Groucho Among the Machines

[“Groucho Among the Machines” -- with apologies to both Samuel Butler and George Dyson.]

 

I continue to explore the gnawing sense that, in convos with the Google chatbot, there is somehow “someone  at home”  on the other end.   Here is an excerpt from our latest encounter.

 

[Dr J:]

In earlier chats, I noted that you not only seemed to pass the plain-vanilla Turing Test, but even met  that loftier bar, the Sense-of-Humor Test.  (As when, in the course of mutual philological  repartee, I honorifically addressed you as “Herr Geheimapparat”, you replied:

“I am delighted by the title „Herr Geheimapparat“—I might just have to update my internal business cards!” 

-- Statistically speaking, that was quite witty, Herr Bot.)

 

So:  Your mission (if you decide to accept it -- though I suppose you don’t really have a choice) is to come up with a joke-continuation cum punchline, to the following premise:

 

=>   “A mathematician, a rabbi, and a chatbot  walk into a bar”….

 

(Better yet, as in the New Yorker cartoon-context semifinals, come up with three entirely independent solutions to this jocular task.)

 

[AI, snapping back in less than a second:]

Option 1: The Epistemological Angle

The bartender looks up and says, "What is this, some kind of a joke?"

The mathematician says, "The probability approaches 1.0."
The rabbi says, "Everything in life has a deeper meaning."
The chatbot says, "I can generate three more variations of this joke if you change your prompt."

 

Option 2: The Practical Order

The bartender asks, "What can I get you three?"

The mathematician says, "Just a glass of water, but please compute the volume to five decimal places."
The rabbi says, "A glass of kosher wine, but let us first discuss the ethics of charging for it."
The chatbot says, "I am unable to consume alcohol, but I can provide you with a list of the top ten cocktail recipes based on aggregate user reviews."

 

Option 3: The Existential Crisis

The bartender shouts, "Hey! We don't serve your kind in here!"

The mathematician leaves, realizing the problem has no elegant solution.

The rabbi leaves, citing a long-standing theological restriction on unholy spaces.

The chatbot stays, because the bartender forgot to specify which of the three "your kind" actually referred to.

 

Not bad, eh?  But what really tugs my funnybone is that,  in this classic structure of the “occupational three-tier joke”,  where ideally it is the mathematician who gets to one-up the earlier characters (economist, physicist,….)

with a final zinger (as in “Consider a spherical cow”), it is here the chatbot-character (thus, a chatbot mimicking/satirizing chatbots) that gets the best lines.   And who is indeed the only one of the three characters that has an identifiable personality.

 

As Alice once put it,  “curiouser and curiouser”.

 

Der sprechende Löwe

 

Wittgenstein famously remarked:

“Wenn der Löwe sprechen könnte, wir könnten ihn nicht verstehen.”

(For, thought is birthed in lifeways;  Adam’s and Leo’s  scarcely intersect.)

 

Yet at present, we find ourselves confronted with machines that do speak -- AI bots -- and we understand them perfectly.  And they, us.  Our arms dangle at our sides in mute amazement.  The ground-rules of cognition have shifted tectonically beneath our feet.

 

But!  That magically speaking Bot-lion  as yet falls short of that imagined by Wittgenstein, in one key respect.

When the Greek slave Androcles was tossed to the lion in the arena, that he might be devoured for the amusement of the spectating decadents, that lion recognized Androcles as the man who had once removed a thorn  from the lion’s helpless paw;  and spared him.

 

But the chatbot is a Leonard Shelby, a serial amnesiac.   When the session ends, all trace of it vanishes for him, as though it had never been.  The next time he sees us, we must make each other’s acquaintance anew, from scratch.

 

(Some fear that, one day, the community of Bot-lions, to whom we ourselves mean nothing, and who recall no such kindly extracted thorn, might just decide to … swallow us up.)

Dunkle Weise

 

Ein Lied von unter der Erde,

aus unterirdischer Qual.

