Ordered Structures and Cognition in Infinite Jest

Taylor, Stuart J.

doi:10.1007/978-3-031-48671-5_4

Stuart J. Taylor⁵

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

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Abstract

This chapter examines intersections of mathematics and literature within encyclopedic narratives by David Foster Wallace. 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’—ordered structures—is used to analyse Wallace’s Infinite Jest. Expanding on the preceding chapters’ exploration of topological, Möbian structures of allusion in DeLillo’s Ratner’s Star and algebraic structures of metaphor in Pynchon’s use of mathematics in Gravity’s Rainbow, ordered structures in this chapter form the basis of analysis of Wallace’s models of cognition in Infinite Jest. Incorporating interdisciplinary readings of Georg Cantor’s transfinite mathematics, this chapter compares Wallace’s cognitive strategies and endnotes in both Infinite Jest and Everything and More with Oulipian writer Jacques Roubaud’s The Great Fire of London. This reading prepares the reader for further explorations of topological, algebraic, and ordered structures in recent American fiction in the concluding chapter of the monograph. 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.
Natalini, ‘Mathematics of Infinity’, p. 46.
2.
This problematic yet persistent division can be seen in two recent collections—cf. Stuart J. Taylor, ‘“getting to the Core of Things”: A Review of Robert K. Bolger & Scott Korb, Eds. Gesturing Toward Reality: David Foster Wallace and Philosophy and Steven M. Cahn & Maureen Eckert, Eds. Freedom and the Self: Essays on the Philosophy of David Foster Wallace’, Postmodern Culture, 26.1 (2015).
3.
Silverblatt, “David Foster Wallace: Infinite Jest.”
4.
C.f., respectively, Chapter 1: Topological Structures and Allusion in Ratner’s Star and Chapter 2: Algebraic Structures and Metaphor in Gravity’s Rainbow. For a further exploration of the mathematical infinite in Wallace’s works, see Stuart J. Taylor, ‘David Foster Wallace’s Mathematics of the Infinite’, in Clare Hayes-Brady (ed.), David Foster Wallace in Context (Cambridge: Cambridge University Press, 2023), pp. 169–80.
5.
Mashaal, p. 82; cf. Nicolas Bourbaki, Theorie Des Ensembles, Éléments de Mathématique, 1 (Berlin: Springer-Verlag, 2006), ch. III, pp. 1–5. Cf. Chap. 1: Introduction.
6.
Taylor, ‘Mathematical Clinamen’, pp. 160–4.
7.
In this reading, mathematical ordered structures complement the ‘cognitive structures’ of cognitive literary studies—c.f. Ellen Spolsky, Gaps in Nature: Literary Interpretation and the Modular Mind (Albany: State University of New York Press, 1993), p. 2. Mary Thomas Crane, Shakespeare’s Brain: Reading with Cognitive Theory (Princeton: Princeton University Press, 2000), p. 34; Jamie Redgate, Cognition, Consciousness, and Dualism in David Foster Wallace’s Fiction (London: Routledge, 2019), p. 7.
8.
N. Katherine Hayles, Postprint: Books and Becoming Computational (New York: Columbia University Press, 2021), p. 8.
9.
Sam Potts, ‘A Diagram of Nearly All the Characters in David Foster Wallace’s Infinite Jest, with Connections and Relations Shown Thereamong.’, 2010 http://sampottsinc.com/ij [accessed 10 September 2023].
10.
Markus Mottl, ‘POMAP—Partially Ordered Maps for OCaml.’, 2017 http://github.com/mmottl/pomap/blob/master/README.md [accessed 10 September 2023].
11.
