Numbering, a Resonant Silence


Prof. Enrica Colabella

Generative Design Lab, DiAP, Politecnico di Milano University, Milano, Italy.




An eastwards curved tree generates brightness

In “the milk of human kindness”



These non-linear investigations are about the hidden numbering structures inside a poetic text/work. Towards a total organic aesthetics. Ione and Pound. Vox and music. Ad libitum.In contado. As in music resonant words become tools for codes in Architecture generative processes. Meta-codes generate variations. Subject at a distance in a silence site; the memory of heart. The concept of abduction. Not-Euclidean experiences. Variant in ending.


An observation: poetry is a strong guide for performing a complex system; always it remains" to the absurd pretension to fix what time leaves behind".  “The first function of poetry, as of all the arts, is to make us more aware of ourselves and world around us “ W. H. Auden

1.Towards a total organic aesthetics

By learning to discover reality. It is a visionary procedure that defines the dual structure between a discovered reality and a new idea of transformation as a coherent system, open toward complexity. This system is organic for the reason that is able to generate endless variations, as in Nature; it is total too for representation in 360° performing, using Not-Euclidean geometry.

1.2 Aim

To discover idea/codes, defining meta-codes as not-linear systems.

1.3 Hypothesis

It is the memory of heart the key of discovering reality. Children discover similarity and affinity between very uneven things thanks to imagination. 

2. Numbering

Code = text (t = K open to performing)



Socrates: Then is this who possesses the art of numbering?

Ione: Yes, he is………


Socrates: Therefore are you not performer of performers?

Ione: Doubtless…


Socrates if there was a science having the same objects, why would we say that there is a difference between one art and another ever since it might be possible to gain the same knowledge from both of them?……….And if I will ask you if we have the same type of knowledge through the same art, that is arithmetic, either through another one, you will surely reply to me through the same.

Ione: Yes, this is true.


2.1 Number as an index


This World is not Conclusion.
A sequel stands beyond -
Invisible, as Music -
But positive, as Sound –


Emily Dickinson, 501


The memory of heart can generate artworks, as a process of discovering and charging fragments of our children life. This process is a sound of numbering as a synthetic tool able to identify a lot of different elements (words, colors, smells, pictures, feelings etc.) in a single impression that rises as a resonant moment in the silence of mind.


2.2 Number as an order, Imagist effect


Number is not only an order for quantity; it is also an organized quality.

“Haiku”, i.e., is an ancient order, 5+7+5, of an open structure able to generate endless results.

Ezra Pound spent 3 years following this order for writing



In a Station of the Metro


The apparition of these faces in the crowd;

Petals on a wet, black bough.


Pound defines the image as that which "presents an intellectual and emotional complex in an instant of time." "It is the presentation of such a complex instantaneously."

The Book of Poetry (Shih Ching). Copy owned and annotated by Ezra Pound.

Upon receiving Fenollosa's scholarly papers, Pound poeticized a number of Fenollosa's line-by-line translations of the works of Chinese poet Li Po (Rihaku in Japanese), publishing the result as the much-noted volume Cathay.

Ezra Pound. "Canto LXXIV," part of The Pisan Cantos, with a "note to base censor" that the ideograms contained nothing seditious. T.MS. with autograph corrections and ideograms.

2.3 Visual Poetry, figurations

Fisches Nachtgesang







2.4 Vox + numbering, dare i numeri

Venticinque trenta quaranta    

Ottanta sedici venti trentadue

Uno quarantacinque trentadue!


2.5 Ad libitum, an exercise

Tracce di germogli tra cenere umettata

Sul poetico, genuflesso sito


2.6  In contado

Dante, Divina Comèdia (finale del Canto XXXIII)

Quella circulazion che sì concetta
pareva in te come lume reflesso,
da li occhi miei alquanto circunspetta,
dentro da sé, del suo colore stesso,
mi parve pinta de la nostra effige:
per che'l mio viso in lei tutto era messo.
Qual è 'l geomètra che tutto s'affige
per misurar lo cerchio, e non ritrova,
pensando, quel principio ond' elli indigne,
tal era io a a quella vista nova:
veder voleva come si convenne
l'imago al cerchio e come vi s'indova;
ma non eran da ciò le proprie penne:
se non che la mia mente fu percosa
da un fulgore in che sua voglia venne.

