Dreaming The Square Root Of Negative One: Jacques Lacan And Space-time Relativity Essay, Research Paper

(c) 1998 by Daniel du PrieThe resistance of dreams to the transparency of the egoic consciousness, as opposed to structural meaning per se, lies not in their ‘objective presentation’, that is, in the way in which objects appear phenomenologically in terms of an eidos, under the order of the symbol. It lies, rather, in a noetic resistance, in an opacity on the order of the image, the imaginary: a lacking in the ‘narrative’ flow of meaning as it flows forwards in time, the non-conformity of the ordered text. Or so it appears at first glance. Dreams seem to hide from imaginary order, protesting against a psychological model of sense/reference. This due to the trieblich (drive-ish) source of dreams’ contents.

In this frame, it appears that when I wake from this dream, or that one, confused, it is not so much because there were no recognisable signifiers, symbols or objects: the cat in my dream I know as a cat, that tram I understand as a tram, the gun looked like a gun which shot bullets and killed the monster. To my understanding, it is in the diachronic flow that meaning seems to elude me. In the syntagmatic disjunctions, dislocations and disordering of the ‘normal’, everyday and waking flow of signifiers’ differences and associations. Not these as such, but in the flow thereof.

The diachronic flow of signifiers which appears transparent due to repetitive reification in the meaningful discourse of the everyday is undermined and turned upside down in my night-life. It is because the cat is eating pizza with knife and fork, because the tram has now become a train (while I was not looking), because shooting the monster had ‘nothing’ to do with ‘anything else’ in my dream narrative that meaning escapes my consciousness. These alien patterns of flow alienate me from my dreams’ meanings.

I am aware, generally, that this lack of meaning is grounded in the manners by which the wish-fulfilments of my Triebe (drives) tend to function, as Freud has variously written, that is, dreams are “disguised fulfilments of repressed wishes” (see endnote 1) [emph. in original]. However, the signifying chain generated by this or that Trieb (drive) in this or that dream by the unconscious is radically obscured in its translation to the symbolic by the censor: that is, in the Trieb’s translation subject to law and reality, which need to preserve their own particular order. Reality (see endnote 2) refuses to accommodate the fulfilment in terms of the latent meaning of this or that Trieb, and hence the flow of meaning is, not edited, but rather ciphered altogether. It is not so much that certain sections are ‘cut’, like a censor might edit a film, but narrative flow itself appears bizarre. The above confusion is, because to my consciousness, where the symbolic or signifying order understood discretely yet remains transparent, analogous meaning is henceforth censored and made secretive and latent.

All this, however, is in fact a clever ruse intended to sustain the ’sanity’ or coherence of the symbolic under the real while repression has become the destiny of the disallowed Triebe. In fact, ‘in’ reality, it is the signifiers (the symbolic – cats and guns and trams) which are always metaphors and metonyms of unconscious signifieds. Dreams have more in common with surrealist poetry than with a film or play in which the story has been cut into pieces and re-arranged at random. If we were to identify or open the symbols in relation to what is being repressed (the aim of analysis), then, no doubt resisted by the real, the diachronic flow, or narrative process would, without alteration, make complete sense. For, of course, a diachronic ‘flow’ itself cannot be ‘dislocated’: it can only move ‘forward’ in time. Even a re-arranged film while making non-sense, still begins at time one, and ends at time two.

What of dreaming sex? Not frustrated sex, but dreaming sex in a utopian type of dreamy freedom? Here there could be no proper bar or resistance between the symbolic and the imaginary – for whatever reason or lack, symbolic reality appears to have ‘forgotten’ to get in the way – the dream becomes real (in a Freudian sense), so to speak: transparent, non-latent, there is nothing to analyse. That is, there’s no dialogue of repression – the sign stands un-occulted. If it be possible (and it is not at all sure whether such utopian, uncensored dreaming even be possible), then dreaming orgasmic sex as just that with an ideal ego is not going to involve confusion or narrative rupture, unless the censor moves back in to blip or expurgate it by fucking with associations of the petit objet ‘a’ : ideal ego – the looked at signifier, symbol for example. Perhaps the ideal ego (ie, who you’re doing it with in your naughty dream) turns into a cloud and suddenly you’re falling to earth, or whatever. But if that doesn’t happen, in this case we could say that the Trieb as articulated demand appears (as closely as seems possible) simply fulfilled. Dreaming sex is then a ‘primary’ Freudian metaphor, but not of what we have grown up to signify with ’sex’. Dreaming sex is, in the sense that it escapes symbolic metaphor violated by reality, is understood wholly by small ‘r’ reality (the symbolic order). Transparent, dreamy sex refers rather to none other but,

