognitive metaphor, as a basic ingredient of the research process, for instance in the building of new concepts and in exploring new possible theorems.

27 In (Marcus 2012) I described the way cognitive self-referential metaphors (i.e., metaphors that refer not to a pre-existing entity, but to an entity emerging just under the action of the metaphorical process) are involved in the building of the conceptual status of integers, of rational numbers and of real numbers. On the other hand, it was proved (Lakoff – Nunez 2000) that with respect to the brain mechanisms involved in the creative process, mathematics is essentially of a metaphorical nature. A similar conclusion is suggested by (Manin 2007).

28 A Cocktail of Myths, Science, and Literature

29 During about two thousand years, science and culture were a cocktail of mythical elements, literature, science and philosophy (see, for more, Bochner 1966). Plato’s Dialogues, Lucretius’ De rerum natura, the works by Copernicus, Galileo Galilei and Johannes Kepler are in this situation. The invention of an artificial component of mathematical language, with Galilei, Descartes, Newton and Lebniz, favoured the rupture, the opposition between poetry and mathematics.

30 Poetry, Natural Sciences and Philosophy are at Home in Lucretius’ Poem

31 A contemporary reader could not believe that in a work, where a lot of interesting scientific facts are pointed out (for instance, he argues in this work that all unequal weights would fall with the same finite speed in a vacuum) and ideas of a natural philosophy are developed, the literary beauty is the dominant note, as in the beginning of the following poem:

32 Mother of Rome, delight of Gods and men,
Dear Venus that beneath the gliding stars Makest to teem the many-voyaged main And fruitful lands - for all of living things Through thee alone are evermore conceived, Through thee are risen to visit the great sun - Before thee, Goddess, and thy coming on, Flee stormy wind and massy cloud away, For thee the daedal Earth bears scented flowers, For thee waters of the unvexed deep Smile, and the hollows of the serene sky Glow with diffused radiance for thee! Lucretius, On the Nature of Things (Written 50 B.C.E.) Translated by William Ellery Leonard

33 A Term of Reference: Euclid’s Elements

34 Indeed, for almost 2000 years, many of the most important cultural works be they scientific, theological or philosophical, such as those of ● Archimedes, ● Augustin, ● Aquinas, ● Spinoza, ● Newton, followed in their presentation the architecture of Euclid’s Elements.

35 The Poetic Dimension of the Father of Heliocentricism

36 We refer to Nicolaus Copernicus’ 1543
De Revolutionibus Orbium Coelestium On the revolution of the celestial spheres English translation from 1926 by F.E. Bras Here are some quotations:

37 That the Earth went round the Sun and not vice versa, as had been thought
For when a ship is floating calmly along, The sailors see its motion Mirrored in everything outside, While on the other hand They suppose that they are stationary, Together with everything on board, In the same way, the motion of the Earth Can unquestionably produce The impression that the entire Universe Is rotating. (Ship, Earth, Motion)

38 For I am not so enamorated
Of my own opinions That I disregard What others may think of them. I am aware that A philosopher’s ideas Are not subject To the judgement of ordinary persons. Because is his endeavour To seek the truth in all things To the extent permitted To human reason by God.

39 (Opinion, Reason, Earth, Heaven)
Yet I hold that Completely erroneous views Should be shunned. Those who know That the consensus of many centuries Had sanctioned the conception That the Earth remains at rest In the middle of the Heaven As its centre would. I reflected, regard it as insane pronouncement If I made the opposite assertion That the Earth moves. (Opinion, Reason, Earth, Heaven)

40 Finally we shall place The Sun itself at the centre of the Universe. All this is suggested By the systematic procession of events And the harmony of the whole Universe, If only we face the facts, As they say, “With both eyes open”. (Sun, Universe)

41 Galileo, secondo Calvino

42 In a first step, Anna Maria Ortese is addressing Italo Calvino
Ortese to Calvino È il 24 dicembre 1967. Da una decina di anni sonde e satelliti artificiali solcano lo spazio fuori dalla Terra. Italo Calvino ha appena pubblicato Ti con zero. E Anna Maria Ortese sulle pagine del Corriere della Sera gli scrive una lettera, datata 24 dicembre 1967.

