ATD 615-643

Revision as of 18:51, 2 September 2010 by Bangorang (Talk | contribs) (Page 636)


Page 615

German: letter of credit.

Page 616

Building housing auditoriums (and in this case a library).

Riemann's Habilitationsschrift
In Germany a new faculty member presents a lecture or, in this case, a thesis on taking up office.
Riemann's lecture, On the Hypotheses that Lie at the Foundation of Geometry, delivered on June 10, 1854. It became a classic of mathematics.

In particular, it provided the mathematical concepts used later by Einstein to formulate his General Theory of Relativity, in which our actual physical space and time are seen to be curved by the action of gravity. Riemann's modern reputation as a "prophetic physicist" thus rests on this lecture. Wikipedia

The Habilitation is actually a formal process for giving a person the right to teach university courses independently (i.e. without a formal assignment) and supervise doctoral candidates. This right is usually referred to as venia docendi or venia legendi in Germany. The process consists of delivering a thesis (Habilitationsschrift) and giving a lecture.

the 1859 paper on primes
In August 1859 Riemann presented a paper, On the Number of Prime Numbers Less Than a Given Quantity, to the Berlin Academy of Science. In the middle of that paper he made what later was called the Riemann Hypothesis (Cf page 496:conjecture). Today, after nearly 150 years of careful research and exhaustive study, it remains unproved.

German: the "aha" phenomenon.

Tchetvyortoye Izmereniye
Today more likely transliterated Chetvertoe izmerenie. Russian: (the) fourth dimension.

"Yob tvoyu mat'"
Russian: Fuck your mother. It's as impolite as it looks, but used way more often than in English.

A splinter Bolshevik faction. The name comes from the noun otzyv meaning "recall"; it does not mean "god-builders." The group (existing under this name only in 1908-9) demanded the recall of Social Democrats from the national legislature.

Vladimir Ilyich Ulyanov aka Lenin (1870-1924), Russian revolutionary and founder of Bolshevism and the major force behind the October Revolution, 1917. He studied law at Kazan University but only practiced law for a couple of years before becoming a professional revolutionary. He was arrested in 1895 for his opinions and activities, and was exiled to Siberia in 1897 for three years. At the end of his exile he went to Switzerland in 1900 and became the leader of the Bolsheviks in 1903, and returned to Russia in 1905 during the 1905 Revolution. He left Russia in 1907 and only returned in April, 1917 with Germany's connivance. Lenin inaugurated the dictatorship of the proletariat after the October Revolution. He died on January 21, 1924 and became the demi-god of the Soviet Union. According to Chambers Biographical Dictionary (1988) Lenin was "shrewd, dynamic, im[placable, pedantic, opportunist, as ice-cold in his economic reasoning as in his impersonal political hatreds that could encompass millions. . . . He inspired in the name of democracy a despotism boundless in the power of its ambition and sense of destiny.

Commonly called Bolsheviks. At the Second Congress of the Russia's Social Democratic Labor Party in August, 1903 there was a dispute between Lenin and Martov, two of the party's leaders. Lenin argued for a small party of highly disciplined, centralized and dedicated professional revolutionary elites with a large fringe of non-party sympathizers and supporters. Martov disagreed believing it was better to have a mass party of activists. At the end of the debate Lenin won a narrow victory: 28 to 23 (the only time in the party history up to then Lenin had a majority behind him). From then on, the Party was split into Lenin's faction called themselves Bolsheviks (majority) and Martov's faction known as Mensheviks (minority). The split became permanent as both groups' policy and practice diverged more and more. In 1912, Lenin's Bolsheviks faction formed a separate Social Democratic Labor Party (Bolsheviks) which in 1918, after they came to power, changed its name to All-Russian Communist Party (Bolsheviks). It finally became Communist Party of Soviet Union in 1952 which was dissolved in 1991.

Marxism belongs to the materialist [1] strain of the Western philosophical tradition, stating that the only objective reality is matter. The orthodox Marxist doctrine is divided into historical materialism (which claims that changes of society and even the non-material "superstructure" are determined by economical processes, and thus materially caused); and dialectical materialism, proposed by Engels and then Lenin, which is basically a philosophy of nature combined with a rather crude gnoseology. The latter maintains that matter is the only substance and it is inherently and objectively dialectical in nature, i.e. it is in constant development due to the interactions of conflicting forces on all levels. An anti-Materialist (like Mach, who was denounced as a "subjective Idealist") is one who is against such belief.

Austrian physicist and philosopher. A strong critic of Newtonian absolute time and absolute space. Cf page 412:Ernst Mach (1838-1916). He was the target of Lenin's attack in his best-known attempt to create a Marxist philosophy (in the technical sense), Materialism and Empiriocriticism.

Russian mystic and author of The Fourth Dimension. Cf page 602:Young Ouspensky (1878-1947).