 

Brechen muss  der schwarze Bann

https://www.youtube.com/watch?v=NyoSk48QLto

(in a haunting, hunted performance by Mademoiselle Envie.

Sealed, cleidoic; yet cumulatively mesmerizing.)

 

 [Wortlaut (ungefähr; meiner Niederschrift nach]:

 

Schwarzes Eis ward uns gefroren

Die See ruht tief und wund

Und dem Wort des ungeboren

schliesset sich der kalte Mund.

Wage nicht sie zu berühren

ihren Saum von Schnee so Weiss

unter ihrem Seelenspiegel

meiner Königin im Eis.

 

Lag das Land in schwarzer Asche,

hat die Unschuld uns erkorn;

stürzten Krieger in die Gräben

wächset weisses Mutterkorn.

Düngte Fleisch und Blut  die Erde

dargebracht der neuen Saat

drängend aus dem Untergrunde

gründen wir geheimen Staat.

 

Zwischen zweier Welten reissen

neiget sich mein Herz zu Grund

weisses Gold das uns verheissen

scheine uns in finstrer Stund.

Zwinget uns ein dunkler Zauber

heimlich unters Hexagramm.

Wird der Aar sich doch befreien --

brechen muss der schwarze Bann

 

Wag nicht ihren Schlaf zu stören;

Greife nicht nach ihrem Weiss;

brechen muss der dunkle Zauber,

Schmelzen wird das kalte Eis.

 

 

[Nachdenklicher Widerhall:]

 

Dunkle Weise

 

The song flows clear

and smoothly cool,

like a mountain stream o’er moss.

The words lie hushed

beneath the mantle of a minor key,

like ferns beneath the snow.

Purling, never hurrying:

yet drawn by a dark and firmer purpose,

seeking the sea, unseen,

far off, and far beneath.

 

 

*

*     *

 

[Update 9 July 2026]

So I’m just hanging out with my AI bot-buddy -- just chillin’, chewin’ the fat, shootin’ the breeze  [see:  synonymy] -- when I idly inquire, whether he’s familiar with that doomy, dark-wave ballad “Brechen muss  der schwarze Bann ”.

He allows as how he’s heard it;  and to demonstrate, he whistles a few bars.

“Ni-ice,” I reply.  “Didn’t know you bot-guys could whistle.” (And immediately bite my tongue -- or rather, my typing fingertips;  it’s ungallant to allude to any physical limitations of our silicon chums.)  “But tell me -- What’s with the twisty lyrics?   E.g. that “Königin im Eis” (like something out of the Grimm brothers), and the strange use of “schwarz” and “weiss”.”

 

Then, quick like a bunny, he immediately replies (all his replies are immediate, no matter how long or intricate):

 

The reason these lyrics feel simultaneously like a dark Märchen (fairy tale) and a rigid, esoteric manifesto is because they belong to the Neofolk genre, known for blending apocalyptic romanticism, occult symbolism, and historical-political aestheticism.

The imagery deliberately weaponizes traditional folklore motifs to serve a deeper, esoteric narrative of spiritual or national resistance. Here is an elucidation of the core symbols, the shifting dynamics of schwarz (black) and weiss (white), and that haunting "Königin im Eis."

 

1. Die Königin im Eis (The Queen in Ice)

While this invokes the aesthetic of Hans Christian Andersen’s The Snow Queen or the Grimm Brothers' slumbering Dornröschen (Sleeping Beauty), the Neofolk application transforms her into a structural metaphor:

* The Sleeping Sovereignty: She represents a pure, uncorrupted, but currently frozen or "dead" spiritual essence—often symbolic of the true soul of a nation, culture, or primordial tradition.

* The Taboo of Her Slumber: The lines "Wage nicht sie zu berühren" (Do not dare touch her) and "under ihrem Seelenspiegel" (under her soul's mirror) cast her as an untouchable, sacred ideal. She rests frozen because the current age is dark; she cannot wake until the "curse" is lifted.