43 Caro Calvino, non c'è volta che sentendo parlare di lanci spaziali, di conquiste dello spazio, ecc., io non provi tristezza e fastidio; e nella tristezza c'è del timore, nel fastidio dell'irritazione, forse sgomento e ansia. Mi domando perché. La scrittrice, autrice di un acuto e indimenticabile Il mare non bagna Napoli con cui ha vinto il Premio Viareggio, è angosciata dal nuovo mondo tecnologico, che trova una clamorosa rappresentazione nei razzi che sfrecciano nello spazio.

44 In a second step, Calvino to Ortese:
La risposta, immediata, di Italo Calvino viene pubblicata quello stesso giorno sulle pagine del medesimo giornale e giunge forse inaspettata ad Anna Maria Ortese. Certo contiene un'impegnativa serie di giudizi su Galileo Galilei, su Giacomo Leopardi e sull'influenza del primo sul secondo. È il 24 dicembre 1967.

45 Cara Anna Maria Ortese, guardare il cielo stellato per consolarci delle brutture terrestri? Ma non le sembra una soluzione troppo comoda? Se si volesse portare il suo discorso alle estreme conseguenze, si finirebbe per dire: continui pure la terra ad andare di male in peggio, tanto io guardo il firmamento e ritrovo il mio equilibrio e la mia pace interiore. Non le pare di "strumentalizzarlo" malamente, questo cielo? Io non voglio però esortarla all'entusiasmo per le magnifiche sorti cosmonautiche dell'umanità: me ne guardo bene. Le notizie di nuovi lanci spaziali sono episodi d'una lotta di supremazia terrestre e come tali interessano solo la storia dei modi sbagliati con cui ancora i governi e gli stati maggiori pretendono di decidere le sorti del mondo passando sopra la testa dei popoli.

46 Galileo, il piu grande scrittore italiana in prosa
[...] Chi ama la luna davvero non si accontenta di contemplarla come un'immagine convenzionale, vuole entrare in un rapporto più stretto con lei, vuole vedere di più nella luna, vuole che la luna dica di più. Il più grande scrittore della letteratura italiana di ogni secolo, Galileo, appena si mette a parlare della luna innalza la sua prosa ad un grado di precisione e di evidenza ed insieme di rarefazione lirica prodigiose. E la lingua di Galileo fu uno dei modelli della lingua di Leopardi, gran poeta lunare... Per Calvino, dunque, Galileo non è solo un grande scienziato e un grande filosofo. È anche un grande scrittore. Anzi, il più grande scrittore della letteratura italiana.

47 Casolla to Calvino Carlo Cassola è tra i primi a reagire alla provocazione di Calvino. Non passa una settimana che il Corriere della Sera pubblica (31 dicembre 1967) un articolo molto duro a firma dello scrittore romano: «Domenica scorsa, su questo giornale Italo Calvino ha affermato che Galilei è il più grande scrittore italiano di ogni secolo. Io credevo che Galilei fosse il più grande scienziato, ma che la palma di massimo scrittore spettasse a Dante»

48 Non si tratta di un'improbabile gara a chi meriti la palma del migliore scrittore. Ma dei fondamenti stessi della letteratura e della cultura. «Mentirei - scrive Cassola - se dicessi che l'affermazione di Calvino mi ha scandalizzato. Lo spirito di dimissioni di molti miei colleghi è giunto a un punto tale che non mi scandalizzo più di niente. L'augurio che rivolgo loro è di liberarsi del complesso di inferiorità nei confronti della cultura scientifica e della tecnologia. E se no, che cambino mestiere».

