Course "Algorithmic Art & A.I."
Het combinatorisch perspektief
op de wereld en de kunst
"The caprice or fancy or utopia of the
Total Library contains certain traits that could be confused
with virtues. Actually, it is astonishing how long it took
mankind to dream up the idea. Certain examples Aristotle attributes
to Democritus and to Leucippus clearly prefigure it, but its
late inventor is Gustav Theodor Fechner and its first expounder
is Kurd Lasswitz. Its connections are illustrious and multiple:
it is related to atomism and combinatory analysis, to typography
and to chance. In The Race with the Tortoise (Berlin,
1929), Dr. Theodor Wolff suggests that it is either a derivation
from or a parody of Raymond Lull's mental machine; I would
add that it is a typographical avatar of the doctrine of the
eternal return which, adopted by the Stoics or by Blanqui,
by the Pythagoreans or by Nietzsche, eternally returns."
Jorge Luis Borges: "The total
library.", p.94.
Veel (maar lang niet alle) verwijzingen hieronder
zijn ontleend aan: Jorge Luis Borges: "La biblioteca total." Sur
(August 1939). [I quote from the English translation: "The Total
Library", in Emir Rodriguez Monegal and Alasteir Reid (eds.): Borges/
A Reader/ A selection from the writings of Jorge Luis Borges (New
York: Dutton, 1981), pp. 94-96.]
Antique roots
Cosmologie van Demokrites/Leukippos: de wereld als compositie van
atomen. (Beschreven in Aristoteles' Metaphysica, eerste
boek.)
[Leucippus's cosmology: the formation of the world
by the fortuitous conjunction of atoms. The atoms are homogeneous
and their differences derive from position, order, or form.] "A
is different from N in form; AN from NA in order; Z from N in position."
Aristotle: Metaphysics. (First Book.) [@ Jorge
Luis Borges: "La biblioteca total.", p.94.]
Aristoteles: De Generatione et Corruptione. Discussie van
physisch atomisme. In dat verband: a tragedy is made up of the same
elements as a comedy - that is, the twenty-six letters of the alphabet.
Cicero: De Natura Deorum: Leuke omkering: Physisch atomisme
is onzinnig, want: random tekst-generatie werkt ook niet.
"At this point must I not marvel
that there should be anyone who can persuade himself that there
are certain solid and indivisible particles of matter borne along
by the force of gravity, and that the fortuitous collision of those
particles produces this elaborate and beautiful world? I cannot
understand why he who considers it possible for this to have occurred
should not also think that, if a countless number of copies of the
one-and-twenty letters of the alphabet, made of gold or what you
will, were thrown together in some receptacle and then shaken out
on the ground, it would be possible that they should produce the
Annals of Ennius, all ready for the reader. I doubt whether
chance could possibly succeed in producing even a single verse!"
Cicero: De Natura Deorum. [@ Jorge Luis
Borges: "La biblioteca total.", p.95.]
Theo Lutz: Zum "Problem des Cicero". In: Elisabeth
Walther and Ludwig Harig: Muster möglicher Welten. Eine
Anthologie für Max Bense. Wiesbaden: Limes, 1970.
"The soul can make new compositions, but it cannot
make new things."
St. Bonaventura: Commentarium in
III Sententiarum, 37, 1, dub. 1. [@ Umberto Eco: The Aesthetics
of Thomas Aquinas, trans. Hugh Bredin (London: Radius, 1988), p.
173. [Il problema estetico in Tommaso d'Aquino (Milan, 1970)]]
"Aquinas does not refer to artistic production
as "creation." His position is that man must have the humility to
acknowledge that he does not bring forms into existence ex nihilo,
since the forms which he produces are dependent upon a preexisting,
concrete, and organic reality. In fact Aquinas suggests that they
arise out of the preexisting reality, that they were already present
there in potency."
Umberto Eco: The Aesthetics of Thomas Aquinas,
trans. Hugh Bredin (London: Radius, 1988), p. 179. [Il problema
estetico in Tommaso d'Aquino (Milan, 1970)]
Cf. Teilhard de Chardin. (Zie voetnoot in: Scha
(1992).)
Combinatorische technologie
Raymond Lull.
Leibniz.
Wilkins. (Borges heeft ook een essay over Wilkins geschreven
wat online staat.)
