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ISSN 1556-4975

Published by Ricardo and Isabel Nirenberg since 1998

# Chapter 15. Fourier Series and Ironic Horseplay.

October 12, 1958, is a beautiful spring Sunday; I am home, sitting at our patio on the steps leading to the main entrance, facing the rose bushes, a book on my lap.  Joyful noises of boys playing ball in the street.  I don’t see them; I hear mostly the echoes of “¡Dale! ¡Dale!” (“Go! Go!”)  Five years later, freshly arrived in New York and still drenched in nostalgia, I joined my Argentine friends Porta and Fattorini, fellow graduate students at NYU, in mock soccer games, in the Lower East Side. We studious young men who had never played in the streets as young boys, called at each other as we fondly remembered street urchins calling, “¡Dale, Beto!” or “¡Centro, Ruben!”  A young Catholic priest stood watching us at our pretend game a good half hour; whether his interest was athletic, or linguistic, or purely erotic, we didn’t find out — theological, I bet, it was not.

Back in October 1958, the street was filled with noises. The manisero or peanut vendor pushing his smoking miniature locomotive, sounding his tin post horn, the barquillero who sold rolled wafers, calling the kids with his Pan pipe, and the fishmonger with his two baskets balanced on a pole on his shoulder, who announced himself, “Pissscatore,” with tremendous emphasis on the sibilant: Calabrese, I conjecture. The sounds, accompanied by the continuous chirping of fledglings begging for food in the Southern springtime, composed in my mind a wonderfully harmonious experience of the world — not just the sounds in and by themselves, however, but in communication with the book I was reading, a math textbook on trigonometrical series.

You may remember that Pythagoras is credited with the discovery that musical intervals correspond to simple numerical proportions — for example, 2:1 (octave), 3:2 (perfect fifth), 5:4 (major third), 6:5 (minor third). Proportions which brought to my mind, there, facing Mother’s rosebuds, the marriage of music and arithmetic, which lasted more than two-thousand years: music was said to be “number in time.”

Aristotle knew that sounds require not only a voice, or the plucking of a tense string or the striking of a brass plate, but an intervening medium, a metaxú, which could be air or water: sounds, he says, are motions of the medium impinging on our ears. By the 17th century, the pioneers of modern science, Galileo, Descartes, and Newton, were agreed that those motions of the medium are periodic; in other words, that they are waves. But it was only about 1800 that a second revolution occurred: the decomposition or analysis of a sound wave, or actually any wave, into its harmonics, and this is what I am studying on this sunny spring Sunday in this book, whose title and author I don’t remember, but which will have a fairly decisive influence on my life. But let me first finish the little lesson in acoustics.

Numbers, just numbers, can only go so far; to keep abreast of the new, and to undergird acoustics, math had to invent functions that assign number to number; later, in a similar way, math had to move up again, to operators that assign function to function, in order to ground quantum mechanics.  To make things simple, take a straight line from the gong we’re going to strike to the ear that’s going to hear, and call x the distance from the gong.  The function P(x) denotes air pressure along the x-axis: it is a wave, a periodic function. Jean-Baptiste Joseph Fourier became immortal by showing how such a periodic function can be expressed as the sum of multiples of sines or cosines. The n-th term of the sum is called the n-th harmonic of the sound. Enough acoustics for now, and please excuse the technicalities: no idea how else to describe my thoughts and communicate my feelings while in the rose garden on that October day. It was probably the first time I had been reading material in advance of the corresponding lecture. And it was the first time I felt, considering the poetry and the physics of sound, that everything fit, that pace Voltaire, Leibniz was right with his pre-established harmony. Then on top of that, as a surplus, I realized that having just read about Fourier series I had thought of Leibniz, who is the foremost master of infinite sums: something, therefore, was clicking in my mind.

A week later I was sitting in the old classroom on the ground floor of Perú 222 where Professor Alberto González Domínguez taught the Third Course of Analysis. His style was unique and there was in his speech plenty of Andalusian grace, as both his parents were from Southern Spain. A man of fifty-four, he got his doctorate in math in his mid-thirties under Rey Pastor; before going into math, he had been at Filosofía y Letras, where he became a classicist, a polyglot, and a lover of literature. I’ve often thought that his life road was the inverse of mine, but who knows, for as Heraclitus famously said, the way up and the way down are one and the same.