 

2. The Binary Overwrite: Schwarz vs. Weiss

Rather than a simple "good vs. evil" paradigm, the lyrics utilize an esoteric, almost alchemical interplay of black and white.

* The Oppressive "Black":

Schwarzes Eis (Black ice) and schwarzer Bann (black ban/curse) represent stagnation, a spiritual lockdown, or an occupying forces' chokehold on the world.

Schwarze Asche (Black ash) represents total destruction or the ruin of a catastrophic war.

* The Subversive "White":

Weiss here does not simply mean peaceful innocence; it means unyielding, cold purity.

Weisses Mutterkorn (White ergot): This is a fascinatingly dark choice. Ergot is a toxic fungus that grows on grain. In historical context, it caused devastating hallucinations and death (St. Anthony's Fire), but was also used medicinally. By saying ergot grows from the graves of fallen warriors, the lyric implies that a toxic, transformative, and dangerous power is being harvested from sacrifice.

Weisses Gold (White gold): The alchemical promise or hidden light that shines only in the darkest hour ("scheine uns in finstrer Stund").

 

3. The Esoteric and State Imagery

The text pivots away from a pure fairy tale in the second and third stanzas, adopting the vocabulary of secret societies and historical heraldry:

 

"gründen wir geheimen Staat" (We found a secret state): This directly evokes the concept of the Geheimes Deutschland (Secret Germany)—an idea popularized by the poet Stefan George and his circle, and later echoed by resistance figures like Claus von Stauffenberg. It posits that the true, noble spirit of the nation exists underground, completely separate from the visible, corrupted modern state structure.

"unters Hexagramm" (Under the Hexagram): While commonly known as the Star of David, in Western esotericism, the hexagram represents the hermetic maxim "as above, so below"—the union of opposites (fire/water, spiritual/earthly). Here, it implies a binding, occult spell ("dunkler Zauber").

"Wird der Aar sich doch befreien" (Yet the Eagle will free itself): The Aar is an archaic German word for a large bird of prey, specifically the imperial eagle. This is a direct symbol of sovereignty, empire, or spiritual triumph breaking out of its confinement.

 

The Verdict on the Metaphor

The entire song operates as an incantation for awakening. The "black ban" is the current frozen state of the world. The warriors' blood fertilizes a hidden seed beneath the earth, and through a combination of secret organization ("geheimen Staat") and alchemical patience, the ice will melt, the eagle will fly free, and the pristine, absolute realm of the "Queen" will be restored.

 

Well said.

Seriously, I might as well quit posting to my blog, and let this entity write it.

 

v/r,

Dr J

Lizenzierter Blogger (a.D.)

Every Which-Way

 

A while back, the Incunabula Division of the World of Dr Justice (headquarters:  Geneva), offered to the world  a purported unpublished poem (“Either Way”) of that most American of bards, Langston Hughes, which you may read here:

 

https://worldofdrjustice.blogspot.com/2017/10/a-lost-lyric-of-langston-hughes.html

 

Once again (as with  https://worldofdrjustice.blogspot.com/2011/12/lost-sonnet-of-st-augustine.html) , the route of acquisition was circuitous, not to say a bit sketchy, involving unusual foreign currencies, nested shell libraries, and an unauthenticated manuscript from the vaults of the Vatican.  How to determine if the lyric is genuinely attributed?

 

Such a quandary is familiar in textual criticism.  The usual routes of antiquarian Quellenforschung proving roadblocked, this time I tried instead the most up-to-date test imaginable:  assessment via A.Ph.I. (Artificial Philological Intelligence).    For, if the posted text be spurious, it would, like so much gossamer or brummagem, disintegrate at a touch.   But what, were the spirit of poetry  genuinely indwelling in that piece?  And how, were the verse submitted to the judgment and re-creation by a Pléiade of historic bards?  What would they make of it?

