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Tag: Mersenne

September 2, 2016

Eco: Translation

Diego de Torres Rubio de la Copania de Jesus, 1616

Diego de Torres Rubio (1547-1638), Arte de la lengua aymara, Lima, Francisco del Canto, 1616. Digitized courtesy of the John Carter Brown Library. 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.

“Today more than ever before, at the end of its long search, European culture is in urgent need of a common language that might heal its linguistic fractures.

Yet, at the same time, Europe needs to remain true to its historic vocation as the continent of different languages, each of which, even the most peripheral, remains the medium through which the genius of a particular ethnic group expresses itself, witness and vehicle of a millennial tradition.

Is it possible to reconcile the need for a common language and the need to defend linguistic heritages?

Both of these needs reflect the same theoretical contradictions as well as the same practical possibilities. The limits of any possible international common language are the same as those of the natural languages on which these languages are modeled: all presuppose a principle of translatability.

If a universal common language claims for itself the capacity to re-express a text written in any other language, it necessarily presumes that, despite the individual genius of any single language, and despite the fact that each language constitutes its own rigid and unique way of seeing, organizing and interpreting the world, it is still always possible to translate from one language to another.

However, if this is a prerequisite inherent to any universal language, it is at the same time a prerequisite inherent to any natural language. It is possible to translate from a natural language into a universal and artificial one for the same reasons that justify and guarantee the translation from a natural language into another.

The intuition that the problem of translation itself presupposed a perfect language is already present in Walter Benjamin: since it is impossible to reproduce all the linguistic meanings of the source language into a target language, one is forced to place one’s faith in the convergence of all languages.

In each language “taken as a whole, there is a self-identical thing that is meant, a thing which, nevertheless, is accessible to none of these languages taken individually, but only to that totality of all of their intentions taken as reciprocal and complementary, a totality that we call Pure Language [reine Sprache].” (Benjamin 1923).

This reine Sprache is not a real language. If we think of the mystic and Kabbalistic sources which were the inspiration for Benjamin’s thinking, we begin to sense the impending ghost of sacred languages, of something more akin to the secret genius of Pentecostal languages and of the language of birds than to the ideal of the a priori languages.

“Even the desire for translation is unthinkable without this correspondence with the thought of God (Derrida 1980: 217; cf. also Steiner 1975: 64).

In many of the most notable projects for mechanical translation, there exists a notion of a parameter language, which does share many of the characteristics of the a priori languages.

There must, it is argued, exist a tertium comparationis which might allow us to shift from an expression in language A to an expression in language B by deciding that both are equivalent to an expression of a metalanguage C.

If such a tertium really existed, it would be a perfect language; if it did not exist, it would remain a mere postulate on which every translation ought to depend.

The only alternative is to discover a natural language which is so “perfect” (so flexible and powerful) as to serve as a tertium comparationis. In 1603, the Jesuit Ludovico Bertonio published his Arte de lengua Aymara (which he supplemented in 1612 with a Vocabulario de la lengua Aymara).

Aymara is a language still partially spoken by Indians living between Bolivia and Peru, and Bertonio discovered that it displayed an immense flexibility and capability of accommodating neologisms, particularly adapted to the expression of abstract concepts, so much so as to raise a suspicion that it was an artificial invention.

Two centuries later, Emeterio Villamil de Rada described it as the language of Adam, the expression of “an idea anterior to the formation of language,” founded upon “necessary and immutable ideas” and, therefore, a philosophic language if ever there were one (La Lengua de Adan, 1860). After this, it was only a matter of time before the Semitic roots of the Aymara language were “discovered” as well.

Recent studies have established that unlike western thought, based on a two-valued logic (either true or false), Aymara thought is based on a three-valued logic, and is, therefore, capable of expressing modal subtleties which other languages can only capture through complex circumlocutions.

Thus, to conclude, there have been proposals to use Aymara to resolve all problems of computer translation (see Guzmán de Rosas n.d., which includes a vast bibliography). Unfortunately, “due to its algorithmic nature, the syntax of Aymara would greatly facilitate the translation of any other idiom into its own terms (though not the other way around)” (L. Ramiro Beltran, in Guzmán de Rosas n.d.: III).

