MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Three Plates on the Table [Tres platos en la mesa] (1961)
José María Gironella
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Contributed by Vijay Fafat

An emotional, sensitively written example of a short story of magic realism, in the classic tradition of Borges and Cortazar. Most of the story revolves around the main character’s frame of existence, which is also the rationale for the story, building toward its slow finale. Indeed, the story is in keeping with the author’s assertion about his stories in general (which assertion he makes in the foreword of his collected stories):

“In these tales I have not intended to DEMONSTRATE anything; I simply intend to SUGGEST. We are not dealing with a mathematical lesson, but on the contrary, we are trying to pull the reader out of his mathematical lethargy, from his exclusive faith that two and two are four, to shake his drowsiness and get him on his feet; and trying to pursue “fugitive” thoughts – phantoms and fugitives – to capture those anemic agitations which sometimes last a single instant and which we cannot retain with precision.”

Story Summary: A lonely, exhausted man, a school teacher of arithmetic, lived in modest house outside a cemetery. All he had was his daily immersion in his arithmetic on the blackboard, and conversations with the memories of his daughter:

(quoted from Three Plates on the Table [Tres platos en la mesa])

“Always standing in front of the blackboard, with the chalk in his hand. No one knew what he was trying to prove. And it was useless to wait for him to intersperse, between the numbers and symbols, a caricature of a childish house with a chimney, symmetrical windows, lambs around it and, somewhere, a spring time. While he worked—and he did for hours and hours—he never ever gave in to this kind of impulse. He was a man of modest science, domesticated, for himself alone, but he took it very seriously. To be diverted from algebra or from the simplest arithmetical operation would have been to transgress a beautiful law.”

His neighbors and village children thought he was daft, wasting his life and falling into bad habits of smoking and drinking. He had his own thoughts:

(quoted from Three Plates on the Table [Tres platos en la mesa])

“And this was because they did not know that those four walls, his home, sufficed the man of modest science. Within them was everything that satisfied him. There was his brain, his blackboard; in each corner were fragments of memories; in the garret, dreams of childhood; in the ash can, his sins. In the closets he kept old mufflers, the stained smocks of the intellectual, some photographs. No railroad, no ship, no airplane could take him to such a place as that one. And if this was not enough, within those walls—and very often in his own workroom —there was his daughter. A girl of ten, slightly cross eyed, but with blonde braids and an even blonder smile. A girl that would come into the room cautiously, in spite of all the prohibitions, and who, approaching from behind, would cry out, startling him, “Papa, do you want a candy?” A girl with a capacity for tenderness comparable to that of autumn. Always barefoot on the wooden floor. With a little metal brace over her front teeth that rebelled against being straightened. With dolls and everything there was to be had. Bursting with questions and strange thoughts.

[…]

Yes, the modest man of science had this daughter, ten years old, and he asked himself many times if, had she not existed, he would have continued drawing symbols on the blackboard.”

The mathematics teacher often wondered if he would ever have put any effort in drawing his signs and symbols on the blackboard if his daughter had never existed. The daughter was his true miracle, and she gave meaning to his continued existence. He was also aware that he needed to take care of the child’s upbringing and health:

(quoted from Three Plates on the Table [Tres platos en la mesa])

“It was evident that a girl could not live on abstractions. In a house so full of formulas and X's and astronomical calculations, it was essential that there were little monkeys that played the cymbals, as well as clowns and miniature kitchens that worked like real ones, electrically.”

But then the author drops a hammer: that the daughter never really existed at all!

(quoted from Three Plates on the Table [Tres platos en la mesa])

“ Well, actually, this ten-year-old girl, with all that she represented, was the great lie of that silent and hard-working man, mathematical and gray. The blonde braids of the girl, just as the pleasure he experienced explaining the value of a word or winding up her toys, were the personification of a great desire that had never been realized. The child did not exist and the strict truth was this: in the workroom of the man there was nothing but a blackboard, a table, a divan, a wastebasket and the wood-stove.”

