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'''the error of the seismograph recordings . . . singularity'''<br> | '''the error of the seismograph recordings . . . singularity'''<br> | ||
− | "Error" doesn't mean mistake or wrongness. It measures the variability within each instrument; every measurement comes with a plus-or-minus figure. If the Event happened instantaneously, each of the charts would record it as a more or less spread-out peak. The energy released in a process is calculated from the area under the curve of intensity versus time; to get the power (rate of energy release), divide the energy by the duration of the process. Even though he states the math wrongly, Vanderjuice suspects the seismographs of the world have responded to a titanic release of energy that took place in essentially no time at all, so that power = energy divided by zero. When physicists see a ''real'' process apparently demanding division by zero, they call it a singularity and go looking for an explanation. | + | "Error" doesn't mean mistake or wrongness. It measures the variability within each instrument; every measurement comes with a plus-or-minus figure. If the Event happened instantaneously, each of the charts would record it as a more or less spread-out peak. The energy released in a process is calculated from the area under the curve of intensity versus time; to get the power (rate of energy release), divide the energy by the duration of the process. Even though he states the math wrongly, Vanderjuice suspects the seismographs of the world have responded to a titanic release of energy that took place in essentially no time at all, so that power = energy divided by zero. When physicists see a ''real'' process apparently demanding division by zero, they call it a singularity and go looking for an explanation. |
'''the equations of history'''<br> | '''the equations of history'''<br> |
Revision as of 06:52, 2 March 2007
- Please keep these annotations SPOILER-FREE by not revealing information from later pages in the novel.
Contents
- 1 Page XX
- 2 Page 792
- 3 Page 794
- 4 Page 795
- 5 Page 796
- 6 Page 797
- 7 Page 798
- 8 Page 799
- 9 Page 800
- 10 Page 801
- 11 Page 802
- 12 Page 803
- 13 Page 804
- 14 Page 805
- 15 Page 806
- 16 Page 807
- 17 Page 808
- 18 Page 809
- 19 Page 810
- 20 Page 811
- 21 Page 812
- 22 Page 813
- 23 Page 814
- 24 Page 815
- 25 Page 816
- 26 Page 817
- 27 Page 818
- 28 Page 819
- 29 Page 820
- 30 Annotation Index
Page XX
Sample entry
Please format like this.
Page 792
drumfire
Intense, continuous artillery fire, characteristic of the bombardments that preceded the attempted advances on the Western Front in World War I.
Page 794
communicate with the explorer Peary, then in the Arctic Robert Peary did not even leave New York City at the start of his polar expedition until July 6, 1908, 6 days after the Tunguska Event of 6-30-08, and did not reach Ellesmere Island until the summer of 1909(see[1] section on Wardenclyffe Tower).
- But this was one of the 'theories' around the time and long after attempting to explain the Tunguska Event. See Tunguska Event in Wikipedia.
Tom Swift
Tom Swift is a fictional character in youths' books. He is an inventor of ingenious machines that take him and his chums on adventures, usually by air.
Not published until 1910.
Wiki
Semipalatinsk
Town on the Irtysh River, a long way southwest of Vanavara. Soviet nuclear tests were administered from here.
obstanovka
Russian: situation.
Page 795
Zdorovo!
Russian: hello!
Neutral Moresnet
Tiny "country" between Belgium and Germany; existed 1816-1919; see, oh do see, Wikipedia entry.
tchudak
Now transliterated chudak. Russian: crank.
Kiakhta
Or Kyakhta, only two syllables. Town on Russian (Buriat)-Mongolian border south of Lake Baikal, a center of Russian trade with China.
Not even Russian army does that!
And it cost them dearly in 1914 when intercepted "clear" radio traffic helped the Germans crush them at the Battle of Tannenberg.
