Algebraic Structures and Metaphor in Gravity’s Rainbow

Taylor, Stuart J.

doi:10.1007/978-3-031-48671-5_3

Stuart J. Taylor⁵

Part of the book series: Palgrave Studies in Literature, Science and Medicine ((PLSM))

Abstract

This chapter examines intersections of mathematics and literature within encyclopedic narratives by Thomas Pynchon. My interdisciplinary approach draws upon the case of Nicolas Bourbaki, whose ‘encyclopedic’ treatise, Éléments de mathématique, provides an important cultural touchstone for contemporary visions of mathematics as a totalized system. One group of Bourbaki’s three ‘great’ or ‘mother-structures’—algebraic structures—is used to analyse Pynchon’s Gravity’s Rainbow. Expanding on the preceding chapter’s exploration of topological, Möbian structures of allusion in DeLillo’s Ratner’s Star, algebraic structures here permit analysis of metaphor in Pynchon’s work. Thus, the difficult equations in Gravity’s Rainbow are compared with similar structures in works by Bunyan and Catherine Asaro to highlight mathematical models of Thomas Pynchon’s metaphorical processes. This reading prepares the reader for further explorations, in subsequent chapters, of David Foster Wallace’s use of enumerated endnotes in Infinite Jest and Everything & More, understood through ordered structures as Wallace’s hierarchical manipulation of narrative containers as mathematically informed cognitive models. By regarding the topological, algebraic, and ordered structures of mathematics as modelling DeLillo, Pynchon, and Wallace’s figurative strategies—respectively, of allusion, metaphor, and cognition—the interplay between mathematics and encyclopedic narrative can be better appreciated.

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Notes

1.
Hayles, Cosmic Web, p. 27.
2.
Hayles, Cosmic Web, pp. 168–169.
3.
Hayles, Chaos Bound, p. 6.
4.
Hayles, Chaos Bound, p. xii.
5.
Mark R. Siegel, ‘Creative Paranoia: Understanding the System of Gravity’s Rainbow’, Critique: Studies in Contemporary Fiction, 18.3 (1977), 39–54 (p. 44).
6.
Bersani, p. 182.
7.
Safiya Umoja Noble, Algorithms of Oppression: How Search Engines Reinforce Racism (New York: New York University Press, 2018), p. 149. C.f. Yves Citton, ‘Triangulate: Literature and the Sciences Mediated by Computing Machines’ in The Triangle Collective (ed.), The Palgrave Handbook of Twentieth and Twenty-First Century Literature and Science (London: Palgrave Macmillan, 2020), pp. 97–115, p. 102.
8.
Bersani, p. 198.
9.
Frye, p. 352.
10.
George B. Moore, ‘Paranoia and the Aesthetics of Chaos in Thomas Pynchon’s Gravity’s Rainbow’, in Allegory Old and New: In Literature, the Fine Arts, Music and Theatre and Its Continuity in Culture, ed. by Marlies Kronegger and Anna-Teresa Tymieniecka (Dordrecht: Springer, 1994), pp. 203–18 (pp. 203–205).
11.
Ibid., p. 212.
12.
Steven H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Reading, MA: Perseus Books, 1994), p. 2.
13.
Strogatz, pp. 8–9.
14.
Strogatz, p. 5.
15.
G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge: Cambridge University Press, 2000), p. 147.
16.
Bourbaki, p. 226.
17.
David Rayner, Higher GCSE Mathematics: Revision and Practice (Oxford: Oxford University Press, 2001), p. 63. E.g. ‘if a + b = c, where b = 2 and c = 3, find the value of a’.
18.
Tubbs, p. 39.
19.
Mashaal, p. 79.
20.
Claude Berge, ‘For a Potential Analysis of Combinatory Literature’, in Oulipo: A Primer of Potential Literature, ed. by Warren F. Motte, Jr. (London: Dalkey Archive Press, 1998), p. 56.
21.
By extension, the S + 7 version now bears an ‘S – 7’ relation to the ‘original’ text. This extension, called ‘eclipse’, liberates the original text from a position of primacy, and the calculated text from a secondary position.
22.
Euclid, The Thirteen Books of The Elements, trans. by Sir Thomas L. Heath, 2nd edn, 3 vols (Cambridge: Cambridge University Press, 1968), 1 (Books I and II), p. 155.
23.
Lescure arrives at this transformation after going through the preceding iterations of the algebraic structure,+2, +4, +5, + 6, yielding (respectively), ‘drôles [funny (things)]’, ‘drôlesses [(funny) wenches]’, ‘dromadaires [camels]’, ‘druides [druids]’—Jean Lescure, ‘La Méthode S + 7 (Cas Particulier de La Méthode M ± N)’, in La Littérature Potentielle: Créations, Re-Créations, Récréations, ed. by Oulipo (Paris: Gallimard, 1973), pp. 143–48 (p. 148, my translation).
