One recurring theme we enjoy reading and writing about is the intersection, as well as the union of mathematics and literature. Their connection is only natural, considering that literature is defined as the art of the written or spoken word, hence expressed through language. Moreover, the artistic nature of mathematics was exposed by numerous researchers.
But let us not get bogged down in technicalities from the beginning and assume, in what follows, that we are working with the general understanding of literature—that of fiction, expressed through poems, stories, novellas, novels, plays and more.
Setting aside the works drawing obvious inspiration from science (as most of the science fiction subgenre), what else can we add that connects mathematics and literature?
Our article can be read as a preamble for the Poligon Educational event on February 25th. Furthermore, the topic will be expanded in articles and events in the coming months, so make sure you follow our updates on Facebook.
Figures: of Speech and of Geometry
A category of geometric figures which we study since high school is that of conics. Naming them—circle, ellipse, hyperbola, parabola—doesn’t ring any conic bell. But the picture below clarifies the situation: conics are the traces on a plane which cuts two cones with a common tip.
Imagine the cones in a vertical position, one with the opening downwards, and the other, upwards. A vertical cut not through the common tip[1] produces a hyperbola; a horizontal cut produces a circle; skewing the plane at a small angle produces an ellipse and increasing the angle produces a parabola. Such curves can also be defined using algebra or geometric locus, but we are mostly interested in their appearance here.
Historically, conics are said to have appeared first in the works of the Greek Menaechmus (350 BC), but his writings were not found. A thorough study that has indeed survived, including their presentation as conics is that of Apollonius of Perga (200 BC), who wrote an eight-volume treatise titled Conic Sections. In 1710, the English astronomer Edmond Halley—who used Newton’s gravity laws to predict the comet named after him but died before seeing it—published a Latin translation of Apollonius’ works. Below you can see the cover and an illustration from the eighth volume.
Hyperbola
In literature, the hyperbole[2] is a figure of speech which contains an intentional exaggeration, for impact. One could say they are so hungry they could eat a horse and (most likely) not literally meaning it, but instead use hyperbole for effect.
Etymologically, the origin of the word is the Greek word ὑπερβολή ((h)iper + voli), meaning throwing over, at some distance (of a target).
Mathematically, the hyperbola can be called a divergent curve, meaning one which goes further away from a point called its centre.
Therefore, not only does the hyperbola miss the target, but it also strays further and further away from it. The same could be said about the literary hyperbole: its meaning is over, at some distance from reality, going further as the exaggeration is more pronounced. Nevertheless, the centre of a hyperbola is essential for its symmetry, hence for its overall look, as the central (true) meaning of a hyperbole is crucial—even if both the curve and the figure of speech distance themselves from them.
Parabola
The parable is a moralistic story, in which one expresses abstract ideas by means of the concrete. The most well-known parables are those told by Jesus Christ in the Christian Bible, where we find religious and moral values expressed through stories.
For mathematicians, a parabola is a curve which represents a quadratic function, but also one which is drawn with respect to an important point, its focus. And while the hyperbola is a divergent curve, the parabola is convergent, gathering some information in said focus. Remarkably, most of us see and use parabolas almost daily, by means of parabolic mirrors or antennas, which are built so that they gather light or radio waves in a device placed precisely in the focal point.
The etymology again supports the present meaning: the word comes from παραβολή (paravoli), which is made of para (along, near) and shares the voli (to throw) with the hyperbola.
The relation one can see between Jesus’ parables and the mathematical parabola is clear: both the biblical moralistic stories and the devices that have a parabolic shape gather the information along some curve or plot and concentrate it into a focus, which can be a moral principle, or an electronic device.
Ellipse
Commonly called an oval, the ellipse is another conic curve and a literary tool. In geometry, an ellipse is, loosely speaking, an imperfect circle, flattened along some axis.
In literature, the ellipsis appears when one intentionally leaves out some information or there appears a pause in one’s speech or thought. We know it better from its graphical representation: the three dots (…). The word also appears in expressions such as elliptical statement, which shows some lack of information; the speaker or writer avoids or is not aware of some subject, hence they are vague. For example, if asked about what you were doing two weeks ago at 13:15, most likely you will be elliptical in answering. The same could be said if one tries to give a speech they didn’t prepare enough, producing ellipses, commonly accompanied by lots of uhhhms and errrs.
The connection between the two is showed yet again by etymology: the Greek word έλλειψης (elleipsis) shows a shortcoming, an omission, a defect. Hence, one can see the ellipse as an imperfect circle, whereas the imperfection in speech or writing that causes the ellipsis is informational.
Point
We close the article predictably—but slightly off-topic—with the point. Known in writing as the period, it is not actually a figure of speech, but a graphical sign. Nevertheless, the point is indeed a conic curve, albeit a special one, called degenerate—one which pushes the definition to the extreme. To parallel this special character, one can call a coin or a circular piece of paper a cylinder—one with a very small height, hence a degenerate case.
Historically, the point as a geometric object appears first at Euclid of Alexandria (300 BC), where the author uses the word σημεῖόν (simeion), translated generically as sign, and defines it as that which has no parts. Later, the word was Latinized and connected to the verb pungere, to pierce. Its meaning is clearly related to its representation: the smallest sign left by a sharp object piercing or touching some surface—as the quill’s ink-filled tip on a sheet of paper.
By its very generality, the point led to many expressions with various meanings: point of view, punctured, punctuation, weak/strong point.
We close the article with these examples and hope we made a point towards opening a preliminary discussion to our event on February 25th, where we invite you to talk about words and expressions we commonly use that have scientific origins.
[1] If the plane cuts the two cones through the common tip, we get special cases, rather extreme ones, called in mathematics degenerate, which push the definition of a curve to the edges of meaning. We will only briefly address one such case in the last section, and as such, assume here that the plane never contains the common tip of the cones.
[2] The English language remarkably distinguishes between the words used in science and those in literature. As such, we will find the words hyperbola, parabola, ellipse and point in science, while their literary correspondents are hyperbole, parable, ellipsis and period. However, their common origin is indisputable, hence we will explore them together.