Page 617

above this galley-slave repetition of days
ATD motif i.e. rebel against the quotidian day.

the already seen
. . . which we know better under the French term déjà vu.

Staring at the wallpaper.
A parallel to Kovalevskaya, whose father used Ostrogradsky notes to cover the walls. Cf page 500:Sofia Kovalevskaia and wiki.

I couldn't get away with only one plane...
Riemann surface of the log function

Yashmeen was trying to visualize the Riemann surface of a complex function, which details how the function transforms its 2D input (i.e. argument) to its 2D output (i.e. function). Presumably, reading Riemann's geometric works (Cf previous page) would help her understand how to correctly do this.

i, j, and k, the unit vectors
Cf page 526:Gibbsian Vectors.

Page 618

Plural of Schnitt. German: cuts.

cuts ... sheets
Referring to the picture on the right, the horizontal planes are called "sheets". The transitions are called "cuts". This is because the picture can be constructed by taking multiple planes, cutting them, and then glueing the edges of the cuts to connect the planes.

Also consider cuts in films as viewed by a film editor (God?). What appear to the viewer as scene changes in time appear to the editor as segments of film glued together in space.

multiply-connected spaces
In topology, geometrical objects or spaces that are connected but not simply connected are called multiply-connected spaces.
A geometrical object or space is simply connected if it consists of one piece and doesn't have any "holes" that pass all the way through it. For example, balls and planes are simply connected since they have no holes. Neither a donut nor a coffee cup with handle is simply connected, and so both are multiply connected.
Also see Wikipedia for a fine, relatively nontechnical explanation.
Sea-ice and Venice were described as multiply connected spaces on p. 136.

'vector space'
In mathematics, a vector space is a collection of objects, vectors, that may be scaled and added.

That's when it really...
A Riemann surface (e.g. the picture to the right on the previous page) is a 2D Riemannian manifold. In a 3D Riemannian manifold (what Yashmeen saw), the multiple connected 2D planes are replaced with multiple 3D spaces. One can sympathize with her discomfort.

space of higher dimensionality
Hypersphere. A four-dimensional hypersphere is currently considered the possible shape of our universe. (A 4-D hypersphere is to a 3-D sphere, what a 3-D sphere is to a circle.) In mathematics,
Hypersphere can be n-dimensional with n = 4 and greater. Also see Hypersphere of Wiki Entry.

Cf Riemann's Habilitationsschrift on p. 616

Russian: nothing, "it doesn't matter".

if it doesn't work with gold, the next step will be lead
Cowboy alchemy. If you can't settle your dispute with money, you will have to shoot it out. There's a reference to this process on page 105.

it's this damned English practice of talking in code
Refers to commonly noted English cultural tendency to avoid direct expression in conversation.

the Anglo-Russian Entente
The Britain and Russia settled a number of differences in Asia. And with both countries concerned about Germany but friendly with France they concluded the Anglo-Russian Entente on August 31, 1907, in St. Petersburg. It defined their respective spheres of interest in Persia, Afghanistan and Tibet, with Russia taking the northern areas of Persia and Britain taking the Persian Gulf area in the south. Its primary aim was to keep Germany out of that region.

Page 619

German: tavern, beer hall.

Page 620

In AtD the plural akousmata occurs more often. Look it up in the alphabetical "A" page.

From Greek: image, picture.

minié ball
Rifle bullet with a conical head used in muzzle-loading firearms. See the fuller annotation on p. 101.

A steel-gray hard ductile metallic element with a high melting point that occurs widely in combined form, is highly resistant to corrosion, and is used especially in alloys and in refractories and ceramics.
Zirconium is often confused with zircon and even more often with zirconia. Zircon is a gemstone consisting chiefly of zirconium silicate. Zirconia is the oxide of zirconium. "Cubic zirconia" became a popular surrogate gem a couple of decades ago.


Page 621

Reckon yo tengo que get el fuck out of aquí
Macaronic Spanish/English: Reckon I'd better get the fuck out of here.
Kit said the same thing when he decided to leave Yale (page 318).

Zum Mickifest! Komm, komm!
German: To the Mickey party, come, come! "Mickey Finn" = knockout drops such as chloral hydrate (see any film noir).

German: K.O. (= knockout) drops.

Page 622

Group-theoretical implications
Introductions to group theory often use "symmetry under rotation" as an illustration. You can rotate a square 90 degrees and get the same square, and likewise 180 and 270 degrees, so the square has fourfold symmetry. Here Gottlob applies a similar concept to the printed words pun and und, which alternate with every 180 degree rotation.

a whistling or snoring sound heard on auscultation of the chest when the air channels are partly obstructed.

Gottlob! Wo ist deine Spritze?
German: Gottlob, where is your syringe?

"Streng reserviert für den Elefanten!"
German: Strictly reserved for the elephant (not elephants).

Page 623

a bitter poisonous alkaloid that is obtained from nux vomica and related plants, and is used as a poison (as for rodents) and medicinally as a stimulant of the central nervous system.