24.
Alison James, p. 129.
25.
Alison James, p. 130.
26.
For example ‘You never did. | The Kenosha Kid’; ‘you never did the “Kenosha Kid”’; ‘You, Never? …. Did the Kenosha Kid?’ (GR 60; 71).
27.
Strogatz, pp. 8–9.
28.
“linearize, v.” OED Online, Oxford University Press, June 2018, www.oed.com/view/Entry/108620 [accessed 10 September 2023]. Cf. Krzysztof Kowalski and W. H. Steeb, Nonlinear Dynamical Systems and Carleman Linearization (London: World Scientific Publishing, 1991), pp. 7–8.
29.
Sokal and Bricmont, pp. 131–133.
30.
Tony Tanner, Thomas Pynchon (London: Methuen, 1982), p. 75, emphasis added.
31.
E.g. Hugh Caviola, In the Zone: Perception and Presentation of Space in German and American Postmodernism (Basel: Birkhäuser Verlag, 1991); Theophilus Savvas, American Postmodernist Fiction and the Past (Basingstoke: Palgrave Macmillan, 2011), pp. 40–66.
32.
Zofia Kolbuszewska, The Poetics of the Chronotope in the Novels of Thomas Pynchon (Lublin: Learned Society of the Catholic University of Lublin, 2000), p. 117.
33.
Kolbuszewska, p. 142.
34.
Hanjo Berressem, Pynchon’s Poetics: Interfacing Theory and Text (Chicago: University of Illinois Press, 1993), p. 121, original emphasis.
35.
Frye, p. 321.
36.
John M. Krafft, ‘Chronology of Pynchon’s Life and Work’, in The Cambridge Companion to Thomas Pynchon, ed. by Inger H. Dalsgaard, Luc Herman, and Brian McHale (Cambridge: Cambridge University Press, 2012), pp. x–xii.
37.
Linda Hutcheon, A Poetics of Postmodernism: History, Theory, Fiction (London: Routledge, 1988), p. 203.
38.
Jean Bricmont, ‘Science of Chaos or Chaos in Science’, in The Flight from Science and Reason, ed. by Paul R. Gross, Norman Levitt, and Martin W. Lewis (New York: The New York Academy of Sciences, 1996), pp. 131–75 (p. 149).
39.
Tubbs, p. 39.
40.
Christopher Clapham and James Nicholson, The Concise Oxford Dictionary of Mathematics, 5th edn (Oxford: Oxford University Press, 2014), p. 472.
41.
Kiyosi Itô, Encyclopedic Dictionary of Mathematics, 2nd edn, 2 vols (Cambridge, MA: MIT Press, 1993), ii (p. 1678). Cf. Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality (New York: Alfred A. Knopf, 2004), pp. 156–176.
42.
Molly Hite, Ideas of Order in the Novels of Thomas Pynchon (Columbus: Ohio State University Press, 1983), p. 97.
43.
This reading of poetics is counter to that of the rhetorical tradition of Cicero and Quintilian, which collapse distinctions between metaphor and allegory. Thus, Gordon Teskey argues that allegory is that ‘which gives meaning a place to occur but which does not become meaning itself’ and thus can situate metaphorical surprise—Gordon Teskey, Allegory and Violence (London: Cornell University Press, 1996), p. 19. This conception of allegory-as/from-metaphor is that used by some critics of Gravity’s Rainbow—cf. Lynette Hunter, ‘Allegory Happens: Allegory and the Arts Post-1960’, in The Cambridge Companion to Allegory, ed. by Rita Copeland and Peter T. Struck (Cambridge: Cambridge University Press, 2010), pp. 266–80 (p. 270); Maureen Quilligan, ‘Twentieth-Century American Allegory’, in Thomas Pynchon, ed. by Harold Bloom (Philadelphia: Chelsea House, 2003), pp. 93–108 (p. 93). While Quilligan reads Gravity’s Rainbow as ‘a great allegory’, it is so as an ‘allegory of language’—the less definitive type conceived also by Teskey and Hunter—and not the more restrictive sense of allegory, which she defines as a ‘static superstructure’ in ‘service to a dogma’—Quilligan, p. 106. It is this restrictive, static sense which, I argue, Pynchon resists with his metaphorical system of algebraic structures. By distinguishing between the allegorical and the metaphorical, my reading follows Angus Fletcher who argues that ‘Equating allegory with metaphor is likely to lead to a narrow, stultifying view of those works that are most interesting’—Angus Fletcher, Allegory: The Theory of a Symbolic Mode (Princeton, NJ: Princeton University Press, 2012), p. 71.
