"Orpheus Still Sings", an essay by Ricardo Nirenberg

Dedicated to my wife Isabel and
to Elizabeth Sewell, teachers mine.

Chapter I

1.

 

On the day of Orpheus’ and Eurydice’s wedding, the bride is playing with the Naiads on the flowery plain, when a viper bites her in the heel, she collapses and dies.  So starts the narrative in Ovid’s Metamorphoses, Book X.  Orpheus is desperate.  “Che farò senza Euridice”, he heartbreakingly intones in Gluck’s opera, “che farò senza il mio bene” (What will I do without Eurydice, what will I do without my comfort.)  He goes down to Hades to look for his dead beloved.  Somehow, he knew the way: through a cave.  Which cave has been the subject of controversy; the likeliest candidate seems to be the cave in Cape Tainaron, the Southernmost point of Mainland Greece, where Heracles had made the dreaded descent before.

There is agreement on the remainder of the story.  With his divine music (song and lyre — or perhaps sitar?), Orpheus enchants every soul in Hades, from Cerberus the hound to Persephone the queen, who, in tears, grants to Orpheus the return of his beloved to the lightsome world, on the condition that while Eurydice’s shade is following him, he must not look at her.  Yet, steps away from the gates, Orpheus turns to check if Eurydice is truly following, thus sending her back to be trapped in the Underworld forever.  For us to mull over what might have moved the hero to such catastrophic climax.

Perhaps, his ears not detecting her shady footsteps, Orpheus has a fatal lapse in faith, a growth of disbelief in the presence of the hitherto absent beloved.  That seems to be Ovid’s take:

hic, ne defieret, metuens avidusque videndi
(here, afraid that she might fail him, eager to see her) (Line 56)

Christianity too, we must remember, highly valued belief bereft of the testimony of the senses:

Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed. (John 20:29).

Yet, there is no general agreement on the causes of Orpheus’ behavior.  Here is Virgil in Georgics IV, the passage where Orpheus looks back at Eurydice and sends her back to the gloom:

... terque fragor stagnis auditus Avernis.
illa ‘quis et me’ inquit ‘miseram et te perdidit, Orpheus,
quis tantus furor?
(... three loud crashes are heard in the stagnant pools of Avernus. / Eurydice cries: what madness, Orpheus, what madness has condemned both you and my miserable self, / what dreadful madness?) (Lines 493-5).

Not a word here about lack of belief or faith.  And in a well-known painting Camille Corot depicts the hero holding his bride by a wrist, so there can be no question that Orpheus is sure that Eurydice is there with him.  Well then, we ought to look for other possible reasons why Orpheus sends his bride back into Avernus.  Perhaps he suddenly felt that an absent beloved was preferable to, more truly loved than, a present one, as was felt by the Occitan troubadours with their amor de lohn, by Beethoven and the German Romantiker with their ferne Geliebte, by Paul Celan with his “Lob der Ferne”, or perhaps by Johannes Brahms with Clara Schumann. 

Is it truly a question of belief, or faith? is it a question of love?  Or does the Orphic myth raise two rather different and more fundamental questions?

Number one: perhaps Orpheus loved Eurydice but also hated her at the same time?  In traditional logic and in mathematics such situations are forbidden, impossible: the fundamental law of non-contradiction ensures that for any proposition P, P and not-P cannot be simultaneously true.  But myth is not math and logos is not mythos.  In myths, the simultaneity of the feelings of love and of hatred or indifference is far from exceptional; in one of the most ancient myths known to us, Inanna is the Sumerian goddess of both erotic love and war; she loves her husband Dumuzi, yet she chooses him and no other to replace her in the Underworld and condemns him to death.

And number two: is there a limit to how much presence we humans can bear or how much our world can hold?  If so, must destruction and catastrophic absence necessarily follow an excess of presence?  Here we are assigning the word “presence” its ancient meaning of being in some human or divine consciousness.  The kabbalist rabbi Isaac Luria (1534 - 1572) conceived the idea that God was a plenum and that He had to undergo a contraction, in Hebrew a tzimtzum, so there would be room for Creation.  God’s tzimtzum was the first in time: from then on, the alternation presence-absence-presence appears to function like a deep breathing.  Greek pneûma and Latin spīritus came to mean inspiration, in both senses: filling the lungs with air and of being spiritually filled with a divine afflatus.