Thus, because of its perfection, Aymara can render every thought expressed in other mutually untranslatable languages, but the price of this is that once the perfect language has resolved these thoughts into its own terms, they cannot be translated back into our natural native idioms.

One way out of this dilemma is to assume, as certain authors have recently done, that translation is a matter to be resolved entirely within the destination (or target) language, according to the context.

This means that it is within the framework of the target language that all the semantic and syntactic problems posed by the source text must be resolved.

This is a solution that takes us outside of the problem of perfect languages, or of a tertium comparationis, for it implies that we need to understand expressions formed according to the genius of the source language and to invent a “satisfying” paraphrase according to the genius of the target language.

Yet how are we to establish what the criteria of “satisfaction” could be?

These were theoretical difficulties that Humboldt had already foreseen. If no word in a language exactly corresponds to a word in another one, translation is impossible. At most, translation is an activity, in no way regulated, through which we are able to understand what our own language was unable to say.

Yet if translation implied no more than this it would be subject to a curious contradiction: the possibility of a relation between two languages, A and B, would only occur when A was closed in a full realization of itself, assuming to had understood B, of which nothing could any longer be said, for all that B had to say would by now have been said by A.

Still, what is not excluded is the possibility that, rather than a parameter language, we might elaborate a comparative tool, not itself a language, which might (if only approximately) be expressed in any language, and which might, furthermore, allow us to compare any two linguistic structures that seemed, in themselves, incommensurable.

This instrument or procedure would be able to function in the same way and for the same reason that any natural language is able to translate its own terms into one another by an interpretive principle: according to Peirce, any natural language can serve as a metalanguage to itself, by a process of unlimited semiosis (cf. Eco 1979: 2).

See for instance a table proposed by Nida (1975: 75) that displays the semantic differences in a number of verbs of motion (figure 17.1).

Umberto Eco, The Search for the Perfect Language, Figure 17.1, p. 348.png

Umberto Eco, The Search for the Perfect Language, 1995, Figure 17.1, p. 348.

We can regard this table as an example of an attempt to illustrate, in English–as well as by other semiotic means, such as mathematical signs–what a certain class of English terms mean.

Naturally, the interpretative principle demands that the English speaker also interpret the meaning of limb, and indeed any other terms appearing in the interpretation of the verbal expression.

One is reminded here of Degérando’s observations concerning the infinite regress that may arise from any attempt to analyze fully an apparently primitive term such as to walk.

In reality, however, a language always, as it were, expects to define difficult terms with terms that are easier and less controversial, though by conjectures, guesses and approximations.

Translation proceeds according to the same principle. If one were to wish, for example, to translate Nida’s table from English into Italian, one would probably start by substituting for the English verbs Italian terms that are practically synonymous: correre for run, camminare for walk, danzare for dance, and strisciare for crawl.

As soon as we got to the verb to hop, we would have to pause; there is no direct synonym in Italian for an activity that the Italian-English dictionary might define as “jumping on one leg only.”

Nor is there an adequate Italian synonym for the verb to skip: Italian has various terms, like saltellare, ballonzolare and salterellare; these can approximately render to skip, but they can also translate to frisk, to hop or to trip, and thus do not uniquely specify the sort of alternate hop-shuffle-step movement specified by the English to skip.

Even though Italian lacks a term which adequately conveys the meaning of to skip, the rest of the terms in the table–limb, order of contact, number of limbs–are all definable, if not necessarily by Italian synonyms, at least by means of references to contexts and circumstances.

Even in English, we have to conjecture that, in this table, the term contact must be understood as “contact with the surface the movement takes place upon” rather than as “contact with another limb.”

Either to define or to translate, we thus do not need a full fledged parametric language at our disposition. We assume that all languages have some notion that corresponds to the term limb, because all humans have a similar anatomy.

Furthermore, all cultures probably have ways to distinguish hands from arms, palms from fingers, and, on fingers, the first joint from the second, and the second from the third; and this assumption would be no less true even in a culture, such as Father Mersenne imagined, in which every individual pore, every convolute of a thumb-print had its own individual name.

