ISSN 1556-4975

OffCourse Literary Journal

 Published by Ricardo and Isabel Nirenberg since 1998


"The Dining Room Table: the View from Below",
part of a memoir by Ricardo L. Nirenberg

 I was nine when Mother started working full-time at Father’s businesses.  She started by going every day to the fabrics store on Cabildo Avenue, in the barrio of Belgrano, very far from home.  She would walk the five or six blocks to Plaza Flores and there take bus number 55.  At the end of the day, she would take the bus back and walk from Plaza Flores back home.  She left in the early morning and came back around seven PM, almost dinnertime.  This meant that my sister and I were mostly alone, under the care or rather carelessness of the maid, all through the afternoon and early evening.  Where Father was, I don’t know.  He was supposedly running from bank to bank — “corriendo bancos” as he said — to secure credit, to cancel the more pressing debts by incurring some future, larger ones, and whatever else he might have been doing — and likely and additionally corriendo minas, chasing broads.  The running and chasing though, were not on foot: Father drove his aviation-fuel-guzzling ’47 Cadillac Hydramatic from place to place.

I found it heartbreaking to see my mother arrive home every day exhausted and in a bad mood.  But Father was far too busy with financial arrangements which were extremely important, and meanwhile the stores, the lingerie shop, the textile factory in Lanús, outside the city limits: all those businesses were suffering, since “only under the owner’s eye do cattle thrive.”  This is how Mother put it to my sister and me.  And this was especially true of the fabric stores, where employees were helping themselves wholesale to the finest silks.  But no explanation could assuage my pain.  I would spend lots of time under the dining-room table, moping.    

Sometimes I was there with my sister, lying side by side on the rich Persian rug, which would be there for only a couple more years, before it was seized for debts and the floor left bare.  “Why are you crying?” my sister would ask.  And I would tearfully respond, “Because Mummy’s not home.”

My sister didn’t get it.  “We are alone.  Just imagine.  We can do whatever we want.”

“I miss her singing,” I’d try to explain, “I miss the songs she sang when she was in the kitchen.”

“Don’t be silly,” said my sister, “let’s turn on radio Excelsior, and we can listen to some nicer songs.”

She was right, I was being inexplicably silly.  Silly?  That’s putting it mildly.  Till well into adulthood, I’ve been worrying that perhaps I am by nature and inclination slavish, that I rather enjoy the feeling of being a marionette pulled by a martinet, so much so that when I read in the Confessions about young Rousseau taking pleasure at being spanked by Mademoiselle Lambercier, I remembered how often, while at the dinner table, Mother slapped me in the face without warning and for a trifling cause, like wiping my mouth with my hand instead of using the napkin, and in spite of her brutality I missed her to the point of crying under that same table because she wasn’t home.  Remembering that and similar occasions, I thought I smelled miasmas of sado-masochism, and I was afraid I had lived inside a swamp, from which no effort could pull me out.

With all that, when Mother had been working every day for a while, first at the Belgrano fabrics shop, then, after that went kaput, at the Lanús textile factory, I was already twelve or thirteen when I gathered up the courage to confront my parents on the issue.  On a Saturday afternoon, as they were both of them reclining on their bed and my mother was as usual pouring the mate, I stood before them and rather solemnly preached, “In the Bible God says to the woman, you will bear children in pain, and to the man, you will gain your bread with the sweat of your brow.  Then how come in this house Mommy has to do both?”

At first, they were surprised, yet I could tell that my mother was moved.  I was a champion to her liking, and I thought of Ivanhoe when he rides into the Templars’ field to save Rebecca from the stake.  My father spoke at length to reassure me that it was only a temporary situation, that soon his business would be set aright and there would be no more need for Mother’s presence in the factory.  The notable fact is, as I realize now, that I had not read Genesis at that point in my life but was just repeating words my father had taught me.  Adonai Elohim had talked to me only through my father’s lips.  This was one instance, among many, of my father’s early teachings being turned later, as I reached puberty, into fingers pointing at him, silently reproaching, “You have not lived up to your own standard, you have not kept your word!”

