- Please keep these annotations SPOILER-FREE by not revealing information from later pages in the novel.
- 1 Page 525
- 2 Page 526
- 3 Page 527
- 4 Page 528
- 5 Page 529
- 6 Page 530
- 7 Page 531
- 8 Page 532
- 9 Page 533
- 10 Page 534
- 11 Page 535
- 12 Page 536
- 13 Page 537
- 14 Page 538
- 15 Page 539
- 16 Page 540
- 17 Page 541
- 18 Page 542
- 19 Page 543
- 20 Page 544
- 21 Page 545
- 22 Page 546
- 23 Page 547
- 24 Page 548
- 25 Page 549
- 26 Page 550
- 27 Page 551
- 28 Page 552
- 29 Page 553
- 30 Page 554
- 31 Page 555
- 32 Annotation Index
Cf page 521:Ostend, a seaport in northwest Belgium. Among English-speaking tourists, Ostend (or Ostende) is best known as a ferry port. Ships have shuttled between Dover and Ostend for more than 150 years, and today's high-speed catamarans move hundreds of passengers and vehicles between these two ports in just two hours. But this thousand-year-old city is a popular beach resort with Belgians, who flock to Ostend for sun, surfing, sailing and the Kursaal (Casino). The fishing harbor and old town draw many visitors. Ostend is the only Belgian coastal resort that is as lively in the summer as in the winter. For more and pictures Ostend.
Fishermen's Quay, also called De Trap. The shrimp boats come home here from the sea in the morning. Along the quay many stands sell lots of seafoods.
Boulevard van Isenghem
A major thoroughfare in Ostend, locally called Van Iseghemlaan, extending diagonally from seafront southwest through the city.
Quai de l'empereur
Since Ostende is in the Flemish part of Belgium this should be the Keizerskaai, a street along the old part of the harbour, 1919 renamed Vindictivelaan.
According to the OED - A café in which smoking is allowed. Now, any small establishment selling alcoholic liquor.
one centime is the French eqivalent of one cent. A twelve-centime beer would cost 12/100 of a franc.
Cf page 130:Quaternions. Quaternions are a non-communtative extension of complex numbers (Hamilton, 1843).
Analogy with the complex numbers (Cf page 132:complex number) being represented as a sum of real and imaginary parts, a + bi, where i² = −1, a quaternion is defined as a combination a + bi + cj + dk, where i² = j² = k² = i j k = −1, and a, b, c, d are four explicit real numbers. The non-commutative property refers to i j = −j i = k; j k = −k j = i; k i = −i k = j. (i.e. i j ≠ j i; j k ≠ k j; k i ≠ i k; etc.) The using of i, j, k, the imaginary numbers (Cf page 133:imaginary number), led to the phrases of "the ijk lot" of page 533 and "creature of i-j-k" of page 534.
German: waiter, barman. Use of the German word would be insulting to the Belgian barman.
A half-pint glass (25 centilitres, actually).
Pron. lahm-BEEK. Unique Belgian beer style, sour and often thin in body.
Straw hat ("Panama").
Or "octonion," an innovation of English mathematician W.K. Clifford, referred to on p. 249.
Pun on a term from heraldry, barry nebuly. Barry (rhymes with "starry," not "carry") refers to a shield divided into an even number of parts by horizontal lines. Nebuly signals that the lines are deformed into stylized "cloud" shapes. Here you can see an example. If a British author had a character with a heraldic name, it would suggest a pseudonym.
University of Dublin
The Alma Mater of Hamilton, the father of Quaternion. He studied, graduated and taught at Trinity College, the University of Dublin, Ireland's oldest university.
If University College, Dublin, then Joyce had graduated in 1902.
Vector Analysis (or Vector Calculus) developed by Willard Gibbs (Cf page 29:Professor Gibbs) in 1881 and 1884. It is a branch of calculus that deals with vectors and process involving vectors. It is much more easily applied to phsics and other applied sciences than Hamilton's Quaternions (Cf page 525:Quaternions).
A vector is defined by not only a magnitude but also a direction, such as a velocity vector, v is defined by v = ai + bj + ck, where a, b, and c are the magnitudes of the velocity components in directions of i, j and k which are unit vectors, (not imaginary numbers as in Quaternion), with magnitude of 1. In three dimensional cases and xyz coordinate system is used then i, j, k are related to x, y, z directions ("xyz people" of page 533); but they, in general, may be used irrespective of the notation of the coordinates. Mathematical operations (addition, subtraction, multiplication), differentiation (curl — Cf page 326:Curl and p. 536, Laplacian — Cf page 326:Laplacian and p. 536, etc) and integration can be applied to vectors. It is interesting to know that one of the two multiplication operations is called cross product; for unit vectors (i, j, k) perpendicular to each other, then, i × i = j × j = k × k = 0, i × j = k, j × i = -k, etc. (Vector Calculus).
A simple vector anyalysis example here: if k, the unit vector, stands for the direction upward and g is the gravitational acceleration, then the acceleration vector, a, for a projectile, is defined for downward action, (the i and j directions have zero components):
- a = -g k
Integrating a would give the velocity vector, v
- v = -g t k
for zero initial velocity case, and t standing for time.
And integrating v would yield the position vector, h, for the projectile
- h = -½ g t² k
toward the sea level.
Quaternion believers, same as Quaternioneers.
Tasmania is an island of the southern coast of Australia. Known for its relative isolation, it was a prison for English convicts in the 1800s
Having been inseparable from the rise of the electromagnetic
In his 1865 work The Dynamical Theory of the Electromagnetic Field, James Clerk Maxwell unified electricity and magnetism. He put forth twenty equations, with twenty unknowns, in vector form (though different in notation and form than the equations that now bear his name) that completely described all known electromagnetic phenomena. In his 1873 treatise on the subject, he expressed the equations in the mathematics of quaternions. It appears that the quaternion form of the equations remained popular even though, at the behest of his publisher, Maxwell reverted to the 1865 form in the second edition (1881)--though they remain scattered throughout. In 1892 Oliver Heaviside (On the Forces, Stresses, and Fluxes of Energy in the Electromagnetic Field. Philosophical Transactions of the Royal Society of London. A, Vol. 183. pp423-480), while spewing scientific vitriol at the Quaternionists, reformulated Maxwell's original 1865 equations (Heaviside chose to remove the vector potential and scalar fields from the equations; the inclusion of these terms had served as Maxwell's justification for the use of quaternions), and provided the notation still in use today. See this PDF for the evolution of Maxwell's equations.
The Quaternion faction, after William Hamilton, who devised the scheme.
Grand Hôtel de la Nouvelle Digue
There is a Hotel Digue in the Seychelles; this is a New Hotel Digue by Pynchon?
Grand Hotel of New Dyke, may be a made up hotel name.
anterooms of death
This metaphor is sometimes applied to concentration camps. Here the lyric "feel like I'm fixin' to die" seems more apposite.