There seems to be a limit to how much presence we humans can bear.  As Emily Dickinson put it, adding to Orpheus a pinch of Pythagoras:

“For each ecstatic instant
We must an anguish pay
In keen and quivering ratio
To the Ecstasy.”

And Goethe seems to say as much in his poem “Spruchweisheit” (Wise Saying):

“Alles in der Welt läßßt sich ertragen,
Nur nicht eine Reihe von schönen Tagen.”
(Everything in the world can be endured,
except a succession of beautiful days.)

We now choose an example that shows Rabbi Luria in a bright prophetic light.  The beginning of the seventeenth century — let’s say the first fifteen years of the century — saw Shakespeare’s Hamlet and King Lear, The Winter’s Tale and The Tempest, Cervantes’ First Part of Don Quixote in 1605 and the Second in 1615, Monteverdi’s music, including his opera L’Orfeo (1607).  It saw Galileo refuting, with his inclined plane experiment of 1604, the Aristotelian tenet that bodies fall with constant velocity, and concluding that, instead, they fall with constant acceleration, a conclusion that led to the new physics and the mathematical toolkit of the calculus, invented later in the century.  And let us not forget that Johannes Kepler in his Astronomia nova of 1609 established the laws of planetary motion.  As if such prodigious production called for an equally prodigious destruction, the Thirty Years’ War started in 1618.

Eighteen years ago in Offcourse,Spring 2007, I was writing that one cannot be blamed for speculating that the catastrophe of WWI played a big role in the fading away of esthetic as a discipline and the falling of the word “esthete” into disrepute.  Whatever European artistic culture had been up to before that terrible event, had been proved evil after the fact, or at least very ill judged.  What had European artistic culture been up to during the so-called Belle Époque?  Like the cicada of the fable, it had been singing for the pleasure of it, with no heed for the approaching winter.

There is some truth, it still seems to me, in the above paragraph, although I forgot to mention some of the diverse alternations that seem to be the essential rhythms, the breathing, so to speak, of all that belongs to life on earth.  The alternation of night and day and the alternation of the seasons are of course the most familiar, but there are countless others; my grandson Jared, who is a geologist, tells me that Peak Neogene warmth and minimal polar ice volumes occurred during the Miocene Climatic Optimum (ca. 16.95–13.95 million years ago), followed by cooling and ice sheet expansion during the Middle Miocene Climate Transition (ca. 13.95–12.8 million years ago).  Just so, the alternation presence-absence-presence, appears to function like the deep breathing of human history. 

 

2.

 

As I am writing this, The New York Review of Books publishes a review by Adam Kirsch, titled “In Search of Fullness” (Nov 11, 2024), of the Canadian philosopher Charles Taylor’s book, Cosmic Connections: Poetry in the Age of Disenchantment.  Kirsch’s word “fullness” may, in general, mean the same as the word “presence” that I’m using here, but I think that in this particular instance it does not: the fullness spoken of by Taylor and his reviewer, to begin with, is restricted to poetry.  Taylor acknowledges this, both in his title and in his preface — “There are parallel movements in the music and visual art of the time, but I will speak mainly in this book about poetry” — and of course it is his unchallenged right to restrict the scope of his book; however, when I speak of an era of presence, I am purposedly including not only poetry, prose, music and the visual arts, but, equally importantly, philosophy, mathematics and the natural sciences.  Of this unrestricted kind was the period of presence shattered by the Thirty-Year War.

