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Tag: 1548

Eco: Infinite Songs & Locutions


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.

Eco: Bruno: Ars Combinatoria & Infinite Worlds, 3


Giordano Bruno (1548-1600), a mnemonic diagram, which appears towards the end of Cantus circaeus (Incantation of Circe), 1582, which also appears on the cover of Opere mnemotecniche, Vol. 1: De umbris idearum, 1582, Rita Sturlese, et al, ed. 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.

“In her critical edition of De umbris (1991), Sturlese gives an interpretation of the use of the wheels that differs sharply from the “magical” interpretation given by Yates (1972). For Yates, the wheels generated syllables by which one memorizes images to be used for magical purposes.

Sturlese inverts this: for her, it is the images that serve to recall the syllables. Thus, for Sturlese, the purpose of the entire mnemonical apparatus was the memorization of an infinite multitude of words through the use of a fixed, and relatively limited, number of images.

If this is true, then it is easy to see that Bruno’s system can no longer be treated as an art where alphabetic combinations lead to images (as if it were a scenario-generating machine); rather, it is a system that leads from combined images to syllables.

Such a system not only aids memorization but, equally, permits the generation of an almost unlimited number of words–be they long and complex like incrassatus or permagnus, or difficult like many Greek, Hebrew, Chaldean, Persian or Arabic terms (De umbris, 169), or rare like scientific names of grass, trees, minerals, seeds or animal genera (De umbris, 152). The system is thus designed to generate languages–at least at the level of nomenclature.

Which interpretation is correct? Does Bruno concatenate the sequence CROCITUS to evoke the image of Pilumnus advancing rapidly on the back of a donkey with a bandage on his arm and a parrot on his head, or has he assembled these images so as to memorize CROCITUS?

In the “Prima Praxis” (De umbris, 168-72) Bruno tells us that it is not indispensable to work with all five wheels because, in most known languages, it is rare to find words containing syllables with four or five letters.

Furthermore, where such syllables do occur (for instance, in words like trans-actum or stu-prans), it is usually eash to devise some artifice that will obviate the necessity of using the fourth and fifth wheel.

We are not interested in the specific short cuts that Bruno used except to say that they cut out several billion possibilities. It is the very existence of such short cuts that seems significant.

If the syllabic sequences were expressing complex images, there should be no limit for the length of the syllables. On the contrary, if the images were expressing syllables, there would be an interest in limiting the length of the words, following the criteria of economy already present in most natural languages (even though there is no formal limit, since Leibniz will later remark that there exists in Greek a thirty-one-letter word).

Besides, if the basic criterion of every art of memory is to recall the unfamiliar through the more familiar, it seems more reasonable that Bruno considered the “Egyptian” traditional images as more familiar than the words of exotic languages.

In this respect, there are some passages in De umbris that are revealing: “Lycas in convivium cathenatus presentabat tibi AAA. . . . Medusa, cum insigni Plutonis presentabit AMO” (“Lycaon enchained in a banquet presents to you AAA . . . Medusa with the sign of Pluto presents AMO”).

Since all these names are in the nominative case, it is evident that they present the letters to the user of the system and not the other way around. This also follows from a number of passages in the Cantus circaeus where Bruno uses perceivable images to represent mathematical or abstract concepts that might not otherwise be imaginable or memorizable (cf. Vasoli 1958: 284ff).

That Bruno bequeathed all this to the Lullian posterity can be seen from further developments of Lullism.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 137-9.

Eco: Bruno: Ars Combinatoria and Infinite Worlds


Ettore Ferrari (1845-1929), The Trial of Giordano Bruno by the Roman Inquisition, bronze relief, Campo de’Fiori, Rome. This bas relief graces the pedestal of the statue of Bruno at Campo de’Fiori in Rome. The collected works of Giordano Bruno (1548-1600) are in the Bibliotheca Bruniana Electronica at the Warburg Institute, with others at the Esoteric Archives. This photo dated 2006 by Jastrow is in the public domain. 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.    

Giordano Bruno’s cosmological vision presented a world without ends, whose circumference, as Nicholas of Cusa had already argued, was nowhere to be found, and whose center was everywhere, at whatever point the observer chose to contemplate the universe in its infinity and substantial unity.

The panpsychism of Bruno had a Neoplatonic foundation: there was but a single divine breath, one principle of motion pervading the whole of the infinite universe, determining it in its infinite variety of forms.

