Abstract
When speculative realists argue that objects should be considered apart from subjects, they frequently call on the support of George Spencer-Brown’s ‘calculus of indications’; however, they domesticate binary oppositions (e.g., day/night, good/bad, etc.) at the expense of the radical antagonism of Spencer-Brown’s identification of indication with distinction, a ‘pre-Boolean’ alliance that echoes Lacan’s own topologies of the ‘extimate’ (inside-out). Antagonism is not so easily dispelled. Speculative realists should accept the ‘thirdness’ that Spencer-Brown and, later, Lacan employ strategically to address central questions about self-reference. I use evidence from Poe’s ‘The Purloined Letter’ to show how much Lacan’s, Freud’s, and Spencer-Brown’s ‘triplicities’ have to offer to the project of the nonhuman.
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Notes
- 1.
Levi Bryant , ‘Introduction: Towards a Finally Subjectless Object,’ in The Democracy of Objects (Ann Arbor: Open Humanities Press, 2011). Online text accessed August 2016, http://www.oapen.org/view?docId=444377. Note that Bryant reverses Spencer-Brown’s convention of designating innermost spaces as unmarked and external graphic grounds as marked, suggesting that he considers being contained equivalent to being marked. Spencer-Brown’s calculus is a favorite reference for other scholars working in this area, such as sociologist Niklas Luhmann, autopoieticists Francisco Varela and Humberto Maturano, and architectural theorist Patrik Schumacher. For an overview of extensions of Spencer-Brown’s calculus, see Michael Schiltz, ‘Space Is the Place: The Laws of Form and Social Systems,’ Thesis Eleven 88 (February 2007): 8–30.
- 2.
Bryant , ‘The Closure of Objects,’ 4.1, in op. cit: ‘Spencer-Brown’s point is any indication requires a distinction if the indication is to be made.… Form is the condition under which indication is possible.’
- 3.
George Spencer-Brown , Laws of Form (London: Allen and Unwin, 1969), p. 1. I have benefited greatly from Ellie Ragland’s pioneering study of Spencer-Brown’s Lacanian connections in ‘Lacan’s Topological Unit and the Structure of Mind,’ in Lacan: Topologically Speaking, ed. Ellie Ragland and Dragan Milovanovic (New York: Other Press, 2004), pp. 49–72. Ragland was the first Lacanian, I believe, to stress the coincidence of distinction and indication. (Ragland uses ‘indiction’ for ‘indication,’ which has the supplementary sense of a decree or declaration). I wish also to thank Todd McGowan, Alireza Moharar, and my editors, Jonathan Michael Dickstein and Gautam Basu Thakur for their helpful reviews of this chapter and its ideas in its various stages.
- 4.
Louis Kauffman, ‘Laws of Form: An Exploration in Mathematics and Foundations,’ Rough Draft, 2014. Online text accessed Aug 2016, http://homepages.math.uic.edu/~kauffman/Laws.pdf; hereinafter cited as ‘Exploration.’
- 5.
Pierre Skriabine, ‘Clinic and Topology: The Flaw in the Universe,’ in Ragland and Milovanovic, op. cit., p. 88.
- 6.
Ellie Ragland , ‘Lacan’s Topological Unit and the Structure of Mind,’ in Ragland and Milovanovic, op. cit., p. 54. Ragland quotes Lacan in Seminar XX (1972–1973), pp. 118–119.
- 7.
George Spencer-Brown , Laws of Form, Limited Edition (Portland, OR: Cognizer Co., 1994), p. vii.
- 8.
Louis Armand comments on Lacan’s need for non-Boolean logic in ‘Symptom in the Machine: Lacan, Joyce, Sollers,’ 2007. Online text accessed Aug 2016, http://www.lacan.com/sympmach.htm
- 9.
Ibid.
- 10.
Ibid.
- 11.
James Joyce , Finnegans Wake, Viking Compass Edition (New York: The Viking Press, 1967), p. 185.
- 12.
Spencer-Brown (1994), p. 76.
- 13.
Robert Samuels, ‘Logical Time and Jouissance,’ Newsletter of the Freudian Field 4, 1/2 (Spring/Fall 1990): 69–77; Jacques Lacan (1945), ‘Logical Time and the Assertion of Anticipated Certainty,’ in Écrits, trans. Bruce Fink (New York: W. W. Norton., 2002), pp. 161–175.
- 14.
Bruce Fink , The Lacanian Subject: Between Language and Jouissance (Princeton: Princeton University, 1995), p. 14ff. Analyzing Lacan’s use of ciphering to describe the unconscious , Fink makes this astounding claim on page 22: ‘…[T]his way of conceptualizing the unconscious [as an automaton] apparently leaves no room for a subject of any kind. …[T]here is absolutely no need to postulate any kind of consciousness of this automatic movement…[which] contains “indelible knowledge” which at the same time is “absolutely not subjectivized”’ (Seminar XXI, February 12, 1974). Any objective reader of the texts of speculative realists would have to wonder, is this not precisely what they have been looking for?
- 15.
Louis Kauffman details the ways the calculus connects to the primary algebra of x 2 + ax + b = 0, a recursive condition that leads to the ‘Hegelian’ paradox, J = ~J. ‘Knot Logic and Topological Quantum Computing with Majorana Fermions,’ in Quantum Physics (Ithaca: Cornell University Library, January 2013). Online text accessed Feb 2017, https://arxiv.org/abs/1301.6214
- 16.
Louis Kauffman’s interest in the form’s inherent capability of reentering itself is summarized in the idea of the eigenform: ‘What is an eigenform? An eigenform is a solution to an equation, a solution that occurs at the level of form, not at the level of number. You live in a world of eigenforms. You thought that those forms you see are actually “out there”? Out where? It has to be asked. The very space, the context that you regard as your external world is an eigenform. It is your organism’s solution to the problem of distinguishing itself in a world of actions.’ Kauffman seems to provide Lacan with the mathematical basis for his rejection, on the behalf of triplicity, of the need for ‘pictorial’ ideas of settings, contexts, and temporalities . Kauffman (2014), op. cit.