A second look at Taylor’s title reveals another, more crucial point of disagreement: it refers to our age as one of disenchantment.  This designation had been advanced by Max Weber in his 1917 lecture “Science as a Vocation”: it may have been justified at that moment, during the calamities of the Great War, but it would have been entirely inappropriate five years later, because after the Great War of 1914-18 and the influenza epidemic of 1918, which killed unprecedented millions, came a period, roughly from 1920 to 1926, that was exceptionally rich in poetic masterpieces — think of Valéry’s “Le Cimetière marin”, Rilke’s Sonetten an Orpheus and his Duineser Elegien, César Vallejo’s Los heraldos negros, Eugenio Montale’s Ossi di seppia, T.S. Eliot’s “The Wasteland” and Wallace Stevens’ Harmonium, and, to trust those who read Russian (I do not), Marina Tsvetaeva.  And not only rich in poetry.  Think of other masterpieces like Thomas Mann’s Zauberberg, Alban Berg’s Wozzeck and his Lyrische Suite, Charlie Chaplin’s “The Kid,” or Picasso’s pictures of mother and child that rival the ones of 12th-century Western art.  Then think of Schrödinger’s wave mechanics.  The early 1920s appear, at least to my mind, my ears, and my eyes, a blooming era almost as miraculous as the first decade and a half of the 1600s.

Even within Taylor’s chosen restricted field, poetry, I detect an antipathy to modern science, regarded as an instrument of disenchantment, that can only be attributed to ignorance, and his opinions about twentieth-century poetry seem to be driven more by his religious (Christian) commitments than by a sense of beauty.  He writes near the end of his Preface:

“But some of the most significant poetry invoking higher times comes with early twentieth-century “modernism” (Eliot) and continues in the work of Czesław Miłosz.”

That Eliot’s “Wasteland” is at the root of twentieth-century “modernism” has been often said, too often in my judgment; but that poetic modernism continues in the work of Miłosz comes as a shock.  There’s an obvious way in which continuity could be said to hold, that is, in the Christian bent of both poets.  But as a poet and as a critic, Miłosz cannot seriously sustain a parallel with Eliot.  Since our theme here is the Orphic myth, let us take Miłosz’ poem “Orpheus and Eurydice” (ca. 2002) as a gauge of his poetic inspiration.  Here the myth is rehearsed in a modern setting: the gates of Hades are glass paneled, there are elevators to take the shades to their appointed levels, and electronic dogs replace Cerberus, while automobiles go by.  I read that the Polish poet conceived the idea of this work while visiting the hospital where his wife was dying of cancer, which suggests that he presumed to identify himself with the Master of Song.  In any case, Orpheus in a modern setting was not a new conceit: I remember watching around 1959 or 60, Marcel Camus’ film “Black Orpheus,” located in a Rio favela during the carnival.

Miłosz doesn’t trouble himself about the cause of Orpheus’ fatal looking back, he doesn’t ask what might have been in the mind of the hero right before he turned his head.  Without further ado, he ascribes to Orpheus a lack of faith in the reality that the shade of his beloved was following him:

“He knew he must have faith and he could not have faith.”

A plight that has beset countless spirits, among them that of Gotthold Ephraim Lessing in the eighteenth century, who spoke of the filthy wide ditch separating the truths which are certain and can be proved from those we can only know through hearsay, like the murder of Caesar, or the rising of Jesus from the grave: those truths require faith.  And a few lines down Miłosz goes on:

“He turned his head
And behind him on the path was no one.”

If we compare Miłosz’ Orphic poem with Rilke’s German poems on the same subject predating it by almost a century, we cannot avoid the feeling that here a total void of poetic inspiration has followed one of miraculous fullness. 

My feelings are aggravated to the point of despair when I try to make something of John Ashbery’s poem on Orpheus parading the title “Syringa”, meaning “lilacs,” which begins:

“Orpheus liked the glad personal quality                                  
Of the things beneath the sky. Of course, Eurydice was a part
Of this.”

We can either say that this is a view from very high up, from above the suns and galaxies, a godly view of Orpheus in which Eurydice is but an atom — or we can take it as a poor joke. 

 

3.

 

 

What keeps me going — in spite of feelings of weakness and insufficiencies in my body and the frequent hurricanes of hatred and madness out there all over the world — is the evidence of alternances I detect when scrutinizing the past.  It is not something that began sustaining me in my old age; I remember already squeezing hope out of the bulk of my memories at an early age, perhaps in my mid-teens, long before I discovered Kierkegaard’s Repetition and its profound if dubious distinction, that repetition, when and if it happens, makes us happy whereas recollection makes us sad; that was some years before I read Proust.  I was in high school and had already learned to let the winter winds remind me of the breezes of the previous spring by the time I first read Miguel de Unamuno’s masterpiece, Del Sentimiento Trágico de la Vida (The Tragic Sense of Life), published one or two years before the onset of the Great War.  It was there, in that book, I found this unforgettable thought:

“Se vive en el recuerdo y por el recuerdo, y nuestra vida espiritual no es, en el fondo, sino el esfuerzo de nuestro recuerdo por perseverar, por hacerse esperanza, el esfuerzo de nuestro pasado por hacerse porvenir.”
(We live in remembrance and by remembrance, and at bottom, our spiritual life is but our remembrance’s effort to persevere, to turn itself into hope, the effort of our past to turn itself into future.)