Noncommutative . . . Asymmetric
A relation like "cures" is commutative if "A cures B" implies that "B cures A" and vice versa. Here the situation is fuzzier because a total cure is not at issue: "Chloral alleviates the effects of strychnine" and "Strychnine alleviates the effects of chloral" are both true, so noncommutative doesn't quite apply, but one is more true than the other, so asymmetric is a better choice of word.

Verfluchte cowboy!
German: Damn cowboy! (should be Verfluchter Cowboy)

Achtung, Schwester!
German: Hey, Nurse!

German: nut factory. (Er hat einen Klaps means "He's nutty"; Mühle is a mill.)

one of his canonical outfits
"Canonicals" is a term for priestly vestments.
But also, in the psychology of perception, means 'typical' or 'most easily recognised as'

Dr. Willi Dingkopf
German: Thinghead. Possibly, given other meanings of "thing", Dickhead.

Page 624

Kit: '...You just hit me with, with that stick?'
This scene was revealed earlier in the book on page 596: "This is the world, Kit reflected, a couple nights later, around 3 A.M., as an extra smack of the bamboo stick, She is the world."


you are not also Hebraic
Anti-Semitic Dingkopf considered Kit Jewish by his name Traverse.

Jew Cantor, the Beast of Halle, . . . to demolish the very foundations of mathematics
Greg Cantor (1845-1918) taught mathematics at University of Halle from 1869-1918. (Cf page 593:Greg Cantor). He introduced the concepts of infinity and continuum into mathematics and thus brought about one of mathematical crises mentioned on page 594. (Cf page 594:crisis in mathematics).
Dingkopf regarded Greg Cantor Jewish by his name Cantor.

Page 625

"Cantor is a practicing Lutheran." "With a name like that? Please."
Dingkopf hears the name and obsessively thinks of the many Polish Jewish families that bear it. But the connection is not as strong as he surmises: The church of St. Thomas (Thomaskirche) in Leipzig had a staff member called Cantor or Kantor, and noted practicing Lutheran Johann Sebastian Bach held the position in his prime years. Cantor/Lutheran is not an absurdity.

Cantor just means singer in Latin, and it has been used for persons who have a singing part in both Jewish and Christian (and possibly other) rites.

"Dr Hilbert . . ." "Dr. . . . David Hilbert"
Cf page324:David Hilbet (1862-1943), a German mathematician. Again, Dingkopf regarded him as Jewish because of his name, David.

German: colony, compound.

The principles of this (apparently) fictional school of design bring to mind Buckminster Fuller's concept of ephemeralization, which notes that as design and technology improve -- "the more rationally a structure was designed" -- the more that can be done with less, process waste converges toward zero and things become physically smaller, "less the point" -- the "Penultimate Term" -- of being all but invisible. A simple example, the telephone cord is quickly disappearing as we go to cordless phones, and transistors "grow" smaller and smaller as a corollary to Moore's law. The principle of ephemeralization can be applied to design, construction, transportation, computer and other technologies and tools.

into its own metastructure
A German SAP engineer once explained "we control complexity through abstraction."

one is left with only traces in the world, a few tangles of barbed wire
The Invisibilist principles are paramorphosized into a future of kolonies where only the barbed wire outlines are visible. Within the context of antisemitism in the preceding paragraphs, the text is moving from kolonies to concentration camps, concentration camps empty perhaps except for the traces of consciousness remaining, outlined in barbed wire, the plan-view of, not the Penultimate Term, but the Final Solution.

certain odors
cf. p. 408 This has less to do with Proust and involutary memory than with "perhaps certain odors[Italicized in the original] steming from a few tangles of barbed wire upwind, a wind "which itself possesses now the same index of refracton as the departed Structure..." As is explained to Kit by someone in a guard's uniform who may not actually be a guard. That certain odor seems to be the odor of smoke from the ovens.

refraction index
Among other things a refraction index can be used to measure concentration (camps) and confirm purity (ethnic).

someone . . . whom Kit . . . assumed was a guard
Error in grammar by Pynchon or, more charitably, introduced by a copy editor. Punctuating as someone who/whom (Kit assumed) was a guard makes the choice of pronoun clearer. Alternatively: did Kit assume someone? No, he assumed a proposition about someone: someone was a guard. When the subject of that is transformed to "who/whom" for the purpose of linking it into the sentence, it remains the subject: who was a guard.
A quibble over a fine point? Yes, but Pynchon is renowned for his fine points, and this mistake seems to put him on a level with a news intern at a third-tier TV station. So let's consider this a teaching moment: Copy editors, don't impose your ignorance on good writers.

So Gut Wie Neu
German: as good as new.

Dirigible Field
The inmates' occupational therapy is a disguise for constructing this landing facility.

a real Dirigible
The inmates have established a cargo cult Wikipedia article or a UFO cult.