Belgian Art Nouveau
Art Nouveau, 1890(or 80) to 1914, explores a new style in the visual arts and architecture that developed in Europe and North America at the end of the 19th century. At its height (~1907), Art Nouveau was a concerted attempt to create an international style based on decoration. It was developed by a brilliant and energetic generation of artists and desisgners, who sought to fashion an art form appropriate to the post-Industrial Revolution modern age.
Brussels was one of the Art Nouveau centers and represented different style from the others. The jewelers there, accepted as artists rahter than craftsmen, (together with those in Paris) defined Art Nouveau in jewelery and achieved the most renown. (Art Nouveau).
British slang for "sleeping", "staying overnight"
- The following four are local, Belgian, not Russian, nihilists !
Female. Possibly named for Empress Eugénie (1826-1920), consort of French Emperor Napoleon III. Ultimately for St. Eugenia, 3rd-century Roman martyr whose feast is celebrated on December 25.
Female. A pseudonym? In view of the date of the action, certainly not named after the mathematician Fatou (1878-1929).
Male. Named for St. Denis or Dionysius, patron saint of Paris and of France, 3rd-century bishop of Paris, martyr, beheaded on the hill now called Montmartre. "Montjoie St. Denis!" was a warcry used by French troops in the Middle Ages. His intercession is effective against demonic possession and headache.
Male. Saint Polycarp was a Christian bishop of Smyrna (now İzmir in Turkey) in the second century. He was stabbed and died a martyr after an attempt to burn him at the stake failed. His intercession is sought against earache and dysentery.
Probably in reference to the Young Turks, a Turkish revolutionary movement
A part of the Belgian army. According to the 1911 Britannica, "the mass of the garde civique does not pretend to possess military value. It is a defence against sedition and socialism."
French Second Bureau boys
Deuxieme Bureau; French Intelligence.
French: phalanx. A military (here mock-military) group ready for combat.
It also conjures up memories of the early 19th century utopian socialist Charles Fourier, who theorized that people should live communally in "phalanxes" of a specific number based upon their "passions." His solid ideas included equality of the sexes, but he also taught wacky things such as the moon being made of lemonade. Of particular relevance is his rejection of industrial civilization. 
"...until something had happened, something too terrible to remember..."
Again this theme of an unknowable past transgression, here invoked almost as if the unknown signifies the other 'lateral' (a word which has cropped up at least a dozen times already) 'vector'.
French for "dyke"
The Belgian colonisation of the Congo was, as Conrad's Heart of Darkness makes clear, notable for its greed and brutality.
Leopold, King of the Belgians
1835-1909, reigned 1865-1909. A man of almost Nixonian fiendishness. In the Congo he acted as sole proprietor and absolute ruler. The positive outcomes of his exploitation include Heart of Darkness and the phrase "crime against humanity."
mental processes outside the main stream of consciousness but sometimes available to it — from Merriam-Webster's Medical Dictionary.
Belgian armed forces operating in the Belgian Congo (Wikipedia). "King Leopold's private army" may be a more accurate description.
See above: One of the early missions of the FP was to increase rubber export quotas through forced labor and related atrocities.
an informal term used by French students for Classes Préparatoires Littéraires, the two-year cycle of classes taken after the Baccalaureat (taken at age 17-18), to prepare for the entrance examination to the Ecole Normale Supeieure. (khâgne).
J. J. Élisée Reclus (1830-1905), French geographer but mainly educated in Germany. Several times he was forced to leave France because of his political views; he traveled widely in Europe, the British Isles, the United States, and South America and for many years lived in Switzerland. He was professor of comparative geography at the University of Brussels from 1895 to 1905. He had quite an extensive connection with various socialist and anarchist circles (met Bakunin while in Florence).Once he was imprisoned in Versailles in 1871 for his part in the Paris Commune. In 1882 he initiated the Anti-marriage movement while in Geneva. [Reclus).
Follower of Max Stirner, 19th century German philosopher and author of The Ego and Its Own, a work influential in anarchist thought. Wikipedia entry.
Max Stirner's (1806-56) attacks on systematic philosophy, his denial of absulutes, and his rejection of abstract concepts of any kind often places him among the first philosophical nihilists. For Stirner, achieving individual freedom is the only law; and the state, which necvessarily imperils freedom, must be destroyed. Even beyond the oppression of the state, though, are the constraints imposed by others because their very existence is an obstable compromising individual freedom. Thus Stirner argues that existence is an endless "war of each against all" (1845). (taken from the paragraph about Max Stirner in Nihilism)
Sourcing here? Much complexity in properly understanding Stirner, who has some Pynchon-like qualities, to say the least. From the Stanford Dictionary of Philosophy
His major work: The Ego and Its Own Much of Stirner's prose—which is crowded with aphorisms, italicisation, and hyperbole—appears calculated to disconcert. Most striking, perhaps, is the use of word play. Rather than reach a conclusion through the conventional use of argument, Stirner often approaches a claim that he wishes to endorse by exploiting words with related etymologies or formal similarities. For example, he associates words for property (such as ‘Eigentum’) with words connoting distinctive individual characteristics (such as ‘Eigenheit’) in order to promote the claim that property is expressive of selfhood. (Stirner's account of egoistic property—see below—gives this apparently orthodox Hegelian claim a distinctive twist.)
This rejection of conventional forms of intellectual discussion is linked to Stirner's substantive views about language and rationality. His unusual style reflects a conviction that both language and rationality are human products which have come to constrain and oppress their creators. Stirner maintains that accepted meanings and traditional standards of argumentation are underpinned by a conception of truth as a privileged realm beyond individual control. As a result, individuals who accept this conception are abandoning a potential area of creative self-expression in favour of adopting a subordinate role as servants of truth. In stark contrast, Stirner insists that the only legitimate restriction on the form of our language, or on the structure of our arguments, is that they should serve our individual ends. It is the frequent failure of ordinary meanings and standard forms of argument to satisfy his interpretation of this criterion which underpins Stirner's remorselessly idiosyncratic style.
The Ego and Its Own has an intelligible, but scarcely transparent, structure. It is organised around a tripartite account of human experience, initially introduced in a description of the stages of an individual life. The first stage in this developmental narrative is the realistic one of childhood, in which children are constrained by material and natural forces such as their parents. Liberation from these external constraints is achieved with what Stirner calls the self-discovery of mind, as children find the means to outwit those forces in their own determination and cunning. The idealistic stage of youth, however, contains new internal sources of constraint, as individuals once more become enslaved, this time to the spiritual forces of conscience and reason. Only with the adulthood of egoism do individuals escape both material (external) and spiritual (internal) constraints, learning to value their personal satisfaction above all other considerations.
Stirner portrays this dialectic of individual growth as an analogue of historical development, and it is a tripartite account of the latter which structures the remainder of the book. Human history is reduced to successive epochs of realism (the ancient, or pre-Christian, world), idealism (the modern, or Christian, world), and egoism (the future world).
What about these "successive epochs" in understanding ATD?
Stirner's major work, The Ego and Its Own has been reissued in English a number of times in Pynchon's lifetime,from the 60s on. (Not that TRP could not have read it in German!)
i.e. he has doctrinal differernces with Stirnerism, strictly speaking; see P. 324, and "Eigenheit".