Yes, my sister was right: it was silly of me to want my mommy at home with us, when I could have all the freedom I wanted.  But I guess freedom was not what I wanted most.  In fact, freedom was never high in my wish list, although it is there, definitely: I only wish for so much freedom as to make me feel at home in the world.  When there is too little, of course, the world feels more like a prison than a home; but when there is too much freedom I tend to panic.  I hate driving in the middle of a five-lane road or swimming where no coastline is visible.  May William Blake and other freedom freaks forgive me, but I need boundaries.  Is that crass, is that philistine?  It may be so, but all that Existentialistic emphasis on absolute freedom and self-creation, it seems to me, smacks of perversity.  I can understand pretty well, I even sympathize with, those who feel a nostalgia for the garden of Eden where they suppose we dwelt before the Fall, but I cannot share an enthusiasm for the tohu wa bohu the world was before the Creator separated the elements.  Chaos leads directly and always into torture chambers.  With my sister it was different because, strange as it may sound, she did not need a mommy to feel at home in the world.  Perhaps she did not need a daddy either, and anyway, our dad was no good as a girl’s dad.  Besides, she always was more daring than I: it was by her initiative that we smoked our first cigarette.  Which brings another of her daring deeds to memory.

When we were staying at the Grand Hotel in the month of February 1947, during a Carnival celebration with the usual confetti, paper ribbons, and perfumed sprays, my sister, who was not yet six at the time, noticed a lady sitting somewhat apart looking at the revelers with something like dour disapproval, and had the unusual idea of grabbing some ice cubes and dropping them into the back of the lady’s dress.  Ah, what a delicious ruckus followed, the dour lady screaming, trying in vain to get rid of the ice cubes and calling my sister all kinds of names!  My parents felt obliged to take Olgui to our room and spank her, but she actually deserved the Grand Medal of Merit Carnivalesque.

I often lay under the dining-room table by myself, no sister.  It was my way of letting things be.  Up there, on top of the table, Father used to teach me the arduous physical, philosophical, and mathematical ways of getting to the center of things, as he used to say, to the heart of the mind and/or of the universe.  Here, it seemed as if I was able to reach that fabled center just by slipping underneath the table and quietly lying there, facing up, looking at the intricacies of the inner woodwork.  No one knew I was there, in my hideout; I was invisible to the world and tried to make me invisible to myself as well.  In other words, I tried to imagine I was dead.  All sorts of thoughts, however, hovered in my mind, either trying to get admittance to further and more careful reflection or to hinder, like a malign moscardón, a pesky fly, all possibility of sequence in the ideas.  When the house was silent, I tried to experiment with nothingness.

No, I hasten to explain, I wasn’t experimenting with mind-cancelling drugs or with suicide: those never tempted me.  Nor could I then have any notion that nothingness is actually the one idea that may be said to characterize us as humans, whether by our fear of it and being distraught by it, or by our embracing it as our close ally.  With only a bit of oversimplification we can say that myth making and all that goes with the design of Netherworlds — funeral rites and most religions — have their origin in the human fear of nothingness.  That wasn’t clear to me when I was lying under the table.  It became a little clear only later, when I was in high school, when I read Miguel de Unamuno, Del sentimiento trágico de la vida, where “the tragic feeling of life” is the rather fancy way don Miguel calls his own fear of nothingness, and then, about the same time, I found the haunting Latin line, “Timor mortis conturbat me”, in some medieval poem.

Much later, when I was studying Greek in my early thirties, I came upon Socrates’ own feelings about death and its beyond.  Towards the end of Plato’s Apology Socrates tells the Athenian jurors who have condemned him that there are two possibilities about what happens to us after death:
(a) Being dead is a kind of nothingness (hoion mēden), so that the dead have no perceptions or feelings at all, no, not even a single one; or
(b) That what the people often say is true, and death is a migration of the souls, from this to another place (Elysium, let us say).
If (a) is the case, if to be dead is like to sleep without dreams, anyone in his senses will agree that such a sleep is to be preferred to a dream-haunted night or to a wakeful day: why, even the Great King of Persia would agree to that.  If the case is (b), what greater pleasure can you imagine than to be able to converse with the likes of Homer or Hesiod, or with Palamedes, or with Ajax son of Telamon, to compare each other’s experience of being unjustly condemned.