Page 796
By dusk . . . running-lights
An enigma. The ordinary way of analyzing it: Make a model, say a flashlight, an orange and a toothpick mooring line with a raisin balloon at the top. As the orange rotates toward the east and the flashlight appears to set in the link titlewest, what gets dark first? The base of the toothpick, the shadow progressing upward. But the text says the raisin does, the shadow arc moving downward.
It's very curious that immediately following this apparently topsy-turvy paragraph Miles says "As above, so below." Significant?
Are the Chums watching from above?..."as the boys watched"..."as above,so below."?--[User: MKohut] January 28, 2007
- I suggest there's no error, and the "ordinary way" is not the right way to understand the text. It definitely is worth looking for a way that the narration--and Miles' benediction--can be technically as well as thematically correct.
In wizardry (developed from shamanry) Hermes Trismegistus wrote an
Emerald Tablet on which he wrote his wisdom (9-14 precepts).
Sir Isaac Newton translated one precept as:
"That which is below is like that which is above & that which is above is like that which is below."
So, magic? Wiki
--User:mrplong 13:36, 31 January 2007 (AST)
The precept has been linked to numerology [2]; These words circulate throughout occult and magical circles, and they come from Hermetic texts. The concept was first laid out in The Emerald Tablet of Hermes Trismegistus, in the words "That which is Below corresponds to that which is Above, and that which is Above, corresponds to that which is Below, to accomplish the miracles of the One Thing."[24]
In accordance with the various levels of reality: physical, mental, and spiritual, this relates that what happens on any level happens on every other. This is however more often used in the sense of the microcosm and the macrocosm. The microcosm is oneself, and the macrocosm is the universe. The macrocosm is as the microcosm, and vice versa; within each lies the other, and through understanding one (usually the microcosm) you can understand the other.[3]. Card I of the Major Arcana of the Waite Tarot Deck (alluded to throughout AtD) shows The Magician, simultaneously pointing up toward the sky and down toward the earth.
Slowly as God's justice
Must be noted given title and everything religious in ATD.
Page 797
upriver from Vanavara
"Ground zero" of the Event was 40 miles north of Vanavara.
"simultaneity" . . . Special Relativity
Einstein's special theory of relativity (1905) refutes the idea that two observers seeing two events can ever agree on whether the events were simultaneous. Adopters of the theory (and in 1908 they were all early adopters) would be asking one another if it applied to this phenomenon.
the error of the seismograph recordings . . . singularity
"Error" doesn't mean mistake or wrongness. It measures the variability within each instrument; every measurement comes with a plus-or-minus figure. If the Event happened instantaneously, each of the charts would record it as a more or less spread-out peak. The energy released in a process is calculated from the area under the curve of intensity versus time; to get the power (rate of energy release), divide the energy by the duration of the process. Even though he states the math wrongly, Vanderjuice suspects the seismographs of the world have responded to a titanic release of energy that took place in essentially no time at all, so that power = energy divided by zero. When physicists see a real process apparently demanding division by zero, they call it a singularity and go looking for an explanation.
the equations of history
Perhaps an allusion to Isaac Asimov's Foundation Trilogy, in which the Psychohistorian Harry Selden calculates equations of history. His equations are (seemingly) thrown off by the advent of a mutant with unusual powers that his predictive equations do not take into account--not unlike the advent of the Tunguska Event.
Tchernobyl, the star of Revelation
city in Ukraine where a nuclear meltdown occurred linked to Book of Revelation.
something that had not quite happened yet
In short, an Omen. The Tunguska Event could be seen as an omen of the destructive forces unleashed over the entire course of the 20th Century.
Circassian slave
Common figure in European literature about the "Lustful Turk." Circassia is a region in the Caucasus.
teppisti
Italian: hooligans, hoodlums, thugs
Page 798
mala vita
Italian: evil life. With more specific reference to Mafia style criminal organizations like the Malavita del Brenta of Venice. There is also a genre of songs glorifying Mafia life called canto di Malavita.
brides picotees
French: tickle straps
Page 799
"Bevis Moistleigh"
Bevis Mostly? Bevis Wetly?