See p. 527.
going down lately
Jean-Baptiste Sipido (1884-1959), a Belgian socialist. Accusing the Prince of Wales of causing thousands of inocents were killed in the Boer War in South Africa, on April 5, 1900, Sipido leaped onto the foot board of the royal compartment right before the train left the North Railway Station (Gare du Nord), Brussel, and fired two (or one? as reported in The Manchester Guardian, or four? as stated in the text here) shots through the window but missed everyone inside. He was arrested, tried and acquitted. The leader of the House of Commons called the acquittal a "grave and most unfortunate miscarriage of justice." (Sipido).
Prince... of Wales
(Maud Gonne's husband claimed to have been involved in another such plot.)
Hippodrome Wellington, a horse racing track in Ostend built in 1883. The facility hosts both harness and flat racing events. (Hippodrome).
Royal Bathing Hut... twenty francs
A bathing machine (bathing machine)? The King of Belgium certainly would not want to be seen in a swimsuit on a public beach... It seems unlikely, though, that such a royal bathing machine would be for hire.
The explosive picric acid (2,4,6-trinitrophenol) and its derivatives. For picric acid, Brugère's powder and Designolle's powder, see this Britannica article.
See "picric family" above.
See "picric family" above.
Alberto Santos-Dumont (1873-1932), a pioneer of aviation from Brasil. Check out Wikipedia to get a look at the way he was wearing his "trademark Panama hat".
Green Hour and l'heure vertigineuse
Absinthe-drinking time. The liqueur is green. In French, l'heure verte, so vertigineuse (vertiginous, causing dizziness) is a pun on the word for "green."
Rocco and Pino
Rabid Quaternionists and sudden friends of Kit Traverse.
- No, they were not mathematicians at all, let alone Quaternionists, but two "Italian naval renegades" !!
- "Rocco and Pino" are, in temperament, something like the "Mason and Dixon" of manned-torpedoes... cf. the "torpedo" (i.e., "Electrick-Eel") of Mason & Dixon.
Whitehead works in Fiume
Anticipating GR's V2 works.
Robert Whitehead (1823-1905), an English engineer. He developed the first self-propelled torpedo in 1866. He attended Manchester's Mechanics Institute, worked in a shipyard in Toulon (1844), France, and as a consultant engineer in Milan (1847), Italy. Later he moved to Trieste and in 1856 became a manager of a company called Founderia Mettali (later, Stabilimento Tecnico di Fiume) in Fiume producing ship steam boilers and engines which were the most advanced of that era. He also developed the first self-propelled torpedo which was very popular. Whitehead's torpedo was propelled by a compressed air engine, carried 18lbs dynamites and a self-regulating device which kept the torpedo cruising at a constant preset depth. [Whitehead].
Fiume is now Rijeka, Croatia. Trieste is on the northwestern edge of the Istra Peninsula, Rijeka is east of it. [Fiume].
Interesting sidebar: Whitehead's fortune from Fiume and the torpedo went solely to his granddaughter Agatha Whitehead, who married Baron von Trapp. The Von Trapp money came from Robert Whitehead, and most of the von Trapp singers were his great-grandchildren.
Siluro Dirigibile a Lenta Corsa
or S.L.C. "slow course torpedo", "slow-running torpedo". Wikipedia Italy‘s Navy was among the first to experiment with manned torpedos. Though according to this site this did not happen until 1935, Italian frogmen as early as October 31, 1918 made it into the harbour of Pula with the help of a modified german torpedo and sank the former Austrian but by then since a few hours Croatian/Slovenian/Bosnian battleship SMS Viribus Unitis. website
The Wikipedia entry linked above doesn't contain the Italian word dirigibile (steerable), which sets up the torpedo as a counterpart of the dirigible Inconvenience.
- I suspect there's a connection between the torpedo and "Not the usual lateener, in fact appearing to have neither sails, masts, nor oars" in Miles' reversed vision, page 250. Needs work, though.
Make a surreptitious escape (as "infiltrate" means to make a surreptitious entrance).
Italian: certainly not, not a chance. And in Pynchon's Italian is used as an all-purpose exclamation.
Ehi, stu gazz', categoria
Stu gazz' is a dialect representation of sto cazzo, literally meaning this dick here. Normally you could translate the sense of the sentence as: yeah, why not, a fucking category! . -- blicero2 - 2007.02.22
Denigrating the Italian South. Mezzogiorno means midday in Italian but refers generally to Southern Italy.
An exceptionally beautiful Belgian town of canals which is thus one of several towns known as the 'Venice of the north'. In the 14th cettury Burges already became an international finanacial and trading center, but started to decline in the 15th century. In the 20th century, however, the city was discovered by the international tourism and the medieval heritage turned out to be a new source of wealth. A new harbor of Zeebrugge, 10 miles outside of Bruges at the North Sea coast, brought new developments and new industries to the region. For the city and its history see (Bruges).
Raoul's Atelier de la Vitesse
French: Ralph's Speed Shop.
Belgian city, less than 30 miles southeast of Bruges, on the rail line about halfway between Ostend and Brussels. It is the fourth largest city of Belgium. It is bigger than Bruges but not as famous as a tourist attraction. But the city is a showcase of medieval Flemish wealth and commercial success. See (Ghent).
a hundred horsepower
italian (dialectal) = boy, young person
Umeki is typically made with some combination of the various kanji for "plum" (ume) and "tree" (ki), though one has the ki being the character for "ghost/devil" and one obscure reading that's entirely redundant, where ume is "plant" (usually read ue). There is one where ume is the kanji for "buried or embedded". Tsurigane, means a "temple bell", which can stand alone or be followed by the grass kanji to mean "bellflower" (lots of botanical stuff happening here, if that means anything; hardly the only example in AtD). Given the search for Shambhala going on, "Buried Temple Bell" seems a likely translation, at least at this point; the botanical meanings could perhaps emerge later.
Or, another terrible name-pun? "You make [m]e sore again." See another on P. 757
Cargill Knott (1856-1922), professor of physics; seismologist. See his biography here.
Japanese all-purpose cloth. Can be worn, used as wrapping, or used as a bag.
A brownish gray.
boilermakers and their helpers
See annotation to p. 360.
Pencil is a term commonly used in Synthetic Geometry. Straight lines incident with a plane - coplanar lines - and passing through a common point are said to be concurrent lines and the set of all such concurrent coplanar lines is called the pencil. (Cf page 456:Pencil). For a figure and a not quite precise definition see pencil. If a, b, c and d, are four distinct coplanar lines and their double ratio λ = (abcd) = -1, then a, b, c, d are called a harmonic quadruple of lines; they are said to constitute a harmonic pencil. A pencil which is not harmonic then is known as anharmonic pencil. See Pencil (lines 8-9), Double Ratio λ (lines 32-35) and Harmonic Pencil (line 39) of Mathworld.
