# Category Archives: Psychoanalysis

## Lacan on the Number 13 and the Logic of Suspicion

###### [A pdf version is available here.]

Lacan once remarked on the Cartesian cogito that etymologically, “the French verb penser (to think)…means nothing other than peser (to weigh)” (1961-2: 14). Lacan’s mix of bad puns, abuse of notation, cryptic aphorisms & immense erudition has created a new style of writing, and even of thinking. A new language, in short, lacking any method for non-experts to weigh its words.

Of all things, Lacan’s earliest papers take the form of math puzzles—a lucid (albeit horrendously verbose) derivation, then reframing of the problem as metaphor. One such paper—“The Number Thirteen and the Logical Form of Suspicion”—has largely been forgotten. This post aims to recast the puzzle using discrete mathematics, and show how it bears upon Lacan’s later ideas.

What I like about this mathematical allegory is that even if one believes Lacan is a charlatan, here there’s no need to immerse oneself in psychoanalytic concepts, but only to think.

I hope that Lacanians will find working through my derivation a challenging exercise, and that mathematicians will be piqued at the idea of treating a math problem as a philosophical ‘text’. I for one would be glad to see more such texts.

#### 1. Lacan’s Algorithm

We are given 12 identical pieces, and told one of them is ‘bad’—either lighter or heavier than the rest, we’re not sure which. Having only a scale with two plates, and no way to gauge numerical weight, we must find the bad piece in 3 weighings.

If we knew whether the bad piece was lighter or heavier, the problem would be easy: just split the pieces into two groups of 6, then split the ‘bad’ half into two groups of 3, then simply weigh two of the bad three. But we don’t.

Here, we’ll overview Lacan’s account for 12 pieces, and then in the next section we’ll consider n pieces, and try to explain why Lacan’s algorithm works.

Lacan begins by placing on the scales two groups of 4. Suppose they balance. Then the bad piece is in the remaining 4, so we can just weigh any 2 of the 4. If those balance, the 2 left-out pieces are bad; if they don’t, the 2 pieces on the scale are bad. So weigh one of the bad 2 against a good piece: if they balance, the other piece is bad; if they don’t, then the piece on the scale is bad. Simple.

Note how this was equivalent to the sub-problem of finding a bad piece out of 4 pieces, in 2 weighings. The sub-problem is embedded in the larger problem.

If the two groups of 4 don’t balance, we use the method of tripartite rotation.

Tripartite rotation

The scales don’t balance, so one is heavier (H), one lighter (L). So, we select 3 pieces from H, L, and the remainder (R), and rotate them: H → L → R → H.[1]

Case 1: Scales balance — the bad piece is in the 3 moved to R, and too light.
Case 2: Balance shifts — the bad piece is in the 3 moved to L, and too heavy.
Case 3: Unbalance doesn’t change — the bad piece is in the 2 unmoved pieces.

In cases 1 and 2, just weigh 2 of the bad pieces: if they’re equal, the remainder is bad; if not, we know the bad piece is the lighter (case 1) or heavier piece (case 2). For case 3, just pick one and weigh it against a good piece. And we’re done.

Lacan then considers the case of 13 pieces: 4 on each scale, 5 remainders. It’s clear that if the scales don’t balance, the problem is the same as with 12 pieces when the scale didn’t balance—the remainders are all good, whether 5 or 4.

Here, when the scales balance, we have a new problem. Recall how we could treat 4 pieces as a separate problem. So let’s examine the 5-piece sub-problem.

Start with 2 pieces on each scale and 1 remainder. If we’re lucky, the scales balance and the remainder is bad. If not, we have 4 pieces, but we know the 4-piece case takes two weighings, so the 5-piece case must take three weighings.

It’s the same even for 1 piece on each scale and 3 remainders. If we’re unlucky, the scales balance, giving a new sub-problem with 3 pieces—the smallest solvable version of Lacan’s problem. Weigh any 2. If they balance, the remainder is bad. If not, weigh a piece on the scale against the good piece. Total: three weighings.

So both the 3-piece and 4-piece cases take two weighings, 5 pieces takes three weighings, so it would seem that 13 pieces must take four weighings. Nope.