Cf. Sir Bevis from Lang's Red Romance Book around this time. or a Twilight Zone story, Bevis 1960. See Wikipedia.
Or, see later in ATD, Bevis is an allusion to Beavis & Butthead. [Idiot]
Possibly, given what follows, an allusion to the Bevis Marks Synagogue in London, oldest extant Jewish house of worship in Britain [4], but more likely a reference to (p.800)Bevis,the Story of a Boy.
Glagolitic alphabet
See excellent annotation to page 252.
gematria
As described in the text, each letter of teh Hebrew alphabet is also a number. In the simplest form of Gematria, words, phrases and sentences with eqivalent numerical value are somehow linked, in a way promoting exegesis of Torah and Midrash (Torah commentary). More complex, mystical gematria systems are described in [5].
Page 800
fatkeqëse
Albanian: translated in the text as "disaster." Is this correct?
gongs
Medals.
Irredentism
A policy appealing to the idea that "our" lands are unredeemed, i.e., ruled by some outsider, and must be brought into our domain. See annotation to "Eurasia Irredenta" (page 761).
Bevis . . . the Story of a Boy
Theign taunts Bevis with the title of a popular novel, Bevis: the Story of a Boy (1882), by Richard Jefferies. From bits and pieces of the work quoted online (the book is apparently still in print), the narrative style and dialog writing appear similar to what we've seen in the early Chums passages. What's more, themes associated with this and other books by Jefferies (e.g., the beauty of the untouched countryside) align with some of the AtD themes. Jefferies also published a "post-Apocalypse" novel called After London. The Jefferies-Pynchon link may merit a closer look. --Volver 09:58, 30 January 2007 (PST)
Page 801
unprovided for in the future tense of any language
I.e., we have no simple way to describe future events in a chaotic system. You can't say that Chinese butterfly will cause a windstorm in Brazil.
High susceptibility to primordial variables
Chaos theorists talk about "extreme sensitivity to initial conditions."
"an emigration of reason itself".......Crusade"
Notice war talk and natural destruction around the Event.
Page 802
croakers
Slang: doctors, especially quacks.
Also: One who croaks, murmurs, grumbles, or complains unreasonably; one who habitually forebodes evil.
"Croaker" is a long-established (slang) word for "doctor," and in this passage it is quite clear that the doctors (performing curative activities to earn their fees but not really curing anything) feel they are putting one over on everybody else.
Some online citations:
- http://www.allaboutjazz.com/php/article.php?id=19757
- http://www.whysanity.net/monos/requiem.html
- http://cancer.iu.edu/news/research/archives/2000/06.pdf ("In the Spotlight," 2nd graf)
- http://www.classiccrimefiction.com/hardboiled-slang.htm
- http://www.hobonickels.org/alpert04.htm
- http://www.acsu.buffalo.edu/~jcnewman/definition.html
- In short, it wasn't the complainers who "thought they were putting one over," it was the quacks who administered expensive treatments for all ills.
- Slang, sic. I see. Another possible multiple TRP meaning, the complaining doctors, esp. quack "shrinks", relatively new at the time?
radioactive mud-bath slime
Treatment with naturally radioactive waters from hot springs was thought to cure many ailments. An example of a radioactive hot spring resort in Austria is Badgastein.
Mariahilf
The Sixth District of Vienna, known as a shopping district.
Page 803
midinettes
salesgirls (of Paris).
Facharbeiter
German: technician, specialist, skilled worker.
Gabika
"Cute" double diminutive for the Hungarian male name Gábor (Gabriel) and also, more commonly, for the female name Gabriella. The ambiguity (also his looks) fits finely the subversion of gender roles in his relationship to Noellyn Fanshawe.
