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Tag: Faust

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: The Nationalistic Hypothesis, 3


Athanasius Kircher (1602-80), his interpretation of the legendary sphere of Archimedes, using magnets to simulate the rotation of the planets. From Magnes, sive de Arte Magnetica, 1643, p. 305. 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.  


“Ideas similar to these were expressed by Schottel (Teutsche Sprachkunst, 1641), who celebrated the German language as the one which, in its purity, remained closest to the language of Adam (adding to this the idea that language was the expression of the native genius of a people).

Others even claimed that Hebrew had derived from German. They repeated the claim that their language had descended from Japheth, who, in this rendition, had supposedly settled in Germany.

The name of the exact locality changed, of course, to fit the needs of different authors; yet Japheth’s grandson, Ascenas, was said to have lived in the principality of Anhalt even before the confusio. There he was the progenitor of Arminius and Charlemagne.

In order to understand these claims, one must take into account the fact that, during the sixteenth and seventeenth centuries, Protestant Germany rallied to the defense of the language of Luther’s Bible.

It was in this period that claims to the linguistic primacy of German arose, and many of these assumptions “should be seen within the context of Germany’s political fragmentation after the Thirty Years War. Since the German nation was one of the main forces capable of uniting the nation, its value had to be emphasized and the language itself had to be liberated from foreign influences” (Faust 1981: 366).

Leibniz ironized on these and other theories. In a letter of 7 April 1699 (cited in Gensini 1991: 113) he ridiculed those who wished to draw out everything from their own language–Becanus, Rudbeck, a certain Ostroski who considered Hungarian as the mother tongue, an abbé Francois and Pretorius, who did respectively the same for Breton and Polish.

Leibniz concluded that if one day the Turks and Tartars became as learned as the Europeans, they would have no difficulty finding ways to promote their own idioms to the rank of mother tongue for all humanity.

Despite these pleasantries, Leibniz was not entirely immune himself to nationalist temptations. In his Nouveaux essais (III, 2) he made a good-natured jibe at Goropius Becanus, coining the verb goropiser for the making of bad etymologies.

Still, he conceded, Becanus might not always have been entirely wrong, especially when he recognized in the Cimbrian, and, consequently, in Germanic, a language that was more primitive than Hebrew.

Leibniz, in fact, was a supporter of the Celto-Scythian hypothesis, first advanced in the Renaissance (cf. Borst 1957-63: III/1, iv, 2; Droixhe 1978).

In the course of over ten years collecting linguistic materials and subjecting them to minute comparisons, Leibniz had become convinced that at the root of the entire Japhetic stock there lay a Celtic language that was common to both the Gauls and the Germans, and that “we may conjecture that this [common stock] derives from the time of the common origin of all these peoples, said to be among the Scythians, who, coming from the Black Sea, crossed the Danube and the Vistula, and of whom one part may have gone to Greece, while the other filled Germany and Gaul” (Nouveaux essais, III, 2).

Not only this: Leibniz even discovered analogies between the Celto-Scythian languages and those which we would today call the Semitic languages, due, he conjectured, to successive migrations.

He held that “there was nothing that argues either against or for the idea of a single, common origin of all nations, and, in consequence, of one language that is radical and primitive.”

He admitted that Arabic and Hebrew seemed closer than others, their numerous alterations notwithstanding. He concluded, however, that “it seems that Teutonic has best preserved its natural and Adamitic aspect (to speak like Jacques Böhm [sic]).”

Having examined various types of German onomatopoeia, he finally concluded that the Germanic language seemed most primitive.

In presenting this scheme in which a Scythian language group progressively diffused throughout the Mediterranean world, and in distinguishing this group from the other group of southern or Aramaic languages, Leibniz designed a linguistic atlas.

Most of the conjectures in Leibniz’s own particular scheme were, in the end, erroneous; nevertheless, in the light of comparative linguistic work which would come afterwards, he had some brilliant intuitions (cf. Gensini 1990: 41).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 99-102.

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