A l'alta fantasia qui mancò possa;
ma già volgeva il mio disio e 'l velle,
sì come rota ch'igualmente è mossa,

l'amor che mouve il sole e l'altre stelle.


La Divina Comedia is one of the most complex opera in the world, but in the same time she is very clear and simple.

People in contado song a lot of times some frames.

2.7 Numbers = Alphabets, translation in prose from poetry, the grammar of permutations

The Alphabets “poems” by Georges Perec present on the same page in a site a square of 11 letters for 11 and in the other site the same letters explained, with fragments of different spaces-silences. Perec defines poetry a closed square out of other representations and instead prose is the site of punctuation, of spaces, of representations. Each of 176 texts is an onzain, a poem of 11 lines; each line has 11 letters; each line uses a same series of different letters inside themselves. All poems shares the ten most used letters of French alphabet: E_S_A_R_T_I_N_U_L_O: The 11th letter is one of 16th rest. There are 11 poems in B, 11 poems in C etc.; on the whole 16X11=176 poems.

L A N G E S O U R I T L'ange sourit. 
A L O R S G E I N T U Alors geint un glas tiré ou
N G L A S T I R E O U grelot a su nier salut.
E R S A L U T O N G I On gisait.
S A I T O L U R N E G O, l'urne, gourant le si guignart,
O U R A N T L E S I G le sorti sang, élu, oint, eu, gras,
U I G N A R T L E S O lotion à sûr gel!

With the same diagram, the combination in C, Perec arranged a unique text, Ulcerations, composed by 400 permutations: this is the first publication of” La Bibliothèque Oulipienne".


2.8 Poetry in prose

maxima (sententia)
La véritable éloquence consiste à dire tout ce qu’il faut, et à ne dire que ce qu’il faut. 

Maxime N°250 de La Rochefoucauld


3. Idea as a code

Idea is represented with creative algorithms that define multiple paths from an existing world towards possible worlds. Idea is like a natural DNA, a transformation code that identifies a lot of different relationships starting from the designer’s idiom. These algorithms can be used in a creative complex process for every project and it is possible to upgrade them as an increasing experience. So we define a set of not linear procedures (words, matrixes, schemes, paradigms) able to perform open generative systems. This creative methodology brings to formalize an artificial Dna, which is based on the observation of the environment that surrounds us and on our cultural references. This is a possible expression of a lot of impressions of our life.

3.a MetaCode for endless variations

 If we define a code, as open strata of diachronic matrixes, we can generate new endless variations.

3.1 Key words, generative tools for idea

      Words as attributes

We can use creatively our mother tongue defining some words as attributes, minimum three or more, as a possible significance of our iter. This is a very important tool that connects words with pictures in a logical procedure, as in ancient time, ut pictura poiesis. But this is also peculiar to the classic music. We have a lot of different attributes as indications for playing Mozart, Bach Rossini etc. The author can gain an open number of variations with these multiple topic suggestions.


STRUCTURE: 1 FIST ATTRIBUTE,generic also random

                         2 SECON ATTRIBUTE, dual, hendiadys

                         3 THIRD ATTRIBUTE, versus

                         = performing open CATEGORIES

3.2 Abduction 

As happens in every creative act, such observation activates a fixing up of our impressions, as a performing of our subjective interpretation. This procedure was defined by Pierce as an abduction process, able to define an “how to reason”. The interpretation is an experience. The aim of the formal logic is to delineate a table of categories, able to be a faneron, a manifestation of experience. We can read and record what fascinated us as a code of transformation. Hume described this mental process as an idea that reminds an impression about an absent object. In this way what is observed and appreciated becomes a strong deep indication for identifying a process of transformation that will operate on the existing environment to transform it into a possible scenario. So we call abduction this type of performing rules because the interpretation of the events is managed with the aim to represent a rule as an algorithm.