Sounds like an echo and/or parody of the "He Who Must Come" material on page 543. Both are in close proximity to the name Richard Strauss.

German doof means comically stupid (possibly an origin of English "doofus").

Or maybe a version of "Tiefland" [2], the 1903 Eugen d'Albert opera which was turned into a film directed by Leni Riefenstahl [3]. The latter, which began filming in 1940 and wasn't released until 1954, turned out to be the most expensive b&w film made in Nazi Germany. Additional notoriety for the film comes from Riefenstahl's having used Roma and Stinti extras who were being held in Nazi collection camps, so-called "Zigeunerlager."

O Tempora, O Mores
Latin: Oh, the times! Oh, the customs! (Was there really music under this title?)

Famous sentence by Cicero in his First Oration against Catiline, which means Oh the times! Oh the morals! In his opening speech against Catiline, who had previously tried to kill him, Cicero deplores the viciousness and corruption of his age. This sentence is now used as an exclamation to criticize present-day attitudes and trends, often jokingly. So, it is, indeed, an "old favorite"

The Black Whale of Askalon
"Im Schwarzen Walfisch zu Askalon," comic song. The "Black Whale" is a tavern in the ancient Persian town of Askalon. A paraphrase of the lyrics.

Page 626

the head of Jochanaan
In Strauss' opera Salome the title character asks for and receives as tribute John the Baptist's head on a platter. John in the opera is called Jochanaan.

Richard Strauss's opera Salome
Cf page 498:Richard Struass's one-act opera Salome was performed first time in Dresden, Germany, on December 9, 1905. It was a sensation of the year 1905. The opera was based on the French play Salomé by Oscar Wilde. The time of action: about 30 A.D.; place of action: Jerusalem . . . for the story see Salome.

the Five Jews
In the middle of the opera Salome five Jews argued concerning the nature of God.

Judeamus igitur, Judenes dum su-hu-mus
German university students used to sing Gaudeamus igitur, juvenes dum sumus ("Then let us be joyful while we are young men"); the melody forms the climax of Brahms' "Academic Festival" overture. Dr. Dingkopf, the Johnny One-Note of anti-Semitism, sings in bastard Latin, "Then let us Jew while we are Jews."

Ich Bin Ein Berliner
JFK said "Ich bin ein Berliner" at the Berlin wall in 1963. According to Wikipedia, there is an urban legend:

Kennedy should have said "Ich bin Berliner" to mean "I am a person from Berlin." By adding the indefinite article ein, his statement implied he was a non-human Berliner, thus "I am a jelly doughnut". The statement was followed by uproarious laughter.

However, Wikipedia goes on to state:
There is no grammatical error in Kennedy's statement; the indefinite article does not change its meaning. In German, the statement of origin "Ich bin ein Brandenburger" (I am a Brandenburger) is more common than "Ich bin Brandenburger" (I am Brandenburger), but both are correct. The article "ein" can be used as a form of emphasis: it implies "just one of many." As Kennedy did stress the "ein", the usage was, according to German linguist Jürgen Eichhoff [1], "not only correct, but the one and only correct way of expressing in German what the President intended to say."

--Btchakir 07:51, 19 December 2006 (PST)

And Kennedy's motto drew tumultuous cheers, not laughter; the Berliners had no trouble understanding what he meant.

Maybe a Simpsons connection as well:[4]

German: pastry shop.

German: powdered sugar.

Page 628

Halfcourt? what kind of a name is that?
This is Dingkopf speaking, in the context of his obsession with Jewish infiltration of British society. "What kind of a name is that?" has the subtext "Is that a Jewish name?"

Der Wall
In German there are at least three words for "wall": Wand (the wall of a room), Mauer (a masonry wall) and Wall (a wall of a fortification). The infamous Berlin Wall was die Mauer.

In this case 'der Wall' means the rampart on which the town wall stood. After this was razed in the 18. century a path was made on top of 'der Wall' along which Yashmeen and Kit take their walk.

dotted quarter rest
Musical notation: brief pause.

Page 629

Likely to be the Hainberg-Gymnasium at Göttingen

A wine from the Rhine-Palatinate region in western Germany.

Three different wines.

do a bunk

Page 630

a Theosophist
an adherent of theosophy professing to achieve a knowledge of God by spiritual ecstasy, direct intuition, or special individual revelation.

Sidney Reilly
Sidney Reilly, aka The Ace of Spies--a real early 20th century British--and other--intelligence agent [5].

Bumpkin; capitalized, it has a different meaning.

Countries of Central Asia (Kazakhstan, Turkestan, etc.). Possible anachronism; term gained currency after the breakup of the Soviet Union.

No anachronism - in many central-asian languages (Pashtu, Dari, Farsi, etc.) '-stan' means 'land of', i.e. Afghanistan = Land of the Afghans, Nuristan = Land of Light, Frankistan = France, Germanistan = Germany, etc.