Blaise Pascal: Referentie naar random tekst-generatie.
(Waar?)
Jonathan Swift: Referentie naar random tekst-generatie. (Preamble
to: "Trivial Essay on the Faculties of the Soul.")
En: Gulliver's Travels. (Illustratie: Grandville.)
Finiteness
When things around
me seemed once more to be real, Arthur was saying “I’m
afraid there’s no help for it: they must be finite
in number.”
“I should be sorry to have
to believe it,” said Lady Muriel. “Yet, when one comes
to think of it, there are no new melodies, now-a-days.
What people talk of as ‘the last new song’ always
recalls to me some tune I’ve known as a child!”
“The day must come –
if the world lasts long enough –” said Arthur, “when
every possible tune will have been composed and every possible
pun perpetrated –” (Lady Muriel wrung her hands, like
a tragedy-queen) "and worse than that, every possible book
written! For the number of words is finite."
“It’ll make very little
difference to the authors,” I suggested. “Instead
of saying ’what book shall I write?’ an author
will ask himself ’which book shall I write?’
A mere verbal distinction!”
Lady Muriel gave me an approving
smile. “But lunatics would always write new books,
surely?” she went on. They couldn’t write
the same books over again!”
“True,” said Arthur.
“But their books would come to an end, also. The number
of lunatic books is as finite as the number
of lunatics.”
Technisch detail: De redenering gaat alleen op als we een bovengrens
stellen aan de lengte van de melodies, puns en books.
Kurd Lasswitz, stimulated by Gustav Theodor Fechner, imagined
the Total Library. He published his invention in "Die Universalbibliothek",
in: Traumkristalle. Lasswitz's basic idea is the same
as Carroll's, but the elements of his game are the universal
orthographic symbols rather than the words of a language. [In:
Borges: La Biblioteca Total.]
Theodor Wolff: The Race with the Tortoise (Berlin,
1929). Gebaseerd op Lasswitz.
The Eternal Return
Louis Auguste Blanqui: L'éternité par les astres
(1872).
Friedrich Nietzsche: Eternal return.
Evolution
Six eternal apes, randomly striking the keys of
six eternal typewriters with unlimited amounts of paper and ink would
be able to produce Shakespearean sonnets, complete books, and the
23rd Psalm. In the same way, molecular movement, given enough time
and matter, could produce Bishop Wilberforce himself, purely by chance
and without the work of any Designer or Creator.
Thomas Henry Huxley, in a debate with Samuel Wilberforce,
Anglican Bishop of Oxford, about Darwin's theory of natural evolution.
Meeting of the British Association, Oxford, June 30, 1860.
[Russell Grigg: "Could
Monkeys Type the 23rd Psalm?" Creation Ex Nihilo
13(1): 30Ð33 (December 1990 Ð February 1991). Reprinted in:
Apologia 3(2):59Ð64 (1994).] Illustratie: Typewriter-piece Arman;
plaatje in Catalogus Sonnabend-collectie.
"If an army of monkeys were strumming
on typewriters, they might write all the books in the British Museum."
Sir Arthur Eddington, The Nature of the Physical World, 1928.
One version of the infinite monkey theorem states that a single
(immortal) monkey typing randomly will ultimately reproduce the
script of Hamlet. Estimate the time needed for this, assuming
that the monkey can type two characters per second and that the
play has 50 pages, each containing roughly 80 lines and 40 characters
per line. Assume there are 30 possible characters (a through z,
space, period, exclamation period, and carriage return). Compare
this time to the estimated age of the universe, 10^10 years.
Richard O. Duda, Peter E. Hart & David G. Stork: Pattern
Classification. Second Edition. New York: John Wiley &
Sons, 2001. [Chapter 7: "Stochastic Methods." Problem
1, p. 383.]
After a minute or two he began again. “If I’m
not wearying you, I would like to tell you an idea of the future Life
which has haunted me for years, like a sort of waking nightmare--I
ca’n’t reason myself out of it.”
“Pray do,” Arthur and I replied, almost
in a breath. Lady Muriel put aside the heap of music, and folded her
hands together.