The construction of an artificial Dna is also a basic process that can grow toward complexity using algorithms as a useful answer to the contemporary needs of Quality and Beauty.

Is Poetry in relation between musical variations a stochastic process? This is a false problem. Also variation is stochastic, when it is defined. But musical theme is more soft and variations run copious. But why doesn’t Poetry need variation? The condition of eternity is iteration. Poetry represents this procedure. This is a unique way to gain eternity. She is a site of loneliness. Text is iteration. The sounding expression is a collective listening as the addition of hearing singularity. The listening impressions are not possible to add. Each people perceives and takes a peculiar aspect, also if all together perceive the same significance. And emotions can be strongly similar.


4. natural infinite

Leonardo defined philosophy as “images of mental talk” by drawing a deep parallelism between Nature and Reason. Luca Pacioli suggested Leonardo to read the V book by Euclide. This was a basic point that he extended with genial intuition, by using proportions also in time, space, sounds, weights, sites etc. By this scientific investigation he discovered  “… varie e strane forme fatte dalla artificiosa Natura…” (…variant strange shapes made by Artificial Nature..), that he fixed in sketches  and used later as codes in his works.

His scripts edited only in 1881 were pressed as a simple first draft on a wax table in only one passage, by using a Roman technique. These were written all in a reverse way. It is possible to read them only in front of a mirror, for emerging a similarity between natural process and interpreted reality.


5. Resonant words as numbers

5.1  Poetry and geometry

E questo 72 basi molto dagli architecti fia

frequentato in loro dispositioni de edificii,

per esser forma assai accomodata maxime

dove occoresse fare tribune o altre volte,

o vogliamo dire cieli.

(L. Pacioli, De Divina Proportione, 1498)


5.2   Algebra in poetry

5.2.1 Voltaire:
A Madame du Châtelet

Sens doute vous serez célèbre
Par les grands calculs de l'algèbre,
Où votre esprit est absorbé.
J'oserais m'y livrer moi-même;
Mais hélas! A+D-B
N'est pas = à je vous aime.

(Madame du Châtelet va traduir al francès els Principia de Newton... i fou l'amant de Voltaire)


5.2.2 Tartaglia  sent this poem to Cardano, in which the solution of equations of 3° was hidden, from him discovered in 1534, when he was in Venice, nella città dal mare intorno centa:


Quando che 'l cubo con le cose appresso
se agguaglia a qualche numero discreto
trovan dui altri differenti in esso.
Da poi terrai questo per consueto
che il loro produtto sempre sia eguale
al terzo cubo delle cose netto,
El residuo poi suo generale
delli lor lati cubi ben sotratti
varrà la tua cosa principale.
In el secondo de codesti atti
quando che 'l cubo restasse lui solo
tu osserverai quant'altri contratti,
Del numero farai due tal partà volo
che l'una in l'altra si produca schietto
el terzo cubo delle cose in stolo
Dalla qual poi, per commun precetto
torrai li lati cubi insieme gionti
et cotal somma sarà il tuo concetto.
El terzo poi de questi nostri conti
se solve col secondo se ben guardi
che per natura son quasi congionti.
Questi trovai, et non con passi tardi
nel mille cinquecente, quatro e trenta
con fondamenti ben saldi e gagliardi
Nella città dal mare intorno centa.

In the first two lines it is shown the equation  ('l cubo con le cose appresso) it is equal("se agguaglia") to q ("a qualche numero discreto).
This equation

is in fact, as mathematics of 500th century know very well, the equation to which is reduced every equation of 3°1

with some simple passing.
Let’s suppose that


6. Ideazione, imparando dalla Natura

Il ricordare con amore traccia la strada del ritorno.