These diagrams may appear familiar to readers of Franco Morretti’s Distant Reading, in which he schematizes the plot of Hamlet using data modelling. My approach is more fluid in that it allows for multiple ordered structures to coexist rather than form a single structure from the entire dataset of the text (and its intertexts? Derrida may rightly ask ‘Where does it stop, Mr. Moretti?’). By using the most abstract structures of mathematics—topological, algebraic, and ordered—I gain an effective model with which to read authors of a certain mathematical literacy; as a result, my method provides a more general, more malleable, and therefore more inclusive model than Moretti’s distant reading—Franco Moretti, Distant Reading (London: Verso, 2013), p. 213.
12.
Potts, emphasis added.
13.
Potts’s diagram suggests that Infinite Jest is, in fact, analogous to the general formulation of an ordered set known as a ‘partially ordered set’ or ‘poset’ in mathematics, an arrangement in which, unlike the specific example of a ‘totally ordered set’, not every element may be comparable.
14.
Timothy Jacobs, ‘American Touchstone: The Idea of Order in Gerard Manley Hopkins and David Foster Wallace’, Comparative Literature Studies, 38.3 (2001), 215–31 (pp. 225–6, emphasis added). The ‘readerly exertion’ demanded by Infinite Jest qualifies the novel, in Espen Aarseth’s criteria, as ‘ergodic literature’ (a term with its own mathematical resonances, i.e. ‘ergodic theory’), where ‘nontrivial effort is required to allow the reader to traverse the text’—Espen J. Aarseth, Cybertext: Perspectives on Ergodic Literature (Baltimore: Johns Hopkins University Press, 1997), p. 1.
15.
Hugh Kennedy and Geoffrey Polk, ‘Looking for a Garde of Which to Be Avant: An Interview with David Foster Wallace’, in Conversations with David Foster Wallace, ed. by Stephen J. Burn (Jackson: University of Mississippi Press, 2012), pp. 11–20 (p. 18) (first publ. in Whiskey Island (Spring 1993), 49–57).
16.
David Foster Wallace, ‘David Lynch Keeps His Head’, in A Supposedly Fun Thing I’ll Never Do Again (London: Abacus, 1998), pp. 146–212 (pp. 169–70).
17.
Larry McCaffery, ‘An Expanded Interview with David Foster Wallace’, in Burn, Conversations, pp. 21–52 (pp. 21–2) (first publ.in Review of Contemporary Fiction, 13.2 (1993), 127–50).
18.
Michael Goldfarb (2004) ‘The Connection: David Foster Wallace’, in Burn, Conversations, pp. 136–51 (p. 145) (first broadcast on The Connection (90.9 WBUR, 25 June 2004)).
19.
David Foster Wallace, ‘E Unibus Pluram: Television and U.S. Fiction’, in A Supposedly Fun Thing I’ll Never Do Again, pp. 21–82 (p. 74).
20.
Wallace, ‘E Unibus Pluram’, p. 79, original emphasis.
21.
McCaffery, p. 33, original emphasis. Wallace would later define the importance of such work of ‘triage of saliency or value’ of ‘an educated adult, a.k.a. an informed citizen’ as ‘Decidering’ in his introduction to The Best American Essays 2007—David Foster Wallace, ‘Introduction: Deciderization 2007—a Special Report’, in The Best American Essays 2007, ed. by David Foster Wallace, The Best American Series (Boston: Houghton Mifflin Company, 2007), pp. xii–xxiv (p. xv).
22.
David Foster Wallace, ‘Tennis Player Michael Joyce’s Professional Artistry as a Paradigm of Certain Stuff about Choice, Freedom, Discipline, Joy, Grotesquerie, and Human Completeness’, in A Supposedly Fun Thing I’ll Never Do Again, pp. 213–55 (p. 235). Subsequent citations will appear in main text, in parentheses, as ‘SF’.
23.