Song is the means, the catalyst, the platinum moss, by which remembrance is turned into hope. The aoidoi were the priests of remembrance in ancient Greece, the guardians of the sacred relics of the past, and the singers who turned remembrance into beauty, without which life is but hapless and hopeless noise.  And Orpheus is the father of the aoidoi, as Pindar calls him in the fourth volume of the Pythian Odes.

 

4.

 

Breathing is alternation — of void and plenum, in and out, to be sure, but also of presence and absence, of sameness or abiding and difference or mutation.  If we are forced to remain steadily in one of those reciprocal states, we suffocate.  Enough people have drowned in tranquil, windless waters; we, affluent denizens of civilized countries with rapidly changing technologies, are more likely to suffocate in an atmosphere of incessant change.  True disciples of Orpheus, like true disciples of Asclepius, must attend to their spiritual, i.e. pulmonary health.

The first poet I ever met and read was also a medical doctor: Baldomero Fernández Moreno (1886-1950) lived across the street from my house in Buenos Aires and would often stop before our wrought-iron fence to admire Mother’s roses, red, white, and yellow.  Since he died when I was ten, my memories of his aspect are nebulous, but I remember a good number of his poems by heart.  To our times of reckless change he opposed a sweet conservatism:

El tiempo terrible mueve su piqueta...
(Merciless time wields its mattock axe...)

So begins his elegy to his old high school, which was also my old high school except mine occupied a new and very different building, which the poet finds insipid, though I found it imposing.  In another poem he put it in a sad Alexandrine distich:

La ciudad se transforma, dice alegre la gente;
También lo digo yo: mi tono es diferente.
(The city is changing, people merrily say;
I say it too: my tone is different.)

Don Baldomero, steeped in Spanish traditions, was likely familiar with the zarzuela “La Verbena de la Paloma” (1894), where two old men sing jocularly:

Hoy las ciencias adelantan que es una barbaridad, una brutalidad, una bestialidad.
(Today the scientific advances are a barbarity, a brutality, a bestiality.)

I recall those and other lines of verse to help me interpret what Rilke may have meant by those final words, the enigmatic second tercet of his last Sonnet to Orpheus:

Und wenn dich das Irdische vergaß,
zu der stillen Erde sag: Ich rinne.
Zu dem raschen Wasser sprich: Ich bin.
(And if what is earthly leaves you behind,
to the still earth say: I flow.
To the running water speak: I am.)

The two verbs, sagen and sprechen (to say and to speak), serve in both cases to bring to presence that which is absent, adding flow to stillness and stillness to flow, thus completing an earthly plenum, a desideratum for us ephemeral.  Thanks to Orpheus — or to Rilke — difference and sameness, motion and rest, Heraclitus and Parmenides, become reconciled, even dancing partners, and our spirit becomes healthy.

Here I dare talk ethics.  The disciples of Orpheus, whether poets or thinkers, ought to take a Hippocratic oath: to help others in their spiritual healing.  When I say thinkers, I include not only philosophers but mathematicians and scientists, who should profit from the example of the ancient Pythagoreans and of Simone Weil who, in her Commentaires de textes pythagoriciens, connects math with ethics, and even with theology.  Sounds strange?  It sounded mighty strange to my ears when I heard math professor Misha Cotlar say, about John von Neumann, who had died a few months before: “He was a great mathematician but a very evil man.”  Cotlar was exceptional in mentioning math and ethics in the same breath, but then he was also exceptional in his attachment to Vedanta. I was then seventeen, newly admitted to the Facultad de Ciencias Exactas and I wasn’t aware that Oppenheimer, the physicist who held and felt the terrible responsibility for having created the atom bomb, was also a disciple of Vedanta, and that upon the destruction of the two Japanese cities in August 1945 he had exclaimed, quoting the Gita, “Now I am become Death, the destroyer of worlds.”  