44.
Fletcher, p. 156.
45.
Fletcher, p. 157.
46.
John Bunyan, The Pilgrim’s Progress, From This World, To That Which Is To Come: Delivered Under The Similitude of a Dream In Three Parts (Gainsborough: Henry Mozley, 1809), p. 22.
47.
Quilligan, p. 93.
48.
Aristotle, The Works of Aristotle, ed. by W. D. Ross, trans. by W. Rhys Williams (Oxford: Clarendon Press, 1924), 11 Rhetorica (Book III, Chapter 12, 1412a).
49.
Kenneth J. Knoespel, ‘The Emplotment of Chaos: Instability and Narrative Order’, in Chaos and Order: Complex Dynamics in Literature and Science, ed. by N. Katherine Hayles (London: University of Chicago Press, 1881), pp. 100–122 (p. 118).
50.
Steven C. Weisenburger, A Gravity’s Rainbow Companion: Sources and Contexts for Pynchon’s Novel, 2nd edn (London: University of Georgia Press, 2006), p. 75.
51.
Weisenburger, p. 75.
52.
Rainer Maria Rilke, ‘Sonnet 12’, Second Series, in Duino Elegies and The Sonnets to Orpheus, trans. by A. Poulin, Jr. (Boston: Houghton Mifflin Company, 1977), pp. 160–161.
53.
N. Katherine Hayles, How We Became Posthuman: Virtual Bodies in Cybernetics, Literature, and Informatics (London: University of Chicago Press, 1999), p. 22.
54.
Tubbs, p. 39.
55.
Tubbs, p. 41.
56.
Joseph W. Slade, Thomas Pynchon (New York: Warner Paperback Library, 1974), p. 13; Robert L. Nadeau, ‘Readings from the New Book of Nature: Physics and Pynchon’s “Gravity’s Rainbow”’, Studies in the Novel, 11.4 (1979), 454–71, p. 454; Robert D. Newman, Understanding Thomas Pynchon (Columbia: University of South Carolina Press, 1986), p. 3.
57.
Krafft, p. x.
58.
Matthew Winston, ‘The Quest for Pynchon’, Twentieth Century Literature, 21.3 (1975), 278–87 (pp. 284–5).
59.
Adrian Wisnicki, ‘A Trove of New Works by Thomas Pynchon? Bomarc Service News Rediscovered’, Pynchon Notes, 46–49 (2000), 9–34. Katie Muth’s preliminary findings—‘Archival Report’, American Studies in Britain: The BAAS Newsletter, 2015 http://baas.ac.uk/muthfoundersaward2015—are to be developed in ‘The Grammars of the System: Thomas Pynchon at Boening’ in a forthcoming special issue of Textual Practice.
60.
Wisnicki, p. 9. Bomarc Service News features ‘articles attributable to Pynchon’ which ‘contain erudite historical discussions’; some of these articles, Wisnicki argues, ‘relate directly to Gravity’s Rainbow’. For example, the A4/V-2 rocket is discussed in ‘Hydrazine Tank Cartridge Replacement’, included in the 38th issue of Bomarc Service News (September 1962, page 3) and in ‘Missile Ground Support Equipment’, reprinted in Aerospace Accident and Maintenance Review (December 1991, page 3)—Wisnicki, p. 23.
61.
A term coined by P. Schuyler Miller, ‘Review: Islands of Space by John W. Campbell, Jr.’, Astounding Science Fiction, 60.3 (1957), 142–44.
62.
Mendelson, p. 1267; p. 1270.
63.
Thomas Pynchon, ‘Is It O.K. to Be a Luddite?’, The New York Times Book Review, 1984, 40–41.
64.
Linda Hutcheon, ‘Beginning to Theorize Postmodernism’, Textual Practice, 1.1 (1987), 10–31 (p. 12); Poetics, p. 5; p. 112.
65.
Hutcheon, Poetics, pp. 109–110.
66.
Hutcheon, Poetics, pp. 58–9.
67.
Giuseppe Episcopo (ed.), Twentieth-Century Rhetorics: Metahistorical Narratives and Scientific Metafictions (Napoli: Cronopio, 2015), blurb. As supported in the collection by Martin Paul Eve, Nina Engelhardt, Francisco Collado-Rodriguez, Terry Reilly, Giuseppe Episcopo, and Amy J. Elias.
68.
Thomas Moore, The Style of Connectedness: Gravity’s Rainbow and Thomas Pynchon (Columbia: University of Missouri Press, 1987), p. 151, emphasis added.
69.