Actually, for 13 pieces, the 5 remainders aren’t truly a separate sub-problem. There’s a difference: we have 8 good pieces. For 3 or 4 pieces, this doesn’t matter, but for 5 pieces, Lacan can introduce a new trick: the ‘by-three-and-one’ position.

The ‘by-three-and-one’ position

Here, we have 2 pieces in each plate, with one of the 4 a good piece, and 2 remainders. If the scales balance, just weigh one remainder against a good piece and we’re done. If they don’t balance, here’s the trick: we can do the smallest possible tripartite rotation, H → L → R → H, where R is a good piece.

Case 1: Scales balance — the bad piece is in R.
Case 2: Balance shifts — the bad piece is in L.
Case 3: No change — the unmoved piece is bad.

Thus, the 5 remainders take two weighings, and the 13-piece case takes three.

In this case, treating the 5 remainders as a sub-problem was the wrong way to go, making it seem impossible to solve in 3 weighings. More pieces means more ways to divide between scales and remainder, increasing the risk of such pitfalls.

Thus, Lacan’s task is to find a general algorithm for any number of pieces, including a uniform way to divide them. The algorithm must minimize the maximum amount of weighings—i.e. find the minimum, assuming we don’t get lucky.

The problem also raises some new questions. The main one is: for a given number of pieces, how many weighings are needed? As in the solutions outlined above, Lacan answers this question, but fails to explain why his solution works.

Hence, the next section will diverge from Lacan’s exposition, using discrete mathematics to give an algorithm for n pieces. This will help us see how Lacan’s problem relates to the logic of suspicion, which we will outline in the final section.

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## Laruelle’s “Fragments of an Anti-Guattari”

[This may be cited as Laruelle, F.; Wolfe, C. (trans.). (1993). “Fragments of an Anti-Guattari.” Long News in the Short Century 4, pp. 158-164. Retrieved from linguisticcapital.wordpress.com/2013/03/13/laruelles-fragments-of-an-anti-guattari.

The following is reproduced with permission. A pdf version is available here.]

1.1   It was the Post-Modern times
Unlimited becoming-cinema
Image-debris in a state of fixed surview
Thinkers were then producing the Real
A bachelor philosopher a bachelor analyst
A dyad of bachelors was inventing
The reversibility of desire and the concept
The “D-G” desiring-machine
Consider the following diagram

1.2    About-face inversion of the Greek horizon
Great Desirers they went down to the Heraclitus stream
Bathed once-for-two in the same flux
Foreswearing the One-logos of the hospital-schizos – The Sensible
In the Collective-logos of schizo-processes – The Senseless
“The right to madness, superhuman right of the human”
“Take into consideration desire in its entirety”
“A thousand Oedipuses do not make one incest”
“The Same is the Desired and the Desiring—by one machine more or less”
“The stream is the self-production of the stream”

“Heraclitus! Heraclitus!
Only one ‘flash’ can set fire to a thousand plateaus”

“Emblem of necessity
Supreme constellation of Desire
Eternal Yes of Desire
Forever I shall be your Yes”

Thus they spoke of the eternal and cunning speeches
Tautologies linking past and future
New theory of indiscernables – the concept as bridge

1.3    Transcendental cartographers of the thousand eternities of Being
To the proximity constellations Mythos and Logos
Their extinction has not yet reached us –
They have added shining-obscure
The so-called “Chaos” constellation
A stream of neighbouring stars
“Chaosmos”, “Chaosmosis”, “Chaology”, “chaosmology”
And the most recent “Ecology-of-Chaos” also known as “Echaology”

– Its birth has not yet been announced

1.4    A philosopher – an analyst up to one auto-position
An analyst – a philosopher up to one unconscious
Reversible up to an “up to an X”
Naming their common non-sense “Desire”
The archaic originary One-Two of “desiring Desire”
Oh mythology which never ceases to bring back
The D(i)eux [D(y)ei] of grammar

1.5    We have loved these transcendental tautologies
Stretched out like a temple over our heads
Worlding World/nullifying Nothingness/speaking Speech/desiring Desire
Merry-go-round spun around by a Leibnizian ritournelle