Had Cotlar, had Oppenheimer read what Kierkegaard wrote in his Concluding Unscientific Postscript?

“The ethical is and remains the highest task assigned to every human being.  It may also be required of a devotee of scholarship that he understand himself ethically before he dedicates himself to his intellectual discipline, that he continue to understand himself ethically in all his labor, because the ethical is the eternal drawing of breath and in the midst of solitude the reconciling fellowship with every human being.”

I don’t know if they had read it, but I wonder what Cotlar and Oppenheimer would have said of another top mathematician who had died a year or two before von Neumann: Hermann Weyl.  The address he pronounced at the bicentennial celebration of Columbia University in 1954 was titled “The Unity of Knowledge,” and here is one of his final statements:

  

“Being and Knowing, where should we look for unity?  I tried to make clear that the shield of Being is broken beyond repair. We need not shed too many tears about it.  Even the world of our daily life is not one, to the extent people are inclined to assume; it would not be difficult to show up some of its cracks.  Only on the side of Knowledge there may be unity.”

“Unity of science” was not a new topic.  In the decade before WW2 a series of conferences (Kongress für Einheitswissenschaft), had been held in Prague (1929, then in Königsberg (1930), in Prague (1934), Copenhagen (1936), Cambridge (1938), and Harvard (1939).  Still, Weyl’s willful split between being — mortal being — and knowledge is dismaying: Weyl seems to imply that unity can only be attained by artificial intelligence.  And his warlike insistence on shields: had Weyl ever read or heard the poem Rilke wrote in a letter from the Château de Muzot, which he called “improvised”?  I quote only this translated bit:

“... in the end / it is our unshieldedness on which we depend...”

Another question: had Weyl ever read or heard Auden’s poem “The Shield of Achilles,” published in 1952, two years before the Columbia speech?

Whether Weyl was aware of Rilke, or of Auden or of neither, it wouldn’t have made any difference.  For one thing, ever since the times of Pythagoras and of Archytas mathematicians have thought of themselves and their work as well shielded against time and its ravages.  For another, as Weyl also said at the bi-centennial celebration at Columbia:

“Poetry, myth, religion, history, philosophy: all of these, unlike mathematics, are tainted by man’s infinite capacity for self-deception.”

Weyl could not be clearer: what goes for Rilke, Auden, and their ilk goes too for Genesis and the myth of the pair of trees in the Garden, it goes for Inanna and her attempted conquest of the Underworld, and goes for Orpheus, the Master of Song and main theme of these my lucubrations.  Eight years before, in his 1946 address on the occasion of Princeton University bicentennial, confronted with the dreadful prospect opened by the atomic bombing of Japan at the end of WWII, and unlike Oppenheimer, as if opening his arms in powerlessness, Weyl pronounces in Latin: Crescet scientia, pereat mundus! (Let science grow, though the world perish!)  Then he offers a piteous pseudoscientific reason for the plight of the contemporary scientist:

“Technological knowledge is such a dangerous tool in the hands of man, because of the second law of thermodynamics; it is much easier to blow up a building than to build it.”

And he concludes:

“What to do is a question every one of us must answer according to his own conscience. I can suggest no universal solution.”

Hard to dissent from Weyl's statement. I can only add a question: does his vaunted “Unity of Knowledge” include ethics?  No wonder that when, during his first visit to the USA in 1929, a reporter from the Wisconsin State Journal asked Paul Dirac to name a scientist he could not understand, Dirac replied, Weyl.

So much for ethical concerns, most dear to Kierkegaard, to Oppenheimer, and to Cotlar.  “Don’t shed a tear for my shield and its cracks,” says Being, a.k.a. Life, through Weyl’s contradiction-free mathematical tongue.  He often mentions the philosopher Ernst Cassirer, the Neo-Kantian for whom man is not the homo sapiens of Linnaeus but the symbolic animal, Cassirer who devoted as much attention to mathematics and the natural sciences as to the humanistic and artistic disciplines, and with each mention of Cassirer, Weyl does not forget to warn us that “not all human languages are equally truth able,” and that “Poetry, myth, religion, history, philosophy: all of these, unlike mathematics, are tainted by man’s infinite capacity for self-deception.”