That day, González Domínguez was expounding on Fourier series and, having arrived at the problem of proving their convergence — in other words, showing that the more terms you add, the sum becomes closer and closer to the original periodic function — he was finally left with the task of proving that the coefficients approach zero.  — “And now the ball is up on the tile roof,” he declared, and after biting his lower lip, “What are we going to do about it?”

He was about to light a cigarette when I answered, — “Apply the Lemma of Riemann-Lebesgue.” That lemma, ensuring that any periodic function whose integral exists has Fourier coefficients that approach zero, was the most delicate part of the stuff I had been reading at the rose garden a week before. As for the effect, it was immediate: González Domínguez let the lit match fall, took the cigarette off his lips, asked for my name, then used it to congratulate me effusively, as if I had been the discoverer and not merely a reader of that key lemma.  After the lecture, he called me over and we talked.  He inquired about my studies, and after hearing about my heavy load of courses, what with math and with physics (I had already quit chemistry), he commented, — “One shouldn’t force the machine.”

I was reminded of this phrase many years later, when Emilio Lida, my father-in-law, a physician who was the exact contemporary of González Domínguez, felt that death was approaching and expressed that by saying, “the machine is running down,” and I asked myself if the mechanical metaphor was particularly significant for that generation. In any case, the interchange with González Domínguez had two consequences: one, I quit physics, but only after another semester in which I took Classical Mechanics and Electronics (a scramble of triodes and pentodes). And two, Corita Sadosky, daughter of Manuel Sadosky and Cora Ratto, Corita who was there at the time González Domínguez dropped his match, and who had never stooped to say good day, became all of a sudden friendly to me.

She invited me to study with her. I took the bus to the Sadoskys’ apartment on Calle Paraguay, where we’d sit across a neat study table with our books and notes. Often, after completing a few problems, we’d pause and talk, mostly about our common fondness for the novels of Anatole France. It was for me a sweet satisfaction: not since the horrific fall of Madame de la Barre had I had an opportunity to talk about French literature; we variously commented La Rôtisserie de la Reine Pédauque, Thaïs, L’Île des pingouins; I told her about my beloved French teacher, and recalled when Madame lent me a book titled Anatole France en pantoufles (Anatole France in his slippers), a collection of anecdotes and bon mots written by the writer’s secretary, and published right after the writer’s death.

But it wasn’t the same thing, talking French literature with an old lady or with a coquette my age, especially since Corita kept suggesting that we should make love. I felt for her no physical attraction, so I sidestepped her invitations –politely I hope.

I had few illusions about my charms and suspected that Corita would have liked to bring under her sheets all males who were bright students of Exactas. Beata illa. What a fortunate disposition, to have one’s sexual preferences so harmoniously aligned with one’s intellectual ideals. But I was unable to appreciate the merits of Corita's freedom from stagnant sexual prejudices; a hypocrite like mon père, I felt it was a scandal.

From my point of view the strangest fact was that she had a steady, seemingly impassive and unflappable boyfriend, a brilliant student of chemistry, Osvaldo Goscinski. During the four years Corita befriended me, 1958 to 1962, she and Osvaldo appeared together at all formal or family occasions. They did not marry; Osvaldo died on October 30, 2013, exactly ten years ago as I am writing this, a retired professor of quantum chemistry at Uppsala University in Sweden. The reason why Corita stopped being friendly to me is interesting and will be told, if all goes well, in a future chapter.  Cora Susana Sadosky de Goldstein, born May 23, 1940, a professor of math at Howard University in DC, died on December 3, 2010.

* * *

Since early in life and for as long as I lived in Buenos Aires, I was imaginatively pointed to the Southwest. First on foot, I would reach to El Matadero (the slaughterhouse), which happens to be also the title of the first true Argentine novel. Later, on my bike, I would visit la quema, the fields of burning garbage, then ride along the straight, rectified part of the Riachuelo all the way to Puente de la Noria, the Bridge of the Water Wheel, which was, and is, as far Southwest as one can go within the city. All those places were by essence urban: in the burning fields it was the waste of the city that was burnt, in the slaughter house it was the cattle consumed by the voracious citizens that was killed and cut, the Riachuelo was stinking and solidly polluted by the city sewage, and finally, there was no water wheel at all near the eponymous bridge, which was just the end or the beginning of the beltway that defined the Western and Northern limits of the city.