- 17.
Ragland and Milovanovic (2004), p. 53. I would invoke Heraclitus on this matter. Beyond palintropos harmoniē of contradictory elements, Spencer-Brown’s and Kauffman’s idea of Eigenform suggests the Heraclitan alternative, palintonos harmoniē, a ‘musical’ and ‘architectural’ joint to replace the alternating current of contradiction. See this in Plato’s revised terms, in Kelsey Wood, Troubling Play: Meaning and Entity in Plato’s Parmenides (Albany: SUNY Press, 2005).
- 18.
I borrow Lucretius’s word for turbulence with an eye to other Latin terms in Harold Bloom’s description of poetic anxiety : askesis, tesseræ, dæmon, apophrades, and kenosis. The metalepsis of creating something from nothing—‘form’ as Spencer-Brown would refer to it—requires all six, but we might focus first on dæmon, the most mechanical and nonhuman of the set. Harold Bloom, The Anxiety of Influence: A Theory of Poetry (Oxford: Oxford University Press, 1997).
- 19.
Jacques Lacan, Seminar on ‘The Purloined Letter,’ in Écrits: The First Complete Edition in English, trans. Bruce Fink (New York: W. W. Norton, 2002), p. 17.
- 20.
Edgar Allan Poe, ‘The Purloined Letter,’ in The Complete Tales and Poems of Edgar Allan Poe (New York: Vintage, 1975), p. 217.
- 21.
Lacan (2002), p. 20.
- 22.
The double channel idea is the basis of the phenomenon of ‘cross-inscription,’ a fundamental counterpart to relations of extimity ( extimité ). For example, in Ernst Jentsch’s binary of the uncanny , ‘the living person haunted by the specter of death’ and ‘the dead person carried by momentum past the instant of literal dying,’ we say that death is inscribed into life just as life is inscribed into death, in effect that life/death are cross-inscribed binaries that, in ‘ethnographic conditions’ are experienced in one of two ways. Ernst Jentsch, ‘Zur Psychologie des Unheimlichen,’ Psychiatrisch-Neurologische Wochenschrift 8, 22 (26 Aug): 195–198; 8, 23 (1 Sept): 203–205, 1906.
- 23.
Kauffman, ‘Exploration’ (2014). Lacanians will easily see how the converter gate represents the function of jouissance in its ability to ‘create value’ out of either a negative or positive circuit flow. The single-gate circuit is thus Spencer-Brown’s counterpart to the gapped circle of the death drive, where repetition compulsion creates a closed system that mimics the energetics of megalomania in its delusional relations to objects with demonic capabilities (Eros).
- 24.
Lacan (2002), p. 10.
- 25.
To understand the clever relationship between the constructed poché of pickpockets and S(Ⱥ), see Adam Greene, ‘Profiles: Apollo Robbins,’ The New Yorker Magazine (7 Jan 2013). Online text accessed Nov 2016, http://www.newyorker.com/magazine/2013/01/07/a-pickpockets-tale
- 26.
Poe’s description of the poet as being ‘at one remove from a fool’ [emphasis mine] sets up the idea of a poetry with mathematics in a very Spencer-Brownian fashion, especially because Dupin, in stealing the letter , is also fooling the mathematical-poetical Minister by ‘re-entering the form.’
- 27.
For the tradition of Hermes’ secrets, see Norman O. Brown, Hermes the Thief: The Evolution of a Myth (Madison: University of Wisconsin, 1947); and Leonard Barkan, ‘Diana and Actæon: The Myth as Synthesis,’ English Literary Renaissance 10, 3 (Sept): 317–359, 1980. Hermes’ thievery equates with his ability to cross boundaries with impunity, including the arch-boundary separating death from life. Theft-by-stealth indicates that the binary involved with the concealment of the letter is not one of Bryant’s ‘flat binaries,’ such as light/dark, but rather an ‘orthogonal’ binary connecting the intimate (gaze) with the point of view.
- 28.
Richard Kopley, Edgar Allan Poe and the Dupin Mysteries (New York: Palgrave/Macmillan, 2008), pp. 18–24.
- 29.
One should note that the gaze and the acousmatic voice both involve ‘predication reversal,’ an extimacy that locates a subjective function at the kernel of the object. This back-flow of causality and signification invites one to look further into the way the calculus’s inverter gate adjusts the ‘check valve’ uniflow of the Symbolic’s causal and signifying chains.
- 30.
Spencer-Brown (1994), pp. 123–35. Also see Lewis Carroll and William Warren Bartley, Lewis Carroll’s Symbolic Logic (New York: C. N. Potter, 1977).
- 31.
Slavoj Žižek , The Most Sublime Hysteric: Hegel with Lacan, trans. Thomas Scott-Railton (Cambridge, UK/Malden, MA: Polity Press, 2014), pp. 21–34.
- 32.
I would follow and expand on Mladen Dolar’s advice about the uncanny , that is it is not produced by the Enlightenment’s banishment of religion (the standard view) but already present in the ethnographic evidence of rituals, folktales, superstitions, and prophylactic magic from shamanistic times onward. ‘I Shall Be with You on Your Wedding-Night’: Lacan and the Uncanny, Rendering the Real 58 (Autumn): 5–23, 1991.
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Kunze, D. (2018). Triplicity in Spencer-Brown, Lacan, and Poe. In: Basu Thakur, G., Dickstein, J. (eds) Lacan and the Nonhuman. The Palgrave Lacan Series. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-63817-1_8
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