By maintaining that (a) and (b) are equally — and greatly — desirable, Socrates is performing an act of what was to be called “Socratic irony.”  Today, irony is popularly believed to be saying something well knowing that the contrary is the case, like calling a very thin man “Hey, fatso.”  Thus, it is often thought that Socratic irony is manifested in the philosopher’s insistence that he knew nothing, well knowing that he knew a great lot.  That’s a sorry, impoverished view of Socratic irony, and more gravely, of irony in general.  No, irony is the feat of maintaining two ideas which are considered opposite or incompatible in equilibrium, as of equal worth, the way Socrates is here treating both ideas, of nothingness after death and of eternal life, as equally desirable.

Dare you now perform a dizzying jump in space-time?  From about 400 BCE in Athens, over two millennia, to about the first twenty years of the 20th century in Göttingen, the city famous for its sausages and its university, the city Heinrich Heine deemed pretty only when seen im Rückblick, in retrospect.  By1900, almost a century after Heine left Göttingen, its university housed the most important mathematical center in the world, and it was there that a momentous discovery was made: to be logically unimpeachable, mathematics needs a kind of nothingness (hoion mēden), which is called the empty set.  It’s either that, or the outrageously unrealistic hypothesis of the logicians, that everything in the world is always identical to itself.  Ernst Zermelo and John von Neumann, who stayed in Göttingen at different times, were the main contributors to this discovery; let us focus on the latter man, on his genius and his death.

Just as the oracle at Delphi had pronounced Socrates the wisest of Greeks, many consider von Neumann the greatest scientist of his time, the one whose work on math, on physics, and on computer design, among other things, had the greatest impact on our civilization.  There are many differences between Socrates and von Neumann, obviously, but the most remarkable to my mind is their different attitude before the idea of the hoion mēden, the kind of nothingness that’s death.  While for Socrates such nothingness was most desirable, von Neumann felt it was most horrible.  And that in spite of the enormous wealth — I’m thinking of the digital computer and its ever-growing applications — his genius had extracted from numbers.  The numbers which, as he well knew, are all constructed on the empty set, a kind of nothingness: in spite of that wealth, von Neumann was terrified by the proximity of nothingness when he was dying of cancer at Walter Reed (1956-7).  Should we consider von Neumann the Socrates for our time, we who enjoy extracting the most fossil fuels we can, and then worry about the disastrous consequences for our planet?

Socrates was a true agnostic; von Neumann was an agnostic all his life, until death was closing in and then, terrified, he proceeded to pray for eternal life under the guidance of a Catholic priest.  Likely he was aware of the contrast, for von Neumann must have read Plato’s Apology: he might, in fact, have known it by heart as he knew by heart Homer’s Odyssey: by age 8, he was able to converse in ancient Greek.  He must have also remembered Socrates’ saying in Plato’s Phaedo that philosophy is a kind of “training for dying,” but chances are he dismissed it on the grounds that modern scientists are not philosophers, and that they better keep away from that shifty turf.

One might conclude that von Neumann was sturdy brained but faint hearted, and leave it at that, but we should remember that social factors must have played their role too.  Technological advances built on the empty set and on digitized information were, already then, making us feel closer to achieving immortality, and therefore more disconsolate when we feel we are missing it by a few inches, like Moses who died before reaching the Promised Land, or Gilgamesh who got the plant that grants immortality, but right away had it stolen by the serpent.  We shouldn’t forget that another pioneering genius of AI, Norbert Wiener, was proposing about that time (1950), a method to achieve immortality in his book The Human Use of Human Beings: to move all mental contents of a mortal being into the immortal memories of computing machines.

None of those reflections on nothingness and its history were available to me as a child, as I was lying under the dining-room table; in fact, von Neumann was still untroubled by the void, happily working on thermonuclear bombs and MAD strategy, and Wiener’s book wasn’t yet published.  Nor did my concern with nothingness come out of nothing; no, it came directly from the leather pad on Father’s desk.  I’d lift the heavy cover and there, inside, were a few documents in my father’s longhand: they provide the only glimpses I have of his life before I met him.