The summer of 1959-60 splendidly revealed to me a different Southwest. I spent a month as far Southwest as one can go from Buenos Aires without crossing the Andes into Chile, at the Chemistry Camp, a yearly affair managed by the Chemistry Student Center, which accepted students from other fields and from other university schools. Rucksack on my back and woolen cap on my head, standing before the split-flat departure board at the Constitución train station, I felt part of a repetition, a déjà vu, and remembered I had been at the same spot, about to board a train, some years before. Yes, I had been there indeed, when I was leaving for Sierra de la Ventana and the YMCA camp grounds, as told in Chapter 8.

But the differences, how deep and wide! Besides the geographical fact that the YMCA camp was straight South from home and the Chemistry camp was toward the Southwest, besides the fact that now I was five or six years older at an age when age matters, the fundamental difference, I immediately felt, was that here males and females were about equally present, whereas at the YMCA camp I could communicate with only one girl, the pianist Susana Agrest, and that at the risk of my skin, among my brutal fellow campers and under the brutal director, Staude. While we were on the platform, about to board our train, I noticed that men and women were dressed alike and many were wearing boots reaching just above the ankles which they called borceguíes, a word I had never met before. Later I looked it up in the dictionary: they are defined as combat boots, and the etymology of the word is deemed uncertain.

In the train (second class, or even third had there been such), some slept on the wooden seats; I slept on the aisle, in my sleeping bag, rocked to sleep by the regular tricktrack on the tracks and by the monotonous voice of Chaucha, who was lying alongside, telling me of his explorer exploits in the southern suburbs and the status of his favorite soccer team, Racing Club. “Racing is a religion, really,” he would eagerly tell me, and to reinforce his point he asked, “Why d’you think Independiente is called The Red Devils?” Independiente was, and for all I know still is, Racing’s classic rival: their stadiums are close to each other, which quadruples their rivalry, and located in Avellaneda, an industrial and meat-packing suburb just across the lower Riachuelo. I think Chaucha was trying to suggest that just as Racing was God’s team, so Independiente was Satan’s. I ventured to suggest that their red jersey was the real, down to earth reason Independiente is called “los diablos rojos” and I adduced one of those totally useless facts that swarmed in my brain at a young age, namely that there were at least a dozen soccer teams in the world that were called “The Red Devils” because of their red jerseys, and that one of those teams was the old Manchester United, founded way before football had arrived to our shores.

Chaucha said that he didn’t know and didn't care about those foreign teams, and maintained that in the case of Independiente I had gotten it backwards: actually, they wore a red jersey because they were of the Devil.

What would you reply to that? Nothing, unless you don’t mind saying, “You’re crazy.” I pretended to fall asleep, and he went on talking for a while until I heard him snoring. Meanwhile I was asking myself what sort of madness might afflict my new acquaintance. He seemed to be a mystic, one for whom the world is a battlefield between the forces of Good and those of Evil. The entire world, or just the world of soccer? Or just his local world of Dock Sur and Avellaneda? I vacillated, but concluded that it did not seem to make much of a difference from Chaucha’s point of view. A mystic, in his dry drive to purity, doesn’t distinguish between the local and the global, nor between nature and games, only between good and evil. Yes, he must be some kind of gnostic, a Manichaean. But I had read that the Manichaeans, who were numerous in the times of Augustine of Hippo, had been eliminated by the time of Charlemagne, and I had also read that the Cathars or Albigenses, who are thought to descend from the Manichaeans, had been eliminated by the Roman Church by the time of Thomas Aquinas. But wait. Hadn’t I also read somewhere that some Manichean sects still survive in Southern China? Amazing. And if so, why not in Avellaneda?

I didn’t ask Chaucha in which facultad or university school he was a student or in which career he was; I didn’t think he was in any: he showed all the marks of the autodidact. Perhaps that’s why (I thought) our fellow campers avoided him, as I had noticed even at this early stage of our common adventure.  On the other hand, there were a few students from Exactas I was familiar with. Cantarito Bunge, the son of Mario Bunge, my advisor as a physics student, Edgardo “Buby” Zolhofer the cellist, who had been my partner in the chemistry lab, a German budding physicist, Wolfgang, whose last name I have forgotten, and Luis Saintout, who had been my partner in a physics lab, and whose traces I lost three or so years after the chemistry camp: I don’t even know whether he got his physics degree, cannot find him in the Web either. All I remember is that a couple of weeks before we boarded the train to Patagonia, he had told me in strict confidence that there were two beautiful Polish girls who were going with us, that he knew them, and that he was going to arrange things so he and I would enjoy their favors.  As to which girl would go with each of us, that would be decided on the spot. He also advised me to get a pair of crampons to attach to the soles of my boots or borceguíes because I might wish to join him, Buby, and Wolfgang, in a climb of Cerro Torrecillas and its glacier.