One Savile Row
Seat of the Royal Geographical Society.

Now called Kashi, a city in the extreme west of China; at the western end of the Taklimakan desert; a principal town of Chinese Turkestan. Kāshi (Kashgar).

Auberon Halfcourt
The name Auberon is derived from Oberon and related to Alberich, the dwarf in Wagner's Ring cycle. Half-court describes a reduced form of basketball. Another possible allusion (bit of a stretch, perhaps?) is to Auberon Herbert, a British libertarian whom Benjamin Tucker described as "a true anarchist in everything but name."

Page 631

the recent Anglo-Russian Entente
Cf page 618:Anglio-Russian Entente of 1907 in which the spheres of influence in inner Asia were divided between Britain and Russia in order to keep Germany out of that region.

Baku and Johannesburg
Cf page 168: Johannesburg; Baku.

One vision . . . spiritual, and the other, capitalist.
Competing visions as to the significance of what lies buried beneath the sands in Central Asia. We have already seen a map that reflects dual visions of the area. The Great Game competition shaping up in Asia is a continuation of a global 'metaphysical' conflict between materialist and integrationist tendencies.

lie doggo
Go underground, maintain a low profile.

Page 632

Museum der Monstrositäten
German: museum of monstrosities. Mathematical monstrosities.

Professor Klein
Felix Klein is best known for his application of group theory (roughly, the theory of symmetry) to geometry called the Erlangen Program. Presumably (I've never seen his math models) his collection would contain elegantly beautiful, crystalline forms, in contrast to the Museum der Monstrositäten.

motor diligence
Motor taxi, as opposed to horse-drawn.

the Brocken
The highest peak (3,750 ft) in the Harz Mountains in Germany. It is about 35 miles northeast of Göttingen. (The Brocken).

Appears in GR where Slothrop and neophyte witch Geli Tripping encounter the Brockengespenst p. 330. and ....

"An older Germany .... Deeper"
Meaning pre-Christian Germany, as referenced earlier in the passage with the description 'witchlike'.

weapons somehow not yet decipherable

Sapo venetus (Venetian soap) or sapo hispanicus (Hispanic soap). Some kind of soap, obviously.

Page 633

Knipfel...von Imbiss
Neither one existed. Imbiss is German: snacks, fast food. *** I have a differing opinion: Knipfel is Jim Knipfel. Thomas Pynchon has read Knipfel's memoirs, enjoyed them, and blurbed them.

Weierstrass Functions
Cf page 589:everywhere continuous but nowhere differentiable.

Russell's Letter
Russell's letter of June 16, 1902. (see below "Poor Frege . . .").

the Set of All Sets That Are Not Members of Themselves
Russell Paradox. Cf page 538:Bertie Russell.

parallax effect
the apparent shift of an object against a background due to a change in observer's position.

Poor Frege . . . about to publish his book . . .
Gottlob Frege (1848-1925) was a German mathematician. He was one of the founders of modern symbolic logic putting forward the view that mathematics is reducible to logic.
In 1893 Frege published his The Basic Laws of Arithmetic, Vol. 1 in which he axiomatized arithmetic with an intuitive collection of axioms. While his The Basic Laws of Arithmetic, Vol. 2 was at the printer, Frege received a letter (June 16, 1902) from Bertrand Russell in which Russell pointed out that the Russell Paradox gave a contradiction in Frege's system of axioms.

German: shit.

Crotona in Magna Grecia
Crotona is the old Latin name of the Italian city Crotone in southern Italy on the Gulf of Taranto. Ancient Crotona was long one of the most flourishing cities of Magna Grecia (Latin for Greater Greece), the area in Southern Italy colonised by Greek settlers in the 8th century BC. Pythagoras went to Crotona at the age of 40 and most of his philosophical activities occurred there.

Hilbeert . . . August . . . in 1900 . . . International Congress . . . "Paris Problems"
Paris Problems = Hilbert's Problems. Cf page 604:the outstanding problems in mathematics.

zone of dual nature
One place that is two places: this peculiar Pynchonian form of bilocation again.

part "real"...part "pictorial" or let us say "fictional"
Complex numbers are made up of a real number and an imaginary number (e.g "one plus the square root of negative one"), as AtD is made up of real and imaginary (fictional) parts, the effect of which (continuing into P.635) is described as "taking one beyond four dimensional environs...out into a timeless region..." This seems to be the goal of the protagonists, the author, and the reader.

Page 634

German: set theory.

one is thrust . . . into a timeless region
Like one of those funhouse rooms where gravity is reversed.

German railway stations all have a big sign: ZU DEN ZÜGEN, to the trains. Here it's to the quaternions.