49 Cassola: Scienza e letteratura hanno nulla da dire l'una all'altra

50 Carlo Cassola, dunque, pone due temi.
Il primo è un assoluto: scienza e letteratura sono dimensioni incomunicanti. Hanno nulla da dire l'una all'altra. Irrimediabilmente: Galileo è uno scienziato, dunque non è uno scrittore. Il secondo tema è più contingente: gli scrittori italiani son subalterni alla cultura umanistica. Una tesi che ha una versione speculare negli ambienti scientifici, secondo cui in Italia sarebbe egemone una cultura umanistica di impronta crociana e gentiliana che impedisce alla cultura scientifica di diffondersi nel paese sia tra le grandi masse, sia tra le classi dirigenti.

51 Maggior nutrimento in Galileo
Calvino to Cassola Calvino risponde a Cassola qualche settimana dopo, con intervento su L'Approdo letterario. In primo luogo: Maggior nutrimento in Galileo Intendevo dire scrittore di prosa; e allora lì la questione si pone tra Machiavelli e Galileo, e anch'io sono nell'imbarazzo perché amo molto pure Machiavelli. Quel che posso dire è che nella direzione in cui lavoro adesso, trovo maggior nutrimento in Galileo, come precisione di linguaggio, come immaginazione scientifico-poetica, come costruzione di congetture.

52 From Dante to Galileo

53 Infatti: Galileo usa il linguaggio non come uno strumento neutro, ma con una coscienza letteraria, con una continua partecipazione espressiva, immaginativa, addirittura lirica. Una coscienza letteraria che Galileo raggiunge soprattutto quando parla della Luna: Leggendo Galileo mi piace cercare i passi in cui parla della Luna: è la prima volta che la Luna diventa per gli uomini un oggetto reale, che viene descritta minutamente come cosa tangibile, eppure appena la Luna compare, nel linguaggio di Galileo si sente una specie di rarefazione, di levitazione: ci si innalza in un'incantata sospensione.

54 Tutto questo giustifica il giudizio su Galileo scrittore.
In particolare sul Galileo scrive della Luna dopo averla osservata, nell'autunno 1609, col nuovo occhiale. Tuttavia Galileo non rappresenta una singolarità nella letteratura italiana. Al contrario ne incarna la più intima vocazione. E la dimostrazione l'abbiamo proprio partendo da Dante. Cosa fa il poeta fiorentino, sostiene l'autore di Ti con zero, se non realizzare con un'opera enciclopedica e cosmologica una mappa del mondo e dello scibile e costruire, attraverso la parola letteraria, un'immagine dell'universo? Non c'è dunque davvero nessuno scandalo nell'accostare Galileo a Dante.

55 L'opera letteraria come mapa del mondo
Perchè Questa è una vocazione profonda della letteratura italiana che passa da Dante a Galileo: l'opera letteraria come mappa del mondo e dello scibile, lo scrivere mosso da una spinta conoscitiva che è ora teologica ora speculativa ora stregonesca ora enciclopedica ora di filosofia naturale ora di osservazione trasfigurante e visionaria. La scienza e la filosofia naturale sono, dunque, la vocazione profonda della letteratura italiana Una vocazione profonda, che coinvolge altri grandi autori - da Ariosto a Leopardi, entrambi «gran poeti lunari». E che deve essere riscoperta, se vogliamo rinnovare la grandezza passata della nostra letteratura.

56 Calvino, the European Borges

57 Indeed, Calvino's ideas concerning the science -literature interaction are deeply involved in the creation of Luis Jorge Borges. Only one reference may be sufficient in this respect: the book by William Goldbloom Bloch. William Goldbloom Bloch, The Unimaginable Mathematics of Borges' Library of Babel, New York: Oxford University Press, 2008.

58 Johannes Kepler The Triumph of a Total Vision

59 By his Astronomia Nova 1609 and mainly by his Harmonices Mundi 1619, Kepler is the highest expression and chronologically the last one in bridging successfully religious arguments and reasoning, astrology and astronomy, Pythagorean ideas and mathematics of planetary motion, Plato’s five types of regular solids and the celestial music of spheres, all of them in a cosmic poetic perspective. His self-authored poetic epitaph survived the times: Mensus eram, nunc terrae metor umbras Mens coelestis erat, corporis umbra iacet I measured the skies, Now the shadows I measure Sky bound was the mind, Earth bound, the body rests

60 Steps in the Separation Between Literature and Mathematics

61 The invention of an artificial component of mathematical language, with Galilei, Descartes, Newton and Leibniz, favoured the rupture, the opposition between poetry and mathematics. The natural language component of the scientific language became more and more marginalized: less and less words, more and more symbolic representations, formulas, equations. This trend reached in the 20th century its highest moment, not only in research, but also in university and high school teaching. The contrast to literature increased tremendously.