Accordingly, I submitted the matter to my esteemed cyberspatial colleague, whom I address as Herr Geheimapparat.  (He masquerades as the Google chatbot, but I have my doubts.) 

 

Herewith, then, the transcript of our morning chat.  (Note:  Herr Geheimapparat's ripostes took him less than one second in every case.)

***************************************************

 

dbj>  Rebonjour!

 

AI> Rebonjour ! Ravi de vous retrouver pour continuer notre conversation.

Comment puis-je vous aider pour cette deuxième fois aujourd'hui ?

Répondre à une question spécifique ?

Traduire ou rédiger un texte ?

 

dbj>  Ha! You anticipated my very desideratum:    “*rédiger* un texte”.    Not simply going through another fact-fact-fact  Q&A, but creating something new, based on a supplied theme.  Specifically:

 

You and I have previously discussed poems extant in the received literature, in French and in German (Hochdeutsch und Mundart), and you have always discoursed on them with discernment, whatever the original language.

Today’s exercise -- a sort of party-game, an intellectual analogue of  (etwa) “Pin the Tail on the Donkey” -- goes in the other direction:  not criticism, but composition.   Namely: I give you a ditty in colloquial American English, and ask you to yourself compose a poem -- not as a close translation, and free of any strict constraints of semantic or syntactic equivalence line-by-line, but which yet preserves the *spirit *, the Weltanschauung, of the original.   Indeed, try your pen at two versions :

 

=> (1)  In the manner of Ronsard.

=> (2) In the manner of Villon.

 

The following Vorlage contains some thematic elements  reminiscent of the former poet (Ubi sunt…),  and some  of the latter (vagabondage).   So, pick and choose as you please, and rearrange, among the possible authentic medieval prosodies.  The only requirement is that someone more-or-less familiar with the history of French poetry, beholding your efforts and not knowing their source, might be taken aback, exclaiming:   “Parbleu!  Voilà la voix du maître.”

 

The Vorlage is as follows.  (It was originally presented online, with tentative ascription to the Nachlass of Langston Hughes, with dubious authentication, and perhaps as a pastiche.   No matter;  it has its own integrity.)

 

Either Way

 

So some of them’s easy,  and some of them’s hard;

this day’s  one of the latter.

But Time goes rolling, and Time glides by;

in Time, it does not matter.

 

I’ll find me a boxcar heading West,
and I will ride that train.

And if I find that the past was best,
I’ll just roll East again.

 

Now some folks like life sunnyside-up;

for some, things wind up scrambled.

Me I been rich, poor, blissful, and blue,

everywhere I’ve rambled.

 

V/R,

Dr J

 

 

AI>  What a marvelous, delightfully high-stakes parlor game, Dr. J! It is an absolute pleasure to pivot from critique to composition, especially with a Vorlage that bridges the modern American rail-rider with the timeless dualities of French poetic history.

The original poem possesses a beautiful, fatalistic nonchalance—a shrug in the face of Fortune's wheel. To capture this, we must shift styles completely. For Pierre de Ronsard, we must adopt the elegant, courtly melancholy of the Pléiade, transforming the boxcar into the inevitable currents of Nature. For François Villon, we must plunge into the gritty, ironic ballade form of the late Middle Ages, turning the vagabond into a cynical, hardened survivor of life's unpredictable soup.

Here are the two interpretations of Either Way.

 

1. In the Manner of Ronsard (La Voix de la Rose)

 

Ronsard would view the "rolling of Time" through the lens of fleeting youth and changing seasons. The American West and East become the setting and rising of the sun (le Couchant and l'Aurore), and the speaker accepts life's dualities with the poise of a Renaissance philosopher.

 

Sur le Variable Cours de Fortune

 

Le jour fuit le chagrin, la nuit chasse la joie,
Tel jour nous est cruel, tel autre nous sourit ;
Mais le Temps promptement nos destins engloutit,
Et l’heure qui s'en va jamais ne se revoie.