Luc Herman, ‘Early Pynchon’, in The Cambridge Companion to Thomas Pynchon, ed. by Inger H. Dalsgaard, Luc Herman, and Brian McHale (Cambridge: Cambridge University Press, 2012), pp. 19–29 (p. 22). Following Anne Mangel’s study—Anne Mangel, ‘Maxwell’s Demon, Entropy, Information: The Crying of Lot 49’, TriQuarterly, 20 (1971), 194–208—important highlights include: Alan J. Friedman and Manfred Puetz, ‘Science as Metaphor: Thomas Pynchon and “Gravity’s Rainbow”’, Contemporary Literature, 15.3 (1974), 345–59; Joseph Tabbi, ‘Pynchon’s Entropy’, Explicator, 43.1 (1984), 61–63; Dan O’Hara, ‘On the Line of Flight: Pynchon’s Entropy Machine’, Pynchon Notes, 34–35 (1994), 56–69; Lance Schachterle, ‘Information Entropy in Pynchon’s Fiction’, Configurations: A Journal of Literature, Science, and Technology, 4.2 (1996), 185–214.
70.
Stephen P. Schuber, ‘Rereading Pynchon: Negative Entropy and “Entropy”’, Pynchon Notes, 13 (1983), 47–60 (p. 48).
71.
Schuber, pp. 48–49, p. 58.
72.
David Letzler, ‘Crossed-Up Disciplinarity: What Norbert Wiener, Thomas Pynchon, and William Gaddis Got Wrong about Entropy and Literature’, Contemporary Literature, 56.1 (2015), 23–55 (p. 53).
73.
Letzler, p. 53.
74.
Shannon, quoted in Myron Tribus and Edward C. McIrvine, ‘Energy and Information’, Scientific American, 224 (1971), 179–88 (p. 180).
75.
A line of enquiry that continues to be prominent in Pynchon studies—c.f. Susanne Schregel, Nicoletta Asciuto, Nina Engelhardt (ed.) Space and culture ‘Special Issue: Above. Degrees of Elevation’ (November 2020) 23:4.
76.
Linda Hutcheon ‘Beginning’, p. 12; Poetics, p. 5; p. 116; p. 133.
77.
Simon de Bourcier, Pynchon and Relativity: Narrative Time in Thomas Pynchon’s Later Novels (New York: Continuum, 2012), p. 198.
78.
Ibid.
79.
‘vector, n.’ OED Online, Oxford University Press, June 2018, www.oed.com/view/Entry/221825 [accessed 10 September 2023].
80.
Sir Arthur Eddington, The Nature of the Physical World (New York: Macmillan, 1929), p. 69.
81.
Eddington, Nature, p. 66.
82.
Eddington, Nature, pp. 66–67.
83.
Moore describes the ‘entropic “arrow of time”’ without reference to Eddington (Moore, 1987, 162) while Hite’s acknowledgment that ‘The second law is frequently called Time’s Arrow because it is the only physical precept that makes physical processes irreversible’ is informed by the Eddington-indebted Time’s Arrow and Evolution by Harold Francis Blum’s—Thomas Moore, p. 162; Hite, p. 106, 165n11. Despite Simon de Bourcier’s slight references to Eddington, Pynchon and Relativity does not contain any reference to Eddington’s The Nature of the Physical World—de Bourcier, p. 114, 120. In a similar omission, Nina Engelhardt cites The Nature of the Physical World but only to contextualize the famous story of Newton ‘discovering’ gravity from a fallen apple—Nina Engelhardt, ‘Gravity in Gravity’s Rainbow—Force, Fictitious Force, and Frame of Reference; or: The Science and Poetry of Sloth’, Orbit: Writing Around Pynchon, 2014, 1–26 (p. 9).
84.
Eddington, Nature, p. 68.
85.
Hite, p. 106.
86.
Schuber, p. 50.
87.
Slade, p. 215, pp. 218–219.
88.
‘In the paradox of the arrow, Zeno has been accused of an (understandable) inability to distinguish between instantaneous motion and instantaneous rest. … Today we assign a meaning to “instantaneous velocity” … through the concept of the derivative. It is important to note, however, that this notion is defined by a limit process, so the value of the velocity at an instant depends logically upon what happens at neighboring instants. Instantaneous velocity is taken as the limit of ratios of space and time increments (average velocities) taken over ever decreasing time intervals’—Zeno’s Paradoxes, ed. by Wesley C. Salmon (Cambridge: Hackett Publishing Company, 2001), p. 24.
89.