After giving some thought to Luisito’s proposals, I had bought crampons just in case I would dare to climb a glacier, and, wondering what I could talk about with those girls from Poland, I first thought about the Polish mathematician Antoni Zygmund and his two thick volumes, Fourier Series, which I had recently acquired, but then I realized that there was no reason to assume that those girls were math students, or, for that matter, that they attended Exactas.  Fortunately, like a flash of lightning: why, I would talk of Chopin’s mazurkas and polonaises! Is there a Pole who doesn’t love talking about Fryderyk Franciszek Chopin?  Or I could try talking about Gombrowicz’ novel Ferdydurke: surely, they must have heard that it had been recently translated from the original Polish into French and published in Paris by Juilliard, propelling the author into world fame.

The Polish girls were indeed pretty, as Luisito had said; but it became evident early on that they had no interest in my company. Had I been a mouse in transit, they would have paid me more attention.

At the railroad station of Ingeniero Jacobacci, a small town in the province of Río Negro, we had to change trains in order to proceed further South, to Esquel in the province of Chubut. We were to board a train like no other train of that time, running on a narrower gauge than all other trains in Argentina, pulled by an old, long-smokestack steam locomotive. The cars had been brought over by the British, who had used them in the Crimean War. To ride that train and to sit in those cars was to be transported a hundred years back or more. No, that does not even start to describe the feeling. It felt rather as if time had become childish and was rambunctiously jumping around, back and forth, playing tricks, hiding in corners and crying peek-a-boo to us poor fools.

The most enchanting thing was the iron stove in the middle of each car, with a chimney that went through the roof.  Whether it burnt wood or coal, whether it was functional or not, I didn’t find out, but the stove returned Descartes to my mind, Descartes and his poêle in Ulm whose warmth hatched a new world. I was approaching the age at which Descartes dreamt his prodigious dreams, and even though I harbored no hope that a fire would be kindled in that centennial railroad stove, I thought — Perhaps if tonight I manage to sleep close enough to it, I may have a couple of dreams that shall guide me and answer my ever more urgent “Whither, whither?”

But it was noontime, the night was many hours away.  I was looking warily at the can of Armour Vienna sausages that was to provide my lunch when Chaucha approached, pointed to the stove and said, — “¿Che, qué tal si nos mandamos un lindo asadito?” (Hey, how ’bout we make us a nice little barbecue?).

— “That’s not a grill, it’s a stove,” I replied rather severely, and those etymologies I had found when, four years earlier, I had been involved with Unamuno and his critique of the Cartesian stove, plus some other etymologies, true or false, I had picked up in the meanwhile, suddenly rushed up to consciousness and thronged behind my vocal cords.  Estufa and stove and Old High German stuba, all from Latin extufare, to fill with vapor or smoke, and when I pronounce that word, extufare, it reminds me immediately of estofado, sort of an opposite of barbecue and a more civilized method of cooking.  Ah, short ribs of beef are so good, so good either way, grilled or stewed!  Whenever Mother makes them one way, I eat them with gusto, while missing them the other way. Estofado in English is stew, and both words originate from French à l’étouffé, meaning cooked in a closed pot, which, again, descends from that Latin word, extufare. All those sounds, all that prodigios progeny, from just one word, the ancient Greek word for smoke, typhos. From it too, in malam partem, comes our word tufo for a foul smell, a stench. And the name of a serious disease. the typhoid fever, so called because it makes the mind feel smokey.

I can’t recall how much of the above I gave voice to while Chaucha, my new bud, frowning, mouth half open, gawked at me as if I was mad or speaking Urdu. Then he pressed his hand to his forehead and said, — “¡Uf! ¡Estoy estufo!” (Oof, I’m fed up with it!)