Wallace also found tennis’s imagistic beauty-through-abstraction occasionally terrifying. For example ‘the most affecting rendition’ of Kate’s Tractatus-imprisonment in Wittgenstein’s Mistress was, for Wallace, her ‘funnysad [sic] descriptions of trying to play tennis without a partner’ while Markson’s ‘continual reference to bunches of tennis balls bounding all over the place’ illustrated the fecundity of tennis balls as ‘about the best macroscopic symbol there is for the flux of atomistic fact’—David Foster Wallace, ‘The Empty Plenum: David Markson’s Wittgenstein’s Mistress’, in Both Flesh and Not: Essays (London: Hamish Hamilton, 2012), pp. 73–116 (p. 91). Subsequent citations in main text, in parentheses, as ‘BFN’.
24.
To differentiate between the enumerated notations of this chapter and those printed in Infinite Jest etc., the latter will be both emboldened and underlined; other quoted interpolations, specifically alphabetic, will not be presented here with added emphasis.
25.
See, for example, Aleid Fokkema’s overview of the predominance of this consideration of the postmodern narrative character and its related problematics—Aleid Fokkema, Postmodern Characters: A Study of Characterization in British and American Postmodern Fiction (Amsterdam: Rodopi, 1991), p. 14. This generational or periodical demarcation is partly a result of Wallace’s self-conscious separation between his own work and those to whom he is clearly indebted—cf. Stephen J. Burn, ‘Second-Generation Postmoderns’, in The Cambridge History of Postmodern Literature, ed. by Brian McHale and Len Platt (Cambridge: Cambridge University Press, 2016), pp. 450–64. By examining his ‘ordered structures’ in terms of a Bourbakian-mathematical approach to literature Wallace shared with DeLillo and Pynchon, this reading simultaneously recuperates postmodern writing from charges of frivolity and understands Wallace’s inheritance of postmodern literary encyclopedism.
26.
Simon de Bourcier, ‘“They All Sound Like David Foster Wallace”: Syntax and Narrative in Infinite Jest, Brief Interviews with Hideous Men, Oblivion and The Pale King’, Orbit: Writing Around Pynchon, 5.2 (2017), emphasis added.
27.
A. O. Scott, ‘The Panic of Influence’, The New York Review of Books, 2000, 1.
28.
Eva Dolo, ‘Too Much Fun—Endnotes in Infinite Jest’, Symbolism, 15 (2015), 75–100 (p. 99).
29.
Cf. Adam Kelly, ‘David Foster Wallace and the New Sincerity in American Fiction’, in Consider David Foster Wallace: Critical Essays, ed. by David Hering (Los Angeles: Sideshow, 2010), pp. 131–46.
30.
Jacobs, p. 229.
31.
Ira B. Nadel, ‘Consider the Footnote’, in The Legacy of David Foster Wallace, ed. by Samuel Cohen and Lee Konstantinou (Iowa City: University of Iowa Press, 2012), pp. 218–40 (p. 218).
32.
Dolo, p. 99, original emphasis.
33.
Stephen J. Burn, David Foster Wallace’s Infinite Jest: A Reader’s Guide, 2nd edn (London: Continuum, 2012), p. 17.
34.
Jacques Roubaud, Hortense Is Abducted, trans. by Dominic Di Bernardi (London: Dalkey Archive Press, 2000), p. 75.
35.
Ibid., pp. 76–7.
36.
Jacques Roubaud, The Great Fire of London: [A Story with Interpolations and Bifurcations], trans. by Dominic Di Bernardi (London: Dalkey Archive Press, 1992), p. 213, emphasis added. In mathematics, ‘bifurcations’ describe specific types of changes in dynamical systems, a usage which Roubaud analogously exploits to highlight their intended ‘transformative effect’ as textual elements. Subsequent citations will appear, in parentheses, in main body as ‘GFL’.
37.
Jean-Jacques F. Poucel, Jacques Roubaud and the Invention of Memory (Chapel Hill: University of North Carolina Press, 2006), pp. 224–5, original emphasis.
38.