In un afoso mezzogiorno di fine Settembre una piccola foglia precipitò dal suo albero.

Sgomenta e piena di paura  si girò a salutare il padre, la madre, i fratelli, le sorelle

ed i cari amici uccelli. Improvviso un tuono la costrinse a guardare in avanti.

E vide la sua piccola ombra  che le gridava: “Stai lontana. Non venire giù, altrimenti morirò”. Vane urla. Planò a terra fragile nel vento.

Sola e piangente sentì sulla pelle un flebile tremore. “Non temere sono una formichina, tua nuova amica. Quando sarai più secca porterò con me nella mia casa un tuo piccolo frammento. Vedrai troverai tante altre foglie cadute prima di te. Non piangere: l’uccello amico riporterà un altro pezzetto sull’albero come coperta per i suoi piccoli e potrai rivedere i tuoi cari. Anche il vento ti trascinerà lontano e vedrai luoghi bellissimi pieni di canti di uccelli e di fiori profumati. Troverai la felicità nel caldo sole improvviso prima del gelo invernale. Il silenzio terrificante della Natura si scioglierà per te, accogliendoti. Segui il tuo destino ed impara ad ascoltare in silenzio“.

La foglia appassì in fretta. Un tenero passero la raccolse per un lembo e l’adagiò nel suo piccolo nido. Subito la foglia ritornata all’albero si sporse per ritrovare i suoi cari. Emise tutti i suoni familiari. Nulla. Il silenzio incombeva terreo sul suo tenero cuore. Disperata iniziò a piangere, ma improvviso il ricordo della formichina la scosse dalla paura. Rammentò come le avesse insegnato a stare immobile, in silenzio ed ad ascoltare il vento, dopo essersi sincronizzata sul suo respiro, lento o forte che fosse. E ripetendo il ritmo del respiro iniziò una piccola nenia:

“Canta, canta dolce piccola

Al mare giungerà il tuo canto

Solo un cane sordo non potrà ascoltarlo.

Chi ti è vicino al cuore

Subito ti seguirà e dolcezza

Emanerai dalle tue piccole note.

Canta, canta, mai non dubitare.

La fata confetto ti ascolterà

Ed i fiori al tuo ritmo danzeranno“.

Subito un gruppo di foglie ad est del nido iniziarono a cantare e piene di gioia riconobbero la sorella smarrita. Un dolce sorriso di api operose smosse l’aria intorno ai fiori, tra il volo di uccelli di ritorno a casa.


6.2 Samuel Taylor Coleridge:

A mathematical Problem

If Pegasus will let thee only ride him, Spurning my clumsy efforts to o'erstride him, Some fresh expedient the Muse will try, And walk on stilts, although she cannot fly.


Dear Brother,

I have often been surprized, that Mathematics, the quintessence of Truth, should have found admirers so few and so languid.--Frequent consideration and minute scrutiny have at length unravelled the cause--viz.--that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in it's proper Paradise, Imagination is wearily travelling on a dreary desart. To assist Reason by the stimulus of Imagination is the design of the following production. In the execution of it much may be objectionable. The verse (particularly in the introduction of the Ode) may be accused of unwarrantable liberties; but they are liberties equally homogeneal with the exactness of Mathematical disquisition, and the boldness of Pindaric daring. I have three strong champions to defend me against the attacks of Criticism: the Novelty, the Difficulty, and the Utility of the Work. I may justly plume myself, that I first have drawn the Nymph Mathesis from the visionary caves of Abstracted Idea, and caused her to unite with Harmony. The first-born of this Union I now present to you: with interested motives indeed--as I expect to receive in return the more valuable offspring of your Muse—

Thine ever,
S. T. C.

[Christ's Hospital,] March 31, 1791.

This is now--this was erst,
Proposition the first--and Problem the first.