Comptes rendus des séances hebdomadaires, Proceedings of the weekly sessions (of the Academy of Sciences), published from 1835, later (ca. 1935) retitled Comptes rendus de l'Académie des sciences, Proceedings of the Academy of Sciences. (Notice that the academy didn't see the need to specify "French." Take that, Royal Society of London!) For about a century, one of two journals so universally circulated and recognized that bibliographies nearly always cited them in nickname form: C.R. The other was Ber., short for Berichte der Deutschen Chemischen Gesellschaft, Reports of the German Chemical Society (from 1868).
Cf page 29:De Forest.
Cf page 29:Professor Gibbs.
Cf page 58:Maxwell Field Equations.
The wallpaper dye; aniline dyes were the first synthetic dyes, discovered by William Perkin in 1858. Their intense and fade-resistant colors were very fashionable at the end of the nineteenth century. The dyes are also significant in GR as the products of I.G. Farben.
Oliver Heaviside (May 18, 1850 – February 3, 1925) was a self-taught English electrical engineer, mathematician and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of mathematics and science for years to come..
Nineteenth century German mathematician and linguist, essentially the inventor/discoverer of vector space. Grassmann showed that once geometry is put into the algebraic form he advocated, then the number three has no privileged role as the number of spatial dimensions; the number of possible dimensions is in fact unbounded..
in the mood for a clambake
Anachronistic Broadway show tune? If so, the clambake in Carousel turns into a brawl; the assmebled factions of mathematicians could be in the mood for either a party or a brawl, apparently.
Monopole de la Maison
Monopole of the House, a fanciful name of a fanciful drink.
There is, since 1898, a well known restaurant called Monopole Lunch & Sea Grill in Plattsburgh of upper New York state. (Monopole Restaurant).
Most probably, it's the Magnetic monopole being referred here. In physics, a monopole is a magnet with a net magnetic charge, i.e. there is only one pole instead of two (so no net magnetic charge) as usual. (Monopole). It's existence had been theoretically predicted by various particle theories (superstring theory, etc) but never been proved experimentally. Proving the existence of a monopole would certainly earn a Nobel Prize.
An invented language, like Esperanto. Idiom Neutral dictionaries first appeared in 1902. It looks like a simplified Latinate language and it grew out of Volapuk, another "auxiliary language." It was abandoned by the Akademi Internasional de Lingu Universal in 1908.
For a list of all the invented languages that linguists are keeping track of, including Klingon, try Eastern Michigan's Linguist List. And don't forget to click on the link to "Browse sites devoted to constructed languages."
Basically, small talk or chatter. Words used to convey fellow-feeling rather than to impart information.
Kampf ums Dasein
German: struggle for existence.
Fellow Quaternioneer or Fellow Quaternionist.
We are the Jews of mathematics, wandering out here in our diaspora--some destined for the past, others the future, even a few able to set out at unknown angles from the simple line of Time, upon journeys that no one can predict
In keeping with the analogy of Judaism, those "few" people within the Quaternionists "able to set out at unknown angles" are most likely being compared to Kabbalists who claim to partake in a mystic "journey to the Throne of God through the mythological realm of the seven heavens" (Armstrong, A History of God--p. 247). Throne Mysticism in Kabbalah is explored extensively in Gravity's Rainbow.
A gown designed by Paul Poiret (1879-1944), a French fashion designer based in Paris. "In the annals of fashion history, Paul Poiret is best remembered for freeing women from corsets and further liberating them through pantaloons . . . it was Poiret's remarkable innovations in the cut and construction of cloting . . . Working with fabric directly onto the body, Poiret helped to pioneer a radical approach to dressmakeing that relied more on the skills of drapery than on those of tailoring." (from MetMuseum, New York Metropolitan Museum's Special Exhibitions, Poiret: King of Fashion, May 9, 2007 to August 5, 2007). For a picture of Poiret gown see Poiret Gown. The New York Times reported on February 1, 2007 that A Poiret Gown Brings $5,500 at Christie's Auction - the gown was made in 1913 when Poiret was at the height of his career. For his bio see Poiret.
green and long
Pickle, or... what?
- A green and long gherkin (a small, immature fruit of a variety of cucumber used in pickling).
1970s idiom for common European practice?
Set theory deals with the properties of well-defined collections, or sets, of entities - the elements or members of the set - conceived as a whole. The elements may be of a mathematical nature or non-mathematical. The set theory grew out of the German mathematician Georg Cantor's (1845-1918) study of infinite sets of real numbers.
The language of sets has become an important tool for all branches of mathematics, but is of very little relevance to the practice of mathematics in everyday life. As a source of metaphors, however, it's been quite productive; "subset," "superset," "universe," "intersection" and "Venn diagram" have found varying degrees of acceptance. Recasting Aristotle's syllogisms in set-theoretic language also makes them easier for many people to understand.
Hamilton . . . early genius
Hamilton, according to Chambers Biographical Dictionary, "at fifteen knew thirteen languages, had read Newton's Principia, and commenced original investigations". At twenty-two, "while still an undergraduate, he was appointed professor of Astronomy at Dublin and Irish Astronomer-Royal"; at thirty "he was knighted".
Hamilton . . . in the grip of a first love
Pynchon probably didn't mean Quaternion was Hamilton's first love, but its effect on him was similar to that of a first love. In 1843 at the age of 38 Hamilton invented the Quaternion, the first non-communtative algebra to be studied. He felt this would revolutionise mathematical physics, and he spent the rest of his life working on it. In 1853 he published a large volume, Lectures on Quaternions, on his grand invention. The last seven years of his life, Hamilton was writing an 800-page book Elements of Quaternions modeling on Euclid's Elements. The last chapter of the book was completed by his son after his death.
the Walt Whitman of English physics
Whitman pops up again, last seen on page 491.
Note that Wilde's Dorian Gray also undergoes a kind of bilocation.
Spa. Casino ?
For serious minds see Cf page 526:Gibbsian Vectors, but let's follow Pynchon's lighter mood, here is a non-mathematical definition by Kamen (1995):
- Many things have more than direction;
- The magnitude is also a question.
- With acceleration or force,
- And many more things, of course,
- It's vectors that make the connection.
Cf page 326:Curl: curl is a vector operator that shows a vector field's rate of rotation.
Pierre-Simon, Marquis de Laplace (March 23, 1749 – March 5, 1827); French mathematician and astronomer who summarized and extended the work of his predecessors in his five volume Mécanique Céleste (Celestial Mechanics) (1799-1825), translating the geometrical study of mechanics used by Isaac Newton to one based on calculus, known as physical mechanics.
He is also the discoverer of Laplace's equation. Although the Laplace transform is named in honor of Laplace, who used the transform in his work on probability theory, the transform was discovered originally by Leonhard Euler. The Laplace transform appears in all branches of mathematical physics — a field he took a leading role in forming. The Laplacian differential operator, much relied-upon in applied mathematics, is likewise named after him. .