  The longest one was a letter Father had written to a Sr. Roque Wainstein, addressed as “Querido amigo”.  It was dated September 12 of 1933 in Darragueira, a small town about 400 miles southwest of the city of Buenos Aires: what my father was doing there when he was twenty-one I haven’t the slightest idea; I can only venture that it was as far southwest as he ever went.  The letter abounds in philosophemes such as “contingent” as opposed to “transcendent,” and “I” is frequently used as a noun instead of a pronoun, as in: “¡Experimento el vacío, mi Yo que se diluye en la nada!” (I experience the void, my I that dissolves into nothingness!)  From which I conclude that by that time he had read J. G. Fichte, his favorite philosopher, and was already Fichticizing, as the Early German Romantics enjoyed doing.

When I used to read that letter as a boy I was most impressed by the references to nothingness and to the void; now I am astonished at my father’s polar-opposite views of the past and the future.  He trashed his whole past as cold, arid, totally devoid of love, the abode of nothingness and gloomy void.  His future he saw as brightly sunlit, with a megalomaniac hope that he would discover what makes the cosmos tick.  I can tell that he was not making it up, that he really abhorred his boyhood, though I know hardly any details of it.  When his father, my zeide Marcos, came for Sunday lunch, maybe three or four times a year, my father would not exchange a word with him; after the meal Father went upstairs to take his nap, and I stayed with the zeide playing dominoes on the dining-room table.  Mother always served his tea in the way Zeide preferred, in a tall glass as was done back in Russia, with a lump of sugar off which he would take a small bite and then a sip from his glass; she liked her father-in-law, in the spring she chatted with him about the season’s new potatoes, and often questioned Father, “I don’t get what you have against him; he’s such a good man.” 

My paternal grandmother, Olga Finkelstein, died when I was a baby.  I vaguely remember going with my parents once, or at most twice, to visit the grave at the Jewish cemetery of Ciudadela, just outside the city limits, when I was three or four; other than that, the only time I remember my father mentioning his mother was in a letter he wrote to me towards the end of his life, when I was living in the U.S.  To my questions regarding his disastrous relations with Olga, his daughter and my sister, he replied with his own question whose pathos I didn’t grasp at the time.  His question was, “Perhaps you’d be able to tell me why I cannot kiss my daughter, just as I could never kiss my mother?”

Nothingness and gloomy void.  My sister has long refused to talk about her past, and the last time I tried to talk with her about our father — that was years ago — she cut me short, “He was a phony ( un farsante).”  To my mind, there may be many interesting things to be said about a phony, especially if that phony is our father, but there’s not much I can do.  The bitterest part is that by her determination to discard her past she most resembles our father, the master past discarder.  Jorge Manrique and his Coplas come to mind:

 “cómo a nuestro parecer
cualquiera tiempo pasado
fue mejor.”
(“Our hearts recall the distant day
 With many sighs.”  Longfellow translation)

and I think, Manrique couldn’t be a discarder of the past because he admired his father.  But let a contemporary poet speak:

“A self is a self.
It is not a screen.
A person should respect
What he has been.
This is my past
Which I shall not discard.
This is the ideal.
This is hard.”
(James Fenton, “The Ideal”).

Enough for now about Father’s letter to his friend Roque Wainstein.  There were a few more loose, yellowing sheets with unfinished philosophical thoughts inside the leather pad on Father’s desk.  In the particular document that hovered in my mind as I was lying under the dining-room table, my father was attempting to invalidate the number zero.  He had no idea that the attempt was an old one, that it had a long history, nor had I.

Zero, my father began, is the symbolic expression of nothingness.  But, he went on, is nothingness imaginable?  Let’s try to do away with all matter and imagine a void.  Still, there remains the extension of space and the flowing of time.  Can we do away with those too?  Even if we were able to, there still would be the I that tries to imagine, without which there could not possibly be any imagining.  Therefore, nothingness is unimaginable, and its symbol, the zero, is illegitimate. 

Why a thing has to be imaginable for its symbol to be legitimate, my father didn’t say, and I didn’t think of asking.  Thus, as I lay on the carpet as quietly as I could, closing my eyes I tried to follow my father’s instructions and erase from my mind all traces of material objects, until I felt there was nothing but darkness.  Good.  Now, how about space, or, in other words, was my darkness extended?  I couldn’t find a way to find out except by motion.  I might have tried to move my eyes from one spot to another to verify distance or extension, but I had to keep them closed, for otherwise the dark void would immediately disappear.  I could move an arm and see if I could reach for a chair leg, for instance, but that would be introducing again material objects, namely my arm and the chair leg, thus going back to the previous stage.  No, I couldn’t see a way to decide whether or not my darkness was extended without the presence of a moving something.  Did it mean that with the erasure of all material objects I had eliminated space as well?  Does taking away all the potatoes eliminate the bag, the basket, or the pot?  I shuddered before the abyss.  As for the flow of time, I didn’t have the courage or the strength to start thinking about it.