The master idea of an infinite number of worlds was compounded with the notion that every earthly object can also serve as the Platonic shade of other ideal aspects of the universe. Thus every object exists not only in itself, but as a possible sign, deferral, image, emblem, hieroglyph of something else.

This worked also by contrast: an image can lead us back to the unity of the infinite even through its opposite. As Bruno wrote in his Eroici furori, “To contemplate divine things we need to open our eyes by using figures, similitudes, or any of the other images that the Peripatetics knew under the name of phantasms” (Dialoghi italiani, Florence: Sansei, 1958: 1158).

Where they did not emerge directly from his own inflamed imagination, Bruno chose images found in the Hermetic repertoire. These served as storehouses of revelations because of a naturally symbolic relationship that held between them and reality.

Their function was no longer, as in previous arts of memory, that of merely helping to order information for ease of recall, or this was, at least, by now a minor aspect: their function was rather that of helping to understand. Bruno’s images permitted the mind to discover the essence of things and their relations to each other.

The power of revelation stored inside these images was founded on their origin in far-off Egypt. Our distant progenitors worshipped cats and crocodiles because “a simple divinity found in all things, a fecund nature, a mother watching over the universe, expressed in many different ways and forms, shines through different subjects and takes different names” (Lo spaccio della bestia trionfante, Dialoghi italiani, 780-2).

But these images possess more than the simple capacity to reawaken our dormant imagination: they possess an authentic power to effect magical operations on their own, and functioned, in other words, in exactly the same way as the talismans of Ficino.

It is possible, of course, to take many of Bruno’s magical claims in a metaphorical sense, as if he was merely describing, according to the sensibility of his age, intellectual operations. It is also possible to infer that these images had the power to pull Bruno, after prolonged concentration, into a state of mystic ecstasy (cf. Yates 1964: 296).

Still, it is difficult to ignore the fact that some of Bruno’s strongest claims about the theurgic potential of seals appeared in a text that bore the significant title of De Magia:

“nor even are all writings of the same utility as these characters which, by their very configuration, seem to indicated things themselves. For example, there are signs that are mutually inclined to one another, that regard each other and embrace one another; these constrain us to love.

Then there are the opposite signs, signs which repel each other so violently that we are induced to hatred and to separation, becoming so hardened, incomplete, and broken as to produce in us ruin. There are knots which bind, and there are separated characters which release. [ . . . ]

These signs do not have a fixed and determined form. Anyone who, obeying his own furor, or the dictates of his soul, naturally creates his own images, be these of things desired or things to hold in contempt, cannot help but represent these images to himself and to his spirit as if the imagined things were really present.

Thus he experiences his own images with a power that he would not feel were he to represent these things to himself in the form of words, either in elegant oration, or in writing.

Such were the well-defined letters of the ancient Egyptians, which they called hieroglyphs or sacred characters. [ . . . ] by which they were able to enter into colloquies with the gods and to accomplish remarkable feats with them. [ . . . ]

And so, just as, where there lacks a common tongue, men of one race are unable to have colloquies with those of another, but must resort instead to gestures, so relations of any sort between ourselves and certain powers would be impossible were we to lack the medium of definite signs, seals, figures, characters, gestures, and other ceremonies.”

(Opera latine conscripta, Naples-Florence, 1879-1891, vol. III: 39-45).

Concerning the specific iconological material that Bruno employs, we find figures deriving directly from the Hermetic tradition, such as the Thirty-six Decans of the Zodiac, others drawn from mythology, necromantic diagrams that recall Agrippa or John Dee, Lullian suggestions, animals, plants and allegorical figures deriving from the repertoire of emblems and devices.

This is a repertoire with an extraordinary importance in the history of iconology, where the ways in which a certain seal, for example, refers back to a specific idea are largely governed by rhetorical criteria: phonetic similarities (a horse, equus, can correspond to an honest, aequus, man); the concrete for the abstract (a Roman soldier for Rome); antecedent for the consequent; accident for subject (or vice versa); and so on.

Sometimes the analogy  is based upon the similarity of the initial syllable (asinus for asyllum); and certainly Bruno did not know that this procedure, as we shall see in chapter 7, was followed by the Egyptians themselves when using their hieroglyphs.

At other times the relations might be based on kabbalistic techniques such as anagrams or paronomasias (like palatio standing for Latio: cf. Vasoli 1958: 285-6).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 132-5.

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