Dominic Di Bernardi, ‘The Great Fire of London: A Story With Interpolations and Bifurcations’, 2013 https://web.archive.org/web/20180318184706/http://www.dalkeyarchive.com/product/the-great-fire-of-london-a-story-with-interpolations-and-bifurcations/ [accessed 10 September 2023].
39.
Jeff Somers, ‘10 Things You Probably Didn’t Know About Infinite Jest’, B&N Reads, 2017 http://barnesandnoble.com/blog/10-things-probably-didnt-know-infinite-jest [accessed 10 September 2023].
40.
Kiki Benzon also suggests that Wallace’s notes are porous in the sense that they form ‘coercive loops’ between the endnotes, main text, and other texts (particularly the OED). This looping forces the reader ‘into a position of repeated “intermediariness,” herself confirming through action the porous borders of the text she is experiencing’—Kiki Benzon, ‘“Yet Another Example of the Porousness of Certain Borders”: Chaos and Realism in Infinite Jest’, in Consider David Foster Wallace, ed. by Hering, pp. 101–12 (pp. 108–9).
41.
Jacques Roubaud, Mathematics: (A Novel), trans. by Ian Monk (London: Dalkey Archive Press, 2012), p. 100§36. Subsequent citations will appear, in parentheses, in main body as ‘M’.
42.
Benzon, pp. 108–9.
43.
Hofstadter p.10. qtd in Benzon, p. 108.
44.
Benzon, p. 112.
45.
Nadel, p. 222.
46.
Baylee Brits, Literary Infinities Number and Narrative in Modern Fiction (London: Bloomsbury, 2018), p. 4.
47.
“order, n.”, 14a, OED Online (Oxford University Press, June 2017) www.oed.com/view/Entry/132334 [accessed 10 September 2023].
48.
Robert Tubbs, What Is a Number?: Mathematical Concepts and Their Origins (Baltimore: Johns Hopkins University Press, 2009), p. 2.
49.
“order, n.”, 15, OED Online (Oxford University Press, June 2017) www.oed.com/view/Entry/132334 [accessed 10 September 2023].
50.
Kenneth H. Rosen, Discrete Mathematics and Its Applications, 7th Edition (New York: McGraw-Hill, 2012), p. 116.
51.
Christopher Clapham and James Nicholson, The Oxford Concise Dictionary of Mathematics (Oxford: Oxford University Press, 2014), p. 314.
52.
Tubbs, Mathematics in Twentieth-Century Literature, p. 57.
53.
Joseph Warren Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (Princeton, NJ: Princeton University Press, 1990), p. 179. An infinite number is also known as a transfinite cardinal number.
54.
Stanley Burris and H. P. Sankappanavar, A Course in Universal Algebra (Waterloo, Ontario: University of Ontario Press, 2012), p. 4.
55.
Lyn D. English, Mathematical Reasoning: Analogies, Metaphors, and Images (New York: Routledge, 2009), pp. 40–2.
56.
Hayles refers to the Concavity/Convexity as a ‘dump’ representative of a ‘widening circle of toxicity’ and a ‘failure to contain damage within a prophylactically enclosed area’—N. Katherine Hayles, ‘The Illusion of Autonomy and the Fact of Recursivity: Virtual Ecologies, Entertainment, and Infinite Jest’, New Literary History, 20.2 (1999), 657–97 (p. 686, emphasis added). This ecological model resists any encyclopedic enterprise which seeks to encircle, and hermetically seal, such generative sites. As these sites are often characterized by information overload, however, the geographic setting maps a cognitive arena, with Wallace representing consciousness as striving to escape its cranial confines and, in this way, connect with others.
57.
Caleb Crain, ‘Approaching Infinity’, in Conversations, ed. by Burn, pp. 121–26 (p. 125) (first publ. in Boston Globe (26 October 2003)).
58.
William M. Mace, ‘James J. Gibson’s Strategy for Perceiving: Ask Not What’s Inside Your Head, but What Your Head’s Inside Of’, in Perceiving, Acting, and Knowing: Toward an Ecological Psychology (Hillsdale, NJ: Lawrence Erlbaum Associates, 1977), pp. 43–65.