Thus, by starting from terms whose meanings are known and working to interpret by various means (perhaps including gestures) terms whose meanings are not, proceeding by successive adjustments, an English speaker would be able to convey to an Italian speaker what the phrase John hops is all about.

These are possibilities for more than just the practice of translation; they are the possibilities for coexistence on a continent with a multilingual vocation. Generalized polyglottism is certainly not the solution to Europe’s cultural problems; like Funes “el memorioso” in the story by Borges, a global polyglot would have his or her mind constantly filled by too many images.

The solution for the future is more likely to be in a community of peoples with an increased ability to receive the spirit, to taste or savor the aroma of different dialects.

Polyglot Europe will not be a continent where individuals converse fluently in all the other languages; in the best of cases, it could be a continent where differences of language are no longer barriers to communication, where people can meet each other and speak together, each in his or her own tongue, understanding, as best they can, the speech of others.

In this way, even those who never learn to speak another language fluently could still participate in its particular genius, catching a glimpse of the particular cultural universe that every individual expresses each time he or she speaks the language of his or her ancestors and his or her own tradition.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 344-51.

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July 27, 2016

Eco: The Last Flowering of Philosophic Languages

Anne-Pierre-Jacques De Vismes, Pasilogie, ou de la musique, consideree comme langue universelle, 1806

Anne-Pierre-Jacques De Vismes (1745-1819), Pasilogie, ou de la musique, considérée comme langue universelle, Paris, 1806. 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. 

“Nor was even this the end of attempts at creating a philosophic language. In 1772 there appeared the project of Georg Kalmar, Praecepta grammatica atque specimina linguae philosophicae sive universalis, ad omne vitae genus adcomodatae, which occasioned the most significant discussion on our topic written in Italian.

In 1774, the Italian-Swiss Father Francesco Soave published his Riflessioni intorno alla costituzione di una lingua universale. Soave, who had done much to spread the sensationalist doctrine to Italy, advanced a criticism of the a priori languages that anticipated those made by the Idéologues (on Soave see Gensini 1984; Nicoletti 1989; Pellerey 1992a).

Displaying a solid understanding of the projects from Descartes to Wilkins and from Kircher to Leibniz, on the one hand Soave advanced the traditional reservation that it was impossible to elaborate a set of characters sufficient to represent all fundamental concepts; on the other hand, he remarked that Kalmar, having reduced these concepts to 400, was obliged to give different meanings to the same character, according to the context.

Either one follows the Chinese model, without succeeding in limiting the characters, or one is unable to avoid equivocations.

Unfortunately, Soave did not resist the temptation of designing a project of his own, though outlining only its basic principles. His system of classification seems to have been based on Wilkins; as usual he sought to rationalize and simplify his grammar; at the same time, he sought to augment its expressive potential by adding marks for new  morphological categories such as dual and the neuter.

Soave took more care over his grammar than over his lexicon, but was mainly interested in the literary use of language: from this derives his radical skepticism about any universal language; what form of literary commerce, he wondered, could we possibly have with the Tartars, the Abyssinians or the Hurons?

In the early years of the next century, Soave’s discussion influenced the thinking of Giacomo Leopardi, who had become an exceptionally astute student of the Idéologues.

In his Zibaldone, Leopardi treated the question of universal languages at some length, as well as discussing the debate between rationalists and sensationalists in recent French philosophy (see Gensini 1984; Pellerey 1992a).

Leopardi was clearly irritated by the algebraic signs that abounded in the a priori languages, all of which he considered as incapable of expressing the subtle connotations of natural languages:

“A strictly universal language, whatever it may be, will certainly, by necessity and by its natural bent, be both the most enslaved, impoverished, timid, monotonous, uniform, arid, and ugly language ever.

It will be incapable of beauty of any type, totally uncongenial to imagination [ . . . ] the most inanimate, bloodless, and dead whatsoever, a mere skeleton, a ghost of a language [ . . . ] it would lack life even if it were written by all and universally understood; indeed it will be deader than the deadest languages which are no longer either spoken or written.” (23 August 1823, in G. Leopardi, Tutte le opere, Sansoni: Florence 1969: II, 814).