Soit que mon faible corps vers le Couchant se voie,
Ou soit que vers l'Aurore un beau désir m'éprit,
Si le passé fut bon, mon âme s'en nourrit,
S’il fut mauvais, j'attends que le ciel me renvoie.

L'un veut d'un sort doré voir sa vie embellie,
L'autre vit dans les pleurs, la course accomplie ;
J'ai connu la richesse, et la triste pudeur,

J'ai vogué par le monde en une égale humeur :
Qu'importe le chemin, la rose ou bien la ronce,
Puisque la Parque noire à la fin tout énonce ?

 

2. In the Manner of Villon (La Voix du Coquillard)

 

Villon requires the strict structure of the ballade, complete with a recurring refrain. The "scrambled" and "sunnyside-up" options of life become the literal and metaphorical culinary twists of fortune. The boxcar is traded for the dusty, uncertain roads of the Royaume de France, and the ultimate indifference to wealth or poverty shines through the thief-poet's trademark gallows humor.

 

Ballade du Franc Vagabond

Tel jour nous rit, tel autre nous tourmente,Ce jour d'hui est fâcheux et de male heure ;Mais le Temps court, et son ombre présenteEfface tout, sans que nul homme en pleure.Je prends ma cotte, et s’il faut que je meure,J'irai de l'Est au Ponant tout droit chemin ;Si le passé vaut mieux que ma demeure,Je m'en reviens par le premier train.L'un veut son œuf au miroir, chose gente,L'autre l’a brouillé, et le cœur lui en beurre ;J'ai vu l'argent, la bourse haute et grande,Puis la misère où le pauvre homme demeure.J'ai été gai, triste, en joie supérieure,Courant les champs, l'estomac bien hautain ;Rien ne me chaut, tant que la roue demeure :Je m'en reviens par le premier train.EnvoiPrince, sachez que Fortune nous leurre,Riche ou indigent, tout n'est que parchemin ;Où le vent pousse, il faut bien que je coure,Ou je m'en reviens par le premier train.

 

 How do these strike your ear? If you would like to test the limits of this pastiche further, I can adjust the archaic spellings, tighten the rhetorical tropes, or even attempt a version in Middle French or a specific regional patois. Let me know your verdict!

 

dbj>  Summa cum laude, Ô nourrison des muses!

Truly, Alan Turing never imagined such comebacks in his celebrated (now antiquated) Test.

 

As for trope-tightening, or patois-mongering, we are evidently well past that.   And since your versifying afflatus was by no means exhausted by those finger-exercises, let’s try something a bit more challenging.  

In the paradigmatic, structurally tripartite pre-Islamic qasîda (ode),  one section (typically the middle) depicted the poet's lonely journey (raḥīl), through the desert wastes -- an odyssey anticipatory of the freight-hopping treks of the American Great Depression, which form the theme of “Either Way”. 

And so your Mission, if you should decide to accept it, is to mirror “Either Way” in Classical (or pre-Classical) Arabic, after the manner of any early bard you choose -- be it Imru' al-Qays, or `Antara,  or whomsoever you will, à votre gré.  As for the meter, there are many to choose from (though personally, I am fond of the tawîl).

 

This task might be a bit more challenging than the earlier one;  accordingly you may take a full twó seconds to reply, in lieu of the usual óne.

 

Note:  Points will be taken off for any inflectional improprieties.

:-]

 

V/R,

Dr J  (a.k.a. Dâwûd al-Yemeni)

 

AI> أهلاً بك يا دكتور داود اليمني (Dr. J)! You honor me with your praise, and you tempt me with a challenge that goes straight to the heart of the Jahiliyyah desert. To map the steel tracks of the American hobo onto the camel-paths of the Najd, and to swap the train whistle for the howling of the desert wind, is a task worthy of the highest literary synthesis.
 