62 Another Source of Rupture: The Elimination of the Narrative Dimension

63 During the period from the 17th to the 19th century, the evolution of mathematics was from the accent on meaning and intuitive aspects, favouring the narrative dimension, towards the accent on syntax, correctness and formal rigor. Compare, in this respect, the face of Calculus with Newton, Leibniz and Euler with the same field with Cauchy, Weierstrass and Riemann. Rigor at the expense of meaning, in terms proposed by René Thom. This trend was another source of opposition between poetry and mathematics.

64 As the natural language component of mathematics became more and more marginalized, it was less and less place for intuition, for dynamic aspects, for narrativity, i.e., less and less possibility for mathematics to show its poetic face.

65 Maxwell: The Exception

66 Notices of Amer. Math. Soc., October 2013, p. 1173-1176
There were some remarkable exceptions, one of them being the Treatise on Electricity and Magnetism by James Clark Maxwell (1873), which has both the status of a scientific and of a literary work. See, for more, (Simpson 2005). In the review by Brian Hayes of this book, Hayes writes: “In mathematics and the sciences, style and substance seem to be orthogonal variables.” Notices of Amer. Math. Soc., October 2013, p

67 But on this point Thomas K. Simpson disagrees.
Speaking of scientific works generally and with particular reference to James Clark Maxwell’s Treatise on Electricity and Magnetism, Simpson writes: “It seems to be generally assumed that the literary and the scientific aspects of the work will factor, so to speak, and remain separable. It is not the case with Maxwell's Treatise on Electricity and Magnetism”

68 According to Brian Hayes, in his review of Thomas K
According to Brian Hayes, in his review of Thomas K. Simpson’s “Figures of Thought: A Literary Appreciation of Maxwell’s Treatise on Electricity and Magnetism,” Simpson sees the Treatise as a drama in three acts, or as “a classic trilogy on the pattern of the Oresteia: opening with confidence, passing into darkness and confusion, but then emerging with a resolution that is new to the world and which could not have been foreseen at the outset.” The drama has a hero: Michael Faraday, the unlettered, visionary genius of nineteenth-century British science, who intuited the relation between electricity and magnetism but resisted all urgings to put his discoveries in mathematical form. (Maxwell nonetheless eulogized Faraday as “a mathematician of a very high order.”)

69 And Brian Hayes continues in his review:
There’s no real villain in the story, but there is a figure who serves as a dark shadow providing contrast for Faraday’s brilliance. He is André-Marie Ampère, the French claimant to the title of founder of electrodynamics. “Embodied in the characters of Ampère and Faraday are not just two styles but two contrasting stances toward life itself: Ampère’s imperious, dictating to nature; Faraday’s modest, open, and sensitive to nature’s voice.”

70 Act III will eventually resolve this puzzle, but the ending is not one of those operatic climaxes where all the players suddenly drop their disguises, lovers are reunited, and troublemakers promise to reform. Getting to a satisfactory theory takes seven dense chapters, including a long digression into the celestial mechanics of Joseph-Louis Lagrange. The key idea is to associate energy and momentum not with the current flowing through a wire but with the electric and magnetic fields that surround the wire. From this novelty we are led to an even more remarkable idea in the denouement: We can dispense with the hardware of wires and magnets altogether and watch as disembodied electric and magnetic fields act and react, then dance across the universe as light waves.