“The philosopher, turning, so to speak, the general system of these tautologies that he deems suitable to be produced to manifest his thought, from side to side and in all ways, and looking over all the facets of this ‘fourfold’ in all possible ways, since there is no relation which escapes his omniscience; the result of each view of this system, as seen from a certain place up to a turn, is a philosophy which expresses this total, if the philosopher deems it suitable to render the thought effective and to produce this philosophy.” From which 12 founding statements [follow]: “take into consideration
the nullifying world
the speaking world
the desiring world
the worldifying nothingness
the speaking nothingness
the desiring nothingness
the worldifying speech
the nullifying speech
the desiring speech
the worldifying desire
the nullifying desire
the speaking desire … in its entirety
For 12 new philosophers among the thousand
Coming up from the bottom of the Future

.

2.1   I call “One (of) desire” desire as One rather than One as desire

Consider the One (of) desire

(up to a point, more or less, up to a being more or less, not
approximating “as close as X”, not on the basis of any
desire, before it disjoins itself into desired and desiring,
and blends in the concept and the unconscious)

… What is called thinking?

2.2   I call “Desiring desire” the doublet which opens analysis
and the difference which implodes it in super-analysis

Either it desires itself
Inverts reverts itself into super-analysis
Big with a thousand desired-desiring amphibologies

Either it ceases in the One (of) desire to desire itself
Emerges to its own manifestation
As three states (of) desire
Categories of a non-analysis

– The One (of) desire
– or the Desired-without-desire
– the order of the real
– The Being (of) desire
– or the Desirings which are [the] multitude
of desire-thinking
– the order of the symbolic
– The Entity (of) desire
– or desiring Desire
– the order of the imaginary

2.3   I call “One (of) desire” or Desired the Enjoyed (of) jouissance

The One (of) jouissance rather than the jouissance of the One
That which in desire is enjoyed from both ends
That to which desire does not give its share
That part of desire which appears to desire alone
Its absolutely un-desirable and just so desired phenomenon

The Enjoyed suspended in its own immanence
What begins and completes itself with no circle
Begins there without departing from it
Completes itself there without return

Deserted without desire
Too simple the desert is not rare

Desired, absolute past of desire
Enjoyed, absolute past of enjoyment
As the Lived
Precedes the living the Affected
Affection the Enjoyed
Jouissance
Solitude of closed eyes before
The confinement of solitude

Reduced form enjoyment spark of desire
The Ir-reduced of the Enjoyed, the intense Extinguished of the Desired
Are a mystical razor
An ante-essential rather than supra-essential state

2.4   If as Desirings it is still possible to say of desire that it desires
Being (of) desire
It is suspended in-
Desired
The Desirings remain

I call Desirings the multitude (of) axioms
Inhabitants
Of the void beyond the Desired
On this side of the desire-Entity

Think in-Desired
Make Being void of desire
Prepare the dwelling of the Desirings

Of the Desired the axiom is never stated
Unless it is also the cause of the axiom
And insofar as it is

The axiomatics of Desirings adds nothing to the Desired
Just itself to itself
The axiom seen-in-full

Consider the fluxion of desired-desiring connections
Its suspension like a photograph
Reveals to the unclear side of the stream
A strict identity between the source and the mouth
The frozen flux of an eidetic Heraclitus
Frozen-in-One like a sky of eternal axioms

Desired is the non-moved and the non-moving
Desirings are the mobile or the flying moved once each time
Desire-desiring is the moved motor

.

The One (of) desire gathers without division all possible (undividable)
The Being (of) desire gathers without division all possible division
Being is particular – oh Desirings
Particle is the partition with nothing to part
A partition from one end to another
Without mixing with the Desired as is
The undiscernable molecule
of desiring Desire

Desire receives thinking not from thinking itself
From the grace of the One (of) desire and then thinking
Thinking receives desire not from desire itself
From the grace of the in-Desired and then of desire

.

Translated by Charles Wolfe

.

Author’s notes

“Desired”: past participle of ‘desire’, which I make into a noun.