“The one idea”, the Earl resumed, “that
has seemed to me to overshadow all the rest, is that of Eternity
-- involving, as it seems to do, the necessary exhaustion
of all subjects of human interest. Take Pure Mathematics, for
instance -- a Science independent of our present surroundings. I have
studied it, myself, a little. Take the subject of circles and ellipses
-- what we call ‘curves of the second degree’. In a future
Life, it would only be a question of so many years (or hundreds
of years, if you like) for a man to work out all their
properties. Then he might go to curves of the third degree.
Say that took ten times as long (you see we have unlimited
time to deal with). I can hardly imagine his interest in
the subject holding out even for those; and, though there is no limit
to the degree of the curves he might study, yet surely the
time, needed to exhaust all the novelty and interest of the
subject, would be absolutely finite? And so of all other branches
of Science. And, when I transport myself, in thought, through some
thousands or millions of years, and fancy myself possessed of as much
Science as one created reason can carry, I ask myself ‘What then?
With nothing more to learn, can one rest content on knowledge,
for the eternity yet to be lived through?’ It has been a
very wearying thought to me. I have sometimes fancied one might, in
that event, say ‘It is better not to be’, and pray
for personal annihilation -- the Nirvana of the Buddhists.”
“But that is only half the picture,” I
said. “Besides working for oneself, may there not be
the helping of others?”
”Surely, surely!” Lady Muriel
exclaimed in a tone of relief, looking at her father with sparkling
eyes.
“Yes,” said the Earl, “so long as
there were any others needing help. But, given ages and ages
more, surely all created reasons would at length reach the same dead
level of satiety. And then what is there to look
forward to?”
“I know that weary feeling,” said the young
Doctor. “I have gone through it all, more than once. Now let
me tell you how I have put it to myself. I have imagined a little
child, playing with toys on his nursery-floor, and yet able to reason,
and to look on, thirty years ahead. Might he not say to himself
‘By that time I shall have had enough of bricks and ninepins.
How weary Life will be!’ Yet, if we look forward through those
thirty years, we find him a great statesman, full of interests and
joys far more intense than his baby-life could give -- joys wholly
inconceivable to his baby-mind -- joys such as no baby-language could
in the faintest degree describe. Now, may not our life, a million
years hence, have the same relation, to our life now, that the man’s
life has to the child’s? And, just as one might try, all in vain,
to express to that child, in the language of bricks and ninepins,
the meaning of ‘politics’, so perhaps all those descriptions
of Heaven, with its music, and its feasts, and its streets of gold,
may be only attempts to describe, in our words, things for
which we really have no words at all. Don’t you think
that in your picture of another life, you are in fact transplanting
that child into political life, without making any allowance for his
growing up?”
“I think I understand you,” said the Earl.
“The music of Heaven may be something beyond our powers of thought.
Yet the music of Earth is sweet! Muriel, my child, sing us something
before we go to bed!”
Modern Art
Interviewer: "Hoe is 't met je nieuwe opera?" Giuseppe Verdi:
"Precies dezelfde noten als de vorige, ik heb alleen de volgorde een
beetje veranderd."
Cage, Morellet, De Vries, etc.
"Man kann soweit gehen, gro§e
Teile des Šsthetischen Produktionsprozesses unter dem Anzahlaspekt
zu betrachten: KŸnstler wechseln den Šsthetischen Raum, wenn eine
genŸgend gro§e Anzahl von Objekten darin realisiert worden ist
- vom KŸnstler selbst oder von anderen; wenn sie herausfinden,
da§ ein solcher Raum schon besetzt ist; KŸnstler suchen sich "gro§e",
"offene" RŠume. Die Definition der Šsthetischen RŠume selbst ist
natŸrlich das eigentliche Problem. Die zwei extremfŠlle sind der
Raum aller Ÿberhaupt mšglicher Bilder, der alle anderen Šsthetischen
RŠume enthŠlt, sowie die durch jedes einzelne realisierte Bild
definierten RŠume, die keinen anderen Raum enthalten."
Frieder Nake: €sthetik als Informationsverarbeitung.
Vienna/New York: Springer Verlag, 1974, p. 104.
Uitdaging: enumereer
alles. "Triviale"
oplossing: enumereer alle pixel-grids. Verschillende kunstenaars hebben
onafhankelijk van elkaar dit idee ontwikkeld en geïmplementeerd.
Zie:
Enumeratie-pagina.
Philosophische esthetica
Immanuel Kant: das Mathematische Erhabene.
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