After hearing that, I cannot but sympathize with Paul Dirac.  At first blush, it may look as if Weyl is only repeating what Francis Bacon wrote on the first page of his Essays, at the dawn of the sun of modern science, that man has “a natural though corrupt love of the lie itself.”  Yet Bacon was writing as a lover of truth, as a lover of words, and as a disciple of Montaigne; for him, the philosopher is able and willing to rescue us from the quagmires of human lies.  But when Weyl makes his indictments and his pronouncements about poetry, myth, religion, history, and philosophy, what language is he using?  Mathematical?  Clearly not.  We might settle and say that he is using the language(s) of history, of social sciences, of anthropology, or of philosophy.  But those languages, he is asserting, are tainted, a prey to human falseness and self-deception: hence, if we trust him, we must distrust his panegyric of mathematics.  The whole thing brings to mind the ancient paradox of Epimenides the Cretan who asserts that all Cretans are liars.

Still in my late teens I discovered this, by twenty-four-years old W.B. Yeats, against the positivistic views of Weyl:

The woods of Arcady are dead, 
And over is their antique joy; 
Of old the world on dreaming fed; 
Grey Truth is now her painted toy; 
Yet still she turns her restless head: 
But O, sick children of the world, 
Of all the many changing things 
In dreary dancing past us whirled, 
To the cracked tune that Chronos sings, 
Words alone are certain good.

Still one more.  Some thirty years ago, in my lecture on Galileo, Descartes, and the birth of modern science I noted this about unity, being, and knowledge: “Modern science achieved unity in the laws that govern the universe, making our earth and the most distant stars parts of the same cosmos.  A practical result, however, has been the specialization and fragmentation of our knowledge, and the abandonment of all attempts at cognitive unity within any single human mind.”

 

5.

 

 

Human languages and their truth ableness.  The earliest Greek philosophical discussion about language had to wait until Plato.  His dialogue Cratylus has three characters: Cratylus, who maintains that names must meet certain standards to be considered correct, Hermogenes, who argues that names are arbitrary and conventional (which is the modern, Saussurean stand), and of course, Socrates, who meanders and goes off on so many tangents, I’m not surprised that it is often considered one of Plato’s most vexing works.  Aristotle in his De Interpretatione offers a compromise between Cratylus’ and Hermogenes’ opinions based on his correspondence theory of truth; I am arrogant enough to offer a different compromise.  In my view, both positions, Cratylus’ and Hermogenes’, are correct, but only partially.  Certainly, in the case Socrates chooses — hippô denotes a horse and anthropos denotes a human being — historical contingencies and conventions play a most important part, and with horses and men it could well have been the other way around; but in other cases there are obvious ways in which a name may be right or wrong.

In the language of chemistry, for example, names like potassium or sulfur are the product of historical contingencies, yet the name sulfur dioxide is right when applied to SO2 (so long as di still means 2) but wrong if applied to the substance whose formula is SO3.  In mathematics, for another example, any contradiction is deadly wrong, and just one occurrence of it would demolish the whole edifice, whereas in the demotic of many cultures it makes perfect sense to call a fat guy, ironically, “Slim.”

But enough about the ancients.  The Middle Ages saw a long contention between realists and nominalists.  The realists were Platonists; for them ideas are eminently real and their proper names call them to mind.  Mallarmé said it more elegantly in Crise de vers:

« À quoi bon la merveille de transposer un fait de nature en sa presque disparition vibratoire selon le jeu de la parole, cependant ; si ce n’est pour qu’en émane, sans la gêne d’un proche ou concret rappel, la notion pure. »
(What use is the marvel of transposing a fact of nature into its vibratory-almost-vanishing by playing the game of language, however, if it is not to extract from it, without the trouble of a near or concrete recall, the idea in its pure state.)