Exhausted, still lying under the dining-room table, my brain switched to less philosophical and more sentimental thoughts.  How long will it be until Mother returns?  How long until she feels it is strange that she hasn’t heard a peep from me, and starts looking around?  I haven’t told anyone that I’m here.  No one knows.  She will go up to the lumber room, my lab and workshop, open the rackety door, see not me, go back to the bedroom, look under the beds and behind the wardrobes, go down to the kitchen, look into the fridge corner, and start searching the whole house, more and more worried.  “Ricardo!” she’ll call me, “Ricardo!” will resound all over the place, making the crystal chandeliers tingle, until finally, sweetly, her screams will yield to, “Ricardito!  My love!  My soul!  Come back!  I’ll never hit you again!  I’ll never force on you those hard-boiled string beans that you detest!  I’ll make niños envueltos every week!”  But I’ll be dead. “Come!  From now on, I promise, you’ll be lord and king in my house!”  Too late.  I’ll be dead from deep, multiple wounds, or rather from a single spiritual undefinable malaise.

And truly I felt I was fainting, as if life were oozing away.  It was a wonderfully voluptuous sensation.  Oh, the unforgettable moment when Mother finally finds me here!  Ah, her tragically charged scream!  Not even Kirsten Flagstad.  Mother’s face will hover over me, caressingly, like the full moon.  She will in vain try to feel my breath: there will be none.  I can see her face, swollen with anxiety, just like when she had me sitting on the potty, forcing me to stay until I had performed.

It was no less than ten years after those under-the-table philosophic and sentimental fancies that I found my father was wrong in his attempt to invalidate the number zero.  Specifically, he was wrong in stating that nothingness is not imaginable: not only is it imaginable, but we do experience it.  Perhaps the simplest example is when we go to bed at night and awake the next morning, having slept through without dreams: we know, because we remember, that we are, upon awakening, the person we were when going to bed, but we have no recollection of the time in between, which for us becomes a hole in time, a kind of nothingness, identifiable only by its borders, the evening before and the morning after.  This is what Socrates talks about in Plato’s Apology, but I hadn't read Plato until I was in my thirties and was studying Greek.  A more dramatic example is the experience of having been under total anesthesia, something that happened to me only much later.  I first became aware of the redeeming yet paradoxical presence of absence, of that which I find pleasure in calling the ontology of holes, when I was eighteen, studying math, and encountered the construction of the real number line.  It was a momentous event in my life.

The ancient Pythagoreans, to their horror, discovered that numbers, which they believed were the eternal and perfect substance of the cosmos, are riddled with voids and thoroughly infected by nothingness.  Numbers, back then, were the integers 1, 2, 3, etc. and the fractions obtained from those: 1/3, 3/11, 785/9, etc.  They could be added and multiplied.  Since 1x1 = 1 and 2x2 = 4 already, it is clear that the square of no integer can be equal to 2, but the question remained, is there a fraction whose square is 2?  The Pythagoreans found that there is not, which was a revolutionary mathematical and philosophical achievement.  Yet, it is quite easy to see that there are fractions whose square is more than 2, yet as close to 2 as you wish, and that there are fractions whose square is less than 2, yet as close to 2 as you wish.  In our decimal notation (which was unknown to the ancients), √2 = 1.41421356237... with infinitely many non-periodic decimals, so if you want a fraction whose square is smaller than 2 but which differs from √2 by no more than 0.001, say, it’s enough to take 1.414, that is, the fraction 1414/1000.  But no matter to what lengths we go, we’ll never get a fraction whose square is exactly 2.  There is a void, a hole, where we would expect √2.  The ancients referred to the infinitely many such holes as incommensurables.