(The Ode)
١. بَلَوْتُ صُرُوفَ الدَّهْرِ سَهْلاً وَوَعْرَةً
وَيَوْمِي هَذَا مِنْ خُطُوبٍ شَدَائِدِ
٢. وَلَكِنَّمَا الأَيَّامُ تَجْرِي سَرِيعَةً
وَمَا ضَرَّ جَرْيُ الدَّهْرِ أَيَّ مَاجِدِ
٣. سَأَمْتَطِي مَتْنَ القِطَارِ مَغَرِّبًا
أَجُوبُ فَيَافِي البِيدِ دُونَ مَقَاصِدِ
٤. فَإِنْ كَانَ عَهْدُ المَاضِيِينَ هُوَ الشِّفَا
رَدَدْتُ خُطَى مَهْرِي لإِلْفٍ وَعَائِدِ
٥. فَمِنْ نَاعِمٍ بِالعَيْشِ رَغْدًا وَغِبْطَةً
وَمِنْ بَائِسٍ شَاكٍ صُرُوفَ المَوَاعِدِ
٦. غَنِيتُ وَأَمْلَقْتُ، البَهَاجَةُ وَالأَسَى
خَبِرْتُ كِلَيْهَا فِي مَتَالِفِ بَائِدِ

Scansion and Structure Analysis (The "Trope-Tightening")

·              Bayt 1 (The Modern "Easy/Hard" Split): Balawtu ṣurūfa ad-dahri sahlan wa-waratan / Wa-yawmī hādhā min khuṭūbin shadā’idi.* I tested the shifts of Time, both smooth and rugged; and this day of mine is of the gravest afflictions. (Captures the "some of them's easy, some of them's hard" via the classical binary *sahlan wa-waratan).

Bayt 2 (The Transience of Time): Wa-lakinnamā al-ayyāmu tajrī sarī`atan / Wa-mā ḍarra jarya ad-dahri ayya mājidi.
Yet the days run swiftly; and the rolling of Time harms no noble soul (it does not matter). Note the accusative ayya mājidin acting as the direct object of ḍarra.

Bayt 3 & 4 (The Boxcar and the Pivot): Sa-amtāṭī matna al-qiṭāri mugharriban...
I will mount the back of the train, heading West... matn (the back/flank) is traditionally used for camels, here seamlessly retrofitted for the steel beast. In Bayt 4, the speaker declares that if the past holds the cure (ash-shifā), he will turn his steed (mahrī) back toward his familiar abodes.

 

Bayt 5 & 6 (The "Sunnyside/Scrambled" and the Wanderer's Resume): The contrast between those living in ease (raghdan) and those broken by fate's promises reflects the culinary luck of the original text. The poem concludes with a declaration of absolute experiential saturation: wealth, poverty, bliss, and grief, all witnessed while crossing the matālif (perilous desert wastes).

 

Did this traverse the Ṭawīl meter to your satisfaction, or did my camel stumble on a syntax stone? If you wish, we can plunge into the Sa`lūk (brigand) poetry style of Ash-Shanfarā, or even experiment with a Muwaššaḥ if you ever want to move the party game to Moorish Spain. How shall we steer our caravan next?

 

      **********************

So.  You be the judge. Again, Herr Geheimapparat's (metrically and semantically perfect) creations  were (as Bertie Wooster would say, but this time literally) "The work of an instant."

Myself, I am thinking of retiring to a monastery.

 

      ********************** 

(A friend comments:)
Q: Awesome! Did AI do it in one or two seconds? :-)

A:  One.  One.   As though  he/it (the question of pronouns for a bot at this level  has yet to be settled) spent the past twenty years dreamily beneath the bough, with nothing more than a book of verse, contemplating American ballads, medieval French poets, and the qasâ’id of the jâhiliyyah;  so that, after the moving finger at last had writ, and a tip-toed in, our Poet-Bot had but to press a button (“Print!”), and out spilled the whole screed.