- Cf page 326:Laplacian: Laplacian is a differential operator named after Laplace. The text here was talking about mathematical operations and operators — rates of change, rotations, partial differentials, Curls, Laplacians, . . .
beginning to appal
By 1905 there had been years of outrage at conditions in the Belgian Congo, King Leopold's private fief. Conrad's Heart of Darkness had been published as a serial in Blackwood's Magazine in 1899 and as a book in 1902. There were missionaries' accounts of the brutality, and newspaper reports. Leopold and his apologists published rebuttals. The Norton Critical Edition of Heart of Darkness contains an extensive collection of both.
Baize is a coarse woolen felt.
Broken symmetry is a concept used widely in mathematics and physics. For a simplest explanation (good enough for the text here), this term means that an object breaks either rotational symmetry or translational sysmetry - when one can only rotate an object in certain angles or when one is able to tell if the object has been shifted sideways. For a little bit more detailed explanation see Identify the Broken Symmetry; or even more On Broken Symmetry.
refers to the Belgian symbolist painter Fernand Khnopff (1858-1921), famous for his painting "The Caress", in which a female sphinx erotically lures a young man. The painting can be seen in the wikipedia entry
in French, "friser" means to curl or twist. "La frisée" could mean "curled," by extension "twisted." The Pleiades is a cluster of hundreds of stars, though only a few are visible, sometimes referred to as The Seven Sisters. If Pleiades are Sisters, Pléiade is one Sister, so her name means Twisted Sister!
Literally "My faith", i.e. "By my faith!", a mild exclamation of incredulity.
ten thousand francs
Based on currency conversions relative to gold, this is equivalent to about $30,000 US today.
Someone cheap or cautious, possibly named after people from PIke County, Missouri, who came to California in the 1800s, looking for work. They were poor, hence cheap.
what is a Quaternino?
Cf page 525:Quaternions for a mathematical definition. From The Random House Dictionary of the English Languages, The Unabridged Edition (1966): Quaternion is "a quantity or operator expressed as the sum of a real number and three complex numbers, equivalent to the quotient of two vectors. The field of quaternions is not commutative under multiplication.".
Bertie ('Mad Dog') Russell
'Mad Dog' seems to be used with heavy irony here. Bertrand Russell was known most for his rationalism, so to speak, his work in modern logic. He did little in his public roles (at this time in AtD) that would have him referred to as "crazy', as we say, beyond the social norm, "mad". It might be argued that his use of 'logic' against philosophers such as Hegel and McTaggart within Against the Day showed up their 'madness'. (Many did think McTaggart was a bit...different...for seriously not believing in Time.) McTaggart broke with Russell after an early influential friendship---Russell was the younger man and the influenced one. He said he was an Hegelian because of McTaggart--Russell wrote in his Autobiography that McTaggart said he no longer wanted to meet/talk with him bcause he could no longer stand Russell's opinions.
Bertrand Russell (1872-1970) was a British mathematician, philosopher, logician and social critic. Best known for his work in mathermatical logic and analytic philosophy. In late spring of 1901 he discovered the so-called Russell Paradox, "the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox." (On-line Stanford Encyclopedia of Philosophy). He won the 1950 Nobel Prize in Literature in "recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".
nebulae: formed from the diffusion of gas in galaxies or as exploded stars (or the last ember-like stage of a star)
Most nebulae can be described as diffuse nebulae, which means that they are extended and contain no well-defined boundaries. In visible light these nebulae may be divided into emission nebulae and reflection nebulae, a categorization that depends on how the light we see is created.
Probably refers to the fact that quite a lot of Hegel's philosophy deals with the is-ness of the world as we know and experience it.
On page 787 of Bertrand Russell's History of Western Philosophy is a summary, perhaps, of this remark about Hegel's puns: "as a result of analysis of the concept "existence", modern logic has proved this [Cartesianism, refuted by Kant, reinstated by Hegel] argument invalid....."
We know from other places that TRP himself seems to 'not like' Cartesianism. See 'cartesian' citations within this wiki.
a vector quotient
The result of one vector divided by another. According to the English dictionary definition of previous page this is just a Quaternion.
Unit vector is a vector with magnitude of one. The unit vectors in 3-dimensional space, i, j, k, associated with x, y, z directions are used in defining a general 3D vector (Cf page 526:Gibbsian Vectors).
A basic yoga pose.
'Quadrantal Versor Asana'
A triangle pose taken that extra dimension.
Looks a lot like the Dutch "Uw moeder!" - a cry of astonishment ("Your mother!"), the equivalent to the black English "yo mama".
A term typical to mathematics. A commutative equation is one that can operate in exact reverse and still yield the same results. 'Noncommutative' then suggests unidirectionality. The ability to go from point A to point B, but not from B to A.
A woman's drawstring handbag; usually made of net or beading or brocade; also: A system of lines forming a pattern of squares at the focal plane of a telescope, used in micrometers. 
- Isn't that sort of a red herring? "[P]roducing from her reticule a . . . watch" doesn't really allow of that second meaning.
- It could be a pun, since a reticule/ handbag always shows its pattern of lines, and a watch (timepiece) is drawn from it. Remember that, e.g. railroad lines of tracks, are a sign of industrialism encroaching on the natural and the spiritual.
Vacheron & Constantin watch
Made by a Swiss company founded in 1755. From 1819 to 1970 the name was as in the text, then the & dropped out. See the Wikipedia entry.
For a pocket watch, a case with a hinged metal cover. More often called "hunter case" (and such a watch a "hunter").
"haar rekening, ja?"
The bill, yes? (Dutch)?
Her bill, yes? I.e., give the check to the lady.
Given the presence of Chris 'Kit' Traverse here, this very much suggests a reference to Christopher 'Kit' Marlowe, Elizabethan poet, playwright and contemporary of Shakespeare. Marlowe was stabbed to death in 1593, in murky circumstances, ostensibly over a bill or 'reckoning', though he was widely believed to have been involved in some form of espionage.
Strictly speaking "haar rekening" means that the lady pays for herself only. If Root wanted to make sure that Pléiade pays for the whole company he would have to say "de hele rekening voor de dame".
The Woëvre is a natural region of Lorraine in north-east France. It forms part of Lorraine plateau and lies largely in the department of Meuse. During World War I, there was much fighting there due to vast mineral resources that had been discovered in the Briey basin or Eastern Woevre at the end of the 19th century. "Piet" is Dutch for "rock" or "stone" and is a fairly common Dutch name, the English equivalent being Peter.
If the surname is pronounced as in Dutch, Woevre is another Pynchon villain with a "V"-name (Vond, Weissman, Vibe).
The Force Publique (FP) was the official armed force for what is now the Democratic Republic of the Congo from 1885, (when the territory was known as the Congo Free State), through the period of direct Belgian rule (1908-60), until the beginning of the Second Republic in 1965. Wikipedia entry
made him reach
Possible allusion to a famous line, "When I hear the word culture I reach for my gun." From Hanns Johst's biographical play Schlageter. The original line is slightly different: "Wenn ich Kultur höre ... entsichere ich meinen Browning," "Whenever I hear of culture... I release the safety-catch of my Browning!" (Act 1, Scene 1). It is spoken by another character in conversation with the young Schlageter. In the scene Schlageter and his wartime comrade Friedrich Thiemann are studying for a college examination, but then start disputing whether it's worthwhile doing so when the nation is not free.