Page 804
eleven
Vienna is 86 degrees west of the Event, more or less. Converting longitude to time at 15 degrees = 1 hour, we get a time difference of 5 hours 44 minutes. At 7:17 a.m. Event time, it was 1:33 a.m. in Vienna. Now, at 11:00 p.m. the same day, Vienna time, it is 21 hours and 27 minutes after the event. The atmospheric effect has propagated west (possibly against the high-level winds?) from Siberia to Central Europe in quite a short time. All these numbers are rough!
Page 805
prepare them against the day
Here the phrase means "in anticipation of" or "to be ready for."
And more. Thematic.
Given what has been said about the Tunguska Event, colored by accounts of the atmospheric effects of the Krakatoa eruption,highly suggestive of Judgment Day.
against the day
I shoulda been keepin' notes, dammit! I am sure that regularly through the book I have been spotting deliberate sentences ending with "... something the day"...but not, until now, with "against the day". And a few score pages ago I'm sure there was a sentence what ended w' "...against the night...", then Tunguska happens, and we now need to be wary o'the day..?
Page 806
Toward the end of October all Hell broke loose...annex Bosnia
The Bosnian Crisis began with the fear on the part of Austria-Hungary of possible reverses of Turkish concessions since the Russo-Turkish War of 1878 by the newly-resurgent Young Turk movement. The answer to this was annexation of Bosnia, which it had ruled as a colony since 1878. Knowing such a move would be opposed by Serbia, in turn supported by Russia, the Austrians offered to support the right of Russia to move warships through the Bosporus, and to support a declaration of independence from Turkey by Bulgaria. This provoked a general crisis [6] from which Serbia had to back down, lacking Russian support. All had been settled in secret meetings in the months before; the Bulgarian (Glagolitic) traffic intercepted by Bevis Moistleigh, above, is thus explained. So is the sense of Grand Conspiracy; all the Great Powers were eventuallly involved.
coconut-shy
A coconut shy (or coconut shie) is a traditional game frequently found as a sidestall at funfairs and fêtes. The game consists of throwing wooden balls at a row of coconuts balanced on posts. Typically a player buys three balls and wins each coconut successfully dislodged. In some cases other prizes may be won instead of the coconuts.
The origins of the game are unclear, although the term is first listed in the Oxford English Dictionary in 1903.
The word 'shy' in this context is a colloquial English term, meaning 'to throw' or toss. Wikipedia.
šlivovica
One of the spellings of this word for plum brandy (also slivovica, slivovitz, etc.).
one to fifty million . . . mile-to-the-inch sheets
Two extremes of mapmaking. A 1:50,000,000 map of the United States would fit comfortably on a page of AtD with most of Mexico and several Canadian provinces. Austria-Hungary at that scale would be about as big as your two thumbprints side by side.
The British Ordnance Survey produced a famous series of inch-to-the-mile sheets (1:63,360); the detail is about fine enough to show the left-turn lane of a city street. At this scale it would take some 200 unhandily large sheets to cover Austria-Hungary.
Decisions of the utmost gravity
that lead to Gravity's rainbows
Page 807
Major B. F. Vumb
Major Bum Fuck Vumb, as in Dumb? Another Pynchonian V-name
with the usual associations.
Judensau
German: Jewish pig.
Christian Socialists . . . Dr. Karl Lueger
Lueger (pronounced in three syllables, LOO eh ger) was a Viennese politician and founder of the anti-Semitic Christian Social Party.
Reichsrath
Austrian parliament.
Wer Jude ist, bestimme ich
German: as translated in text.
der schöne Karl
German: fine Karl. Deeply sarcastic.
Page 808
"Well actually..."
Shanghai, which because of its international status did not require a passport or visa for entry, would become a refuge for Jews made stateless by Nazi Germany or were otherwise refugees in the 1930s. Many tens of thousands were able to reach it, and survived the war and the Holocaust under Japanese occupation. Large numbers reached it using so-called Sugihara Passports, letters of transit issued by the Japanese vice-consul to Lithuania in 1940, with the connivance of Dutch diplomats[7]. Obviously an anachronism, but actually...this is about portents and other bends in Time, perhaps things that echo up and down the Timelines (ours and alternates).
