Anxious Geometries

Abstract

These short poetic texts, the first ones written—many years ago—as a commentary on representation of imaginary arrangements of volumes and architectures, have as their object geometric entities, and a certain melancholy given to them by their inflection in shadow or disappearance in light. They are infused with aching by the unresolved relations between finite and infinite, between truth, uncertainty and doubt; light and shadow; permanence and the inexorable flow of time.

On Quadrato nero by Kasimir Malevic

So many verses have been inspired by the famous painting Black Square of 1914–1915 by the Russian painter Kazimir Malevich, founder of Suprematism, a movement of the Russian avant-garde.

With this work (here liberally interpreted by me), Malevich intended to arrive to the zero degree of painting, that is, the total abandonment of representation, the mimetic relationship with a reality other than self. What remains, and what the artist was striving for, are pure perception and absolute sensitivity (Fig. 12).

In my pictorial interpretation, the black square is perceived frontally, and is not exactly a square, since there are asymmetries, optical corrections. The vertical sides are slightly longer with respect to the horizontal sides; the space below the square is higher with respect to that above it. There are also other, almost imperceptible deformations. The background is not white but vibrant with material and light, the gray has various tonalities; on top, in the upper middle panel, it deepens to black. Not even the black is absolute, but allows the slightest gleams, fragments of light.

However, in all these interpretations, pictorial as well as poetical, there emerges, from the apparent imperturbability of the black square, margins that evoke something, allude to other, and absorbing our gaze, whisper questions to us. In affirming that it signifies nothing and hides no enigma, it raises a subtle anxiety. An archetypal form, the black square evokes, in its dark and almost imperceptible whispering, that most hidden aspect of intimacy that Jung identified as the Shadow. It is the Shadow which is inhabited by removed feelings of guilt, indelible uncertainties of the ego.

Poems/poesie

• 12

• The golden section of the ruler does not voice 

  the wise cartographer’s knowledge, 

  for shade shuns triangulation

  and light isn’t but the unquiet dominion

  of the winged creatures. Arduous to trace

  neat trail in the garden: tracks do clog

  in mill-ponds of shade or in fine clarity

  of vagueness, of outlandishness.

  Among arboreal encumbrances and humid tuffs

  entanglements aren’t but harsh knots of sorrow.

  Let us then yield to a minor outline

  as of the skylark’s bold map-threading,

  to the mocking measure of its singing,

  although almost nothing is left behind

  but the uncertain presentiment of a quietude.

• 12

• Non esaurisce l’aurea misura del regolo

  nessun sapere del cartografo valente

  poiché l’ombra sfugge ad ogni triangolazione

  e la luce è dominio irrequieto dei volatili.

  Arduo comporre limpida traccia nel giardino:

  s’interrompono i sentieri in gore d’ombra

  o in tenue chiarità di lontananze vaghe.

  Tra frangenti arborei e zolle umide

  sono gli incroci aspri nodi d’afflizione.

  Affidiamoci allora al minimo tracciato

  della cartografia audace delle allodole:

  alla misura irridente del loro canto

  sebbene, a noi, quasi nulla resti,

  solo il presagio incerto d’una quiete. (Fig. 3)

Fragment of a theorem never seriously stated (since it has just emerged from shadow…)

Frammento di un teorema mai seriamente enunciato (poiché appena emerso dall’ombra…)

• 17

• Metrication is sought by the universe for

  pathways to blossom into measures to be trodden, 

  outlining spaces unto the boundary of void.

  Pathways, silver slimes in the time of night,

  nights of dreadful eclipses, to go through

  in winding exhausted roaming to the extent

  of unbecoming spaces, whilst betrayed

  by stars once relied upon as fixed.

  Uncertain travelers in the frail cavity of memory,

  may find it sweet to pause at a hollowed border

  overwhelmed by flowing waves of time.

• 17

• Un sistema metrico è necessario all’universo

  a dischiudere sentieri in misure percorribili

  tracciando spazi certi al limite del vuoto.

  Si percorrono sentieri, bave argentee nella notte

  in tortuosi andirivieni stremati ai confini

  di spazi insostenibili, in notti di tremende eclissi

  traditi da quegli astri che si credevan fissi.

