Literature

A HIDDEN LITERATURE
Solomon Marcus
Simion Stoilow Institute of Mathematics
Romanian Academy
[email protected]
Two Lines of
Cultural Evolution
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.
To Get Order,
We Have to Pay a Price
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.
The Great Failure
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
A Quasi General Agreement
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.
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,
► engineering sciences,
► natural sciences,
► economics,
► information sciences,
or to ► some other social sciences.
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
Daughters of the
Ancient Myths
In the Greek tradition of the Western World,
Literature
beginning with
Homer
and
Mathematics
beginning with
Thales and Pythagoras
are both daughters of the ancient myths,
from which they inherited
some of their basic features
Need of a Presence
Accounting for an Absence
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.
Need of a Fictional Universe
Then, all these fields need to place
their action into a fictional universe.
Points
as things having no part
and
Lines
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.
The Holographic Capacity
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.
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.
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.
Transgressing
Classical Logic
Myths, literature and mathematics need to transgress the
logic governed by the principles of identity, noncontradiction 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.
A Special Kind of
Temporality
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.
Metaphor at Home
in Mathematics
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.
In (Marcus 2012) I described the way cognitive selfreferential 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).
A Cocktail of
Myths, Science, and Literature
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.
Poetry, Natural Sciences
and Philosophy
are at Home in
Lucretius’ Poem
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:
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
A Term of Reference:
Euclid’s Elements
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.
The Poetic Dimension of
the Father of Heliocentricism
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:
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)
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.
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)
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)
Galileo, secondo Calvino
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.
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.
In a second step, Calvino to Ortese:
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.
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.
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.
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»
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».
Cassola:
Scienza e letteratura hanno
nulla da dire l'una all'altra
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.
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.
From Dante to Galileo
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.
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.
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.
Calvino,
the European Borges
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.
Johannes Kepler
The Triumph of a Total Vision
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
Steps in the Separation
Between
Literature and Mathematics
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.
Another Source of Rupture:
The Elimination of
the Narrative Dimension
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.
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.
Maxwell:
The Exception
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. 1173-1176
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”
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.”)
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.”
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.
A Big Change of Paradigm
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.
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.
Barthes and Calvino
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 (1967-1968)
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. 29-38;
a translation from the original in Italian,
published by Einaudi, Torino, in 1982
Science and Literature
as Complementary Aspects
of the Same Text
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:
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).
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.
Wonder and Surprise
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.
Invention and Discovery:
From Asymmetry to Symmetry
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.
The Theatrical Dimension
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.
To Conclude
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.
THANK YOU!