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Tag: Marconi

Eco: Descartes and Mersenne


René Descartes (1596-1650), Principia philosophiae, Amsterdam: Apud Ludovicum Elzevirium, 1644. Held by the Chemical Heritage Foundation as accession number Q155.D473.1644, Othmer Library of Chemical History. 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. 

“More or less at the same period, the problem of a real character was discussed in France, with a more skeptical attitude. In 1629, Father Marin Mersenne sent Descartes news of a project for a nouvelle langue invented by a certain des Vallées.

We are told by Tallemant des Réau that this des Vallées was a lawyer who had an immense talent for languages and who claimed to have discovered “a matrix language through which he could understand all others.”

Cardinal Richelieu asked him to publish his project, but des Vallées replied he was only willing to divulge such a great secret against the promise of a state pension.

“This the Cardinal denied him, and so the secret ended up buried with des Vallées” (Les historiettes, 1657: 2, “Le Cardinal de Richelieu“).

On 20 November 1629, Descartes wrote back to Mersenne giving his thoughts about the story. Learning a language, Descartes noted, involved learning both the meaning of words and a grammar.

All that was required to learn new meanings was a good dictionary, but learning a foreign grammar was more difficult. It might be possible, however, to obviate this difficulty by inventing a grammar that was free from the irregularities of natural languages, all of which had been corrupted through usage.

The resulting language would be a simplified one and might seem, in comparison to natural languages, the basic one, of which all the other natural languages would then appear as so many complex dialects.

It was sufficient to establish a set of primitive names for actions (having synonyms in every language, in the sense in which the French aimer has its synonym in the Greek philein), and the corresponding substantive might next be derived from such a name by adding to it an affix.

From here, a universal writing system might be derived in which each primitive name was assigned a number with which the corresponding terms in natural languages might be recovered.

However, Descartes remarked, there would remain the problem of sounds, since there are ones which are easy and pleasant for speakers of one nation and difficult and unpleasant for those of another.

On the one hand, a system of new sounds might also prove difficult to learn; on the other hand, if one named the primitive terms from one’s own language, then the new language would not be understood by foreigners, unless it was written down by numbers.

But even in this case, learning an entire new numerical lexicon seemed to Descartes a tremendous expense of energy: why not, then, continue with an international language like Latin whose usage was already well established?

At this point, Descartes saw that the real problem lay elsewhere. In order not only to learn but to remember the primitive names, it would be necessary for these to correspond to an order of ideas or thoughts having a logic akin to that of the numbers.

We can general an infinite series of numbers, he noted, without needing to commit the whole set to memory. But this problem coincided with that of discovering the true philosophy capable of defining a system of clear and distinct ideas.

If it were possible to enumerate the entire set of simple ideas from which we generate all the complex ones that the human mind can entertain, and if it were possible to assign to each a character–as we do with numbers–we could then articulate them by a sort of mathematics of thought–while the words of natural languages evoke only confused ideas.

“Now I believe that such a language is possible and that it is possible to discover the science upon which it must depend, a science through which peasants might judge the truth better than philosophers do today.

Yet I do not expect ever to see it in use, for that would presuppose great changes in the present order of things; this world would have to become an earthly paradise, and that is something that only happens in the Pays des Romans.”

Descartes thus saw the problem in the same light as Bacon did. Yet this was a project that he never confronted. The observations in his letter to Mersenne were no more than commonsensical.

It is true that, at the moment he wrote this letter, Descartes had not yet started his own research into clear and distinct ideas, as would happen later with his Discours de la methode;  however, even later he never tried to outline a complete system of simple and clear ideas as the grounds on which to build a perfect language.

He provided a short list of primitive notions in the Principia philosophiae (I, XLVIII), yet these notions were conceived as permanent substances (order, number, time, etc.) and there is no indication that from this list a system of ideas could be derived (see Pellerey 1992a: 25-41; Marconi 1992).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 216-8.

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.

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