On a given finite Line
Which must no way incline;
To describe an equi--
--lateral Tri--
--A, N, G, L, E.
Now let A. B.
Be the given line
Which must no way incline;
The great Mathematician
Makes this Requisition,
That we describe an Equi--
--lateral Tri--
--angle on it:
Aid us, Reason--aid us, Wit!


From the centre A. at the distance A. B.
Describe the circle B. C. D.
At the distance B. A. from B. the centre
The round A. C. E. to describe boldly venture.
(Third Postulate see.)
And from the point C.
In which the circles make a pother
Cutting and slashing one another,
Bid the straight lines a journeying go,
C. A., C. B. those lines will show.
To the points, which by A. B. are reckon'd,
And postulate the second
For Authority ye know.
A. B. C.
Triumphant shall be
An Equilateral Triangle,
Not Peter Pindar carp, not Zoilus can wrangle.


Because the point A. is the centre
Of the circular B. C. D.
And because the point B. is the centre
Of the circular A. C. E.
A. C. to A. B. and B. C. to B. A.
Harmoniously equal for ever must stay;
Then C. A. and B. C.
Both extend the kind hand
To the basis, A. B.
Unambitiously join'd in Equality's Band.
But to the same powers, when two powers are equal,
My mind forbodes the sequel;
My mind does some celestial impulse teach,
And equalises each to each.
Thus C. A. with B. C. strikes the same sure alliance,
That C. A. and B. C. had with A. B. before;
And in mutual affiance,
None attempting to soar
Above another,
The unanimous three
C. A. and B. C. and A. B.
All are equal, each to his brother,
Preserving the balance of power so true:
Ah! the like would the proud Autocratorix do!
At taxes impending not Britain would tremble,
Nor Prussia struggle her fear to dissemble;
Nor the Mah'met-sprung Wight,
The great Mussulman
Would stain his Divan
With Urine the soft-flowing daughter of Fright.


But rein your stallion in, too daring Nine!
Should Empires bloat the scientific line?
Or with dishevell'd hair all madly do ye run
For transport that your task is done?
For done it is--the cause is tried!
And Proposition, gentle Maid,
Who soothly ask'd stern Demonstration's aid,
Has prov'd her right, and A. B. C.
Of Angles three
Is shown to be of equal side;
And now our weary steed to rest in fine,
'Tis rais'd upon A. B. the straight, the given line.


6.2 Metrical Feet,Samuel Taylor Coleridge
Trochee trips from long to short;
From long to long in solemn sort
Slow Spondee stalks, strong foot!, yet ill able
Ever to come up with Dactyl's trisyllable.
Iambics march from short to long.
With a leap and a bound the swift Anapests throng.
One syllable long, with one short at each side,
Amphibrachys hastes with a stately stride --
First and last being long, middle short, Amphimacer
Strikes his thundering hoofs like a proud high-bred Racer.

If Derwent be innocent, steady, and wise,
And delight in the things of earth,
water, and skies;
Tender warmth at his heart, with these meters to show it,
WIth sound sense in his brains, may make Derwent a poet --
May crown him with fame, and must win him the
Of his father on earth and his father above.
My dear, dear child!
Could you stand upon Skiddaw, you would not from its whole ridge
See a man who so loves you as your fond S.T. Colerige.

7. Not-eucludean geometry

On Divers Geometries


Euclid Riemann, other geometers,
invented ideas of space. Regarding them,
elation astonishes us: discreteness, shape,
the measure of distances, as though the world
had order in it which were discoverable.
But hardly so; their order is not the world's,
their separately premised spaces not congruent,
as though, besides their spaces, there were space,
not spoken of, unspeakable.

Geometers, all measures measure themselves,
none measures the world. Premise and axiom
are terms of the limited case, to limit it.
There is no limited truth: there is no truth.

William Bronk.

8. Version


“Mathematics has totally false reputation to gain infallible results. Her infallibility is nothing more then her identity.

2x2 is not 4, but it is only 2x2, and we call this “4” for convenience. But 4 is nothing of new. And mathematics goes ahead in this way for her conclusions: only that in the most advanced formulas identity disappears from sight.”