“in-Desired”: en rather than dans, indicating an interiority or a radical inherence/immanence.

Sensés”-Senseless: translation of Heraclitean terms.

“Fourfold”: Heideggerian term (Cf. “The Thing”).

Jouissance”/“Enjoyment”: Lacanian term. I extract from it the past participle Joui (Enjoyed) which I make into a noun.

“Reduced”-“spark”: mystical terms. (Cf. Meister Eckhart).

“Ir-reduced”: not opposed to “Reduced”; cf. “irreducible”.

“Extinct”/“Extinguished”: past participle of ‘extinguish’, which I make into a noun.

“razor”: Cf. Ockham’s razor.

“ante-essential”: cf. the mystical term ‘supra-essential’; before Essence (=Being), above or beyond Essence (=Being).

.

: Editor’s notes:

I have emended the second term in §1.3’s antepenultimate line. It originally read ‘Chaosmose’, while Laruelle doubtless means ‘Chaosmosis’, the title of one of Guattari’s books. Cf. the French osmose, which translates to the English ‘osmosis’.

In §1.4, ‘self-position’ has been changed to ‘auto-position’, in keeping with standard translations of Laruelle.

“Nullifying nothingness” (1.5) refers to Heidegger’s statement “The nothing nothings.” Laruelle clearly has in mind the meaning ‘nothinging nothingness’, which unfortunately does not parse well into English.                                                                     — G.J.

## Goethe on Jakob Michael Reinhold Lenz

Jakob Michael Reinhold Lenz

One is aware of that species of self-torture which, in the absence of any external or social constraints, was then the order of the day, afflicting precisely those possessed of most exceptional minds. Things which torment ordinary people only in passing and which, because unengaged in self-contemplation, they seek to banish from their thoughts, were instead acutely registered and observed by the better sort, and set down in books, letters, and diaries. But now the strictest moral demands placed upon oneself and others were commingled with an extreme negligence in one’s own actions, and the vague notions arising out of this semi-self-knowledge encouraged the strangest proclivities and most outlandish behavior.  This unremitting work of self-contemplation was further abetted by the rise of empirical psychology, which, if unwilling to describe anything that causes us inner unrest as wicked or reprehensible, could nonetheless not entirely condone it; and thus was set into motion a permanent, irresoluble state of conflict. Of all the full- or half-time idlers intent on digging into their innermost depths, Lenz excelled in cultivating and perpetuating this state of conflict, and thus he suffered in general from that tendency of the age to which the depiction of Werther was meant to put a stop; but he was cut from a different cloth, which set him apart from all the others, whom one had to admit were thoroughly open, decent creatures. He, by contrast, had a decided propensity for intrigue, indeed, for intrigue pure and simple, without any particular goal in view, be it reasonable, personal, or attainable; on the contrary, he was always concocting some twisted scheme, whose very contortions were enough to keep him wholly entertained. In this way, throughout his life his fancies played him for a rascal, his loves were as imaginary as his hates, he juggled his ideas and feelings at whim, so that he would always have something to do. By these topsy-turvy means, he would attempt to impart reality to his sympathies and antipathies, and then would himself destroy this creation again; and so he was never of use to anybody he loved, nor did he ever do harm to anybody he hated, and in general he seemed only to sin in order to punish himself, only to intrigue in order to graft some new fiction onto an old one.

His talent, in which delicacy, agility, and extreme subtlety all vied with each other, proceeded from a genuine depth, from an inexhaustible creative power, but, for all its beauty, there was something thoroughly unhealthy about it, and it is precisely talents such are these that are the most difficult to evaluate. One cannot fail to appreciate the outstanding features of his works; they are suffused with by something quite sweet and tender, but this is intermixed with instances of buffoonery so baroque and so asinine that, even in a sense of humor this all-pervasive and unassuming, even in a comic gift this genuine, they can hardly be pardoned. His days were occupied by airy nothings to which, ever assiduous, he managed to give meaning, and if he was able to idle away his hours in this fashion, it was because, given his outstanding memory, the time he actually devoted to reading always proved to be most fruitful, enriching his original way of thinking with a great variety of materials.