Despite these and similar strictures, the ardor of the apostles of philosophic a priori languages was still far from quenched.

At the beginning of the nineteenth century, Anne-Pierre-Jacques de Vismes (Pasilogie, ou de la musique considérée come langue universelle, 1806) presented a language that was supposed to be a copy of the language of the angels, whose sounds derived from the affections of the soul.

Vismes argued that when the Latin translation of Genesis 11:1-2 states that “erat terra labii unius” (a passage to which we usually give the sense that “all the world was of one language”), it used the word labium (lip) rather than lingua (tongue) because people first communicated with each other by emitting sounds through their lips without articulating them with their tongue.

Music was not a human invention (pp. 1-20), and this is demonstrated by the fact that animals can understand music more easily than verbal speech: horses are naturally roused by the sound of trumpets as dogs are by whistles. What is more, when presented with a musical score, people of different nations all play it the same way.

Vismes presents enharmonic scales of 21 notes, one for each letter of the alphabet. He did this by ignoring the modern convention of equal temperament, and treating the sharp of one note as distinct from the flat of the note above.

Since Vismes was designing a polygraphy rather than a spoken language, it was enough that the distinctions might be exactly represented on a musical stave.

Inspired, perhaps, indirectly by Mersenne, Vismes went on to demonstrate that if one were to combine his 21 sounds into doublets, triplets, quadruplets, etc., one would quickly arrive at more syntagms than are contained in any natural language, and that “if it were necessary to write down all the combinations that can be generated by the seven enharmonic scales, combined with each other, it would take almost all of eternity before one could hope to come to an end.” (p. 78).

As for the concrete possibility of replacing verbal sounds by musical notes, Vismes devotes only the last six pages of his book to such a topic–not a great deal.

It never seems to have crossed Visme’s mind that, in taking a French text and substituting tones for its letters, all he was doing was transcribing a French text, without making it comprehensible to speakers of other languages.

Vismes seems to conceive of a universe that speaks exclusively in French, so much so that he even notes that he will exclude letters like K, Z and X because “they are hardly ever used in languages” (p. 106).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 302-4.

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July 12, 2016

Eco: The Problem of the Primitives

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria, frontispiece

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, frontispiece, Dissertation on the Art of Combinations or On the Combinatorial Art, Leipzig, 1666. 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.

“What did Leibniz’s ars combinatoria have in common with the projects for universal languages? The answer is that Leibniz had long wondered what would be the best way of providing a list of primitives and, consequently, of an alphabet of thoughts or of an encyclopedia.

In his Initia et specimina scientiae generalis (Gerhardt 1875: VII, 57-60) Leibniz described an encyclopedia as an inventory of human knowledge which might provide the material for the art of combination.

In the De organo sive arte magna cogitandi (Couturat 1903: 429-31) he even argued that “the greatest remedy for the mind consists in the possibility of discovering a small set of thoughts from which an infinity of other thoughts might issue in order, in the same way as from a small set of numbers [the integers from 1 to 10] all the other numbers may be derived.”

It was in this same work that Leibniz first made hints about the combinational possibilities of a binary calculus.

In the Consilium de Encyclopedia nova conscribenda methodo inventoria (Gensini 1990: 110-20) he outlined a system of knowledge to be subjected to a mathematical treatment through rigorously conceived propositions. He proceeded to draw up a plan of how the sciences and other bodies of knowledge would then be ordered: from grammar, logic, mnemonics topics (sic) and so on to morals and to the science of incorporeal things.

In a later text on the Termini simpliciores from 1680-4 (Grua 1948: 2, 542), however, we find him falling back to a list of elementary terms, such as “entity,” “substance” and “attribute,” reminiscent of Aristotle’s categories, plus relations such as “anterior” and “posterior.”

In the Historia et commendatio linguae characteristicae we find Leibniz recalling a time when he had aspired after “an alphabet of human thoughts” such that “from the combination of the letters of this alphabet, and from the analysis of the vocables formed by these letters, things might be discovered and judged.”

It had been his hope, he added, that in this way humanity might acquire a tool which would augment the power of the mind more than telescopes and microscopes had enlarged the power of sight.

