The Universal Library
A schema allowing finitely many instantiations
is succinctly represented by an algorithm enumerating these instantiations,
one by one, in some systematic order. An alternative (extensional)
representation is the output sequence of such an algorithm.
The first artwork instantiating this format is an early piece of "concept art": the "Universal Library" described
by Kurd Laßwitz in his dialogue "Die
Universalbibliothek" (1901). The Universal Library is the
set of all possible books: the set of all sequences of typographical
characters with a certain maximum length. (Laßwitz notes that
the maximum length does not introduce an essential limitation: longer
texts merely consist of multiple volumes from the library. W.V.O. Quine ("Universal Library") observed that a small pocket library of two one-bit volumes may thus be used to represent the Universal Library in a very efficient way.) The
history of this idea is beautifully summarized by Jorge Luis Borges
in his essay "La Biblioteca Total" (1939). Borges mentions
Lewis Carroll and Gustav Theodor Fechner as direct antecedents of
Laßwitz. The Universal Library re-appears in The Race with
the Tortoise by Theodor Wolff (1929) and "The
Library of Babel" by Jorge Luis Borges (1944).
Quotes
Interviewer: "Can you tell us something about your new opera?"
Giuseppe Verdi: "It's exactly the same notes as the previous one, I merely changed the order a little bit."
[To do: Find source and exact formulation!]
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.”
Lewis Carroll: Sylvie and Bruno Concluded, 1893. Chapter
IX: The Farewell-Party.
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: "La
Biblioteca Total", 1939.
Chaque fois que l'on discute de tel ou tel produit de l'esprit sous le rapport de l'art, il faut s'en tenir à ce dilemme: ou c'est une intuition lyrique, ou ce sera n'importe quoi d'autre, même éminemment respectable, mais non pas de l'art. Si la peinture était, comme pour certaines théories, une imitation ou une reproduction des objets donnés, elle ne serait pas de l'art mais quelque chose de mécanique et de pratique; si les peintres étaient, comme selon d'autres théories, des assembleurs de lignes, de lumière et de couleurs au moyen de nouveautés ingénieuses, de trouvailles efficaces, ils ne seraient pas des artistes mes des inventeurs de techniques; si la musique consistait en de semblables combinaisons de tons il serait possible de composer des partitions sans connaître la musique, en réalisant le paradoxe de Leibniz et du Père Kircher, ou il serait à craindre, avec Proudhon pour la poésie et Stuart Mill pour la musique, que, une fois épuisé le nombre des combinaisons possibles de mots et de notes, poésie et musique disparaissent du monde.
Benedetto Croce: "Aesthetica in nuce." (Laterza, 1935) French translation by Gilles A. Tiberghien
in: Benedetto Croce: Essais d'esthétique (Paris: Gallimard, 1991), p. 47.
References
Louis Auguste Blanqui: L'éternité par les astres (1872).
Jorge Luis Borges: "La Biblioteca Total." Sur (August 1939).
Concept Art 