The truth was that it was only him and his wife of thirty years who had each other’s company:

(quoted from Three Plates on the Table [Tres platos en la mesa])

“The only true consolation of the modest sage, his only effective company, was his wife. And the invention of the daughter had been in fact their joint idea. The two would have wanted to have her and they spent years awaiting the event.

[…]

Sometimes it seemed to him that he was resigned. Because he loved his wife and also because in the mutual proximity, in the mutual solitude, there beat a consolation and even a motive for life. His wife was a woman who never laughed, but neither did she ever despair. She occupied much space sitting, like a large parcel, but when she stood up one could see how small she was. She had not changed at all since they were married, on August 12th of 1918. Only her hair. Her hair had saddened and the line that parted it was now a more uncertain path down the center of her head. But the rest, all intact. The same clear look, the same sunken cheeks. She always seemed to wear the same blouse and the same skirt, except on Sundays, when she tied a bow here and another there. She always seemed to walk on sandals, even when she returned from the street with her shoes full of mud. And when she opened a drawer, one would have said she was looking for a glove. Besides, the man was convinced that his wife had a lovely voice, that she could have sung like the angels, but that she had not even wanted to attempt it because she preferred not to modify things, not to disturb. In fact, the great passion of the woman was to go unnoticed. She had a premonition that her husband was accomplishing meritorious work, and that was enough for her.

[…]

The man loved her deeply, spontaneously, without ever asking himself why, nor supposing that it could be any other way.”

So far, so melancholic… and then the author drops the second hammer in its turn:

(quoted from Three Plates on the Table [Tres platos en la mesa])

“Well, the fact is that this humble wife, born near wheat, was the second big lie of that somewhat gray-haired and sentimental man. This wife did not exist either and was also the personalization of his other great desire, the desire to have company. In reality, in that house—in the kitchen, in the hallways, in the bedroom—only he lived, he briefly, with some furniture, the blackboard and the window. The sugar cubes dissolved ingloriously in his own coffee and there was never a chance for a warm voice to emerge from his side. There was no such thing as sad hair, not even on August 12, 1918, not even the black cat with white spots or the opposite. Simply, he had so desired a wife like that one, for whom he would have brought awakening and joy, the life of every day and eternal that when the wind murmured outside - threatening the lungs - or when it rained gently it was not unusual that for a few seconds He actually came to believe that he was married, that in the room next to his a woman, who was his, was sewing or ironing for him.

And many times, at dawn, he would open his eyes without expression in the darkness, he felt an extreme hollowness in everything that his thoughts could encompass and he wondered if his breathing and the signs on the blackboard had a purpose.”

And thus he was, this school teacher of symbols and figures… himself a symbolically tragic, lonely figure.

(quoted from Three Plates on the Table [Tres platos en la mesa])

“Alone in his solitude. With fifty-five years behind him. […] Fifty-five years with himself, searching for he knew not what, without a wife, without a daughter. Born right there, near the cemetery, whose trees grew at the pave of the new guests that arrived at the enclosure.”

Time kept passing, and he noticed a change in his life:

(quoted from Three Plates on the Table [Tres platos en la mesa])

“Little by little, the old house took on the appearance of a fort, of an ancient and gloomy castle. Had this situation been prolonged, the youngest of the schoolchildren would have woven imaginative legends around him. And in the meantime, in his rooms, the man lived as though, in truth, there did exist his wife and his daughter. It was no longer a matter of imagining tinkling laughs or his wife pressing in an adjacent room. Now it was a matter of putting three plates on the table, three glasses and three napkins. Now it was a matter of asking the postman, “Is it for me or for my wife?” And of wondering why the text books for the next semester should be so much more expensive and why an epidemic of measles should be coming from the east.

