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:'''<big>Please keep these annotations SPOILER-FREE by not revealing information from later pages in the novel.</big>'''<p><br>

==Page 615==

'''''Kreditbrief'''''<br>
German: letter of credit.

==Page 616==

'''Auditorienhaus'''<br>
Building housing auditoriums (and in this case a library).

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

'''the 1859 paper on primes'''<br>
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 ''Reimann Hypothesis'' (Cf [[ATD_489-524#Page 496|page 496:conjecture]]). Today, after nearly 150 years of careful research and exhaustive study, it remains unproved.

'''''Achphänomen'''''<br>
German: the "aha" phenomenon.

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

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

'''Otzovists'''<br>
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.

'''Lenin'''<br>
[http://www.bartleby.com/65/le/Lenin-Vl.html 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 inauguraed 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.''

'''Bolshevists'''<br>
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's 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 finnaly became Communist Party of Soviet Union in 1952 which was dissolved in 1991.

'''anti-Materialist'''<br>
Marxism belongs to the materialist [http://en.wikipedia.org/wiki/Materialism] 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.

'''Mach'''<br>
Austrian physcist and philosopher. A strong critic of Newtonian absolute time and absolute space. Cf [[ATD_397-428#Page 412|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''.

'''Ouspensky'''<br>
Russian mystic and author of ''The Fourth Dimension''. Cf [[ATD_588-614#Page 602|page 602:Young Ouspensky]] (1878-1947).

==Page 617==

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

'''the already seen'''<br>
. . . which we know better under the French term ''déjà vu.''

'''Staring at the wallpaper.'''<br>
A parallel to Kovalevskaya, whose father used Ostrogradsky notes to cover 
the walls. Cf [[ATD_489-524#Page 500|page 500:Sofia Kovalevskaia]] and [http://en.wikipedia.org/wiki/Sofia_Kovalevskaia wiki].

'''''i, j,'' and ''k'', the unit vectors'''<br>
Cf [[ATD_525-556#Page 526|page 526:Gibbsian Vectors]].

==Page 618==

'''''Schnitte'''''<br>
Plural of ''Schnitt.'' German: cuts.

'''multiply-connected spaces'''<br>
In topology, geometrical objects or spaces are connected but not simply connected are called multiply-connected spaces. In mathematics, a geometrical object or space is [http://en.wikipedia.org/wiki/Simply-connected simply connected]<br> if it consists of one piece and doesn't have any "holes" that pass all the way through it.<br> For example, neither a doughout nor a coffee cup with handle is simply connected, and so both are [http://mathworld.wolfram.com/MultiplyConnected.html multiply connected]. [http://en.wikipedia.org/wiki/Simply_connected Also see Wikipedia] for a fine, relatively nontechnical explanation. Sea-ice and Venice were described as multiply connected spaces on [[ATD_119-148#Page_136|p. 136.]]

''''vector space''''<br>
In mathematics, a [http://en.wikipedia.org/wiki/Vector_space vector space] is a collection of objects, vectors, that may be scaled and added.

'''space of higher dimensionality'''<br>
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,<br>[http://mathworld.wolfram.com/Hypersphere.html Hypersphere] can be n-dimensional with n = 4 and greater. Also see [http://en.wikipedia.org/wiki/Hypersphere Hypersphere of Wiki Entry].

'''''nichevo'''''<br>
Russian: nothing, "it doesn't matter".

'''if it doesn't work with gold, the next step will be lead'''<br>
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'''<br>
Refers to commonly noted English cultural tendency to avoid direct expression in conversation.

'''the Anglo-Russian Entente'''<br>
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 Guld area in the south. Its primary aim was to keep Germany out of that region.

==Page 619==

'''''Bierstube'''''<br>
German: tavern, beer hall.

==Page 620==

'''''akousmaton'''''<br>
In ''AtD'' the plural ''akousmata'' occurs more often. [[A|Look it up in the alphabetical "A" page.]]

'''eidolon'''<br>
From Greek: image, picture.

'''minié ball'''<br>
Rifle bullet with a conical head used in muzzle-loading firearms. [[ATD_97-118#Page_101|See the fuller annotation on p. 101.]]

'''Zirconium'''<br>
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.<br>
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.

'''galena'''<br>
a bluish-gray cubic mineral with metallic luster consisting of lead sulfide and constituting the principal ore of lead.

==Page 621==

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

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

'''''K.O.-Tropfen'''''<br>
German: K.O. (= knockout) drops.

==Page 622==

'''Group-theoretical implications'''<br>
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.

'''rhonchus'''<br>
a whistling or snoring sound heard on auscultation of the chest when the air channels are partly obstructed.