It was my turn to look at him open mouthed, this time in admiration. That expression estar estufo is local slang; I was familiar with it, but it never occurred to me to connect and to add it to my etymological search. Amazing, I thought after Chaucha had left, perhaps for the roof of the car, since he preferred to travel al fresco, which wasn’t too dangerous because the train moved slowly and you could always hang on to the chimney; yes, amazing how a clever autodidact catches stuff a college student lets mindlessly slip by. No sooner had I thought those last two words when I became conscious of something incontestably more amazing and more important which I had let slip by. For four years I had been with Descartes in my mind, his poêle, his dreams, his Meditations, his Method.  For ten years or more I had lived with Don Quixote, savoring a hundred turns of phrase belonging to a language that was mine and, at the same time, the language of a loftier I. And those two, Descartes and Don Quixote, although inhabiting the same mind, had never met, had never been connected!

The first connection I made was, naturally, that Descartes might have read Cervantes’ novel. He had surely heard of it, for in his time everyone in Europe who could read, and many who couldn’t, were talking about the adventures of the knight and his squire. Yet when I mentioned Cervantes and Don Quixote to Chaucha the autodidact, he shrugged his shoulders and replied as if I had spoken of some exotic sauce, — ¿Y eso con qué se come? (One eats that with what?).  With the passage of time things have become worse. I used to meet occasionally with Gene Mirabelli, who taught creative writing at the university here in Albany; he maintained in all seriousness that the pretended literary excellence of Don Quixote must be a conspiracy of Spanish Literature professors.

Descartes, perhaps even before that fateful night in Ulm, must have read one of the French translations of the misadventures of the Knight of the Sorrowful Countenance.  The next connection I made, or I should rather say that occurred by itself, was between the unforgettable words pronounced by the battered don Quixote to his neighbor, the peasant who was carrying him home at the end of his first, ill-starred sortie, and the unforgettable words with which Descartes declared his first and most basic indubitable truth.

The peasant was protesting that the wounded hidalgo was not Baldovinos or Abindarráez the Moor, as he claimed, but Señor Quijada his neighbor.  To which don Quixote replied, — “Yo sé quién soy”, — I know who I am, and proceeded to state that he could be, if he so pleased, each of the Twelve Peers of France, or of the Nine Worthies, since his deeds would surpass in glory and fame all of them.

Descartes, for his part, concisely stated his celebrated cogito ergo sum, “I think, therefore I am.”  Too concisely, I thought — and here another connection was established —, for to be able to conclude that “I am” one had first to know that one is thinking, to be conscious that ego cogito.  Here is something, I thought in my youthful arrogance, that Descartes missed.  A thinking machine, like the ones Turing, von Neumann, Wiener, and other prodigies were building or talking about in the 40s and 50s, doesn’t know that it is a thinking machine, you see?  Finally, to be able to know that I think I have first to know who I am, otherwise how could I be sure that it’s really me who’s doing the thinking, or that perhaps, instead, I happen to be nothing but the thought or the dream of another mind or of some thinking machine?  So, I thought, Descartes’ cogito is surely though unacknowledgedly connected to, and logically dependent on, Don Quixote’s axiomatic yo sé quién soy, and not only that but, I thought further, I could spend the rest of my days thinking about those and similar connections and dependences, and the rest of my nights dreaming about them, both for my own metaphysical solace and so as to establish beyond dispute that Don Quixote and not Descartes is the true founder of modern philosophy.

* * *

In Chubut, the train stopped for three or four hours at El Maitén, where about half of our contingent was to get off and be transported by buses to their base camp at Lago Puelo, and where our locomotive could get new loads of coal and water. It was about noontime, there were no clouds in the sky, and the sun was bright and hot. I sat under a covered shelter at the station, next to Cantarito Bunge. The son of Mario Bunge and his first wife, I don’t know why he was called Cantarito, and only recently I checked the Internet and saw that his given name is the more jejune Carlos Federico, and that he has added, after Bunge, his mother’s name, Molina y Vedia. In Spanish, “cantarito” is a small cántaro (a water jar); the word may be connected to ancient Greek κάνθαρος, and may even be traced back to the Sumerian word ⁠gannu-tur⁠, a little vessel. How many of us can boast of a nickname going back to the Sumerians, the authors of the most ancient myths we know? Why, those elegant and traditional Argentine names, Bunge and Molina y Vedia, cannot hold a candle to a nickname like Cantarito.

He handed me canteen he had been holding on his lap.

I took a gulp and exclaimed, — “Yo-ho-ho, and a bottle of rum!”

— “Well, yes, except that it’s not a bottle,” said Cantarito.  “You know what it is?”