Elefant Hotel
The only listed Elefant Hotel in Austria, a building described as "ancient", is in Salzburg, not Graz; it is currently a Best Western. There is also a Hotel Elefant in Prague, once part ot the Empire; perhaps there was a chain?
...common Anglo-Habsburg interests...
All the Great Powers found ways to benefit from the Bosnian Crisis, perhaps explaining Theign providing Italian naval decodes to the Austrians. Or, as Latewood accuses below, he is a double agent; McHugh is at least suspicious here. Either way, sending Latewood and Moistleigh on a suicide mission to Bosnia is one way to cover his tracks.
Murgasse
Street in Graz. The Murgasse was first mentioned in a document from 1346. The part of town to the south was occupied by the farmers.
Murgasse
8490 Bad Radkersburg, Austria
Page 809
Novi Pazar
Novi Pazar also figures briefly in GR (P.14-15, Viking eds.): "...on this obscure sanjak had once hinged the entire fate of Europe" The Novi Pazar desk is manned by Lord Blatherard Osmo. The crisis passed, but Lord Osmo has an adenoid, and this mucoid "lymphatic monster", now independently alive in 1939, is confronted by an agent of The Firm (an outfit very like its temporal predecessor the T.W.I.T. in its interests in the paranormal) , one "Pirate" Prentice; it is "now as big as St Paul's and growing by the hour" threatening all London, but confined successfully--leading to Lord Osmo's neglect of Novi Pazar...A bizarre satiric experience of Crisis Management by Great Power foreign ministries, and the literally sticky mess they created.
the vile Aerenthal
Aloys (or Alois) von Aerenthal (1854-1912), Austrian foreign minister who engineered the annexation of Bosnia in 1908.
in three-quarter time
Two plausible references: events driven by Vienna, the world's waltz capital, and a dark comic song recorded by the Kingston Trio in the 1960s: "Merry Minuet." In 3/4 time, it includes lyrics commenting on ethnic hatred, irredentism and inevitable nuclear catastrophe.
One could also add Ravel's La Valse.
Note the chain-like sliding/closing/turning step sequence in Viennese Waltz, and also the rhythm itself represented by the repeated dactyl "and so on, and so on".
In fact, the sequence of events described here as a possibility in 1908 were realized in 1914, when Russia, in the crisis provoked by a Serbian youth group's assassination of Archduke Ferdinand of Austria, this time backed Serbia, resulting in the cascade of troop mobilizations that became World War I.
Isvolsky
A.P. Izvolsky (Izvolski, Izvolskii) (1856-1919), Russian foreign minister who traded Bosnia-Herzegovina to Austria in exchange for Austria's help in opening the Bosporus and Dardanelles to Russian ships. Pynchon's spelling may well be from a contemporary source; consistent transliteration is a more recent fetish.
Grey
Sir Edward Grey (1862-1933), British Foreign Secretary 1905-16.
Page 810
It's like having the lights brought up for a bit...
As the crisis wound down to war in 1914, Sir Edward Grey (still Foreign Minister) is famously quoted as having said, "The lamps are going out all over Europe; we shall not see them lit again in our lifetime."[8]
Vlado Clissan
His name comes from his hometown of Clissa, but this is the Italian name of the place. In Serbo-Croatian it is Klis. A pseudonym?
Blutwurst Special
German: blood sausage.
Page 811
"iron convergences and receding signal-lamps"
our 'free choices' in...life; so ironic at this point.
Kurt Vonnegut, in Slaughterhouse Five, described the human point of view as from consciousness strapped to a railroad car, forever facing only backward; from this vantage, history looks single and inevitable, whereas in reality the train of history is moving over unknown numbers of (from this perspective unseen) switch points, the settings of which are in fact changeable (the more complex view being taken by an extraterrestrial species, the Tralfamadorians, who can see forward to the many possibilities), alternate histories possible at every switch. The character Pointsman in GR in some ways embodies these possibilities.