In Laws 819D-820D Plato flatly states that those who don’t know about incommensurables are suckling piglets, not human beings.  That gives us some idea of the importance the ancient philosophers attributed to those holes.  Today, very few worry about them: in my own experience with academics, as far as the scientists are concerned the problem has been long solved and transcended; as for the humanists, they have no idea about holes and incommensurables.  The problem was, indeed, logically transcended by the identification of the holes with their borders.  √2, for example, is defined as a pair or couple of sets: the set of all fractions whose square is less than 2, and the set of all fractions whose square is larger than 2 (remember that there is no fraction whose square equals 2).  This pair of set is called a Dedekind cut.  Richard Dedekind (1831-1916) was another bright graduate from Göttingen.

Which reminds us of those two other Göttingen great savants, Zermelo and von Neumann, who saw that, unless we admit the Eleatic cockamamie denial of change and motion, the numbers 1, 2, 3, etc. and therefore the fractions must all be built on the empty set ø, which is the number 0, pace my dad.  When we join Zermelo and von Neumann to Dedekind their predecessor, we realize that the real number line (the collection of all Dedekind cuts) is a vast construct: ideal containers containing only ideal containers which contain only ideal containers... and so on indefinitely; the only thing that all those ideal containers are allowed to contain is ideal containers, and all boils down to the empty set.  Nothing upon nothing, voids within voids: all those holes that so troubled the ancient philosophers are now filled, thanks to the Holey Ghost — by voids.

So vast is the construct called the real numbers, or the real number line, that even if we were immortal and in possession of the fastest possible computing machines, we could become acquainted with only a negligible number of points in it, and the rest will remain forever unknown.  Benevolently you shrug your shoulders and remark that all that rigmarole may be of some interest to the philosopher, the contemplative, but doesn’t concern the man of action: math works, and that is all that counts.  You may be right if by men of action you mean the very many who feel that the examined life is not worth living: you will find among them many scientists, not a few contemporary philosophers, but not a single poet.  Charles Olson explained the mission of the poet, “The work of each of us is to find out the true lineaments of ourselves by facing up to the primal features of those founders who lie buried in us.”

Parents and grandparents, uncles and aunts, are among “those founders who lie buried in us,” and it may not be easy or pleasant, indeed it might be awful, “facing up to their primal features.”  But not only them.  We must reach back and face up to the primal features of those who fashioned and told our oldest myths, like Inanna going down to the Underworld, or the builders of the Tower of Babel, or of Moses, Jesus, Muhammad, and of those who established the foundations of our ever-changing view of our myths and of the world, from Anaximander, Laozi, and the Buddha to Einstein and Wittgenstein.

In his 1922 poem “Le Cimetière Marin” Valéry included, in mitten drinnen, the line,« La vie est vaste, étant ivre d’absence » (Life is vast, being drunk on absence — absence, mind you, not absinthe).  Life, it turns out, is similar to the real number line.  But when it comes to post-war poems having to do with the renewed consciousness of the void, my favorite is this one by Eugenio Montale, followed by my tentative translation:

“Forse un mattino andando in un’aria di vetro,
arida, rivolgendomi, vedrò compirsi il miracolo:
il nulla alle mie spalle, il vuoto dietro
di me, con un terrore da ubriaco.

Poi, come s’uno schermo, s’accamperanno di gitto
alberi, case, colli per l’inganno consueto.
Ma sarà troppo tardi; ed io me n’andrò zitto
tra gli uomini che non si voltano, col mio segreto.”

(Perhaps one morning while walking through a crystal air,
dry, turning my head I’ll see the miracle accomplished:
nothingness at my back, the void behind
me, in a drunken terror.

Then, as on a screen, they’ll relocate themselves at once
trees, buildings, hills, according to the usual deceit.
But it’ll be too late; and I’ll go tight-lipped
among the men who never turn their head, me with my secret.)
(1921-5, included in Ossi di seppia, 1925).

Those men who never turn their head: among them, filling in my mind a vital void, my father still young who wrote to his friend from Darragueira about the sorrow of turning his head and remembering the void of his past, my father who tried to apply crystal logic and Cartesian insight to prove that there can be no nothingness.  I go out into the dry, cold evening and walk the two- or three-hundred yards to the Schoolhouse Road bridge, from which I watch the Interstate below.  The traffic is fierce, uninterrupted — tractor trailers, tank trucks, vans, SUVs, and sprinkles of smaller cars roaring and rolling at 65 miles per hour or more.  Alas for the one who turns his head or looks at the rear-view mirrors to change lanes and sees a void just where another vehicle is about to pass him.  No time nor space for voids.  Traffic was not so bad back in the 1920s.

