Numbering, a Resonant
Silence
Prof. Enrica Colabella
Generative Design
Lab, DiAP, Politecnico di Milano University, Milano, Italy.
e-mail: enrica.colabella@polimi.it
An eastwards curved tree generates brightness
In “the milk of human kindness”
Abstract
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.
Antefatto
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)
Ione
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."
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The Book of Poetry (Shih Ching). Copy
owned and annotated by Ezra Pound.
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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 NachtgesangC.Morgenstern,1905
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2.4 Vox +
numbering, dare i numeri
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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)
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Quella circulazion che sì concetta A l'alta fantasia qui mancò possa; 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.
G
R E L O T A S U N I
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!
R T
I S A N G E L U O
I N
T E U G R A S L O
T I
O N A S U R G E L
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.
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STRUCTURE: 1 FIST
ATTRIBUTE,generic also random |
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2 SECON ATTRIBUTE, dual,
hendiadys |
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3 THIRD ATTRIBUTE, versus |
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= 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.
TO THE REV. GEORGE
COLERIDGE
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.
I
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!
II
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.
III
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.
IV
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.
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6.2 Metrical Feet,Samuel Taylor
Coleridge |
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.”
Goethe
10 Total Version, in anamorphic representations, by Celestino
Soddu using his software Tracce.
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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
Yours
Fryderyk
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
Yours
Fryderyk
Literature
W. H. Auden, The voice of the
poet.
Platone, Ione
http://www.filosofico.net/loionediplatonee.htm
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
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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.
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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.
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et alea, generatim”, Proceedings of Generative Art Conference, Milan, Alea
Design Publischer, December 1998.
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shadow”, Proceedings of Generative Art Conference, Milan, Alea Design
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December 2000
Colabella E:, “Performing
evocations”, Proceedings of Generative Art Conference, Milan, Alea Design
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Colabella E:, “Figura, aura
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