Waxing lyrical over the possibilities of such a tool, he ended with an invocation for the conversion of the entire human race, convinced, as Lull had been, that if missionaries were able to induce the idolators to reason on the basis of the calculus they would soon see that the truths of our faith concord with the truths of reason.

Immediately after this almost mystical dream, however, Leibniz acknowledged that such an alphabet had yet to be formulated. Yet he also alluded to an “elegant artifice:”

“I pretend that these marvelous characteristic numbers are already given, and, having observed certain of their general properties, I imagine any other set of numbers having similar properties, and, by using these numbers, I am able to prove all the rules of logic with an admirable order, and to show in what way certain arguments can be recognized as valid by regarding their form alone.” (Historia et commendatio, Gerhardt 1875: VII, 184ff).

In other words, Leibniz is arguing that the primitives need only be postulated as such for ease of calculation; it was not necessary that they truly be final, atomic and unanalyzable.

In fact, Leibniz was to advance a number of important philosophical considerations that led him to conclude that an alphabet of primitive thought could never be formulated. It seemed self-evident that there could be no way to guarantee that a putatively primitive term, obtained through the process of decomposition, could not be subjected to further decomposition.

This was a thought that could hardly have seemed strange to the inventor of the infinitesimal calculus:

“There is not an atom, indeed there is no such thing as a body so small that it cannot be subdivided [ . . . ] It follows that there is contained in every particle of the universe a world of infinite creatures [ . . . ] There can be no determined number of things, because no such number could satisfy the need for an infinity of impressions.” (Verità prime, untitled essay in Couturat 1903: 518-23).

If no one conception of things could ever count as final, Leibniz concluded that we must use the conceptions which are most general for us, and which we can consider as prime terms only within the framework of a specific calculus.

With this, Leibniz’s characteristica breaks its link with the research into a definitive alphabet of thought. Commenting on the letter to Mersenne in which Descartes described the alphabet of thoughts as a utopia, Leibniz noted:

“Even though such a language depends upon a true philosophy, it does not depend upon its perfection. This is to say: the language can still be constructed despite the fact that the philosophy itself is still imperfect.

As the science of mankind will improve, so its language will improve as well. In the meantime, it will continue to perform an admirable service by helping us retain what we know, showing what we lack, and inventing means to fill that lack.

Most of all, it will serve to avoid those disputes in the sciences that are based on argumentation. For the language will make argument and calculation the same thing.” (Couturat 1903: 27-8).

This was not only a matter of convention. The identification of primitives cannot precede the formulation of the lingua characteristica because such a language would not be a docile instrument for the expression of thought; it is rather the calculating apparatus through which those thoughts must be found.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 275-7.

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July 10, 2016

Eco: Characteristica and Calculus

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, an excerpt from his first doctoral dissertation, Dissertation on the Art of Combinations, Leipzig, 1666. 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. 

“The theme of invention and discovery should remind us of Lull; and, in fact, Lull’s ars combinatoria was one of Leibniz’s first sources. In 1666, at the age of twenty, Leibniz composed his own Dissertatio de arte combinatoria (Gerhardt 1875: IV, 27-102). But the dream of the combinatoria was to obsess him for the rest of his life.

In his short Horizon de la doctrine humaine (in Fichant 1991), Leibniz dealt with a problem that had already troubled Father Mersenne: how many utterances, true, false or even nonsensical, was it possible to formulate using an alphabet of 24 letters?

The point was to determine the number of truths capable of expression and the number of expressions capable of being put into writing. Given that Leibniz had found words of 31 letters in Latin and Greek, an alphabet of 24 letters would produce 2432 words of 31 letters.

But what is the maximum length of an expression? Why should an expression not be as long as an entire book? Thus the sum of the expressions, true or false, that a man might read in the course of his life, imagining that he reads 100 pages a day and that each page contains 1,000 letters, is 3,650,000,000.

Even imagining that this man can live one thousand years, like the legendary alchemist Artephius, it would still be the case that “the greatest expressible period, or the largest possible book that a man can read, would have 3,650,000,000,000 [letters], and the number of truths, falsehoods, or sentences expressible–that is, readable, regardless of pronounceability or meaningfulness–will be 24365,000,000,001 – 24/23 [letters].”