Not sure about the train connection, it reminded me rather of signs found in zoos or circus sideshows pointing to the major attractions (e.g. "Zu den Löwen" - "[This way] To the lions"). WolfgangFaber 14:35, 11 October 2008 (PDT)

It is puzzling to find Quaternions in the musuem, since they weren't part of the "Crises in Mathematics" at the end of the 19th century. Perhaps Pynchon has placed them here because they were largely superseded by vectors, hence were unloved by most mathematicians, just like the other exhibits. Preterite mathematics.

Nernst light
Light from page 437:Nernst Lamp.

Brougham Bridge
Cf page 561:Brougham Bridge.

complex knife
"part real and part imaginary", and there is a "real" reproduction nearby. These are aides memoires, inspirations--perhaps the dimensions beyond are literally located in imagination, mental spaces.

Sofia Kovalevskaia and . . . Weierstrass
From 1870 Weierstrass was Kovalevskaia's mathematics tutor in Berlin. He gave Kovalevskaia private lessons twice a week for four years. Cf page 500:Weierstrass and Sofia Kovalevskaia.
Here, as on page 500, there is a hint of romantic involvement between the teacher and the student.

Henri Lebesgue (1875-1941) was a French mathematician. He formulated the theory of measure in 1901 and the following year he gave the definition of the Lebesgue integral that generalises the notion of the Riemann integral.

Up to the end of the 19th century, mathematical analysis was limited to continuous functions based largely on the Riemann method of integration. However, in 1902, Lebesgue extended the concept of the area below a curve to include many discontinuous functions and thus generalised the notion of the Riemann integral and revolutionised the integral calculus.

Lebesgue's notorious "surface devoid of tangent planes"
The usual calculus method for computing the area of a surface requires that tangent planes to the surface exist at every point. Although smooth surfaces satisfy this requirement, infinitely rough surfaces, such as a "thoroughly crumpled handkerchief" may not. Lebesgue's integration theory can be used in such cases. See Wikipedia.

. . . everywhere continuous and nowhere differentiable
Cf page 589:everywhere continuous but nowhere differentiable, Weierstrass function and page 594:crisis in mathematics.

Poincare - "Yesterday, if a new function was invented it was to serve some practical end; today they are specially invented only to show up the arguments of our fathers, and they will never have any other use" (Collected Works, v.11, p.130)

Hermite - "I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives."

"She was always my inspiration, you know."
Michael Naumann, German minister of culture, stated somewhere (I've searched everywhere for the actual article-- the repeated report is everywhere but there's no link to the original source) that he assisted Pynchon in his research of Sofia Kovalesvskaia. Naumann said (apparently) that Pynchon's new book would pivot around Kovalesvskaia. While we've heard her name all over the place, it seems clear that rather than transform a historical figure into a fictional one (ala mssrs Mason & Dixon) Pynchon invented Yashmeen Halfcourt to play that role. The quote here, while a simple statement by Yashmeen, is also a fairly explicit fourth-wall breach. (Considering the last line of this chapter, this whole visit to the Museum der Monstrositäten is a fairly unusual authorial Hitchcockian walk-on for TRP.)

Page 635

The Kaiser now seeks in Mexico . . . opportunities for mischief toward the U.S.
Now and for years to come: America's entry into World War One was spurred in part by the Kaiser's offer to return part of the Southwest to Mexico.

German: one who shits raisins. More commonly "Korinthenkacker", insulting term for a very pedantic person.

a world line...never travel
A world line is a tensor, a four-dimensional vector through space and time, therefore a history. Here Gunther is describing the closing off of his future possibilities. In quantum theory observation causes possible states to 'collapse' into one measured state; hence, the past observed from the present is deterministic (it has only one possible state), but the present observed from the past has many possible states until our actions cause it to collapse into one state. Our actions will then be seen to have been inevitable, a world line [6]. Hence: "Ach, das Schiksal".

Ach, das Schicksal
German: ah, fate.

chloral to coffee
A depressant to a stimulant, antipodal (opposite) effects on neuronal function.

that terrible ecstasy known to result from unmediated observation of the beautiful
Cf. Rilke, First Duino Elegy: "For beauty is nothing but the beginning of terror, that we are still able to bear, and we revere it so, because it calmly disdains to destroy us. Every Angel is terror."
Rilke features strongly in V and GR (with Weissmann/Blicero). The idea that 'the sublime' involves an element of terror is fundamental to Romanticism.

May also be an allusion to what is known as "Stendhal Syndrome" [7], a psychosomatic illness that causes rapid heartbeat, dizziness, confusion and even hallucinations when an individual is exposed to art, usually when the art is particularly 'beautiful' or a large amount of art is in a single place. The term can also be used to describe a similar reaction to a surfeit of choice in other circumstances, e.g. when confronted with immense beauty in the natural world. It is said that a lot of tourists who visit Florence and Venice experience it.

They moved along in regret...departures...from...mathematical study
In 1964 Thomas Pynchon applied to the graduate program of the Mathematics Department of UC Berkeley and was rejected (Wikipedia). He subsequently pursued a career solely as a writer.