'''''Gottlob! Wo ist deine Spritze?'''''<br>
German: Gottlob, where is your syringe?

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

==Page 623==

'''strychnine'''<br>
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'''<br>
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!'''''<br>
German: Damn cowboy! (should be ''Verfluchter Cowboy'')

'''''Achtung, Schwester!'''''<br>
German: Hey, Nurse!

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

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

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

==Page 624==

'''''Hebraic'''''<br>
Jewish.

'''you are not ''also Hebraic'''''<br>
Anti-Semetic Dingkopf considered Kit Jewish by his name ''Traverse''.

'''Jew Cantor, the ''Beast of Halle'', . . . to demolish the very foundations of mathermatics'''<br>
Greg Cantor (1845-1918) taught mathematics at University of Halle from 1869-1918. (Cf [[ATD_588-614#Page 593|page 593:Greg Cantor]]). He indtroduced the concepts of infinity and continuum into mathematics and thus brought about one of mathematical crises mentioned on page 594. (Cf [[ATD_588-614#Page 594|page 594:crisis in mathematics]]).<br>
Dingkopf regarded Greg Cantor Jewish by his name ''Cantor''.

==Page 625==

'''"Cantor is a practicing Lutheran." "With a name like that? Please."<br>
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.

'''"Dr Hilbert . . ."  "Dr. . . . ''David'' Hilbert"'''<br>
Cf [[ATD_318-335#Page 324|page324:David Hilbet]] (1862-1943), a German mathematician. Again, Dingkopf regarded him as Jewish because of his name, ''David''.

'''''Kolonie'''''<br>
German: colony, compound.

'''Invisibilism'''<br>
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 visible...to 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'''<br>
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'''<br>
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'''<br>
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'''<br>
Among other things a refraction index can be used to measure concentration (camps) and confirm purity (ethnic).


'''someone . . . whom Kit . . . assumed was a guard'''<br>
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.''<br>
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'''''<br>
German: as good as new.

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

'''a real Dirigible'''<br>
The inmates have established a cargo cult [http://en.wikipedia.org/wiki/Cargo_cult Wikipedia article] or a [http://religiousmovements.lib.virginia.edu/nrms/ufos.html UFO cult.]

'''Doofland'''<br>
German ''doof'' means comically stupid (possibly an origin of English "doofus").

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

'''The Black Whale of Askalon'''<br>
"Im Schwarzen Walfisch zu Askalon," comic song. The "Black Whale" is a tavern in the ancient Persian town of Askalon. [http://www.grainger.de/music/songs/schwarzenwalfisch.html A paraphrase of the lyrics.]

==Page 626==

'''the head of Jochanaan'''<br>
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''<br>
Cf [[ATD_489-524#Page 498|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 [http://www.music.lv/opera/Salome/default_E.htm Salome].

'''the Five Jews'''<br>
In the middle of the opera ''Salome'' five Jews argued concerning the nature of God.

'''''Judeamus igitur, Judenes dum su-hu-mus'''''<br>
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'''<br>
JFK said "Ich bin ein Berliner" at the Berlin wall in 1963. According to Wikipedia, there is an urban legend:<br> 
<blockquote>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.</blockquote><br>
However, Wikipedia goes on to state: <br><blockquote>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."</blockquote><br>
--[[User:Btchakir|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:[http://www.anvari.org/fortune/Simpsons_Subtle_Allusions/9.html]

'''''Konditerei'''''<br>
German: pastry shop.

'''''Puderzucker'''''<br>
German: powdered sugar.

==Page 628==

'''Halfcourt? what kind of a name is that?'''<br>
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'''''<br>
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'''<br>
Musical notation: brief pause.

==Page 629==

'''Rheinpfalz'''<br>
A wine from the Rhine-Palatinate region in western Germany.

'''Deidesheimer...Herrgottsacker...Hofstück'''<br>
Three different wines.

'''do a bunk'''<br>
Flee.

==Page 630==

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

'''Sidney Reilly'''<br>
Sidney Reilly, aka The Ace of Spies--a real early 20th century British--and other--intelligence agent [http://en.wikipedia.org/wiki/Sidney_Reilly].

'''hoosier'''<br>
Bumpkin; capitalized, it has a different meaning.

'''stans'''<br>
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'''<br>
Seat of the Royal Geographical Society.

'''Kashgar'''<br>
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. [http://en.wikipedia.org/wiki/Kashgar Kāshi (Kashgar)].

'''Auberon Halfcourt'''<br>
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 [http://en.wikipedia.org/wiki/Auberon_Herbert Auberon Herbert,] a British libertarian whom Benjamin Tucker described as "a true anarchist in everything but name."