We can imagine even larger numbers. Imagine our alphabet contained 100 letters; to write the number of letters expressible in this alphabet we would need to write a 1 followed by 7,300,0000,000,000 (sic) zeros. Even to write such a number it would take 1,000 scribes working for approximately 37 years.

Leibniz’s argument at this point is that whatever we take the number of propositions theoretically capable of expression to be–and we can plausibly stipulate more astronomical sums than these–it will be a number that vastly outstrips the number of true or false expressions that humanity is capable of producing or understanding.

From such a consideration Leibniz concluded paradoxically that the number of expressions capable of formulation must always be finite, and, what is more, that there must come a moment at which humanity would start to enunciate them anew.

With this thought, Leibniz approaches the theme of the apochatastasis or of universal reintegration–what we might call the theme of the eternal return.

This was a line of speculation more mystical than logical, and we cannot stop to trace the influences that led Leibniz to such fantastic conclusions.

It is plain, however, that Leibniz has been inspired by Lull and the kabbala, even if Lull’s own interest was limited to the generation of just those propositions that expressed true and certain knowledge and he thus would never have dared to enlarge his ars combinatoria to include so large a number of propositions.

For Leibniz, on the contrary, it was a fascination with the vertiginous possibilities of discovery, that is of the infinite number of expressions of which a simple mathematical calculation permitted him to conceive, that served as inspiration.

At the time he was writing his Dissertatio, Leibniz was acquainted with Kircher’s Polygraphia, as well as with the work of the anonymous Spaniard, of Becher, and of Schott (while saying that he was waiting for the long-promised Ars magna sciendi of the “immortal Kircher“).

He had yet to read Dalgarno, and Wilkins had still not published his Essay. Besides, there exists a letter from Kircher to Leibniz, written in 1670, in which the Jesuit confessed that he had not yet read Leibniz’s Dissertatio.

Leibniz also elaborated in the Dissertatio his so-called method of “complexions,” through which he might calculate, given n elements, how many groups of them, taken t at a time, irrespective of their ordering, can be ordered.

He applied this method to syllogisms before he passed to his discussion of Lull (para. 56). Before criticizing Lull for limiting the number of his elements, Leibniz made the obvious observation that Lull failed to exploit all the possibilities inherent in his combinatorial art, and wondered what could happen with variations of order, which could produce a greater number.

We already know the answer: Lull not only limited the number of elements, but he rejected those combinations that might produce propositions which, for theological and rhetorical reasons, he considered false.

Leibniz, however, was interested in a logica inventiva (para. 62) in which the play of combinations was free to produce expressions that were heretofore unknown.

In paragraph 64 Leibniz began to outline the theoretical core of his characteristica universalis. Above all, any given term needed to be resolved into its formal parts, the parts, that is, that were explicitly entailed by its definition.

These parts then had to be resolved into their own components, and so on until the process reached terms which could not, themselves, be defined–that is, the primitives. Leibniz included among them not only things, but also modes and relations.

Other terms were to be classified according to the number of prime terms they contained: if they were composed from 2 prime terms, they were to be called com2nations; if from 3 prime terms, com3nations, and so forth. Thereby a hierarchy of classes of increasing complexity could be created.

Leibniz returned to this argument a dozen years later, in the Elementa characteristicae universalis. Here he was more generous with his examples. If we accept the traditional definition of man as “rational animal,” we might consider man as a concept composed of “rational” and “animal.”

We may assign numbers to these prime terms: animal = 2, and rational = 3. The composite concept of man can be represented as the expression 2 * 3, or 6.

For a proposition to be true, if we express fractionally the subject-predicate (S/P) relationship, the number which corresponds to the subject must be exactly divisible by the number which corresponds to the predicate.

Given the preposition “all men are animals,” the number for the subject (men), is 6; the number for animals is 2; the resulting fraction is 6/2 = 3. Three being an integer, consequently, the preposition is true.