Page 636

The preceding sections are a concise, riotous, poignant summary of life at an institute of higher learning; students and to some extent faculty are, notoriously, children at play. Yashmeen, Kit and Gunther are graduating, without diplomas but going out of the hothouse atmosphere of the University into the "real world". But given the preceding 5 pages, how real is that?
But this is not so much about the University as about 'the Museum' on the Brocken, and the issue is really who is speaking. Who would feel qualified to call them 'children'? They're in a 'strange, underground temple' and the Brocken is an ancient, magical place. Associated especially with witches and 'the Spectre of the Brocken', an aerial phenomenon that resembles a human figure (actually the shadow of the viewer on the mist).

The next time you visit...
The University never looks the same after graduation; also, nothing ever does: Heraclitus' dictum that no man ever steps in the same river twice. Time (pace Proust) cannot be reclaimed (even if you can find the tesseract's entrance again)because even if you go back in time, you are not the same person you were; you have been changed by experience.
Again, it's 'the Museum' that's closing. This isn't the Museum of Professor Klein at the University, mentioned on p. 632, it's a 'nocturnal equivalent' out on the Brocken.

the cornerstone of the building is ... a tesseract

3D Projection of a Rotating Tesseract

A tesseract is a four dimensional cube. You can construct a cube in 3-space by connecting the corresponding vertices of two identical squares, each in a separate plane. You can construct a tesseract in 4-space by connecting the corresponding vertices of two identical cubes, each in its own separate 3-space. So a tesseract is an embodiment of bilocation. The picture to the right is the perspective projection into 3-space of a tesseract spinning (click the enlarge button) in 4-space. The two cubes are identical, but appear different-sized due to perspective.

Since the building is constructed from tesseracts, fictionally it can exist in different locations and at different times.

"You know who I am."
Cf. Leonard Cohen:

"You know who I am, you've stared at the sun. I am the one who loves changing from nothing to one."

Some sort of god of mathematics, the curator of the museum? The Spectre of the Brocken (seen by Slothrop and Geli in GR)? Rilke's angel, the terrible ecstasy referred to on p. 635? All three?

Another possibility: the author. After all, the characters are his 'children', his creations. And in a fiction, the author is God. The Museum that he's closing isn't only a museum of mathematics, it's a musuem of narratives about mathematics.

Bravo! Pynchon is speaking to the reader as well as his characters. He is closing his Museum of Monstrous Mathematical Metaphors for now.

Seems too pat to me. Everything can be metafictional or self-referential medium-is-the-message if you look at it from that perspective. Why not just say it's a disembodied voice that calls to mind a "price check on prune juice"-type intercom or loudspeaker annoucement of closing time. It's from the 4th dimension, after all. Thus part and parcel of the high-tech (even holographic) exhibits on display in this museum (from the future?)

Page 637

caldo tlapeno
Mexican chicken vegetable soup.

Tampico means "the place of the otters". As a city, it is Mexico's second most important commercial port along the Gulf of Mexico, is located on the southeastern tip of Tamaulipas. The State of Tamaulipas is on the northeast side of Mexico directly south of Texas; but Tampico is about 300 miles from the US border.

Chiapas is a poor and largely agricultural stat in the southeast of Mexico. It is best known for its 1994 Zapatista movement.

"El Atildado"
Spanish: the neat man. But it also suggests "the man marked with a tilde" (see page 600). When reading this passage aloud, think about how to stress the word "also" in "a gift Günther von Quassel had also been blessed with."

(In mathematical notation, the tilde "~" means "approximately" or "is proportional to," depending on country.)

Page 638

German: beans

As Gunther says, a variety of coffee bean, large in size, grown in Mexico and Central America [8].

Not only a brand of coffee, but a method of preparation also known as "Cowboy Coffee" similar to Turkish/Greek coffee in one boils the grounds in the water [9]. Synonymous here with "plain old, unfancified coffee"--perhaps a swipe at 21st century coffee gourmets and at Starbucks. Another paramorphic-mirror image of the early 21st century in the early 20th.
Cowhands expected their coffee to be ‘brown gargle”, hot, black, strong and thick enough to float a six shooter in.
It's really, really hard to equate cowboy coffee to Greek coffee. Greek (Turkish, Serbian) coffee is made from beans ground to powder and boiled for a few seconds, usually in sugar syrup. Grounds in the cup are a virtue. Cowboy coffee starts as coarse grounds, which are boiled for several minutes (or, heaven help us, longer) and often "refined" with eggshells, which cause the grounds to settle out.

Perhaps as in pistolero; i.e. a barrista.

more likely translates as "coffee man"

el otro lado
Spanish: the other side (in one sense or other).

bucket shop
A stock swindle, in which one set of trades is reported to the customer, while the brokerage is really using the money in other, usually riskier trades ("bucketing"). A place where the public could bet on the daily motions of stock prices before 1929 and before the advent of instant stock quotes via the Internet.