Slade, p. 238. Stefan Mattessich observes similar transformative potential in the critical evaluation of cultural-historical moments: ‘the time retroactively projected on the 1960s by progressives and conservatives alike today has to be a function of how it is read, since in our time, time is a function of language, not a linear and represented series of self-present moments but a catastrophic (or catastropic) and heterological displacement requiring of historical consciousness that it grasp its own symptomaticity in the act of constituting its object’—Stefan Mattessich, Lines of Flight: Discursive Time and Countercultural Desire in the Work of Thomas Pynchon (London: Duke University Press, 2002), p. 211.
90.
Lance Ozier, ‘The Calculus of Transformation: More Mathematical Imagery in Gravity’s Rainbow’, Twentieth Century Literature, 21:2 (1975), 193–210 (p. 194).
91.
Ozier, ‘Calculus’, p. 194.
92.
Ozier, ‘Calculus’, p. 197.
93.
Nina Engelhardt, ‘Formulas of Change, Alternative, and Fiction: Mathematics in Thomas Pynchon’s Gravity’s Rainbow and Against the Day’, Variations, 21 (2013), 131–44 (p. 132).
94.
Ozier, ‘Calculus’, p. 193.
95.
Levey, p. 30.
96.
Ozier, ‘Calculus’, p. 194.
97.
Levey, p. 30.
98.
Lance Schachterle and P. K. Aravind, ‘The Three Equations in Gravity’s Rainbow’, Pynchon Notes, 46–49 (2000), 157–69 (p. 157).
99.
Schachterle and Aravind, p. 157.
100.
Schachterle and Aravind, p. 165.
101.
Clapham and Nicholson, p. 98, pp. 288–290.
102.
Schachterle and Aravind, p. 159.
103.
Schachterle and Aravind, p. 165.
104.
Despite the title of Schachterle and Aravind’s essay, this second mathematical inscription is not an equation: it bears no equals sign.
105.
Schachterle and Aravind, p. 166.
106.
Schachterle and Aravind, p. 165.
107.
Ibid.
108.
Schachterle and Aravind, p. 160.
109.
Nina Engelhardt and Harald Engelhardt, ‘The Momentum of Pynchon’s Secret Formula: Gravity’s Rainbow’s Second Equation Between Archival Sources and Fiction’, Orbit: A Journal of American Literature, 6.1 (2018), 1–27.
110.
Englehardt, ‘Formulas’, p. 132.
111.
Engelhardt, ‘Formulas’, p. 135.
112.
Engelhardt, ‘Formulas’, p. 136.
113.
Albert Einstein, ‘Geometry and Experience’, in Ideas and Opinions, by Albert Einstein, trans. by Sonja Bargmann (London: Souvenir Press, 1973), pp. 232–46 (pp. 232–3).
114.
Einstein, pp. 233–4.
115.
John W. Aldridge, The American Novel and the Way We Live Now (Oxford: Oxford University Press, 1983), p. 54. Richard Locke writes in the New York Times ‘Pynchon doesn’t create characters so much as mechanical men’, while James Wood despairs at ‘what Pynchon does with his characters, increasingly juvenile vaudeville’ and Michiko Kakutani hates his ‘flimsy paper dolls’—Richard Locke, ‘One of the Longest, Most Difficult, Most Ambitious Novels in Years’, The New York Times Book Review, 1973 https://archive.nytimes.com/www.nytimes.com/books/97/05/18/reviews/pynchon-rainbow.html [accessed 10 September 2023]; James Wood, ‘Compliments of Sorts’, London Review of Books, 31.21 (2009), Letters; Michiko Kakutani, ‘Another Doorway to the Paranoid Pynchon Dimension’, The New York Times, 4 August 2009, section Books http://www.nytimes.com/2009/08/04/books/04kaku.html [accessed 10 September 2023].
116.
Thomas Pynchon, V. (London: Vintage, 2000), p. 14; GR 369; Thomas Pynchon, Mason & Dixon (London: Vintage, 1998) (first publ. 1997), p. 21 (subsequently cited as ‘MD’). Bodine first appears in Pynchon’s short story ‘Low-Lands’—Thomas Pynchon, Slow Learner: Early Stories (London: Jonathan Cape, 1985), pp. 53–77 (p. 60). According to Pynchon, Bodine was based on a ‘drinking companion’ of a ‘gunner’s mate on my ship’ during Pynchon’s time in the merchant navy. The day before he was discharged from service, Pynchon met this real-life ‘counterpart’ to his character—Slow Learner, pp. 10–11.
117.
A notable exception to this pattern is his latest novel, Bleeding Edge, in which the closest sentiment to ‘single up all lines’ is a character’s description of post-9/11 Halloween celebrations in New York: ‘Everything collapsed into the single present tense, all in parallel’—Thomas Pynchon, Bleeding Edge (London: Jonathan Cape, 2013), p. 374.
