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Tag: Harmonie

June 16, 2016

Eco: The Egyptian vs. The Chinese Way, 2

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Athanasius Kircher (1602-80), origins of the Chinese characters, China Illustrata, 1667, p. 229, courtesy of Stanford University. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“On the subject of signatures, Della Porta said that spotted plants which imitated the spots of animals also shared their virtues (Phytognomonica, 1583, III, 6): the bark of a birch tree, for example, imitated the plumage of a starling and is therefore good against impetigo, while plants that have snake-like scales protect against reptiles (III, 7).

Thus in one case, morphological similarity is a sign for alliance between a plant and an animal, while in the next it is a sign for hostility.

Taddeus Hageck (Metoscopicorum libellus unus, 1584: 20) praises among the plants that cure lung diseases two types of lichen: however, one bears the form of a healthy lung, while the other bears the stained and shaggy shape of an ulcerated one.

The fact that another plant is covered with little holes is enough to suggest that this plant is capable of opening the pores. We are thus witnessing three very distinct principles of relation by similarity: resemblance to a healthy organ, resemblance to a diseased organ, and an analogy between the form of a plant and the therapeutic result that it supposedly produced.

This indifference as to the nature of the connection between signatures and signatum holds in the arts of memory as well. In his Thesaurus atificiosae memoriae (1579), Cosma Roselli endeavored to explain how, once of a system of loci and images had been established, it might actually  function to recall the res memoranda.

He thought it necessary to explain “quomodo multis modis, aliqua res alteri sit similis” (Thesaurus, 107), how, that is, one thing could be similar to another. In the ninth chapter of the second part he tried to construct systematically a set of criteria whereby images might correspond to things:

“according to similarity, which, in its turn, can be divided into similarity of substance (such as man as the microcosmic image of the macrocosm), similarity in quantity (the ten fingers for the Ten Commandments), according to metonymy or antonomasia (Atlas for astronomers or for astronomy, a bear for a wrathful man, a lion for pride, Cicero for rhetoric):

by homonyms: a real dog for the dog constellation;

by irony and opposition: the fatuous for the wise;

by trace: the footprint for the wolf, the mirror in which Titus admired himself for Titus;

by the name differently pronounced: sanum for sane;

by similarity of name: Arista [awn] for Aristotle;

by genus and species: leopard for animal;

by pagan symbol: the eagle for Jove;

by peoples: Parthians for arrows, Scythians for horses, Phoenicians for the alphabet;

by signs of the zodiac: the sign for the constellation;

by the relation between organ and function;

by common accident: the crow for Ethiopia;

by hieroglyph: the ant for providence.”

The Idea del teatro by Giulio Camillo (1550) has been interpreted as a project for a perfect mechanism for the generation of rhetorical sentences.

Yet Camillo speaks casually of similarity by morphological traits (a centaur for a horse), by action (two serpents in combat for the art of war), by mythological contiguity (Vulcan for the art of fire), by causation (silk worms for couture), by effects (Marsyas with his skin flayed off for butchery), by relation of ruler to ruled (Neptune for navigation), by relation between agent and action (Paris for civil courts), by antonomasia (Prometheus for man the maker), by iconism (Hercules drawing his bow towards the heavens for the sciences regarding celestial matters), by inference (Mercury with a cock for bargaining).

It is plain to see that these are all rhetorical connections, and there is nothing more conventional that a rhetorical figure. Neither the arts of memory nor the doctrine of signatures is dealing, in any degree whatsoever, with a “natural” language of images.

Yet a mere appearance of naturalness has always fascinated those who searched for a perfect language of images.

The study of gesture as the vehicle of interaction with exotic people, united with a belief in a universal language of images, could hardly fail to influence the large number of studies which begin to appear in the seventeenth century on the education of deaf-mutes (cf. Salmon 1972: 68-71).

In 1620, Juan Pablo Bonet wrote a Reducción de las letras y arte para enseñar a hablar los mudos. Fifteen years later, Mersenne (Harmonie, 2) connected this question to that of a universal language. John Bulwer suggested (Chirologia, 1644) that only by a gestural language can one escape from the confusion of Babel, because it was the first language of humanity.

Dalgarno (see ch. 11) assured his reader that his project would provide an easy means of educating deaf-mutes, and he again took up this argument in his Didascalocophus (1680). In 1662, the Royal Society devoted several debates to Wallis’s proposals on the same topic.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 171-3.

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May 25, 2016

Eco: Infinite Songs & Locutions, 2

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Ramon Llull (1232-1315), La Tercera Figura, from Ars brevis, Pisa, 1308. This illustration is hosted on the net by the Centre de Documentacio de Ramon Llull, while the original is held in the Escorial, MS.f-IV-12, folio 6. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“Mersenne and Guldin were anticipating Borge’s Babel Library ad abundantiam. Not only this, Guldin observed that if the numbers are these, who can marvel at the existence of so many different natural languages?

The art was now providing an excuse for the confusio linguarum. It justifies it, however, by showing that it is impossible to limit the omnipotence of God.

Are there more names than things? How many names, asks Mersenne (Harmonie, II, 72), would we need if were to give more than one to each individual? If Adam really did give names to everything, how long would he have had to spend in Eden?

In the end, human languages limit themselves to the naming of general ideas and of species; to name an individual thing, an indication with a finger is usually sufficient (p. 74).

If this were not so, it might easily “happen that for every hair on the body of an animal and for each hair on the head of a man we might require a particular name that would distinguish it from all others. Thus a man with 100,000 hairs on his head and 100,000 more on his body would need to know 200,000 separate words to name them all” (pp. 72-3).