==Page 631==

'''the recent Anglo-Russian Entente'''<br>
Cf [[ATD_615-643#Page 618|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'''<br>
Cf [[ATD_149-170#Page_168|page 168: Johannesburg; Baku]].

'''One vision . . . spiritual, and the other, capitalist.'''<br>
Competing visions as to the significance of what lies buried beneath the sands in Central Asia. We have already seen a map that reflects [[ATD 243-272#Page 249|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'''<br>
Go underground, maintain a low profile.

==Page 632==

'''Museum der Monstrositäten'''<br>
German: museum of monstrosities. ''Mathematical'' monstrosities.

'''motor diligence'''<br>
Motor taxi, as opposed to horse-drawn.

'''the Brocken'''<br>
The highest peak (3,750 ft) in the Harz Mountains in Germany. It is about 35 miles northeast of Göttingen. ([http://en.wikipedia.org/wiki/The_Brocken The Brocken]).

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

'''weapons somehow ''not yet decipherable'''''<br>
Rayguns.

==Page 633==

'''Knipfler...von Imbiss'''<br>
Neither one existed. Imbiss is German: snacks, fast food.

'''''Weierstrass Functions'''''<br>
Cf [[ATD_588-614#Page 589|page 589:everywhere continuous but nowhere differentiable]].

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

'''''the Set of All Sets That Are Not Members of Themselves'''''<br>
Russell Paradox. Cf [[ATD_525-556#Page 538|page 538:Bertie Russell]].

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

'''Poor Frege . . . about to publish his book . . .'''<br>
[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Frege.html 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.<br>
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.

'''''Kot!'''''<br>
German: shit.

'''Crotona in Magna Grecia'''<br>
Crotona is the old Latin name of the Italian city  [http://en.wikipedia.org/wiki/Crotone Crotone] in southern Italy on the Gulf of Taranto. Ancient Crotona was long one of the most flourishing cities of [http://en.wikipedia.org/wiki/Magna_Graecia 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"<br>
Paris Problems = Hilbert's Problems. Cf [[ATD_588-614#Page 604|page 604:the outstanding problems in mathematics]].

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

'''part "real"...part "pictorial" or let us say "fictional"'''<br>
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==

'''''Mengenlehre'''''<br>
German: set theory.

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

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

'''Nernst light'''<br>
Light from [[ATD_429-459#Page 437|page 437:Nernst Lamp]].

'''Brougham Bridge'''<br>
Cf [[ATD_557-587#Page 561|page 561:Brougham Bridge]].

'''complex knife'''<br>
"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'''<br>
From 1870 Weierstrass was Kovalevskaia's mathematics tutor in Berlin. He gave Kovalevskaia private lessons twice a week for four years. Cf [[ATD_489-524#Page 500|page 500:Weierstrass and Sofia Kovalevskaia]].<br>
Here, as on page 500, there is a hint of romantic involvement between the teacher and the student.

'''Lebesgue'''<br>
[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Lebesgue.html 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.

'''"surface devoid of tangent planes"'''<br>
In other words, discontinuous functions.<br>
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 th eintegral calculus.

'''. . . everywhere continuous and nowhere differentiable'''<br>
Cf [[ATD_588-614#Page 589|page 589:everywhere continuous but nowhere differentiabl, Weierstrass function]] and [[ATD_588-614#Page 594|page 594:crsis in mathematics]].

==Page 635==

'''The Kaiser now seeks in Mexico . . . opportunities for mischief toward the U.S.'''<br>
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.

'''''Rosinenkacker'''''<br>
German: one who shits raisins. More commonly "Korinthenkacker", insulting term for a very pedantic person.

'''a world line...never travel'''<br>
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 [http://en.wikipedia.org/wiki/Time_travel]. Hence: "Ach, das Schiksal". 

'''''Ach, das Schicksal'''''<br>
German: ah, fate.

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

'''that terrible ecstasy known to result from unmediated observation of the beautiful'''<br>
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."<br>
Rilke features strongly in V and GR (with Weissmann/Blicero). The idea that 'the sublime' involves an element of terror is fundamental to Romanticism.

==Page 636==

'''Children'''<br>
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?<br>
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 'the Spectre of the Brocken', an aerial phenomenon that resembles a human figure.

'''The next time you visit...'''<br>
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.<br>
Again, it's 'the Museum' that's closing. This isn't the Museum of Professor Klein mentioned on p. 632, it's a 'nocturnal equivalent' out on the Brocken.

'''"You know who I am."'''<br>
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?
Or the Spectre of the Brocken? Rilke's angel? All three?<br>
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.

==Page 637==

'''caldo tlapeno'''<br>
Mexican chicken vegetable soup.

'''Tampico'''<br>
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 [http://en.wikipedia.org/wiki/Tampico Tampico] is about 300 miles from the US border.