59.
John D. Barrow, Pi in the Sky: Counting, Thinking, and Being (Oxford: Clarendon Press, 1992), pp. 280–2, emphasis added. Cf. David Foster Wallace, ‘David Foster Wallace Papers Manuscript Collection’ (Harry Ransom Center, 1971–2008), MS-5155, Container 9.2.
60.
Cf. Lance Olsen, ‘Termite Art, or Wallace’s Wittgenstein’, Review of Contemporary Fiction, 13.2 (1993), 199–215.
61.
James Ryerson, ‘Introduction: A Head That Throbbed Heartlike: The Philosophical Mind of David Foster Wallace’, in Fate, Time, and Language: An Essay on Free Will, ed. by Steven M. Cahn and Maureen Eckert (New York: Columbia University Press, 2011), pp. 1–33 (p. 22).
62.
For more on the way the text ‘enact[s] the difficulties of mathematical abstraction as it relates to our everyday lives and narratives’, see the discussion with Wallace’s technical advisor on the project—Stuart J. Taylor, ‘The making of Wallace’s Everything and More: an interview with Erica Neely’, Lettera Matematica International (2015) 3 pp. 269–73, p. 270.
63.
Gregory Bateson, Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution and Epistemology (London: Granada, 1973), p. 434.
64.
Bateson, p. 439, emphasis added.
65.
Natalini, ‘Mathematics of Infinity’, p. 51, original emphasis.
66.
David Lipsky, ‘The Lost Years and Last Days of David Foster Wallace’, in Conversations, ed. by Burn, pp. 161–81 (p. 172) (first publ. in Rolling Stone 1064 (30 October 2008)).
67.
Nadel, p. 224.
68.
Michael Pietsch and Rick Moody, ‘On Editing David Foster Wallace: An Interview’, in The Legacy of David Foster Wallace, ed. by Cohen and Konstantinou, pp. 208–17 (p. 213).
69.
McCaffery, p. 41.
70.
Shari Benstock, ‘At the Margin of Discourse: Footnotes in the Fictional Text’, PMLA, 98.2 (1983), 204–25 (p. 220n2).
71.
Ibid.
72.
Benstock, p. 204.
73.
Marshall Boswell, Understanding David Foster Wallace (Columbia: University of South Carolina Press, 2009), p. 209.
74.
Ibid., p. 121.
75.
Ugo Panzani, ‘“Mathematically Uncontrolled but Humanly Contained”: Narrative Iteration in Infinite Jest’, Lettera Matematica, 3.4 (2015), 289–93 (p. 289).
76.
Caleb Crain, ‘The Great Postmodern Uncertainty That We Live In’, Steamboats Are Ruining Everything, 2008 http://steamthing.com/2008/09/the-great-postm.html.
77.
Jacques Derrida, Limited Inc., trans. by Samuel Weber (Evanston, Illinois: Northwestern University Press, 1988), p. 20.
78.
Mike Strong, ‘Dubious Math in Infinite Jest’, The Howling Fantods, 2004 https://web.archive.org/web/20221001175010/http://thehowlingfantods.com/dfw/dubious-math-in-infinite-jest.html [accessed 10 September 2023].
79.
