MATHEMATICS IN THE STRUCTURE OF LITERATURE

Gustavo Zubieta Castillo

(translated from Spanish by Michael Moretti)

Published in Spanish at Rinconete of the Centro Virtual Cervantes, Dec 2002.

It does not seem strange, or surprising, that one would intuitively sense the relationship which exists among mathematics, literature and art. When a writer applies an accent to a letter, he is introducing into the language a means of augmenting the intensity in the way a vowel is pronounced, so that the orthography conforms to mathematical rules, in the same way as music theory for the proper effect of the sounds of a musical instrument.

When a human speaks, and the production of the sounds is valid for all beings, he employs a musical instrument composed of organic filaments: the larynx. Upon the physical capacity of the "quality" and intensity of the sound is grounded the classification and subdivision of the human voice—high and low, feminine (soprano, mezzo soprano, contralto) and masculine (barítone and below). All physical phenomena of nature are disposed to be measured, as are the psychic; that is to say that there exists no phenomenon in the universe whose study does not arrive to the conclusion that there exists an intimate correlation among others of a different nature.

Literature being the expression of an ensemble of incorporated knowledge of the language, one cannot exclude from its structure the presence of the sciences known as exact and thereby of mathematics. Mathematics and literature, as all know, are housed and fused in the delicate, higher nervous centers constituting in one of the greatest qualities of intelligence: the memory.

Language, expressed in words, is nothing more than a harmonious association of conscious experiences of diverse nature, which, at a given moment, form an idea, a concept which it externalizes as sounds in spoken language or written medium.

Original ideas are probabilistic events borne of the perpetual exercise of thought and contemplation: the imagination.

PROPORTION AND MEASURE IN POETRY

Metrics in the composition of a quartet in a sonnet are nothing other than the intuititive measure of the use of a specific number of words apportioned evenly in groups of syllables. And consonance is nothing more than the utilization of syllables, harmonic notes, sounds (or physical waves), produced by the articulation of the word, pleasant to the ear, forming a discourse which has a meaning.

The content of verse seems to have little transcendence in recent times, as it had in past eras; thereby, zeal and the pursuit of originality and creativity—giving greater weight to musicality while abandoning the message—thus seems to have yielded modern and surreal poetry, a trend which has had further success in painting, displacing perfection of the depiction for color.

Quartets and tercets are measured of grouped words, with logical sense, which express truths or fantasies; which by containing an demonstrative meaning, are capable of arousing the individual’s most intimate emotional responses.

Who does not know from their first encounters with literature in school or other cultural source, the sonnet of the inspired Spanish poet Félix Lope de Vega y Carpio (1562-1635), as example of knowledge of metrics, a proper term of mathematical significance? With delight we realize the experience of a sonnet born in the imaginative inspiration of the author. Here, as reminder, follows the text:

Instant Sonnet¹

A sonnet Violante bids me write,

such grief I hope never again to see;

they say a sonnet's made of fourteen lines:

lo and behold, before this line go three.

I thought that I could never get this far,

and now I'm halfway into quatrain two;

but if at the first tercet I arrive,

I'll have no fear: there's nothing I can't do!

The tercets I have just begun to pen;

I know I must be headed the right way,

for with this line I finish number one.

Now I am in the second, and suspect

that I have written nearly thirteen lines:

count them, that makes fourteen, and look -- it's done.

The mind of the author carries out a mental operation of mathematical nature; the difference is situated in the use of words in place of numbers.

The author arithmetically analyzes what constitutes a sonnet. This is not novel. Which poet does not know that it is a tercet and a quartet? But, when he is in the act of inspiration, an automatic and intuitive mechanism causes him to employ a measure in the same manner utilized by the consciousness to gauge distance or velocity. While the skill evolves and gains in experience, measurement achieves greater precision, without the need to utilize an measuring instrument, such as a tape measure.

The evolution of oration in poetry concludes with an acoustic analogy which defines the cadence and rhythm of the verse. An acoustic physical phenomenon has been measured subconsciously. The word “sonnet”, comes from the Italian “sonette” which means “pleasing, musical sound to the ear”. And every act of measurement being an essentially mathematical mental process, it has measured the sonette or sonnet.

RELATIONSHIP BETWEEN IMAGINATION AND THE STATISTICAL MIND OF DON MIGUEL CERVANTES SAAVEDRA

In the work Don Quijote of La Mancha, the lives of two characters pass with a series of the most implausible adventures, in the theater of everyday events. The personalities and figures of Don Quijote and Sancho Panza, constitute the center of the creative and imaginative universe of Don Miguel Cervantes Saavedra. Both characters are apparently fictitious, but, at the same time they are present in our daily life; therefore, their existence and presence can be identified in the statistics of any population.

To define the personality and the character of the protagonists of the work Don Quijote of la Mancha with mathematics, we begin by recalling a paper that figures very importantly in the analysis of all natural phenomena, the curve described by the mathematical genius, Karl Friedrich Gauss (1777-1855): the normal curve or bell curve, as it is also called. Not only the sciences, if not human understanding for the analysis of any natural phenomenon, can nowadays do without Gauss’s bell curve.

In the briefest and most illustrative way we remember that the normal curve, or that of Gauss (y=e^-x2), is a graphic in the form of a bell in a system of the distributed coordinates of two variables. The frequency distribution in the ordinate and the changes of the observed phenomena in the abcissa, can be of any nature: for example, stature, weight, trait or personality. It is a curve by which one can statistically analyze phenomena of diverse complexity.

If Gauss’s normal curve in statistics is a tool which has application in the pure and applied exact sciences, and has also utility in the social sciences and psychology, why not ,then, in literature? Let’s see.

The precise description of personality encounters difficulties in the most fastidious methods of psychology; if you consider that the differences among the personalities of the individuals that are found in the norm, significant identity differences are not presented. However, it does not surprise us to confirm Don Miguel de Cervantes Saavedra describing, in an intuitive manner, the two central characters of his work, Don Quijote and Sancho Panza, with diametrically opposing characteristics.

Physically and psychologically, easily identifiable, with a statistical mind, Cervantes Saavedra has placed these two characters at the extremes of Gauss’s normal curve without having a notion of the efficacy of statistics. Gauss did not yet exist and he did not know this science.

If we analyze don Quijote’s body weight by his physical constitution such as we imagine and is illustrated in drawings, he weighs around fifty kilograms, in contrast with Sancho Panza who is situated at eighty or more kilograms. If psychologically we classify these characters and their demeanors statistically, we will see that they withdraw to the extremes, of the individual that we consider "normal".

Don Quijote, by his psychosomatic characteristics, is more inclined to hypochondria, and ailments of the vascular and nervous systems. Today we would say, for example, that he is more susceptible to suffer paranoia and Alzheimer’s disease. In contrast, Sancho’s predisposition inclines more toward digestive and vascular illnesses, and to the afflictions which accompany of arterial hypertension, which today we would say were produced by an excess of cholesterol. Amen, of the figure which to each of them has been assigned by Cervantes Saavedra, in the theater of the life.

Mimicked and sublimated in diverse nuances of their behavior and gesture, they can be objects of studies of multiple variations. Always in agreement with the role that the author makes them represent in their innumerable adventures in la Mancha, the characters also live in a region that geographically exists.

We can conclude saying that literature and mathematics are reciprocal and complementary wisdoms, and without knowing, we daily use them in all our expressions.