IN THE STRUCTURE OF LITERATURE
from Spanish by Michael Moretti)
in Spanish at Rinconete of the Centro Virtual Cervantes, Dec 2002.
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.
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 voicehigh 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.
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.
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.
ideas are probabilistic events borne of the perpetual exercise of
thought and contemplation: the imagination.
AND MEASURE IN POETRY
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.
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 creativitygiving greater weight to musicality while abandoning
the messagethus seems to have yielded modern and surreal poetry, a
trend which has had further success in painting, displacing
perfection of the depiction for color.
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 individuals most intimate
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:
Violante bids me write,
grief I hope never again to see;
a sonnet's made of fourteen lines:
behold, before this line go three.
that I could never get this far,
I'm halfway into quatrain two;
the first tercet I arrive,
no fear: there's nothing I can't do!
tercets I have just begun to pen;
must be headed the right way,
this line I finish number one.
in the second, and suspect
have written nearly thirteen lines:
them, that makes fourteen, and look -- it's done.
of the author carries out a mental operation of mathematical nature;
the difference is situated in the use of words in place of numbers.
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.
BETWEEN IMAGINATION AND THE STATISTICAL MIND OF DON MIGUEL CERVANTES
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.
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
Gausss 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.
Gausss 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? Lets
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.
and psychologically, easily identifiable, with a statistical mind,
Cervantes Saavedra has placed these two characters at the extremes of
Gausss normal curve without having a notion of the efficacy of
statistics. Gauss did not yet exist and he did not know this
analyze don Quijotes 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 Alzheimers disease. In
contrast, Sanchos 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.
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.
conclude saying that literature and mathematics are reciprocal and
complementary wisdoms, and without knowing, we daily use them in all