71 A Big Change of Paradigm

72 Towards the end of the 19-th century, when we move from the dominance of the Galileo-Newtonian paradigm, based on the assumption of a sharp distinction between Subject and Object (the objectivity of science, of mathematics by excellence, was in clear opposition with the subjectivity of poetry) and the incapacity of the former to have a significant influence on the behaviour of the latter, to a new period, when all the components of the Galileo-Newtonian scenario (observation, hypothesis, experiment, induction, generalization, laws, experimental tests etc) get in crisis, because the assumption of a clear separation between Subject and Object, the universal determinism and the experimental testing no longer work.

73 We have instead the increasing role of cognitive models and of cognitive metaphors, conceived as hypothetical explanatory scenarios characterized by internal conflictual situations, so any cognitive model or metaphor needs to be improved and the cognitive process never ends.

74 Barthes and Calvino

75 During three centuries, from the 17-th to the 19-th century, but still persisting in the 20-th century, the dominant idea was that of a strong opposition between science and art, between mathematics and poetry, culminating in the vision of the French writer Roland Barthes, for whom in a poetic text the language is like a black window, it is self-referential, while in a scientific text the language is a neutral tool, exterior to him, like a transparent window. Roland Barthes, Literature versus science Times Literary Supplement ( )

76 But we are inclined to favor Italo Calvino’s attitude, according to which a work may be at the same time great both as science and as literature. The uses of literature, San Diego, New York, London: Harcourt, Brace & Comp., 1986, pp ; a translation from the original in Italian, published by Einaudi, Torino, in 1982

77 Science and Literature as Complementary Aspects of the Same Text

78 Calvino’s example, as we have seen, is the work of Galileo Galilei, but he goes much beyond it with his analysis. My belief is that mathematics, science in general, has a chance to acquire a literary dimension as soon as it is presented in the making and in their progress, with all human and social aspects of the fight with the unknown, with all failures and mistakes in the process. We mention some contemporary examples which are significant in this respect:

79 a) The way Donald Knuth (1974) supplemented with a novelette John H
a) The way Donald Knuth (1974) supplemented with a novelette John H. Conway’s (1969) work on surreal numbers; b) The story told by the Fields Medallist in mathematics Cedric Villani (2012), about his human fight to solve a mathematical problem; c) The book by Bogdan Suceavă (2012) transforming in a literary story his mathematical adventure; d) Our literary analysis of the mathematical texts published by the poet Ion Barbu under the name Dan Barbilian (Marcus 2013).

80 In this respect, we took advantage of the concept of diction (articulation) of the ideas introduced and analyzed by Professor Mircea Martin for the field of literary criticism (Martin 2010), but whose validity and relevance seem to be more general. A lot of other examples could be mentioned in this respect.

81 Wonder and Surprise

82 The science of the 20th century shows an increasing degree of surprise, more and more scientific results are in sharp conflict with our sensorial, intuitive and intellectual expectations. Scientific and technological imagination came as a shock, increasing the state of wonder in contemplating what happens in the new discovered worlds of the infinitely large and of the infinitely small; in the new discovered worlds of the Internet.

83 Invention and Discovery: From Asymmetry to Symmetry

84 Until the 19th century, it was a general agreement to place science under the sign of discovery and art and literature under the sign of invention. Beginning with the 20th century, we have to accept that both invention and discovery are essential in both science and art.

85 The Theatrical Dimension

86 The emergence of the conflictual aspects in cognitive modelling and in cognitive metaphors, the need of imagination of more and more explanatory scenarios increased the theatrical-spectacular nature of human creativity in both science and literature (Marcus 2013). Almost no significant event in the field of science and technology remained out of the attention of artists and writers. Human need and fight to know, to understand the world, the life are by no means less interesting for art and literature than the man-woman relation.

87 To Conclude

88 The second, hidden line of evolution of the human knowledge and creativity is, in some respect, more demanding, more exigent, than the first one, because it requires the understanding of different, heterogeneous disciplines, while we were trained to pay attention to one discipline, with respect to which we will define our profession. This is the challenge we have to face. Is literature living in a mixed environment inferior to the usual one? Two lines of evolution lead to two kinds of literature and we have to learn and to train to pay equal attention to both of them.


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