Slavonian
Today the name applies to the eastern part of Croatia, but a map will confirm that the route passes through the Slovenian plain. Writers before the World War must have had difficulty keeping Slovenia, Slovakia and Slavonia straight, especially since all were inhabited by Slavonic peoples.
Austrian double
Latewood, in light of Theign's treatment of Yashmeen, and the apparent passing of Italian naval decrypts to Austria, accuses Theign of being an Austrain double agent.
Page 812
Mestre Bridge
Mestre is a town in Veneto, northern Italy, a frazione of the comune of Venice. Located on the mainland,the city is connected to Venice by a large rail and road bridge, called Ponte della Libertà (Freedom Bridge).
Page 813
And England's far, and honour a name
Cyprian quoting from the 1897 poem "Vitaï Lampada" ("They Pass the Torch") by Sir Henry Newbolt (1862-1938), previously quoted on page 236.
"honour"
Cf. Falstaff on.
Page 814
Lateeners
A lateener is a boat with a lateen sail: a triangular sail with one edge tied to a long spar, which is supported in the middle on a mast.
Strichmädchen
German: streetwalker.
LLoyd Austriaco
A ship line. Lloyd Triestino was formed in 1919 as the successor to Lloyd Austriaco following the incorporation of Trieste into the Kingdom of Italy on January 3rd 1919.
Page 815
"Nimrod" . . . from Elgar's Enigma Variations
"Nimrod" is the ninth section of this major 1899 work by English composer Edward Elgar (1857-1934). Like the other 13 sections, it characterizes a family friend; this one is A. J. Jaeger (whose name means "hunter" in German, hence "Nimrod," the name of a hunter mentioned in the Bible). Here is a very good description of the work and "Nimrod" in particular.
The "Nimrod" variation is perhaps the most poignant of the piece; it rises to a cresendo and slowly, sadly, fades; an anthem for the fading of the 19th century.
"La Gazza Ladra"
Overture by Rossini to an opera whose title means "The Thieving Magpie." It is as bright and impersonal as "Nimrod" is serious and sentimental.
"The Volga Boatmen" . . . "Auld Lang Syne"
The puzzle in the "Enigma" Variations is this: Variations are based on a theme, but Elgar never states the theme; what is the melody? These are two of the popular guesses.
Δt
Mathematical symbol used for a finite length of time.
In addition, Pynchon is very concerned with dt,(little delta-t) the time differential, an infinitesimal change in time; to quote Pynchon from Lot 49 (Lippincott, 1965 p.129): "a vanishingly small instant in which change had to be confronted at last for what it was, where it could no longer disguise itself as something innocuous like an average rate; where the velocity dwelled in the projectile though the projectile be frozen in midflight, where death dwelled in the cell though the cell be looked in on at its most quick." But, the paragraph goes on, "dt" also suggests DTs, Delirium Tremens (alcohol withdrawal) a state giving access to hallucinatory experiences, "spectra beyond the known Sun, music made purely of Antarctic loneliness and fright." Which is the general mood in the wake of the Tunguska Event and the Bosnian Crisis, or should be, if the characters were not so dutifully repressing it. (In Lot 49 the realization of the dt/DTs connection has to do with Oedipa Maas' realization of the finality of death, and what inaccessible realms of experience are lost with each individual's death).
- Are you confusing Δt, symbolizing a finite duration, with dt, a duration shrunk to an infinitesimal?(Possibly--my physics/calculus may be rusting. The connection may still hold; note emendation above--thanks. Edit further if necessary!).
co-conscious with the everyday
again. Linked to creativity here.
Ramanujan's Formula
an elegant hyperbolic summation, Ramanujan's formula for the Riemann zeta function evaluated at the odd positive integers. Ramanujan didn't come to the attention of Western mathematicians until he wrote to Hardy in late 1912 - early 1913 and travelled to Cambridge in 1914. Is Yashmeen prescient?