_

Lenz eventually came to suffer from paranoid schizophrenia, which inspired Georg Büchner to write a speculative biographical novella based on the diaries of Johann Friedrich Oberlin, at whose house Lenz lodged for a period of three weeks as his mental health steadily deteriorated. I post the above excerpt here due to its incisive analysis of Lenz’s personality, which I admire both for its perspicaciousness and the way it highlights Lenz’s relation to the Romantic zeitgeist.  As well, Deleuze & Guattari refer to Lenz in the opening pages of Anti-Oedipus. See here for an excellent synopsis of Lenz’s life and place within schizoanalysis.

## Guattari’s Glossary of Schizoanalysis

[I figured I might as well post this for fellow confuzzled readers of D&G. One should, however, note the suspicion of ‘tautological’ definitions posed by Bourdieu, following Wittgenstein, who decried the assumption of Western metaphysics that every word references a distinct object. Rather, we should look at words in terms of what they do: as a ‘toolbox’. Here, then, is a glimpse into some of the tools utilized by Guattari and Deleuze, though these are by no means exhaustive, tautological definitions, but merely two-dimensional renditions of multifaceted concepts. For other renditions, the reader is directed to this and this, as well as the following books:

• Parr, A. (Ed.). (2005). Deleuze Dictionary. Edinburgh, Scotland: Edinburgh University Press.
• Bonta, M. & Protevi, J. (2004). Deleuze & Geophilosophy: A Guide & Glossary. Edinburgh, Scotland: Edinburgh University Press.]

_

Arche-writing [arche-écriture]: expression put forward by Jacques Derrida who posits that writing is the basis of oral language. The writing of traces, imprints, conserved in the space of inscription, is logically anterior to time and space, signifier and signified oppositions. Schizo-analysis objects that this concept is still an all too totalizing vision, an all too “structuralist” concept of language.

A-signifier [a-signifiant]: we have to distinguish between signifying semiologies―that articulate signifying chains and signified contents―and a-signifying semiotics that work from syntagmatic chains without engendering any signification effect, in the linguistic sense, and that are susceptible of entering into direct contact with their referents in the context of diagrammatic interaction. An example of an a-signifying semiotics: musical writing, a mathematical corpus, computer syntax, robotics, etc.

Assemblage [agencement]: this notion is larger than structure, system, form, process, etc. An assemblage contains heterogeneous elements, on a biological, social, machinic, gnoseological, or imaginary order. In schizo-analytic theory of the unconscious, assemblage is employed in response to the Freudian “complex.”

Becoming [devenir]: this term related to the economy of desire. Desire flows proceed by affects and becomings, independently of the fact that they can fold over onto [se rabattre sur] persons, images and identifications or not. So an individual, anthropologically labelled masculine, can be traversed by multiple, and apparently contradictory, becomings: becoming feminine [devenir féminin] can coexist with becoming a child, becoming an animal, becoming invisible, etc.

Block [bloc]: This term resembles assemblage. It’s not a question of an infantile complex, but the crystallization of systems of intensities that traverse psychogenic strata and are susceptible of operating through perceptive, cognitive or affective systems of all kinds. An example of an intensity block: musical refrains in Proust, “Vinteul’s little phrase.”

Body without organs [corps sans organe]: Gilles Deleuze borrowed this idea from Antonin Artaud to describe the degree zero of intensity. The idea of the body without organs, unlike that of the death drive, does not implicate thermodynamic reference. Read the rest of this entry

## Richard Webster on Intellectuals

The tragic predicament of such intellectuals [as Lacan] is that, driven by terrifying feelings of emotional emptiness and insecurity, they mistakenly conclude that intellectual truths can be an adequate substitute for emotional warmth. Convinced that difficult or abstract intellectual formulations can alone fill the void they feel within them, they develop a voracious appetite for such formulations, anorexically judging their goodness by the degree of difficulty or abstraction they possess. Believing that what they have devoured is intrinsically nourishing and failing to grasp the poverty of the diet they have adopted through their own self-denying ordinances, they now feel impelled to share their ‘truths’ with others. Indeed they are driven by their own generosity to do so. Like a starving man who compels others to eat the diet of stones he believes has saved him, they give abundantly of their poverty out of a genuine conviction that they are enriching others. Because their own most generous impulses have become inextricably entwined with their impulse to self-denial they are unable to discriminate between generosity and cruelty and unable to understand that by compulsively sharing with others (or compelling others to share) their own chosen form of intellectual or spiritual wealth they are merely disseminating their poverty.