In order to name every individual thing in the world one should thus create an artificial language capable of generating the requisite number of locutions. If God were to augment the number of individual things unto infinity, to name them all it would be enough to devise an alphabet with a greater number of letters, and this would provide us with the means to name them all (p. 73).

From these giddy heights there dawns a consciousness of the possibility of the infinite perfectibility of knowledge. Man, the new Adam, possesses the possibility of naming all those things which his ancestor had lacked the time to baptize.

Yet such an artificial language would place human beings in competition with God, who has the privilege of knowing all things in their particularity. We shall see that Leibniz was later to sanction the impossibility of such a language.

Mersenne had led a battle against the kabbala and occultism only to be seduced in the end. Here he is cranking away at Lullian wheels, seemingly unaware of the difference between the real omnipotence of God and the potential omnipotence of a human combinatory language.

Besides, in his Quaestiones super Genesim (cols 49 and 52) he claimed that the presence of the sense of infinity in human beings was itself a proof of the existence of God.

This capacity to conceive of a quasi-infinite series of combinations depends on the fact that Mersenne, Guldin, Clavius and others (see, for example, Comenius, Linguarum methodus novissima (1648: III, 19), unlike Lull, were no longer calculating upon concepts but rather upon simple alphabetic sequences, pure elements of expression with no inherent meaning, controlled by no orthodoxy other than the limits of mathematics itself.

Without realizing it, these authors are verging towards the idea of a “blind thought,” a notion that we shall see Leibniz proposing with a greater critical awareness.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 141-3.

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May 25, 2016

Eco: Infinite Songs & Locutions

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Giordano Bruno (1548-1600), memory wheel, De Umbris Idearum, 1582, reconstructed by Dame Frances Yates, Warburg Institute. Frances Yates wrote Giordano Bruno and the Hermetic Tradition, Chicago, 1964. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.  

 “Between Lull and Bruno might be placed the game invented by H.P. Harsdörffer in his Matematische und philosophische Erquickstunden (1651: 516-9). He devises 5 wheels containing 264 units (prefixes, suffixes, letters and syllables).

This apparatus can generate 97,209,600 German words, including many that were still non-existent but available for creative and poetic use (cf. Faust 1981: 367). If this can be done for German, why not invent a device capable of generating all possible languages?

The problem of the art of combination was reconsidered in the commentary In spheram Ioannis de sacro bosco by Clavius in 1607. In his discussion of the four primary qualities (hot, cold, dry and wet), Clavius asked how many pairs they might form.

Mathematically, we know, the answer is six. But some combinations (like “hot and cold,” “dry and wet”) are impossible, and must be discarded, leaving only the four acceptable combinations: “Cold and dry” (earth), “hot and dry” (fire), “hot and wet” (air), “cold and wet” (water).

We seem to be back with the problem of Lull: a conventional cosmology limits the combinations.

Clavius, however, seemed to wish to go beyond these limits. He asked how many dictiones, or terms, might be produced using the 23 letters of the Latin alphabet (u being the same as v), combining them 2, 3, 4 at a time, and so on until 23.

He supplied a number of mathematical formulae for the calculations, yet he soon stopped as he began to see the immensity of the number of possible results–especially as repetitions were permissible.

In 1622, Paul Guldin wrote a Problema arithmeticum de rerum combinationibus (cf. Fichant 1991: 136-8) in which he calculated the number of possible locutions generated by 23 letters. He took into account neither the question of whether the resulting sequences had a sense, nor even that of whether they were capable of being pronounced at all.

The locutions could consist of anything from 2 to 23 letters; he did not allow repetitions. He arrived at a result of more than 70,000 billion billion. To write out all these locutions would require more than a million billion billion letters.

To conceive of the enormity of this figure, he asked the reader to imagine writing all these words in huge notebooks: each of these notebooks had 1,000 pages; each of these pages had 100 lines; each of these lines could accommodate 60 characters.

One would need 257 million billion of these notebooks. Where would you put them all? Guldin then made a careful volumetric study, imagining shelf space and room for circulation in the libraries that might store a consignment of these dimensions.

If you housed the notebooks in large libraries formed by cubes whose sides measured 432 feet, the number of such cubic buildings (hosting 32 million volumes each) would be 8,050,122,350. And where would you put them all? Even exhausting the total available surface space on planet earth, one would still find room for only 7,575,213,799!

In 1636 Father Marin Mersenne, in his Harmonie universelle, asked the same question once again. This time, however, to the dictiones he added “songs,” that is, musical sequences.

With this, the conception of universal language has begun to appear, for Mersenne realizes that the answer would necessarily have to include all the locutions in all possible languages. He marveled that our alphabet was capable of supplying “millions more terms than the earth has grains of sand, yet it is so easy to learn that one hardly needs memory, only a touch of discernment” (letter to Peiresc, c. April 1635; cf. Coumet 1975; Marconi 1992).

In the Harmonie, Mersenne proposed to generate only pronounceable words in French, Greek, Arabic, Chinese and every other language. Even with this limitation one feels the shudder provoked by a sort of Brunian infinity of possible worlds.

The same can be said of the musical sequences that can be generated upon an extension of 3 octaves, comprising 22 notes, without repetitions (shades of future 12-tone compositions!).

Mersenne observed that to write down all these songs would require enough reams of paper to fill in the distance between heaven and earth, even if every sheet contained 720 of these 22-note songs and every ream was so compressed as to be less than an inch thick.

In fact the number of possible songs amounted to 1,124,000,727,777,607,680,000 (Harmonie, 108). By dividing this figure by the 362,880 songs contained in each ream, one would still obtain a 16-digit figure, whilst the number of inches between the center of the earth and the stars is only 28,826,640,000,000 (a 14-digit figure).

Anyone who wished to copy out all these songs, a thousand per day, would have to write for 22,608,896,103 years and 12 days.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 139-41.

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