Nominalists, on the contrary, believed that only particulars located in space and time — nostalgic space and doleful time — have full reality, whereas “universals” like beauty, or faith, have only a pale, post rem reality: they are but names, words, and a word is nothing but a soft wind from the mouth, a flatus vocis.  This doctrine and its name emerged from debates in medieval philosophy, more precisely with Roscellinus, who lived from about 1050 to about 1121.  It is a remarkable doctrine.  The question is: are all words nothing but flatus vocis, or only some of them?   If only some, how can we distinguish those who are from those who are not?  If beauty is a universal, hence just a flatus, how come when I add her to it — her beauty — it suddenly becomes a particular and by no means a flatus?  Can two flatus add up to something fully real?

And if all words are flatus, what happens then to promises, oaths, and blasphemies?  Are they vain and ephemeral, and no more binding than embarrassed farts?  And what of the Mosaic commandment, Thou shalt not take the name of the Lord thy God in vain?  I wonder how Roscellinus and his followers avoided the stake.

Another puzzle: what’s the nominalist take on math?  Are numbers abased to the state of mere flatus, or are they fully real stuff located in space and time?  It is true that my senses can detect numerical differences — my tongue, for instance, can tell if I have zero, one, two, or three pills placed on it, and my eyes can number a few trees before them — but let those be many, and I lose count.  On the other hand, without the assistance of numbers, space and time themselves become problematic.  Already as a high-school student I was aware that there is serious logical cheating involved in the geometric axioms: when you are told that “given two different points, there is one and only one line containing both,” what is meant by “different points”?  How can anyone tell if two points are the same or different?  None of the geometric axioms enables us to do so.  Two points can be switched around and none the wiser, and if you say, “they are the same if they are in the same location,” I’ll reply that I have not seen that word, “location,” in any of the axioms.  Such logical problems vanish when we have recourse to Descartes’ invention, numerical coordinates.  Now every point in space and every point in time has its own identity, just as we in this country have our own social security number, and everything can proceed in conformity with legal and logical strictures.

Anyhow, I was curious about what nominalists have said about numbers, or rather what they are saying today, for Roscellinus still has followers.  So I consulted the Stanford Encyclopedia of Philosophy, a precious resource for amateurs like me, and I found the article by Otavio Augusto Santos Bueno which begins as follows:

“Nominalism about mathematics (or mathematical nominalism) is the view according to which either mathematical objects, relations, and structures do not exist at all, or they do not exist as abstract objects (they are neither located in space-time nor do they have causal powers).”

I’m not sure how to interpret what is meant here by “not to exist”, but one thing strikes me as outlandish: how can anyone, at this point in the history of humanity, view mathematical objects and structures as having “no causal powers”?  I take it that having causal powers is synonymous with having effects.  How anyone living today can be blind to the innumerable effects, all around us, of mathematics, of statistics, and of the sciences based thereon?  And if by having causal powers it is meant to have effects strictly by itself, I will argue that nothing in the world, except perhaps for the Elohim of Genesis or for Aristotle’s prime mover, has effects strictly by itself.

After a few more obscure paragraphs I quit trying: to be forced to read Otavio Augusto Santos Bueno’s article is, or at least seemed to me, almost as excruciating as being condemned to die inside the bull of Phalaris.

Nevertheless, since no doctrine is so abstruse or absurd as to lack all beneficial effect, Mr. Bueno’s first names brought to my mind a namesake, Enrique Santos Discépolo, by consensus one of the great tango lyricists, and with him one of his pieces, the tango “Yira, yira” of 1929.  In Buenos Aires yirar means to wander aimlessly about, or to wander about with some purpose — a prostitute or a peddler yiran in search of clients, but in in Discépolo’s tango a desperate man yira in search of a fraternal chest to hug before he dies.  Like many expressions of the River Plate slang, it was derived from the Italian: girare also means to roam, to wander, to mill about, but it has a much wider variety of meanings than the River Plate slang yirar.

It may seem I am yirando; on the contrary, I’m going straight to the point.  Which is how deftly Discépolo combines the universal “faith,” considered by the nominalists a whiff, a flatus, with a most down-to-earth, fully real particular, in his characterization of despair: 

“Cuando no tengas ni fe
ni yerba de ayer
secándose al sol.”
(When you’re left with no faith
nor yesterday’s yerba
drying under the sun.)