~Webster, R. “The Cult of Lacan

[The above is the only thought-provoking paragraph of an otherwise worthless essay.]

## A Question For Lacanians

When Jacques-Alain Miller was a philosophy student at L’Ecole Normale Superieure, Althusser told him to read “all of Lacan,” so he did. Then, one day when Lacan was visiting the school, Miller asked him a now-‘famous’ question that supposedly revealed the key to Lacan’s psychoanalysis, and the two from then on entered into an understanding which was to last all their lives. Miller’s question was: “Does your notion of the subject imply an ontology?” (via)

Another account of the exchange (which includes Lacan’s answer), located here, is:

The ontological concerns of the Cahiers pour l’Analyse themselves are prefigured in a key moment in Jacques Lacan’s seminar in the spring of 1964, when Jacques-Alain Miller asked Lacan if his theory of the subject, grounded in an account of lack and its structuring function of the unconscious, presupposed an ontology. In the seminar, Lacan answered this question with the suggestion that the constitutive gap of the unconscious was essentially ‘pre-ontological’. The Cahiers pursue Miller’s original question along multiple lines, identifying points of contact between Lacan’s theory of subjectivity and the ontological concerns to be found in recent and contemporary developments in logic and the sciences.

As far as I can tell, there are two possible interpretations of the word ‘ontology’ in Miller’s question. Ontology can mean ‘study of being’, or more rarely can mean ‘diegesis’ (fictional ‘world’), though I’m not sure if the latter is still true in the French. In the former case, it would seem that Miller is asking “Does your notion of the subject imply that your work is a study of being?” In the latter case, he would be asking if the ego (which is an imaginary construction) subsists in a distinct diegesis (i.e. a plane of reality separate from everyday existence).

Even after hearing Cahiers pour l’Analyse‘s account, I still do not understand the question (nor how Lacan’s answer can be correct). My question to Lacanians, then, is: what does Miller mean, what does Lacan’s answer mean in relation to Miller’s question, and what are the broad implications of this question?

(Note: the above exchange can be found in The Four Fundamental Concepts of Psychoanalysis.)

## Trying to Get Immanence Out of a (Philosopher’s) Stone: Archetypes, Sociobiology, Harry Potter, and the UK Riots

Click the picture for a more detailed explanation of the notion of signifier/signified.

[To make the parallel of Harry Potter & the Tottenham riots seem less farfetched, see here.]

There are a number of popular (i.e. non-academic) intellectual movements whose objective is to find an immanent basis for the meaning of signifiers. One such example is Jungian archetypes, which states that various symbols are innate in the human mind, and thus that symbols are “universally recognizable.” As well, the sociobiology of Desmond Morris seeks to ground social phenomena in biological instinct (once again, innate), e.g. he ascribes the tradition of women coloring their lips red to the fact that when a woman becomes aroused, her lips become engorged with blood, appearing fuller and redder; thus lipstick is a display of availability for mating, just as is the peacock displaying its feathers. A third, more contemporary instance of this tendency can be found in the Harry Potter series. In Hogwarts, students of witchcraft & wizardry are taught combinations of signifiers (e.g. a “swish & flick” of one’s wand combined with the words “Wingardium Leviosa” pronounced in a specific way) which are somehow inherently connected to their magical function. There is no talk of ‘inventing’ spells; presumably experimental wizards merely spout out Latin-sounding words in hopes that they’ll bring a result connected to their etymology. This essay will outline the three views described above; show how meaning is in fact not immanent, but for the most part purely arbitrary; and show how this immanent treatment of signifiers resonates within the UK riots, perhaps to the point of precluding any significant cultural change.