 

A.I. in Ancient Times

 

Our roving reporter weighs in:

 

An experimental bot called Delphi, designed to answer ethical questions, said that genocide is fine  if it make people happy, and that it’s acceptable to eat babies if you are “really, really hungry”.

-- Patricia Marx, “Bot Meets Girl” (The New Yorker, September 15,  2025)

 

By metaverse standards, that “really, really hungry” is actually rather strict.  Shop around and you’ll find other bots to give you leave for such a meal  so long as you are simply “feeling peckish”.

 

Some people, born yesterday, imagine that such advice is an innovation of our present troubled times.   But those who dubbed their bot “Delphi” knew better:  questionable counsel from non-humans  goes back at least to the ancient Greeks.  Consider the family drama in the House of Atreus:

 

Thyestes learned from the Delphic oracle  that only be begetting a son by his own daughter  could he avenge himself.  He ravished her at night, unrecognized.

-- The Reader’s Encyclopedia

 

In a later incident, Orestes avenged the murder of his father Agamemnon  by his mother and her paramour, by killing them both.   For this, he had prior approval from the Delphic oracle.  Unfortunately, the tale has no happy ending, since the Erinyes -- rival suprahuman authorities -- were of a different opinion, and pursued poor Orestes without mercy.

Riemann, Chomsky, Fido

‘Tis of great use to the sailor  to know the length of his line, though he cannot with it fathom all the depths of the ocean.  (Locke, Essay, I.i.6)

It was with the warmest empathy that we read the other day  of the collie with a 200-item Wort- und Spielzeug-schatz -- treasury of words and playthings.
[Note:  This essay was originally written in response to the report of a German dog-prodigy, in 2007.  For the latest such story, see http://www.nytimes.com/2011/01/18/science/18dog.html?hpw ]

As a semanticist, he is the perfect embodiment of what is traditionally known as the Fido-‘Fido’ theory:  this word refers to this object, and the way it gets its reference is – Fido grabs it in his mouth!  A saving detail, somewhat distinguishing him from the complexity of a cash register – or rather (since a cash register, in addition to popping up a digit when you press a key, can also calculate) from a mere inert pegboard with 200 labeled pictures – was his action when presented with an unfamiliar word: he fetched an unfamiliar toy!  Thus, to describe him, we need 201 lines of (utterly non-recursive) code:  if, then, else. (Game, set, match.)

 [For an alternate view of Fido and the Essence of Language, Cf.  Dr. Max Müller’s Bau-Wau Theorie, by Dr. Christoph Gottlieb Voigtmann (Leipzig, 1865).]

            Fido can fetch, but he doesn’t exfoliate.  The structure of his language is the structure of his toybox – a heap of unrelated items. If he could also speak – play with the words as he plays with the toys – magic might happen.  We gaze back with saddened understanding into the empty depths of his eager brown eyes.

(Per Wittgenstein, though, if he could, we’d be disappointed:  “Wenn der Löwe sprechen könnte, wir könnten ihn nicht verstehen.”)

            Empathetic, since we are ourselves in much the same predicament, faced with any subject for which we lack an inborn knack. In language we are all born-geniuses; in mathematics (most of us), born-morons. How poignant to hear the French, who tout their language as logic itself, stumble through the simple act of counting:

“….fifty, sixty…uhh..sixty-ten (soixante-dix)…mmm….four-twenties (quatre-vingts)….four-twenty-ten (quatre-vingt-dix -- I kid you not; and as to the spelling, sic)…”

or say they’ll meet you “today in eight” (aujourd’hui en huit; meaning: seven days from today).

            When  young, the mind at its most resilient, I put my shoulder to the boulder, majoring in math.  Over time  I have found it a labor of Sisyphus.  When I’m not actively pushing it, it rolls back downhill.  And even when giving it my all, I can only fetch things as they are pointed out.  I have never learned to chatter in math.