118.
Hanjo Berressem, ‘How to Read Pynchon’, in The Cambridge Companion to Thomas Pynchon, ed. by Inger H. Dalsgaard, Luc Herman, and Brian McHale (Cambridge: Cambridge University Press, 2012), pp. 168–77 (p. 175).
119.
As a nautical command, the term refers to the mooring ropes aboard a vessel about to depart. Completing the ‘single up’ renders the vessel to the mooring point (on a jetty, for example) by a single rope, that is, a ‘single line’. ‘Single up’: to ‘[t]ake Take in all additional parts, leaving a single line at each station’—‘Manual of Commands and Orders 1945’, Naval History and Heritage Command https://web.archive.org/web/20190327181122/https://www.history.navy.mil/research/library/online-reading-room/title-list-alphabetically/m/manual-of-commands-and-orders-1945.html [accessed 10 September 2023]; Mike MacKenzie, Seatalk: The Dictionary of English Nautical Language, 2005 https://web.archive.org/web/20160702192036/http://www.seatalk.info/cgi-bin/nautical-marine-sailing-dictionary/db.cgi?db=db&uid=default&FirstLetter=s&sb=Term&view_records=View+Records&nh=11 [accessed 10 September 2023].
120.
Beer, Darwin’s Plots, p. 74.
121.
Catherine Asaro, Spherical Harmonic (New York: Tom Doherty Associates, 2001), p. 16.
122.
Asaro, Spherical Harmonic, p. 48.
123.
Ibid, original emphasis. Asaro’s manifest exploration of ‘what it means to be embodied in high-tech worlds’ is, like Pynchon’s, facilitated by mathematical imagery—Donna J. Haraway, ‘A Cyborg Manifesto: Science, Technology, and Socialist-Feminism in the Late Twentieth Century’, in Simians, Cyborgs, and Women: The Reinvention of Nature (New York: Routledge, 1991), pp. 149–81 (p. 173).
124.
Asaro, Spherical Harmonic, p. 409.
125.
Asaro, Spherical Harmonic, pp. 409–410.
126.
While it may appear that Asaro is less prescriptive in other works—for example, in the ‘Author’s Note’ for her 2003 novel The Moon’s Shadow, Asaro recognizes that ‘Other interpretations exist for the moons, their shadows, and their symbolism’—even here she presents a dominant reading of the novel’s ‘Moons of Glory’ as the moons of Saturn, going as far do describe her narrative as composed of such ‘allegories’—Catherine Asaro, The Moon’s Shadow (New York: Tor, 2004), p. 397, p. 393. See also her mathematical defense of the possibility of time travel—Catherine Asaro, ‘Complex Speeds and Special Relativity’, American Journal of Physics, 64 (1996), 421–9.
127.
Asaro, Spherical Harmonic, p. 167.
128.
John H. Mathews and Russell W. Howell, Complex Analysis for Mathematics and Engineering (Boston: Jones and Bartlett Publishers, 2006), p. 85.
129.
Asaro, Spherical Harmonic, p. 167.
130.
Bersani, p. 193.
131.
Against the Grain: Reading Pynchon’s Counternarratives, ed. by Sascha Pöhlmann (Amsterdam: Rodopi, 2010).
132.
Arthur Saltzmann, ‘“Cranks of Ev’ry Radius”: Romancing the Line in Mason & Dixon’, in Pynchon and Mason & Dixon (Newark: University of Delaware Press, 2000), pp. 63–72 (p. 65).
133.
Theophilus Savvas observes this phrase recurring throughout Mason & Dixon, yet it is also important to note its prevalence throughout Pynchon’s writing—Savvas, p. 78.
134.
Pynchon, V., p. 11, emphasis added.
135.
Pynchon, V., p. 306.
136.
Thomas Pynchon, The Crying of Lot 49 (London: Vintage, 2000), p. 20, emphasis added. Subsequent citations in main text, in parentheses, as ‘Lot 49’.
137.
Cf. M. I. Kalinin and S. A. Kononogov, ‘Fundamental Problems in Metrology: Boltzmann’s Constant, The Energy Meaning of Temperature, and Thermodynamic Irreversibility’, Measurement Techniques, 48.7 (2005), 632–36 (p. 634).
138.
Claude E. Shannon, ‘A Mathematical Theory of Communication’, The Bell System Technical Journal, 27.3 (1948), 379–423 (p. 393).
139.
Hite, p. 133.
140.
Hite, p. 115.
141.
Thomas Moore, p. 173.
142.
Engelhardt and Engelhardt, p. 24.
143.
Hite, p. 150.
144.
Thomas Moore, p. 173.
145.