That’s the depth of destitution and despair.  Most of us believe we know what the universal noun faith means, and the word despair, from the Latin spes = hope, plus the negative prefix des-, means hopelessness.  As for the particular yerba, it is a plant (Ilex paraguariensis) used to make an infusion called mate or cimarrón in Spanish, and chimarrão in Brazilian Portuguese.  The crushed yerba leaves and stems are used only once: to use them again would produce an almost insipid, washed-out beverage.  To be unable to procure a cupful of fresh yerba is to have reached the bottom wastes of neediness.

I never shared nor do I enjoy the monochromatic pessimism of Discépolo’s vision of humanity, but I consider the above three verses of his “Yira, yira” to be a practical Orphic lesson for both Platonists and nominalists, an exhortation to abandon their one-sidedness and the foolishness of trying to rank what’s real into more or less: to utilize the combined resources of universals and particulars for the sake of song.

 

Appendices
1.

When I was working towards a PhD in math at the Courant Institute of New York University in the mid 1960s, my office mate used to expound his thesis to me in great detail.  By 1970 we were in touch no longer.  Then I left math research and more than fifty years passed by.  Not long ago I received mail from him — Why don’t we skype?  — Why not indeed?  So once a month we skyped in the evening for about an hour. Uninterested in my interests, immune to Orphic enchantments, Bernie evokes with gospeler devotion his mathematical deeds of yore.

Trying to sprinkle a bit of my own spice on those encounters, a bit of vital self-assertion, I mentioned the essence of I have written above: my dismay at Hermann Weyl’s two bicentennial addresses.

Bernie was quick to react.  “I greatly admire Hermann Weyl,” he said somberly.  And three seconds later he added, “I’m bored.  I have to go.”  That was it, which leads me to think that the last time we skyped is sure to be the last.  Paraphrasing Poe in Eureka, Bernie would never, thenceforward, have anything to do either with me or with my truths.

I was startled, but in no wise offended; on the contrary, I was grateful to Bernie Borne, for he had taught me a valuable lesson.  Transport yourself five centuries back, and imagine you were talking not to a doctor in math but to a doctor of theology from the University of Paris, telling him that you are dismayed by the doctrines of Saint Augustin or of Saint Thomas Aquinas.  How would he react?  Not nicely, and not very differently from Dr. Borne, I venture to say.  For him, as for Weyl, for Einstein and longer ago for Spinoza, math is the modern sacred doctrine: math happens to be their religion as well as their theology.  An argufier may argue that a religion like Christianity is based on miracles contrary to reason, while math is the basis of our natural sciences and our technology, hence religion and math cannot be compared.  I will only refer the argufier to Eugene P. Wigner’s famous paper, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (Communications on Pure and Applied Mathematics, vol. XIII, 1-14, 1960).

 

2.

Above I was asking myself, had Weyl ever read or heard the poem Rilke wrote in a letter from the Château de Muzot?  I quoted this translation: “... in the end / it is our unshieldedness on which we depend...”  I could have asked the same question about the last tercet in Rilke’s Orphic Sonnet 1. XI: “The constellation deceives us. / To trust it for a while is joy, / and that’s enough.”  I thought that, in light of what he said at Princeton and Columbia, Weyl would have scoffed at those and many other poems — what am I saying?  At most, nay at all poems, excluding perhaps the one Einstein once penned about Spinoza.  Imagine my surprise, then, when I was informed by my son David that at the IAS in Princeton, where Weyl spent all his years in the U.S., there are letters sent in the early 1950s by Weyl to Hermann Hesse: in them the mathematician insisted on his admiration for Hesse’s poems.  No reply from Hesse has been found.

In my adolescence I read all the Hesse novels that could be found in Spanish translation, until I graduated to Thomas Mann, but I had never seen a Hesse poem.  Upon learning of those Weyl’s letters I read a number of Hesse’s poems and was not impressed.  Was their affinity based merely on the facts that they were both named Hermann and that both were Germans turned Swiss?  I don’t know and it’s irrelevant.  The point I want to make is that when he spoke about his preferences, his loves and his life, Weyl could not avoid contradicting himself, which is what happens to all of us, but which within our mathematical profession is a mortal sin.