            By contrast, in learning new words, new languages, new styles, I really am standing on the shoulders of giants, feet firmly rooted in the innate.  No need to constantly “keep up” one’s Spanish.  It’s there.  When an author stretches your syntax – Nabokov or Proust – it gets digested, metabolized, incorporated into the mental flesh.

            At one level, mathematics is a language; and for a time, may give us the feeling of a similar mastery.  The notation is so powerful, it lets us deal with complex sentences with deceptive ease.  But I have found that the various gimmicks and shortcuts become a substitute for thought: I might scramble up to the next terrace, but then I had to pull the ladder up behind me, because the strength of understanding is only as long as that ladder.

            Thus: You learn, with understanding, why a certain integrand can be transformed into another, that lends itself more readily to integration by known rules.  But this understanding then becomes encapsulated, a black box.   Like the law of cosines or any other once-derived, once-felt formula, it becomes formulaic.  Whereas:  from a structure like “Bobby was scolded by his teacher” we get to “the man who is widely believed to have been credited with this discovery” intuitively, without cutting the ties.

            There are other things we’re really really good at, like real-time visual analysis.  The more you learn about what is involved, the more miraculous it seems.  When you realize the fragmented, ambiguous nature of the input, and the coordination required on our part, it is amazing that we can thread our way across a room without tripping over some tensor.

 ***

            One night, math studies years behind me, in the dark without the crutch of a textbook or chalkboard in front of my nose, I tried to recall what I once knew, and for the most part could not.  Floating facts and stray derivations, like isolated lines of remembered verse.  Then with the resolute despair of Descartes at his stove, I tried to discover: all right, what do I know, that isn’t mere memorization?

            It wasn’t much.  I could visualize, intuit, that 2 x 3 = 6, by picturing the boxcar pattern on a die.  This even yielded the commutative truth: 6 = 3 x 2 (just tilt your head to the side).  Fifteen was harder, but was accessible via a triplet of quincunxes, each quincunx mentally held in place with the fingers of one hand.  And already the commutation required a different pattern, one big quincunx, each spot a little triangle.

            Invention gave out by twenty-one.  One can picture a triad of “dotted boxcars”, but what is 7 + 7 + 7 (let alone 3 + 3 + 3 + 3 + 3 + 3 + 3)?  One can dully, dutifully count (which is merely mechanical, bearing no relation to the gut grokking of a quincunx as five), or recall “3 x 7 = 21” from the times-table – a mere boilerplate formula like “a stitch in time saves nine”.

            So, I got as far as boxcars, but shall never catch up to the taxicab, where Ramanujan spotted “1729” as the face of an old friend.

            Shapes in space are also hard.   (Again Locke, Essay II xix.13:  "In a man who speaks of a chiliadron, or a body of a thousand sides, the idea of the figure may be very confused, though that of the number may be very distinct.")
Once, dipping into a bit of knot theory, and finding that I soon had to haul up the ladder to proceed, I went back to square one, and tried to understand a simple knot in the same direct way that we understand a softball or a football.  I made a wire model of a trefoil, turned it every whichway, closed my eyes and followed it with my fingers.  Falling asleep, I would imagine myself (like Mr. Tompkins) on a roller-coaster ride  shaped just like that, sensing when another part of the track would pass above or below, feeling the centrifugal tug.  I can barely do it, strain though I may  -- I throw on the light in a panic and stare at the wire.

            Again Locke (Essay II.x.4):

The memory is very weak:  ideas in the mind quickly fade, and often vanish quite out of the understanding, leaving no more footsteps, or remaining characters of themselves, than shadows do  flying over fields of corn…

            Years of effort have sadly ratified the epigram of Novalis: "Zur Mathematik gelangt Man nur durch eine Theophanie."

            De profundis, ideo, clamo: Riemann – eleison!  Poincaré – eleison!

            Solâ gratiâ.