Alexander Taylor posits that Alice’s arithmetic is logical in a non-decimal system where, starting from base 18, bases increase by three. This system makes Alice’s arithmetic correct until the multiplication of 4 by 13 (with a base of 42)—Alexander L. Taylor, The White Knight: A Study of C. L. Dodgson (Edinburgh: Oliver & Boyd, 1952), p. 47. Following the nineteenth-century arithmetical works of Augustus De Morgan and George Peacock, Francine Abeles suggests a multiplication system for Alice’s arithmetic that ‘is commutative’ but ‘not associative’; in this system, by ‘disregarding order, there is only one way to get to twenty’, by using base six and multiplying 12 by one, which = 20—Francine F. Abeles, ‘Multiplication in Changing Bases: A Note on Lewis Carroll’, Historia Mathematica, 3 (1976), 183–4 (p. 183). Against Abeles’s technical disorder, Martin Gardner’s reading is far less technical. He argues Alice will never get to twenty because of classroom conventions, that is precisely because of a proprietary sense of ‘order’: ‘the multiplication table traditionally stops with the twelves, so if you continue this nonsense progression—4 times 5 is 12, 4 times 6 is 13, 4 times 7 is 14, and so on—you end with 4 times 12 (the highest she can go) is 19—just one short of 20’—Gardner, Annotated, p. 23.
80.
Marta Bono, ‘Reactions to Chaos Theory: The Mathematical References in the Notes of Infinite Jest’, trans. by Kim Williams, Lettera Matematica International, 3.4 (2015), 295–8 (pp. 295–6).
81.
Delillo, End Zone, pp. 219–25 (p. 219; p. 223).
82.
DeLillo, End Zone, p. 223.
83.
DeLillo, End Zone, p. 225.
84.
DeLillo, End Zone, p. 219.
85.
DeLillo, End Zone, p. 223.
86.
Panzani, p. 292.
87.
‘crisis, n.’ OED Online, Oxford University Press, June 2018, www.oed.com/view/Entry/44539 [accessed 10 September 2023].
88.
We may note that Otis P. Lord’s name derives from Emily Dickinson’s lover, Otis Phillips Lord, a Massachusetts Supreme Court Judge—Wendy Martin, The Cambridge Introduction to Emily Dickinson (Cambridge: Cambridge University Press, 2007), p. 19. Thus, in a multi-layered pun, Wallace’s Lord, unlike Dickinson’s, fails to maintain order in court.
89.
“crisis, n.” OED Online.
90.
David Foster Wallace, ‘Derivative Sport in Tornado Alley’, in A Supposedly Fun Thing I’ll Never Do Again, pp. 3–20 (p. 9).
91.
“order, n.”, OED Online.
92.
Susan Schneider, Science Fiction and Philosophy: From Time Travel to Superintelligence (Chichester: Blackwell, 2016), pp. 160–1.
93.
Schneider, p. 160.
94.
Cf. E. C. Zeeman, Catastrophe Theory: Selected Papers, 1972–1977 (London: Addison-Wesley, 1977).
95.
Silverblatt, “David Foster Wallace: Infinite Jest.”
96.
Wallace, HRC, MS-5155, container 8.6.
97.
This taps into the stereotypical division of arts and sciences as captured by the following anecdote: ‘Once Dirac asked Oppenheimer what he would have done in life had he not become a physicist. Oppenheimer replied immediately that he would have become a poet. Dirac was appalled. Finding this an inconceivable alternative, he replied, “As a physicist I take what is complicated and make it simple. But the poet does the very opposite”’—Barrow, p. 24.
98.
A. M. Moore, ‘How to Catch a Tortoise’, London Review of Books, 25.24 (2003), 27–8.
99.
Wallace, HRC, MS-5155, container 8.6.
100.
Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Godel (New York: Atlas Books, W. W. Norton & Company, 2006), p. 17n1.
101.
Cf. Wallace, HRC, MS-5155, container 8.9.
102.
Dave Eggers, ‘David Foster Wallace: Interview’, The Believer, 2003 https://web.archive.org/web/20220627075337/https://culture.org/an-interview-with-david-foster-wallace/ [accessed 10 September 2023].
103.
‘jest, n.2.’ OED Online, Oxford University Press, January 2023 www.oed.com/view/Entry/101132 [accessed 10 September 2023].

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Taylor, S.J. (2024). Ordered Structures and Cognition in Infinite Jest. 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_4

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