10 Total Version, in anamorphic representations, by Celestino Soddu using his software Tracce.






8.1 Two letters written by Chopin


We have in 2 versions almost the same text, only the ending is totally different.


A Jan Matuszynski, Varsavia

Version 1

New Year's eve 1831,Vienna

My darling

………….Excuse me for the disorder of this paper, but I write as drunk




Version 2

New Year's eve 1831,Vienna

My darling

………….When we will talk about a lot of things. I love you and you too love me.

For all friends, for your sister and your father






W. H. Auden, The voice of the poet.

Platone, Ione

Emily Dickinson, The Poems of Emily Dickinson, 1955.

Ezra Pound, Personae, 1926.

James Legge, translator. The Book of Poetry (Shih Ching). Copy owned and annotated by Ezra Pound. Shanghai: Chinese Book Co., 1903.

Ezra Pound. "Canto LXXIV," part of The Pisan Cantos,Pisa,1945.

Poems of Christian Morgenstern, published by Bote&Boch,Germany

Francesco De Sanctis, Storia della Letteratura Italiana, Utet, Torino, 1968.

Georges Perec, Alphabets, Éditions Galilée, Paris, 1985.

Georges Perec,Ulcerations , ” La Bibliothèque Oulipienne".

Colabella, E: 1999, Imaging Humanity, Proceedings, USA, Bordighera  Press,  The imprinting of a man, word as medium for icona (pag.129)  The experiences of the students of Enrica Colabella, a. a. 1997/98 Corso di Rilevamento e Rappresentazione , Faculty of Architecture, Politecnico di Milano. Codes as expression of an hypothesis that comes from the Poetic Test of Giacomo Leopardi. The goal is the building of possible “real” scenerios of Architecture, that represent the formulated idea. 

Pierce Charles Sanders “Categorie”, a cura di R. Fabbrichesi  Leo Ed. Laterza,1992.

Hume David A Treatise of Human Nature, edited by David Fate Norton and Mary J. Norton, Oxford/New York: Oxford University Press, 2000.

Fodor Jerry A., Hume Variations, Oxford/New York: Oxford University Press, 2002.

Colabella, E, Soddu, C,"Il progetto ambientale di morfogenesi", (the environmental design of morphogenesis), Progetto Leonardo Publisher 1992.

L. Pacioli, De Divina Proportione, 1498

Samuel Taylor Coleridge. A mathematical problem. Carta al seu germà George, 1791. Primera publicació 1834.

Colabella E:, “Verba, scripta et alea, generatim”, Proceedings of Generative Art Conference, Milan, Alea Design Publischer, December 1998.

Colabella E:, “The night shadow”, Proceedings of Generative Art Conference, Milan, Alea Design Publischer, December 1999

Colabella E:, “Mater Matuta”, Proceedings of Generative Art Conference, Milan, Alea Design Publischer, December 2000

Colabella E:, “Performing evocations”, Proceedings of Generative Art Conference, Milan, Alea Design Publischer, December 2001

Colabella E:, “Figura, aura uniqueness”, Proceedings of Generative Art Conference, Milan, Alea Design Publischer, December 2002

Colabella E:, “Code, a password to infinite”, Proceedings of Generative Art Conference, Milan, Alea Design Publischer, December 2003

Colabella E:, “Identity, a double vision in a generative process”, Proceedings of De Identitade Conference, Rome, Alea Design Publischer, July 2004

Colabella E:, “Generative identity code”, Proceedings of SIGRADI, Porto Allegre, Brazil, November 2004

William Bronk. On Divers Geometries - Life Supports: New Collected Poems San.Francisco: North Point Press, 1981, 101.

Wolfgang Goethe, in J. R. Newman (ed.), The World of Mathematics.

Vita di Chopin attraverso le lettere, a cura di Valeria Rossella, Lindau, Torino 2003