  Viaggiatori incerti nel cavo esile della memoria,

  dolce è tuttavia sostare laddove il confine è vago

  sommersi dall’onda temporale che trascorre.

• 21

• Everyone knows, in one’s unquiet soul,

  that the beauteous garden is the unfulfilled,

  there the vermilion maple-tree grows with the rose,

  near to the box-tree the hedged thuja

  juts out in full greenery beyond its limits,

  the jasmine is enraptured in dimness

  on the breaking of the path and there

  the faint enclosure yields to the hour of twilight. .

• 21

• Ciascuno sa, nell’animo irrequieto

  che il giardino più bello è l’incompiuto,

  vi cresce l‘acero vermiglio con la rosa,

  accanto al bosso la tuia in siepe

  sopravanza di verzura i suoi confini,

  il gelsomino s’inebria di penombra

  laddove il sentiero s‘interrompe e

  cede il labile recinto all‘ora che rabbuia.

Triangles/Triangoli

• 23

• Some among the triangles unmistakably look 

  vindictive and gloomy- natured.

  Revengeful as they are, then, they rage

  against the cartographer whose fingers tremble

  and anxiety due to the elapsing season

  cracks the light on the declining page.

  Acute angles are sharply severed across,

  more, they are wounded, scratches are pierced

  in the unsteady defenceless paper substance.

  That is why each and one cartographer’s

  woeful look happens to oft betray

  the shadow of shed tears in his eyes

• 23

• Alcuni tra i triangoli esibiscono

  un’indole fosca e assai vendicativa.

  Rancorosi, dunque si ribellano

  al cartografo cui tremano le dita 

  e l’ansia della stagione che trascorre

  incrina la luce sul foglio che declina.

  I lati allora recidono, aspri feriscono

  gli angoli acuti, incidono scalfitture

  nel supporto cartaceo e indifeso.

  Per questo accade che ogni cartografo

  mostri spesso nello sguardo triste

  l’ombra d’un trattenuto lacrimare. (Fig. 8)

(translated by Claudia Azzola)

• 8

• When a mathematician, about to set off

  for a holiday at the seashore

  or for calling on some unavoidable relatives,

  leaves pages of yet unproven theorems,

  resting on white, still untouched papers,

  what do the forsaken glasses look at?

  will the lenses, without eyes shining,

  be bound to magnify delicate golden dust,

  sheaves of convergent curved lines

  of the neat abandoned theorems?

• 8

• Quando un matematico, in partenza

  per destinazione di ferie balneari o

  inevitabili visitazioni parentali, lascia

  carte di teoremi ancora irresoluti,

  posati sui fogli bianchi tuttora intatti,

  dove guardano gli occhiali smessi?

  resteranno le lenti, senza luce d’occhi,

  ormai ad ingrandire pulviscoli dorati,

  fasci d’incurvate linee convergenti

  dei nitidi teoremi abbandonati?

• 15

• Geometry exhibits shadowy anomalies.

  When it simulates the perfection of inviolable certitudes,

  it proliferates deceitful and disquieting theorems.

  In the unnameable chaos, this precarious order,

  brimming with aporias, generates morbid nostalgia

  for quadratures and golden albeit impassive sections.

  But if shadow escapes all triangulation

  and light is the fickle domain of restless winged beings,

  perhaps something remains within exiguous enclosures,

  sorrowful souls and beloved bodies lightly touching each other,

  the transparent fracture of a glance, words engraving

  stubborn crevices in the silence and surviving

  in the fragile geometry of memory.

• 15

• La geometria mostra ombrose anomalie.

  Quando simula perfezione di certezze inalienabili,

  prolifera in teoremi ingannevoli e inquietanti.

  Nel caos innominabile, quest’ordine precario e

  insieme colmo d’aporie, produce insane nostalgie

  di quadrature e d’auree ma impassibili sezioni.