Weisenburger, p. 150; J. M. J. Kooy and J. W. H. Uytenbogaart, Ballistics of the Future: With Special Reference to the Dynamics and Physical Theory of the Rocket Weapons (London: McGraw, 1946). However the chapter he suggests is titled ‘Motion of a Rocket Controlled by a Gyro Pilot’, which does suggest more specific (yet at the same time not fully determinate) readings of this equation, as will be seen.
146.
Schachterle and Aravind, p. 160.
147.
Chris Baldick, The Oxford Dictionary of Literary Terms, 3rd edn (Oxford: Oxford University Press, 2008), p. 309.
148.
Schachterle and Aravind, p. 165.
149.
Schachterle and Aravind, p. 166.
150.
Engelhardt, ‘Formulas’, p. 136.
151.
Engelhardt, ‘Formulas’, p. 135.
152.
Engelhardt and Engelhardt, pp. 6–7.
153.
Engelhardt and Engelhardt, p. 9.
154.
Otto Müller, ‘The Control System of the V-2’, in History of German Guided Missiles Development, ed. by T. Benecke and A. W. Quick (Brunswick: E. Appelhans & Co., 1957), pp. 80–101—quoted in Engelhardt and Engelhardt, p. 24.
155.
Engelhardt and Engelhardt, p. 10; cf. Müller, pp. 90–91.
156.
Engelhardt and Engelhardt, p. 10, p. 24; Müller, p. 90.
157.
Engelhardt and Engelhardt, p. 15.
158.
Ibid.
159.
Engelhardt and Engelhardt, p. 15.
160.
Engelhardt and Engelhardt, p. 20.
161.
Ibid.
162.
Engelhardt and Engelhardt, p. 20; Engelhardt, ‘Formulas’, p. 135.
163.
Jenkins, ‘Beyond Two Cultures’, p. 411.
164.
Jenkins, ‘Beyond Two Cultures’, pp. 412–413.
165.
“line, n.2.”, II 7–9, OED Online (Oxford University Press, June 2018) www.oed.com/view/Entry/108603 [accessed 10 September 2023]. I take inspiration from Tim Ingold’s creative and provocative study (that far exceeds its anthropological origin), Lines: a brief history (London: Routledge, 2007).
166.
‘differentiation’, in Clapham and James Nicholson, pp. 133–134.
167.
H. Jerome Keisler, Elementary Calculus: An Infinitesimal Approach, 3rd edn (Mineola, NY: Dover, 2012). 902. If integration is ‘the process of finding an antiderivative of a given function f”, then its counter-process is differentiation—‘integration’, in Clapham and James Nicholson, pp. 244–246. In other words, integration is to differentiation what multiplication is to division.
168.
Strogatz, p. 6.
169.
Clapham and Nicholson, p. 477.
170.
Strogatz, p. 5.
171.
Ozier, pp. 199–201; Savvas, p. 45; Engelhardt, ‘Gravity’, p. 15.
172.
Schachterle and Aravind, p. 161.
173.
‘partial derivative’ in Clapham and Nicholson, pp. 350–351.
174.
This is shown by the superscript ‘²’ which means that his is a partial differential equation of a higher order, specifically, it is a second-order partial differential equation. This second-order characteristic is not identical to that proposed by Noah Toyonaga in whose reading of Gravity’s Rainbow a first order of ‘monolithic and incomprehensible narrative … gives way to a coherent musicality of second order structure’. Nevertheless, what Toyonaga proposes as Pynchon’s ‘second order poetics’ does find richer meaning as it moves towards a nonlinear-dynamic conception of reality—Noah Toyonaga, ‘A Second Order Poetics in Gravity’s Rainbow’, in Pynchon’s New Worlds (presented at the International Pynchon Week 2017, Hôtel Fleuriau, La Rochelle, France, 2017) http://internationalpynchonweek2017.org/conference/texts.php?t=27 [accessed 10 September 2023].
175.
Nina Engelhardt, ‘Formulas’, p. 135; Thomas Moore, p. 173.
176.
Thomas Pynchon, Against the Day (London: Jonathan Cape, 2006), p. 603. Subsequent citations will appear in the main text, in parentheses, as ‘AD’.
177.
Thomas Moore, p. 173.
178.
Ludwig Prandtl, Essentials of Fluid Dynamics: With Applications to Hydraulics, Aeronautics, Meteorology and Other Subjects (London: Blackie, 1952), p. 72.
179.
Prandtl, p. 27.
180.
Ibid.
181.