The line is often misattributed to better-known Nazis and others .
- In Jean-Luc Godard's 1963 film Le Mépris (Contempt), Jack Palance's character "Jeremy Prokosch," an American movie-producer, intones to Fritz Lang: "Whenever I hear the word culture, I reach for my checkbook."
In Dutch/Flemish, the name means "roofer." (De in these names almost never means "of, from" as in French; it's nearly always the definite article.)
Afrikaans: baboon. (Afrikaans is the language spoken by descendants of Dutch colonists in present-day South Africa. Some items identified as Dutch or Flemish in this wiki may really be Afrikaans.)
The South African song "Bobbejaan klim die berg" ("Bobbejaan climbed the hill") is the source of the stage name of Belgium's most famous country and western musician, Bobbejaan Schoepen (b. 1925). In 1943 he was suppressed by the Nazis after performing a South African song, "Mamma, 'k wil 'n man hê" ("Mama, I want a man"), which contains the line "No, Mama, I don't want a German, because I don't like pork." He founded the Bobbejaanland theme park in Belgium, where he still lives.
MKIV/ODC... Mark Four
This would be the Mark IV Ohmic Drift Compensator (Page 565), a key component of the Q-weapon, which "regulates how much light is allowed to enter the silvering of the mirror! Special kind of refraction! Calibrated against imaginary index! Dangerous! Of the essence!'"
not part of your remit
Not included in your job description, instructions, authorization. "Remit" (noun) is usually a British usage.
Dutch/Flemish: brownnose, ass-kisser.
one on her wrist
All the bruises reflect some refinement or artistry except this one, which may have been inflicted crudely.
over the day
Across the horizon -- " a screaming comes across the sky"
Edmund Whittaker (1873-1956), an English mathematician. He is best known for his work in numerical analysis. And he contributed widely to applied mathematics, mathematical physics and the theory of special functions. He also worked on celestial mechanics and the history of applied mathermatics and physics. (Whittaker).
The Sir Edmund Whittaker Memorial Prize is awarded every four years by the Edinburgh Mathematical Society to an outstanding young mathematician having a specified connection with Scotland .
The cloudy effect caused by the addition of water to absinthe. Dictionary definition: "of questionable taste or morality; decadent."
Standing mirror in a freestanding vertical frame.
as if someone
Sound-cancelling vs opacity-cancelling?
wraith of Pleiade Lafrisee
Pleiade manifests one of her not-visible stars. Perhaps this sister has somehow twisted herself on an imaginary axis ala Dr. V. Ganesh Rao.
Warning, giving advice, by extension ominous or menacing.
Against....the day.... Note: this phrase happens at the exact halfway point of the novel: p.542.3
He Who Must Come
The evil-doer who must come might be Adolf Hitler. It would make sense. The implication being that Europe is precipitating into a no-return situation. Capitalism cannot but end in WW2.
Ah, a lot more and less than capitalism going on here, especially if anyone specific like Hitler is meant.
- When French writers use this phrase (celui qui doit venir) they do mean the Messiah . . . although a few devout quibblers point out that the Messiah has already come. It's rather tiresome Googling the phrase; the first 83 hits definitely refer to Christ and most of them quote the first verses of Matthew 11. But there's also a Camus reference (in English, I think) down at No. 90, if anyone has a JSTOR account:
Recalls Yeats' 'The Second Coming' once again: "And what rough beast, its hour come round at last, Slouches towards Bethlehem to be born?" 
Georges Boulanger, French military man, and War Minister in the late 19th century. He was one of those men "on a white horse" that some conservatives looked to, as he urged an attack on Germany and the end of the French Republic with a return to monarchy. He was also notorious for his harsh reprisals against workers' demonstrations. "'Boulangisme'" threatened a coup in 1889, but the general's procrastination brought the crisis to an end.
In The Infernal Machine: A History of Terrorism by Matthew Carr, 2007, Boulanger is called the "father" of fascism.
what death and what transfiguration
Allusion to Richard Strauss' tone poem "Death and Transfiguration" (Tod und Verklärung), premiered in 1890.
Dead certainty, sure thing.
Alfred von Schlieffen was the author of a German war plan to win a two-front war against both France and Russia by quickly defeating France before Russian troops could be mobilized. The Schlieffen Plan included an attack on France through Belgium, disregarding its neutrality.
Title of Pynchon's first published story. Here, ass?
Main square of Ostend; literally "drill field".
peau de soie
"Skin of silk" A heavy, smooth satin with very fine ribbing; somewhat dull in sheen compared with traditional silk finishes.
Richard Freiherr von Krafft-Ebing, Austro-German psychiatrist and author of Psychopathia Sexualis (1886), a pioneering study of deviant sexual behavior and fetishism. Coined both sadism and masochism as terms for these respective behaviors. Wikipedia entry.
Toque here refers to a lady's hat, originally of fur but here in velvet, which is rather like a flattened chef's hat in shape.
Proust: in À l'ombre des jeunes filles en fleurs the narrator first sees Albertine wearing a toque. There seem to be quite a few Proust themes and references running throughout the novel. Indeed Pliade is the French publisher of Proust's works.
A shopgirl or dressmakers apprentice. A milliner.
A distinctive Belgian style of beer. Wikipedia
Coins. Originally Roman gold coins, latterly any kind of coin.
Specifically small change. She is affecting modesty by claiming that a hat like hers can be had for pennies in any unpretentious shop. In France "sou is used as slang for money, as in sans le sou. 'I'm broke', 'without money'. It is also a slang term for the Canadian cent (standard French, cent)." (Wikipedia)
Brautigan's "Trout Fishing in America" famously ends with the word mayonnaise. GoogleBooks
Another Pynchonic word combination, here denoting the two main ingredients of mayonnaise: 1) eggs, and 2) oil. It's not "fecoventilatory collision" as seen in "Vineland," but it's nice.
Grape commonly used in Rhone Valley wines e.g. Chateauneuf du Pape.
Region north of Paris.
Here the reference is to crème chantilly otherwise known as whipped cream. Chantilly mayonnaise is made by incorporating the beaten egg whites for extra lightness.
Legislative act declaring that a person is guilty of a crime and setting punishment without the benefit of a formal trial. The Constitution forbids the federal government (Article I, Section 9, clause 3) and the state governments (Article I, Section 10, clause 1) from passing bills of attainder. [www.historycentral.com/Civics/B.html]
'Aux armes, citoyens'
To arms, citizens, from the French national anthem, La Marseillaise (1792). Kit confused La Mayonnaise with La Marseillaise.
I don't think he's confused - he suspects Pleiade and is making a point ironically. A James-Bondish sort of quip. In fact this whole incident is Bondish and Pleiade is a Bond-type seductress. And let's not forget, Kit is surrounded by Flemings...