“¿Una cantimplora?” I said, and took several draughts of rum.  The Spanish word cantimplora means canteen, stoup, or flagon.

Cantarito took the canteen back, drank some, and asked, — “Yes, but do you know what cantimplora means, where the word comes from?”

I had no idea and told him so.  The cantimplora went back and forth several times.   I felt I was getting drunk.  — “But little vessels surely know interesting things about one another, so, Cantarito, if you are nice enough why don’t you tell me about it.”

— “It comes from Catalonia.  It’s because it sings and it sobs: canta i plora in Catalan, see?”  Which he demonstrated by kissing the canteen, holding it vertically, and letting the liquor flow: gloo – gloo – gulp! / gloo – gloo – gulp!  And so on.

It was my turn again and little rum remained; as I was wiggling and waggling the cantimplora to rescue any drops, I remembered Cervantes’ invocation to the Sun to help him tell the deeds of the “great Sancho Panza” as governor of the Isle Barataria.  It is one of the most exuberantly enigmatic passages in the novel, and one of the first I learned by heart as a boy; I venture to translate its first period:

Oh perpetual discoverer of the antipodes, world’s torch, eye of the sky, sweet waggle of the canteens (cantimploras).

I could make sense of the antipodes business, since given two antipodal points the sun visits one twelve hours after visiting the other; “world’s torch and “eye of the sky” are clear enough, but no matter how I turned it over in my mind, I couldn’t understand why the sun is called the “sweet waggle of the canteens” — “meneo dulce de las cantimploras”. Until now, that is, when I found myself waggling a canteen for a few drops of rum under a merciless sun.

When I tried to return the empty canteen, I found that Cantarito was no longer sitting next to me. I looked around and didn’t see him. I stood up and walked unsteadily toward the waiting train. Then I saw Cantarito: he was lying on the ties between the rails, less than twenty yards ahead of the locomotive.  I drew closer as best I could and, leaning toward him, I hollered, — “Are you crazy or what?  Get off the rails!”

When I got pretty close to him and managed to get myself heard, my hollers elicited a smile.  — “Why,” he said, “the sleepers are the right place to sleep, aren’t they?”

He used the Spanish word durmientes, “sleepers,” for the railway ties. Since I was quite sleepy myself, I found his argument persuasive and I stretched myself down right behind him, for the gauge was too narrow for two people to lie side by side. I don’t know how long I slept there. I was awakened by the tenuto toot of the locomotive. The motorman was clearly expressing his displeasure and demanding a clear way. I got up, but Cantarito was, amazingly, still asleep, unpertooted by the toot. I whispered softly in his ear, “Cantarito, wake up,” and, as if by enchantment, he immediately did.

By daybreak, when we arrived at Esquel in the Chubut, the terminus of the railroad line, the effects of the rum had dissipated, and we had recovered our energy as well as our wits. We alighted from the train with our baggage and were told to wait there for a couple of hours for a bus which was to take us to Lago Futalaufquen, and then by boat to Lago Verde and our camping grounds. Chaucha approached me.  — “You know, there’s a brothel here in Esquel.” I thought it was odd, for public brothels had been banned in Argentina for more than twenty years, my whole life; was Patagonia an exception?  — “We have enough time to go there and be back here before the bus comes to fetch us.  C’mon! Let’s go!” Chaucha coaxed me and pulled me by the arm.

— “No, thanks,” I said curtly, and I remained strangely perturbed. The idea of visiting a brothel, when the poor idiot had all these camping girls at hand to try his charms on and perhaps strike the gold of love, I found it repellent. Or was I of two minds about it, was there another part of me that found the idea tempting? Every time I sniffed the methane from the swampy soul of a boy my age, instead of avoiding him — all other campers had firmly ignored Chaucha from the beginning — I tried to convince him and the world that I rightfully belonged to his beastly realm with the best of them. Perhaps it was the remnant of my grammar school trauma: no way of avoiding the bullies who daily tormented you and masturbated around you in the classroom; no way of beating them either; therefore you try to join them. For the umpteenth time in my life I re-examined the question, and for as many times reached no definitive conclusion.