If the number for monkey were 10, we could demonstrate the falsity of either the proposition “all men are monkeys” or “all monkeys are men:” “the idea of monkey does not contain the idea of man, nor, vice versa, does the idea of the latter contain the former, because neither can 6 be exactly divided by 10, nor 10 by 6” (Elementa, in Couturat 1903: 42-92). These were principles that had all been prefigured in the Dissertatio.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 271-5.

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June 29, 2016

Eco: Descartes and Mersenne

René_Descartes_1644_Principia_philosophiae

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.

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June 21, 2016

Eco: Polygraphies

Chart_in_the_hand_of_Dr_John_Dee._Steganographiae

John Dee (1527-1609), an excerpt from Steganographiae, aka Peniarth MS 423D, astrological texts in Latin, 1591. Steganographiae was originally composed by Johannes Trithemius in the 1490’s. Infamous as a work of cryptography, this excerpt was copied by hand by Dr. Dee. Peniarth MS 423D is held by the National Library of Wales. This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. All rights are waived worldwide under copyright laws. This file can be copied, modified, and distributed with no permissions required.  

“Steganographies were used to cipher messages in order to guarantee secrecy and security.  However, even though disregarding many terminological details (or differences) used today by the cryptographers, one must distinguish between the activity of coding and decoding messages when one knows the key, or code, and cryptoanalysis (sic); that is, the art of discovering an unknown key in order to decipher an otherwise incomprehensible message.

Both activities were strictly linked from the very beginning of cryptography: if a good steganography could decode a ciphered message, it ought to allow its user to understand an unknown language as well.

When Trithemius wrote his Polygraphiae, which was published in 1518, before his Steganographia, and did not earn the sinister fame of the latter work, he was well aware that, by his system, a person ignorant of Latin might, in a short time, learn to write in that “secret” language (1518: biiii) (sic).

Speaking of Trithemius‘ Polygraphia, Mersenne said (Quaestiones celeberrimae in Genesim, 1623: 471) that its “third book contains an art by which even an uneducated man who knows nothing more than his mother tongue can learn to read and write Latin in two hours.”

Steganography thus appeared both as an instrument to encipher messages conceived in a known language and as the key to deciphering unknown languages.

In order to cipher a message one must substitute the letters of a plain message (written in a language known by both the sender and the addressee) with other letters prescribed by a key or code (equally known by sender and addressee).

To decipher a message encoded according to an unknown key, it is frequently sufficient to detect which letter of the encoded message recurs most frequently, and it is easy to infer that this represents the letter occurs most frequently in a given known language.

Usually the decoder tries various hypotheses, checking upon different languages, and at a certain point finds the right solution.

The decipherment is made, however, more difficult if the encoder uses a new key for every new word of the message. A typical procedure of this kind was the following. Both the encoder and the decoder refer to a table like this:

Umberto Eco, Table, The Search for the Perfect Language, Polygraphies, Trithemius, p. 195

Umberto Eco, The Search for the Perfect Language, p. 195.

Now, let us suppose that the key is the Latin word CEDO. The first word of the message is encoded according to the third line of the table (beginning with C), so that A becomes C, B becomes D and so on.

The second words is encoded according to the fifth line (beginning with E), so that A becomes E and so on. The third word is encoded according to the fourth line, the fourth according to the fifteenth one . . . At the fifth word one starts the process all over again.

Naturally the decoder (who knows the key) proceeds in the opposite way.

In order to decipher without knowing the key, if the table is that simple and obvious, there is no problem. But even in cases of more complicated tables the decipherer can try with all possible tables (for instance, with alphabets in reverse order, with alternate letters, such as ACEG), and it is usually only a matter of time before even the most complex of codes are broken.

Observing this, Heinrich Hiller, in his Mysterium artiis steganographicae novissimum (1682), proposed to teach a method of learning to decipher messages not only in code, but also in Latin, German, Italian and French, simply by observing the incidence of each letter and diphthong in each language.

In 1685, John Falconer wrote a Cryptomenysis patefacta: or the Art of Secret Information Disclosed Without a Key, where he noted that, once someone has understood the rules of decipherment in a given language, it is possible to do the same with all the others (A7v).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 194-6.

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June 16, 2016

Eco: The Egyptian vs. The Chinese Way, 2

kircher_099-590x1024

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

50arbreu_fig3_escorial

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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