King of France 1715-1774 .
Cléo de Mérode
Glamorous French ballerina (1875-1966), later Follies Bergere dancer and famous beauty. Her reputed intimacy with King Leopold was only a rumor . The character Madame Leonora Armfeldt in Stephen Sondheim's A Little Night Music has some features in common with her.
Marquise de Pompadour
Mistress of Louis XV,once friend of Voltaire and a power behind official scenes..
duc de Richelieu
Duc de Richelieu (1696-1788), marshal of France, was a grandnephew of Cardinal Richelieu, and born in Paris. Apart from his reputation as a man of exceptionally loose morals, he attained, in spite of a defective education, distinction as a diplomatist and general. (duc de Richelieu and cf page 490:duc de Richelieu)
dubious 'victory' in 1756
As part of the Seven Years' War (1756-1763), duc de Richelieu (1696-1788), a Marshal of France, won a victory in the Battle of Minorca (May 20, 1756) over John Byng (1704-1757), a British Admiral. In spring of 1756 John Byng was sent with a small and undermanned fleet to relieve the British Port Mahon on the Mediterranean island of Minorca. During the battle ensued, several British ships were badly damaged by the French squadron while others, including Byng's flagship, were still out of effective firing range. Instead of engaging the enemy directly, Byng decided to keep the formation, allowing the French fleet to get away undamaged. (Battle of Minorca).
the ill-fated Admiral Byng
John Byng, convicted by court-martial of failure "to do his utmost" in the battle, shot in 1757. Remembered because of (1) his being the last officer of flag rank to be put to death for conduct in battle and (2) Voltaire's gag in Candide: "In this country it is good to kill an admiral from time to time in order to encourage the others."
"Spanish fly," contact irritant sometimes ill-advisedly used as aphrodisiac.
Pertaining to the Marquis de Sade. The acts the chef performs on the egg and oil have the same names as acts of Sadean sex.
Right? (Isn't that so?)
A grass (Vetiveria zizanioides) of tropical India, cultivated for its aromatic roots that yield an oil used in perfumery. [www.answers.com/topic/vetiver]. So, a perfume with, llterallly, roots in India.
Vetiver makes frequent appearances throughout À la recherche du temps perdu.
A beaut; in current parlance, a hottie.
Quaternion Probability, page 536.
French: as translated in the text.
disjunctive effects of thunderstorms
Folk wisdom says a thunderstorm will cause mayonnaise to separate (oil from yolks).
Mayonnaisse like Smegmo and Crisco is a hydrogenated fat; cottonseed oil is a common factor to all three. Indeed, the name Crisco derives from the intial sounds of "crystallized cottonseed oil". Note in the next few pages a mention of Candlebrow -- underscoring a tie-in between Mayonnaisse and Smegmo.
It may be of interest to note that hydrogenation may have a symbolic use for Pynchon. The process entails bubbling hydrogen through oil in the presence of a metal catalyst such as nickel, platinum, aluminum at 248 to 410 degrees. Remnants of these metals stay in the finished product, and when consumed can lead to an increase in heavy metals in the human body.
Eating hydrogenated oils is like eating plastic. The body does not recognize that these molecules have been mutated and tries to use them as essential fatty acids. But they cannot perform the same function, and as a result hydrogenated oils can cause short circuits in the electrical flow that controls the heartbeat, nerve functions, cell division and mental balance. They also create free radicals (anarchists!) that are linked to cancers. Free radicals plus metal remnants are a major contributor to cancer, heart disease, immune system dysfunction, osteoporosis, depression, chronic fatigue, Alzheimers, and neurological diseases. It is estimated that over 200 million people have died prematurely because of the hydrogenated oils found in our diets.  Not to mention innocent bystanders killed by mentally imbalanced people whose imbalance may stem from the ingestion of hydrogenated oils -- there may be some underlying reality to the "Twinkie defense."
A lounge suit is another name for business suit consisting of a matching jacket and trousers or skirt.
ankle high shoes with elastic gussets in the sides (wordweb online)
Suggestive of Adam Smith's metaphor for market forces in economics.
To make mayonnaise, beat together egg yolks, salt, mustard and vinegar, then drip in oil while beating to form the emulsion. If you scale the process up for industrial production, you will automate the introduction of the oil, using nozzles that release it a drop at a time—but in a large vat you can have many such nozzles.
Vat or tank in which the mayonnaise is agitated or beaten.
Clinique d'Urgence pour Sauvetage des Sauces
French: Emergency Clinic for Salvage of Sauces.
Literally, "Dick, cretin." Cazzo is a common Italian interjectionary obscenity, especially in the south. "Cazzo, cretino," is akin to someone saying, "Well shit, dummy," or "F-ing moron!"
È il cowboy!
Italian: It's the cowboy!
Le bambole anarchiste, porca miseria
Italian: Anarchist babes, oh boy.
A southeast suburb of Ostende.
Quai de l'Entrepôt
Italian: boys, guys.
That the General was 'reactionary' and that the C of C bureaucracy had a 'defiant residue' of Boulangism, continues the characterization of the organization for which the Chums 'work'.
See p. 543 above, regarding a 2007 book in which Boulanger is called the 'father of fascism'.
French: fictive postage stamps. Cf "Lot 49".
Yes, stamps mean something in Pynchon's works; here, it seems important that these stamps are characterized as frauds.
As explained in the text.
"Section IIIB (Intelligence) of the German High Command. After WWI, was funded by Alfred Hugenberg (financial backer of Nazi party)". From Sabotage by Sayers & Kahn, 1942.. The authors state in the Forward, in 1942, "that 'Nazi Germany' is the creation of spies and saboteurs". See V. & Gravity's Rainbow, of course.
Germany might stand a better chance...
That is, if the French were to push into Alsace (per Boulanger) as the Germans executed the Schlieffen Plan  for the encirclement of Paris, it would put the French at an even greater disadvantage...as actually happened in 1914. Had the Belgians and British not delayed the Germans in Flanders, and had the French railroads not performed speedily to bring the French troops back to the Marne, World War I could have had a very different outcome...an alternate history.
Policies based on revenge, or a person following such policies. In General Boulanger's case, revenge against Germany for the Franco-Prussian War (that is, retaking Alsace, lost in 1871).
the somewhat discomposed General
Having died in 1891, the General by the time of the action is certainly somewhat decomposed; brief biographies do not suggest he was non compos mentis, that is, mentally discomposed.
grow more and more invisible
What could be meant? Clearly, they inhabit bodies that people interact with?, as well as being characters in works of fiction.
Given what happens with the Chums as the story progresses [Spoiler bit, thematically], I suggest that their invisibility here means the entering of simple human life, to live out their lives 'anonymously' in history. I want to suggest this is largely a positive vision, indicated in other ways and places as well in TRPs work. Here is an overt bit of circumstantial evidence from Pynchon's introduction to Jim Dodge's novel Stone Junction:
"Equally difficult for those who might wish to proceed through life anonymously and without trace has been the continuing assault against the once-reliable refuge of the cash or non-plastic economy." 