Now, however, sixty-four years after my disgusting experience with Chaucha, as I was typing those very words, “for the umpteenth time...,” an old, at first unwelcome memory  appeared from nowhere and called me from a distance like a great kiskadee, implying that my dipsychia, my simultaneous being repelled by, yet willing to play the game with, certain boys, goes back to an earlier stage in my life; earlier, I mean, than my torments at the hands of my nasty classmates in sixth and seventh grades. You may remember from Chapter 3 that when I was five or six my older cousins Davel and Hugo told me about the secrets of genetics and the non-urinary use of the genitals. It’s okay if you don’t remember, and do not bother going back, for I’m retelling it here, as well as retelling that after my cousins left, I asked my parents if such horrendous news were true, and they confirmed it. Years later they told me that I had been shaken. Well, two or three years after the collapse of my innocence — and here comes the almost forgotten memory — I was entertaining my two older cousins with vulgar mixes of gibberish and gesticulation.

I try to decide whether those acts started before or after I watched Chaplin in “Modern Times,” his famous rendition of “Je cherche après Titine”.  I cannot be sure, but I think my encounter with Chaplin’s movie came later. In any case, I had concocted several acts, each consisting in a mumbo jumbo associated with a car make. There was a “language of the Pontiac,” another “of the Oldsmobile,” and a “language of the Buick.” This last one displaced the others since it was my cousins’ favorite by far.  — “C’mon, speak to us in the language of the Buick,” they would plead, and they would start giggling in advance.

The high point, the climax of our fun, had to do with the Buick hood ornament, a sort of torpedo going through a ring. I would replicate the ring with the index finger and thumb of my left hand, and the torpedo with the index finger of my right hand which I moved back and forth while uttering blather I fancied to be sex talk.

I pause here to inspect in myself the surfacing of this Loch Ness monster from my deep past. I let myself fall into a waking somnolence, the best state of mind to revisit the scenes from a distant time in one’s life. Gastaldi is sitting next to me, to my left, masturbating, his face a mask of idiocy; Peralta and Páez are masturbating in the back row, their pricks the size of those in the Phallological Museum of Reykjavík; the teacher is writing on the board moral maxims about the value of an ever-wakeful conscience. I’m about to throw up. Then I see myself lying on my back inside the lumber room, my head against the door, concentrated on the stimulation of my modicum of a penis, imagining that a gypsy woman, in gratitude for having rescued her child from the floods, has given me a penis-lengthening ointment, which I now hold in my left hand: it’s my mother’s Pond’s C cream. Paradoxically, this scene provokes a smile but no revulsion. Now Rodolfo Mattarollo and I are walking along a marbled cloister, around a healing-murmur fountain, talking about things — parlando cose che ’l tacere è bello, sì com’era ’l parlar colà dov’era. Actually, we’re talking about Wozzeck at the Teatro Colón, about Alban Berg and the revolution he brought to operatic music, to the manner of singing — his Sprechgesang —, and the end of the post-Wagnerian style. I’m finding our dialogue sublime. Then — switch — I’m in a tête-à-tête with Ramón Falcón, the boy who ended up killing women and burying them in his backyard. We’re laughing idiotically and drawing plans for a giant brothel, a labyrinth with a Bovine Whore or Slutty Cow lodged at the center. Then I’m standing face to face with Rodolfo, raising my hand with two extended fingers above his head and then, as if knighting him, touching both his shoulders with a ruler and solemnly declaring, “In the name of God, of Saint Michael and Saint George, I hereby make you a Slutty Cow.” Again, I’m not disgusted at myself, not about to puke, but strangely satisfied and smiley.

All those Kinderszenen are from age twelve, but the clownish “language of the Buick” strikes me as belonging to an earlier stage, not more than two years after my cousins revealed that we come from those holes where pipi and caca come from and I tried to imagine my parents doing it and was crushed, gulped down into the abyss as by a toilet flush. I was five or six then. Father had taught me to play chess, and had already begun to indoctrinate me with the notion that there is a center from which the All should be viewed; why, he might have begun to talk about his favorite philosopher, Fichte. I guess that before my cousin-caused catastrophe I vaguely believed I had come from my father’s brain, like the goddess Athena from her father's. Now I find it incomprehensible that soon after the catastrophic loss of my innocence I was making fun of it and entertaining my older cousins with a vulgar parody of sex. At age seven or eight I had already become two-masked, a double hypocrite. Realizing this, and realizing that now I’m about to reach page 200 of this memoir and year 84 of my long and idle age, where everything turns out to be both true and false and double edged, I can only conclude that there’s a lot to be said for the unexamined life.

Ricardo Nirenberg is an editor of Offcourse