With all this there came an unexpected moment of mental clarity in front of the blackboard. As with the contraction that precedes the avalanche, he found that operations that he had scrutinized for years were now, as he attacked the final stretch, resolved in one swoop, as though he were copying. The man was astonished. He called his two possible companions, the two columns of his being, and explained with enthusiasm what that particular x signified, and that 2:4. His wife and daughter opened their mouths in admiration and they clung to the long smock that conformed to his body, as though they were birds, numb with cold. To sum up, he grew old and exhausted, but he felt happier than ever before. The compassion of the town was ridiculously useless. And it was also useless for his friends, among them the constable, to take periodic turns down his street, peering inside through the window, fearful of discovering his body fallen face down or hanging from a rope. Actually, he was strong, he was an oak, thanks to his parents and because he had always lived a correct life. He would see his name on the doorplate for a long time, and who knew whether, before he repaired to the call of the trees in the cemetery, he would not, to everyone’s bewilderment, in fact hit upon the key to the extermination of all rats or the irrigating without water of the immense arid lands of the world. Oh, yes, he would last a long while”

Till the final denouement…

(quoted from Three Plates on the Table [Tres platos en la mesa])

“Well now, it’s necessary to confess that this man did not exist in the town, either. His humility, his gray hair, his silhouette in front of the blackboard and his impetuous interior anxieties were nothing but the personification of a great desire of the neighbors in that solitary street, tired of seeing an empty and smelly lot in front of the fountain in the graceful park. Yes, often, when the wind murmured outside or when it rained drearily, they had thought about that lot —where the weeds grew raggedly and where passersby dumped their rubbish—and they had wished for a modest building to rise there, with a smoking stove-pipe perforating the upper pane of a window. The oldsters and the children —especially a cross-eyed boy with a splendid set of teeth— had gone further: in dreams they had more than once imagined what the inhabitants of that building would be like. And among the innumerable possibilities that had crossed their minds like gusts of wind, the image of that domestic intellectual, grayhaired and sentimental, who went out with his wife under the same umbrella and who lifted his daughter into the air, holding her under the arms, had been miraculously repeated.”

The mathematical content is very low except in its symbology and some references, but it does hit home, imagining an imaginary mathematics teacher appearing in the village’s collective imagination. Might not that village itself be an apparition wafting out of Nothing, the entire sequence a self contained loop of non-existence rising as a perfect bootstrap?

Indeed, the story does not have to say that the village also does not exist. The reader knows that it was just a creation of the author. But, I still have to wonder whether the author's decision to make the lonely and delusional father/husband into a math teacher reflects some prejudice about mathematics or mathematics teachers. The character could have been a poet or a welder or a chef or a member of any other profession. But, there is something about mathematics which seemingly resonates with mental illness and sorrow for writers and readers. However, this does not agree with what I see when I look at the community of mathematicians and math teachers, who seem no more prone to these sorts of personality traits than those in any other profession.

Publication History:

  • The story appears in Spanish in the 1961 collection, "Todos Somos Fugitivos" by José María Gironella.
  • An English translation appeared in the 1964 collection “Phantoms and Fugitives – Journeys to the Improbable” which was translated by Terry Broch Fontsere (and from which the quotes in Vijay's review were taken).

(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Three Plates on the Table [Tres platos en la mesa]
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Library of Babel by Jorge Luis Borges
  2. The Lottery in Babylon [La lotería en Babilonia] by Jorge Luis Borges
  3. Ibn Hakkan al-Bokhari, Dead in his Labyrinth by Jorge Luis Borges
  4. El matemático by Arturo Azuela
  5. Colonel Lágrimas by Carlos Fonseca Suárez
  6. The Secret Integration by Thomas Pynchon
  7. Three Days and a Child by Abraham B. Yehoshua
  8. Lost in the Funhouse by John Barth
  9. The Geometry of Love by John Cheever
  10. An Old Arithmetician by Mary Eleanor Wilkins Freeman
Ratings for Three Plates on the Table [Tres platos en la mesa]:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
1/5 (1 votes)
..
Literary Quality:
5/5 (1 votes)
.

Categories:
Genre
MotifMental Illness, Math Education,
Topic
MediumShort Stories,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)