Given the year, this may be related to the Panic of 1907. Steve/Ramon bought stocks on margin and when they went south he was slammed.

Probably = indulging in flimflam (fraud, swindles)

north wind.

Plaza de Toros
A bullring.

[S]louching away into the yellow opacity, he invited them all up to a wingding [...] that evening.

Compare with T.S. Eliot's Love Song of J. Alfred Prufrock:

The yellow smoke that rubs its muzzle on the window-panes

Licked its tongue into the corners of the evening

remy 09:52, 28 December 2006 (PST)

Page 639

Rio Bravo
Mexican name for the river known in the US as the Rio Grande.

Ramos gin fizzes
The original Ramos gin fizz was invented in the 1880s by Henry C. Ramos, in his bar at Meyer's Restaurant, this is one of New Orleans' most famous drinks.

jungles of Tehuantepec
Jungles of The Isthmus of Tehuantepec in Mexico. The isthmus represents the shortest distance between the Gulf of Mexico and the Pacific Ocean.

unnatural boom
Another paramorphic mirroring of the 21st/20th centuries; tech stock boom/bust of ~2000.

Cf page 168: Baku.


adios chingamadre
Spanish: goodbye, motherfucker.

Page 640

In Norse mythology the Valkyries are minor female deities.

Mondragón semiautomatics
A self-loading rifle designed and patented by Mexican General Mondragón in 1896 — so it was only 10 years ago. It's magazine capacity was of 8-round or 10-round box, or later 30-round drum (for German service). For a picture of the refined 1908 model and its 1907 patent see Mondgragón M1908 rifle.

An American magazine-fed, bolt-action rifle. See Springfield.

Schnecken rigs
A possible anachronism, but it is hard to be sure. The German word Schnecken in the small-arms context (Schneckenmagazin) refers to what's called a "cylindrical magazine" in English. The best-known weapon using this magazine is the Russian PP-19 Bison submachine gun, but the Bison is based in part on Kalashnikov technology and hence could not have been developed until after World War II. The definitive online information on the Bison not only identifies it as using the Schneckenmagazin but also contains excellent cutaway drawings of the "helical feed" system; use your browser's search function to find the word Bison. This page has a photo and specs in English. The Schnecken rig is definitely not the drum magazine used with the American Thompson submachine gun in the 1920s.

Opponents of the dictatorship of Porfirio Diaz, hence left wing. Eventually, ten years later, to become the Mexican Revolution led by Pancho Villa and Emiliano Zapata.

the Pánuco
Río Pánuco, a river in Veracruz state, east-central Mexico. It is formed by the junction of the Moctezuma and Tamuín rivers on the San Luis Potosí-Veracruz state line, the Pánuco meanders generally east-northeastward past the town of Pánuco to the Gulf of Mexico about 6 miles below Tampico.

Page 641

Mondragóns will get you through
Echoes the wonderful 1970s slogan "Dope will get you through times of no money better than money will get you through times of no dope."

Coin with a portrait of Miguel Hidalgo (1753 – 1811), hero of the Mexican war of independence against Spain.

este . . . perdón
this . . . sorry

Page 642

La Fotinga Huasteca
Fotinga is Spanish: jalopy. Huasteca is a region of the Sierra Madre Oriental north of San Luis Potosí. A local equivalent to "Tijuana Taxi"?

Spanish: battery (collection of percussion instruments).

[T]hat dirty li'l back-shootin Bob Ford.
Ford shot notorious outlaw Jesse James in the back on April 3, 1882; Ford himself was shotgunned to death in 1892. The event inspired one Billy Gashade to pen the verse that became the popular folk ballad "Jesse James," recorded by Pete Seeger, Bruce Springsteen, and many others.
bnilsson 01:41, 2 January 2007 (EDT)


eight seconds . . . rodeo
A bull rider must stay aboard for eight seconds to score.

cerverzas Bohemias
Bohemias (brand) beers, a Mexican beer.

Cuervo Extra
Brand of tequila.

José Cuervo is a well-known brand of tequila; the wikipedia does not mention Extra but Especial.

Page 643

Spanish: frontier.

Ambushed, betrayed.

Repeating-bolt-action rifles designed by the Norwegians Ole Krag and Erik Jorgensen in late 19th century (1886). From 1892 Krag-Jorgensens were used by the United States army as standard arms. And now it is a popular collector item.

Ciudad Juárez, or simply Juárez, is a city in the Mexican state of Chihuahua. It stands on the Rio Grande across the border from El Paso, Texas. Juárez is the major port of entry and transportation center of north central Mexico.

Vaya con Dios, pendejo
Spanish: Go with God, asshole.

Annotation Index

Part One:
The Light Over the Ranges


Part Two:
Iceland Spar


Part Three:


Part Four:
Against the Day


Part Five:
Rue du Départ


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