Page 816
dolce far niente
Italian: sweet doing-nothing.
divided second
A dt.
of his entry
Vlado the Impaler?
the Karst
Generic "karst topography" takes its name from this area of Slovenia and Italy (locally called kras and carso). The terrain features limestone with fissures and cavities eroded by water. Caves as well as underground streams and lakes are common.
Illyria
The Roman province in which modern Trieste is located.
Page 817
quiet spaces between trams, unpredictable, even, she imagined, mathematically so
Two familiar "rhythms" have this quality of chaotic intervals: the beating of the human heart and the sound of water dripping from a faucet. The second part of the phrase is subtle: the time of the next drip can't be mathematically predicted (to arbitrary accuracy), but it is possible to describe in mathematical terms the way in which it's unpredictable.
never farther than half a block from the counter-soporific fluid
Perhaps an allusion or parallel to the 21st century ubiquity of Starbucks.
Svr šavam!
Croatian/Serbian: I'm finishing. Also, implausibly, written Svršavam.
Velebit
A ridge that runs parallel to the Croatian Adriatic coast a few tens of miles south of Trieste. Lying a short distance inland, it is made up of limestone karst.
Page 818
persisted from day to day
The image again of the storm that retains its identity over a long time.
Stationary waves
Crests and troughs that don't move. Seen more often where water is flowing (up/downstream of rocks in rapids), but also where waves coming onshore interact with those reflected from the shore.
Uskok
Serbian/Croatian: fugitive. Writers even in antiquity noted that piracy was a main economic activity along this coast.
In all, Vlado seems very like the Traverse brothers, set against the modern world, or anyway modern power arrangements, a bit of an anarchist in his own way. But his grievances have historic depth and resonance, more of what Pynchon in V. called "Temporal Bandwidth".
Clissa
Town from which Vlado Clissan takes his nom de guerre. Locally called Klis.
Page 819
Page 820
John of Asia
John of Asia, also called John of Ephesus, was a 6th-century church leader and historian. The ruins of Ephesus are located in western Asia Minor, now in Turkey.
coastline approaching infinite length
Another reference to the "crisis" in mathematics. The closer you look at the coastline, the longer it gets. If you could view it from infinitely close up, it would become infinitely long. This is a specific reference to Fractal Geometry (another fractal reference self-similarity over scale occurs on page 575) Benoit Mandelbrot, in Fractals: Form, Chance and Dimension discusses the infinite coastline of Britain: "We will see that...the final estimated length is not only extremely large but in fact so large that it is best considered infinite."). The Euclidean view of the coastline's length would be akin to simply measuring off the distance around the island. The fractal view suggests however, that the coastline is far from straight. The fact that a coastline is usually rugged with twists and turns both small and large leads us to conclude that the actual length of the coastline is much larger than the straight-line distance. The more we examine the twists and turns, the more we realize that they are smaller and smaller copies of the larger original, making their way deeper and deeper into the coastline itself. Depending upon how small a yardstick we choose to measure the coastline, the numeric outcome becomes larger. The final length of our measured coastline becomes bigger and bigger as the essence of what we measure becomes smaller and smaller, i.e., the estimated length continues to increase as the ruler length decreases.
Annotation Index
Part One: The Light Over the Ranges |
|
---|---|
Part Two: Iceland Spar |
119-148, 149-170, 171-198, 199-218, 219-242, 243-272, 273-295, 296-317, 318-335, 336-357, 358-373, 374-396, 397-428 |
Part Three: Bilocations |
429-459, 460-488, 489-524, 525-556, 557-587, 588-614, 615-643, 644-677, 678-694 |
Part Four: Against the Day |
695-723, 724-747, 748-767, 768-791, 792-820, 821-848, 849-863, 864-891, 892-918, 919-945, 946-975, 976-999, 1000-1017, 1018-1039, 1040-1062 |
Part Five: Rue du Départ |