'''Chiapas'''<br>
[http://en.wikipedia.org/wiki/Chiapas Chiapas] is a poor and largely agricultural stat in the southeast of Mexico. It is best known for its 1994 Zapatista movement.

'''"El Atildado"'''<br>
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==

'''''Bohnen'''''<br>
German: beans

'''Maragogype'''<br>
As Gunther says, a variety of coffee bean, large in size, grown in Mexico and Central America [http://coffeeplus.com.au/coffees/7443.html].

'''Arbuckles'''<br>
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 [http://www.ineedcoffee.com/02/04/cowboycoffee/]. 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.<br>
Cowhands expected their coffee to be ‘brown gargle”, hot, black, strong and thick enough to float a six shooter in.<br>
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.

'''''cafetalero'''''<br>
Perhaps as in ''pistolero''; i.e. a barrista.

'''''el otro lado'''''<br>
Spanish: the other side (in one sense or other).

'''bucket shop'''<br>
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.

'''flimming'''<br>
Probably = indulging in flimflam (fraud, swindles)

'''''norte'''''<br>
north wind.

'''Plaza de Toros'''<br>
A bullring.

'''[S]louching away into the yellow opacity, he invited them all up to a wingding [...] that evening.'''<br><br>
Compare with T.S. Eliot's ''Love Song of J. Alfred Prufrock'':

<blockquote>
The yellow smoke that rubs its muzzle on the window-panes<br>
Licked its tongue into the corners of the evening</blockquote>
[[User:Bean|remy]] 09:52, 28 December 2006 (PST)

==Page 639==

'''Rio Bravo'''<br>
Mexican name for the river known in the US as the [http://en.wikipedia.org/wiki/Rio_Grande Rio Grande].

'''Ramos gin fizzes'''<br>
The original [http://www.gumbopages.com/food/beverages/ramos-gin-fizz.html 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'''<br>
Jungles of [http://en.wikipedia.org/wiki/Isthmus_of_Tehuantepec The Isthmus of Tehuantepec] in Mexico. The isthmus represents the shortest distance between the Guld of Mexico and the Pacific Ocean.

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

'''Baku'''<br>
Cf [[ATD_149-170#Page_168|page 168: Baku]].

'''skeeters'''<br>
mosquitoes

'''adios ''chingamadre'''''<br>
Spanish: goodbye, motherfucker.

==Page 640==

'''Valkyrie'''<br>
In Norse mythology the [http://en.wikipedia.org/wiki/Valkyrie Valkyries] are minor female deities.

'''Mondragón semiautomatics'''<br>
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 [http://world.guns.ru/rifle/rfl26-e.htm Mondgragón M1908 rifle].

'''Springfield'''<br>
An American magazine-fed, bolt-action rifle. See [http://en.wikipedia.org/wiki/M1903_Springfield_rifle Springfield].

'''Schnecken rigs'''<br>
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. [http://88.198.24.206/invisionboard/lofiversion/index.php/t20170.html 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. [http://world.guns.ru/smg/smg08-e.htm 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.

'''anti-Porfiristas'''<br>
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'''<br>
''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 Guld of Mexico about 6 miles below Tampico.

==Page 641==

'''Mondragóns will get you through'''<br>
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."

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

'''''este . . . perdón'''''<br>
this . . . sorry

==Page 642==

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

'''''batería'''''<br>
Spanish: battery (collection of percussion instruments).

'''[T]hat dirty li'l back-shootin Bob Ford.'''<br>
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.<br>
[[User:bnilsson|bnilsson]] 01:41, 2 January 2007 (EDT)

'''''resentimientos'''''<br>
resentments.

'''eight seconds . . . rodeo'''<br>
A bull rider must stay aboard for eight seconds to score.

'''cerverzas Bohemias'''<br>
Bohemias (brand) beers, a Mexican beer.

'''Cuervo Extra'''<br>
a kind of tequila ?

==Page 643==

'''''frontera'''''<br>
Spanish: frontier.

'''drygulched'''<br>
Ambushed, betrayed.

'''Krag-Jorgensens'''<br>
Repeating-bolt-action rifles designed by the Norwegians Ole Krag and Erik Jorgensen in late 19th century (1886). From 1892 [http://en.wikipedia.org/wiki/Krag-J%C3%B8rgensen Krag-Jorgensens] were used by the United States army as standard arms. And now it is a popular collector item.

'''Juárez'''<br>
''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. [http://www.juarez-mexico.com/ Juárez] is the major port of entry and trnasportation center of north central Mexico.

'''''Vaya con Dios, pendejo'''''<br>
Spanish: Go with God, asshole.

==Annotation Index==
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