  Ma se l’ombra sfugge ad ogni triangolazione

  e la luce è volubile dominio di volatili irrequieti,

  forse entro recinti esigui qualcosa resta,

  dolenti anime e corpi amati che si sfiorano,

  la limpida frattura d’uno sguardo, parole

  che incidono tenaci spiragli nel silenzio e

  sopravvivono nell’esile geometria della memoria.

Parallels/Parallele

• 27

• The anxious enigma lies in the axiom

  of two lines perfectly defined

  in their unquestioned parallel condition.

  Geometry, we known, outlines neat certitudes

  detached from time and shadows,

  but if the meeting point lies at infinity,

  the system wobbles, loosens its meshes

  and unlocks the unexpected threshold of a foreign,

  unexpressed beyond where thought founders.

• 27

• Giace l’ansioso enigma nell’assioma

  di due rette perfettamente definite

  nell’indubbia loro condizione parallela.

  La geometria, si sa, delinea nitide certezze

  sottratte al tempo e alla penombra, ma,

  posto all’infinito il luogo dell’incontro,

  il sistema vacilla, allenta le sue maglie

  e schiude imprevista la soglia di un altrove

  informulato laddove naufraga il pensiero. (Fig. 7)

(translated by Giuseppe O. Longo)

• 1

• The long side of the rectangle in the shadow does descend.

  The short one, in the bare light, wears thin

  And vanishes, merely inscribed in the thought

  Of an illusory imagined fulfillment.

• 1

• Declina il lato lungo del rettangolo nell’ombra.

  Quello breve, nella luce sgombra, s’assottiglia

  e svanisce, soltanto inscritto nel pensiero

  d’un illusorio compimento immaginato.

Malevich’s black square/Il quadrato nero di Malevich

• 32

• As black, in the square looks frightened, yet

  settled in its derisory perimeter

  prides itself of a vague, rarefied beauty.

  Confident in the absolute perfection of its sides

  mutely encloses within scant boundaries

  than secret, unperturbed pulse

  that breezes beyond any known threshold.

• 32

• Nero, il quadrato pare spaurito, ma,

  concluso nel suo perimetro irridente

  vanta una bellezza vaga, rarefatta.

  Certo dell’assoluta perfezione dei suoi lati

  muto racchiude entro confini esigui

  quel pulsare segreto e imperturbato

  che spira oltre ogni soglia conosciuta.

• 34

• The invasion of sense

  and the anxiety of any minimal emotions

  the suprematist black square repels.

  If you look at it, it seem to be loftily staring at you

  with Gorgon’s square pupil,

  as if wanting to tell you in a murmur:

  why do you tremble and question

  lost within vain enigmas?

  The black square IS, nothing it means.

• 34

• Respinge l’invasione del senso

  e l’ansia d’ogni minima emozione

  il quadrato nero suprematista.

  Se lo guardi, pare fissarti altero

  con la quadra pupilla di Gorgone,

  come volesse dirti sottovoce:

  perché tremi e t’interroghi

  perduto entro enigmi vani?

  Il quadrato nero È, nulla significa.

• 40

• The name, any name, comforts

  even the most fearful child,

  smoothens frayed drooling at the edges

  allows the caressing, lightly touching

  in the rustling forest of fhe other names.

  But the black square, it has no name

  it might be called darkness

  that blueish blackening of his,

  or sumptuous veil of panther;

  though, hearing the whispering

  cruel buzzing of a fly

  or the echo of scornful laughs, over

  his discreet dark threshold

  it whisperingly seems to allude

  to the light clue of a fault.

• 40

• Il nome, ciascun nome, rassicura

  perfino il bimbo più spaurito,

  smussa sfrangiate bave ai bordi

  permette un carezzevole sfiorarsi

  nella selva frusciante d’altri nomi.

  Ma non ha nome il quadrato nero,

  potrebbe chiamarsi tenebra

  quel suo bluastro nereggiare

  oppure sontuoso vello di pantera;

  sebbene, udendo bisbigliare

  il ronzio crudele d’una mosca

  o l’eco d’irridenti risatine, oltre

  la sua discreta soglia oscura

  pare sommessamente alluda

  all’indizio lieve d’una colpa.

(translated by Silvio Raffo)