Doug McLean, Understanding Aerodynamics: Arguing from the Real Physics (Chichester: Wiley, 2013), p. xxii. This ‘arises from the fact that owing to the existence of the boundary layer the external flow’ of a frictive medium, specifically air, ‘is displaced from the boundary through a distance δ* as compared with the frictionless case’ which would require only δ which is just the ‘boundary layer thickness’ in quantum mechanical ‘superfluids’—Prandtl, p. 109.
182.
Rilke in a letter to Marie von Thurn und Taxis, 12^th September 1912—quoted in Slade, p. 211.
183.
F. S. Schwarzbach, ‘A Matter of Gravity’, in Pynchon: A Collecion of Critical Essays, ed. by Edward Mendelson (Englewood Cliffs, NJ: Prentice-Hall, 1978), pp. 56–67 (p. 63).
184.
Fabienne Collignon, ‘Atomic-Antarctic Terminal Zone’, Textual Practice, 2017, 1–19 (p. 11). In her reading of the militarization of the Earth’s poles using such technologies, Collignon argues that ‘the gyrocompass is the means to, and beyond, the end of the world’—Collignon, p. 9.
185.
Kenneth Ian Trevor Richardson, The Gyroscope Applied (London: Hutchinson, 1954), p. 352; Judith R. Walkowitz, ‘Science and the Seance: Transgressions of Gender and Genre in Late Victorian London’, Representations, 22 (1988), 3–29 (p. 5). Walkowitz notes that ‘The seance reversed the usual sexual hierarchy of knowledge and power: it shifted attention away from men’, traditional gatekeepers of scientific institutions ‘and focused it on the female medium, the center of spiritual knowledge and insight’—Walkowitz, p. 8. ‘More than mere fantasy,’ Patrick Whitmarsh claims that Pynchon’s séance ‘serves as an analogue for advanced communication and media technologies of the twentieth century. Spiritual mediumship enacts a reimagining of communications networks that undermines the intentional participation of human agents’—Patrick Whitmarsh, ‘Specters of Communication: Supernatural Media in Thomas Pynchon’s Gravity’s Rainbow’, MFS: Modern Fiction Studies, 63.3 (2017), 524–46 (p. 527). Whitmarsh also contends that ‘the invocation of mystery in Gravity’s Rainbow is not intended merely to reflect an attitude of antirationalism in the face of a cold, calculating bureaucratic state. Rather, it actively opens new corridors of political thought by speculating on the inhibitions and empowerments of technological organization’—Whitmarsh, p. 540n6.
186.
It is informed by many trusted sources—including A. L. Rawlings, The Theory of the Gyroscopic Compass and Its Deviations (New York: Macmillan, 1944)—as well as technical military sources—cf. Davenport’s bibliography, in Gyroscopes: Theory and Design with Applications to Instrumentation, Guidance and Control (London: McGraw-Hill, 1961), p. 130.
187.
Paul H. Savet, Gyroscopes: Theory and Design with Applications to Instrumentation, Guidance and Control (London: McGraw-Hill, 1961), pp. 77–8.
188.
Not least because such a reading develops the implication of Schacterle and Aravind’s claim that Pynchon’s equation bears resemblance to those of a ‘damped driven oscillator’, or pendulums—Schachterle and Aravind, p. 162. These are essentially simplified gyroscopes.
189.
This is where Schachterele and Aravind conclude their explorations of ‘damped driven oscillators’ as ‘mimic[king] the simpler aspects of rocket flight’—Schachterle and Aravind, p. 162.
190.
cf. ‘function’ in Clapham and Nicholson, pp. 193–194.
191.
Richardson, p. 352.
192.
Richardson, p. 51.
193.
Richardson, pp. 353–4.
194.
Richardson, pp. 353.
195.
Clinton, p. 28.
196.
“precession, n.2” OED Online, Oxford University Press, July 2018 www.oed.com/view/Entry/149609 [accessed 10 September 2023], 1b., emphasis added.
197.
Taylor, ‘Mathematical Clinamen’, pp. 151–7.
198.
As seen earlier in the double integration procedure at Brennschluss, described by Ölsch—GR 358.
199.
These are attributes of the rocket which von Braun believes might ‘free man from his remaining chains, the chains of gravity which still tie him to this planet. [The rocket] will open to him the gates of heaven’—Walter Saunders, ‘The Seer of Space: Lifetime of Rocket Work Gives Army’s Von Braun Special Insight into the Future’, Life, 19th November, 133–39 (p. 133); quoted in Engelhardt, ‘Gravity’, p. 5.
200.
Savvas, p. 13, emphasis added.
201.
Max, pp. 213–4.

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Taylor, S.J. (2024). Algebraic Structures and Metaphor in Gravity’s Rainbow. In: Mathematics in Postmodern American Fiction. Palgrave Studies in Literature, Science and Medicine. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-48671-5_3

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