(When did he lose his innocence?)
a modification of any salsician metaphor toward the diminutive
Salsician: pertaining to sausage. Lindsay says Suckling's penis is better compared to a wiener than a knockwurst.
"Why you little–and I do mean 'little'–"
Another Simpsons reference?
Noseworth, the Master-At-Arms of the Chums division of this organization with a defiant residue of 'fascism', who had no smell to Pugnax early on, is called out, either for real or in a sex-bashing putdown, for homosexuality. cf. homosexuality as a metaphor in Gravity's Rainbow.
dunes between Nieuport and Dunkirk
Nieuport is a Belgian seaport about 10 miles southwest of Ostend. Dunkirk is a French port (less than 10 miles inside the French border) about 20 miles southwest of Nieuport. The latter was a site of one of the bloodest battle in World War I. The general area between Niewport and Dunkirk was the well traversed battle fields of two world wars. (Dunkirk was (in)famous for the British Army's escape from the Nazi German's assault in World War II.)
Not information, energy.
Angels of God led Lot and his family out of Sodom as it was being destroyed and told them not to look back at the mayhem. Lot's wife, Edith, imprudently looked back and was transfigured into a pillar of salt.
In Mason & Dixon, p. 354 , the interiors of some coaches were larger than their exterior dimensions. Interiors have importance in Pynchon's worldview. Cf. "invisibility", and a 'human life' above.
an imitating recess or structure made to resemble a natural Italian grotto.
a highly developed taste, moreover, for human blood
Since Pugnax developed this taste in the Carpathians, home of Castle Dracula, this seems a clear reference to Bram Stoker's novel.
Major mountain range running northwest-southeast through Poland, Slovakia, western Ukraine and Romania.
Uhlan regiments belonged to the light cavalry. They wore splendid uniforms (model for some U.S. marching band uniforms). Wikipedia article.
Now Timişoara, extreme western Romania.
prefiguration...of the holy City
City of God, ala Augustine? The Heavenly City of the 18th Century Philosophers , as explored in the book Ian McEwan says he lent Pynchon? 
...separated by only a slice of Time...
Miles is beginning to experience Time almost as a spatial dimension, his personal vector as traversing (!) 4-dimensional space, or perhaps multidimensional space, the mathematics for which is being debated in Ostend.
securing the mess decks
The Chums follow U.S. Navy idiom in orders (frequently prefixed with "Now") and shipboard activities ("secure" meaning "whatever you did before, undo it now," in this case put away the dishes and fold up the tables).
Tolkienesque name? Or perhaps it's a nod to the Ryder-Waite Tarot deck and to Kevin Thorn (Kevin Matthew Fertig, 1977-), the American professional wrestler better known by his ring name Kevin Thorn who is currently signed to World Wrestling Entertainment wrestling on its ECW brand. He has appeared in vigniettes with Ariel (Shelly Martinez, 1980-), the tarot card reader, who spits blood at the camera while she "predicted the future of ECW." Yup, a stretch...
- The name also evokes the Four Horsemen of the Apocalypse.
He was at Candlebrow.
Presumably a 'trespasser.'
the four-note chord in the context of timelessness
A melody is formed by notes following one another in time; a chord on the ukulele violates that practice by having all the notes sound at once. A really clever little passage. Note: Jazz musicians describe musical improvisations as horizontal (with the melody) or vertical (with the chord)
20 kilometers south of Ostend (about halfway to Ypres).
The terrain was flat...lowlands
Not, this time, a reference to Pynchon's Lowlands, but to the two-dimensionality of Flanders, as in Edwin A. Abbott's Flatland ; most humans, like the inhabitants of Flanders and Abbott's Flatlanders, experience life in two dimensions.
Somewhere up in the sky was Miles' home...
Whereas Miles and the Chums of Chance, in contrast, live in three dimensions. The mathematicians gathered in Ostend are trying to calculate how to experience and use vectors to live in four dimensions; in a way, to experience Time as a kind of spatial dimension. Miles, on P. 551, is demonstrating the beginnings of an intuitive discovery of how to experience Time as an almost spatial dimension. Which would be a sort of "time travel", or at least an expanded view of life and history.
soaked in water or exposed to moisture (as flax or hemp) to facilitate the removal of the fiber from the woody tissue by partial rotting.
Ypres and Menin
Municipalities in West Flanders that were sites of some of the bloodiest battles of WWI. At the beginning of the war, the British and Belgian stand helped save Paris from encirclement by the Germans, and saved the Channel ports, but as Thorn points out, the area became the western anchor of the Western Front trench system. The several Battles of Ypres saw the first uses of poison gas (Mustard Gas, dichlorodiethylsulfide, was first called Yperite), the use of enormous mines, and the legendary mud of Passchendaele .
Ten years from now
(1914?) through 1918? and beyond?. Another paramorphic mirror--what do we now face. Whatever it is, it is nuclear.
Hieronymous Bosch (1450-1516), Dutch painter of nightmares. Wikipedia entry.
Pieter Brueghel the Elder(1525-1569), Flemish painter.Wikipedia entry.
League of Nations? The League of Nations was formed after WWI to prevent future wars. Didn't succeed.
No. In this case a historical unit of length, approximately three miles - "league on league" = tremendous masses
where the needles went and which way to rotate them
I.e., how to push Thorn's buttons; the image is from acupuncture.
simpletons at the fair
Making Pynchon's metaphor explicit.
Chopin E-minor Nocturne
Frédéric Chopin (1810-49), a Polish pianist and composer (Chopin). He was born in Warsaw, Poland to a Polish morther and a French father. He went to Paris at the age of 20 and died there at the age of 39. He was widely regarded as one of the most famous and influential composers for the piano. From 1837-47 he had a 10-year stormy relationship with the French writer George Sand. His E-minor Nocturne is a 4-minute long Romantic style piano solo composed in 1827. (A nocturne is usually a musical composition that is inspired by, or evocative of, the night Nocturne.)
???glimmering or imperfect light or twilight hours.
A coined term, apparently similar in meaning to Miles’ phrase “failure of physical translation.” Plasma would take an older meaning of “form” or “shape." Hysteresis, according to Webster's, refers to “a retardation in effect when the forces on an object are changed.” Hysteresis is used to describe magnetic phenomenon as well as plastic or elastic materials, that involve changes to a rest state that last beyond the forces that cause them. Examples include recordings on magnetic tape or a thumbprint slowly disappearing from putty. In the context of this passage, plasmic hysteresis appears to describe the lingering visage of someone who is no longer present – a hysteresis of form only and thus a failed physical translation. See etymology of plasma and this nifty explanation of hysteresis.
Hysteresis has also been used to refer to “loops” in time, certainly apropos in this case. I stumbled across an excellent example in a 1980 episode of Dr. Who, in which the eponymous Dr. is trapped in “chronic hysteresis,” an endless loop or return to a previous point in time – very similar to the situation of Ryder Thorn. Check it out for yourself!
The Light Over the Ranges
Against the Day
Rue du Départ