I return to the best filler of voids who ever was, Richard Dedekind, who filled at one stroke of genius the infinitely many voids that gaped inside the infinite line of fractions.  For the beginner, it is difficult to imagine the situation: imagination must be cultivated, it doesn’t come ready made with our genetic endowment.  Between two different fractions there are always infinitely many other fractions; for example, if we’re given 1/3 and 1/2, we can see that 2/5 lies between them, then, repeating, we see that 3/8 lies between 1/3 and 2/5, and that 3/7 lies between 2/5 and ½, and so on indefinitely.  We’ll never find two fractions with nothing in between; still and all, there are invisible holes, infinitely many.  It dismayed the Pythagoreans when they discovered that there is no fraction expressing the length of the hypothenuse of a right isosceles triangle (there is no √2), a shattering discovery that, to my mind, precipitated the birth of Western metaphysics.

I was teaching calculus at Exactas in Buenos Aires, my last semester in my native land before leaving for New York in August 1963 with the fellowship that allowed me to get a doctorate at NYU.  Among my calculus students there was one Isabel Lida, a remarkably self-assured eighteen-year-old who would come up after class and ask questions, visibly less wishing to dispel any mathematical doubts she might have had than because she had conceived the rough sketch of a life plan for both of us. 

We were married on 20th February 1964 at the Brotherhood Synagogue in Greenwich Village, New York, by Rabbi Allen Block, with cantor Leib Mirkovic, two months after Isabel arrived from Buenos Aires for a visit.  It was a very small wedding, no more than a dozen guests in our rented studio apartment, and of our relatives, only Raimundo Lida and his wife Denah, Isabel’s uncle and aunt from Cambridge, Mass.  On many occasions through these fifty-nine years of being together, Isabel told me that she had been captivated by my way of explaining Dedekind cuts.  In retrospect, it seems crazy to explain Dedekind cuts in Calc One.  Way too complicated, too hard.  But there you are: throwing in a humongous infinity of nothings or almost nothings to achieve plenitude, that is, in few words, what Dedekind did to construct the real numbers.  And that is, too, what we did, Isabel and me, to construct our reality.

We started with tidbits from childhood books, the fables of La Fontaine and of his Spanish imitators, the picture of a boa that has swallowed an elephant in St. Exupéry’s Le Petit prince, which surprisingly looks like a Gauss curve, or the adventures of Perucho and Naricita as told by Monteiro Lobato.  Isabel contributed the rhymes and tongue twisters of Lo que sabía mi loro (What my parrot used to know) by José Moreno Villa, a poet from Málaga.  And we shared a good amount of Walter Scott and Dumas père, Kipling, Stevenson, and Louisa May Alcott.  Ten years before I learned to read Homer in Greek, Isabel remembered by heart long stretches of the Iliad in the 1831 Spanish translation by José Mamerto Gómez Hermosilla.  Each of us threw into the mix a repertory of linguistic and gestural expressions culled from our grandparents, mostly Yiddish or Yiddish accented but not all, for Isabel’s maternal family, the Schmucklers, had arrived in Argentina well before 1900, and her grandfather Salomón was a true gaucho judío, capable of riding on horseback hunting Pampa ostriches with bolas.  Once, in 1966, he took me to a country store and bar near the Lida’s country house in Pilar, some 35 miles from the capital, and invited me to a glass of rum ( caña).  We were drinking and smoking at the counter, and a gas tank driver in a Shell uniform was drinking and smoking next to us, exchanging pleasantries with Isabel’s grandfather, who, quite out of the blue, declared that he was a Jew.  The truck driver burst out laughing and said, “You a Jew, don Salomón, that’s really a good one!”  The old man may have wanted to impress me, his grandson-in-law, by showing how easily he could “pass,” yet how courageously he refused to hide his Jewish identity.

Almost nothings by the trainload, holding on to Being by thin threads of ephemeral memories, now all tangled, matted, and packed down into a thick rug.  On which Isabel and I lie entwined and study the woodwork over us, marveling about it, knowing that we have been the joiners.

Ricardo L. Nirenberg is editor of Offcourse

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