The promotion of consciousness as being essential to the subject in the historical after-effects of the Cartesian cogito [being] for me the deceptive accentuation of the transparency of the I in action at the expense of the opacity of the signifier that undermines the I; and the sliding movement (glissement) by which the Bewusstsein [Consciousness] serves to cover up the confusion of the Selbst [Self],[which] eventually reveals, with all Hegel’s own rigour, the reason for his error in the Phenomenology of Mind.(see endnote 3)

If the operation of the signifier that undermines the I in the capacity of -1 is given already as retarded (past to future), all other signifiers will appear falsely transparent. Falsely ‘recognising’ the signified, I affirm the reality of the signifier undermining the I, while colluding in my own repression, while in the case of the sex dream I think my desire is fulfilled.

The sex dream transcends need, and the alienating demand, to aim at desire, or rather, nothing taken as desire. It is for this (lack of) concept that the sexual dream is a metaphor, and a metaphor that aims at a prototypical or (if I may) an original Trieb. In other words, it signifies the fundamental action of the ‘I’ within the obscurity between the synchronicity of the statement, on the one hand, and the signified on the other to exhaust itself in that operation written by Lacan as the square root of negative one(see endnote 4) : an Imaginary number.

The use by Lacan of the square root of negative one in his psychoanalytic theory is controversial and no doubt misunderstood. The “s = √-1″ is not just about an operation that is impossible. In relativity theory, “the parameter that represents temporal displacements…is represented by a negative square: [eg] ?t 2. But…what does that tell us about t? What is the square root of, say, -9?”(see endnote 5)

This is not analogous to the unconscious ciphering the glow of meaning in a dream, as it is the signifiers which are ciphered: the negative ones. Rather √-1 refers to the ‘Real which resists symbolization absolutely’ – that is, the retarded historical flow of time (past – future). The way the maths deal with a negative square is to invent an imaginary number: the solution of √-1, signified as i. (It cannot be symbolised any other way, by the way, as this ’solution’ does not exist symbolically.) So, if you multiply this imaginary number you get -1. When we add i to time to make imaginary time, or i t, (which physics allows), and do this in psychoanalysis also, we can make time just like space, we can remove its ‘flow’ which should allow us to do better analysis.

In the case of i t, when time measurements are squared we get units of I 2 x t 2, which is simply (-1) x t 2, or ?t 2. Now, we have to multiply this negative number by the minus sign that comes into Einstein’s equations themselves, which cancels out the (-1) we got from I 2 and leaves us with just t 2 (remember the old adage ‘two negatives make a positive’).”(see endnote 6)

Leaving aside the algebra – the crucial factor is that for the symbolic order really to work, it incorporates a symbol, I 2, the meaning of which is wholly imaginary, and literally stands in the place of what it represents, an inexpressible operation. More than that however, this Imaginary symbol also makes historical time symmetric, that is structural and spatial, and in the equations, positive t squared is actually time moving backwards.

This second point is the key to understanding that it is not the narrative flux in dreams which obscures their meaning, but the opacity of signifiers, or, to be more accurate, it is not so much the direction of diachronic flow which cannot be dislocated (as I suggested above), but, the imaginary nature of the statement shows up time (on the other hand) to be structural and symmetric – not in any sense subject to psychology (or the psychological arrow).

The ‘true’ significance of symbols in dreams is in this structural sense actually governed by a fundamental indeterminacy, as long as the equation which realizes ?t 2 with t 2 is not realized by the consciousness. In this context meaning is smeared out. But the censoring tendency moves in, in a sense with exactly that equation to collapse the indeterminacy of meaning into classical signifiers by repressing freedom. This is an equation that gives a certain pre-determined but groundless value to “I 2 = -1″, a psychological value that has nothing to do with the value of i but which passes undetected by the Bewusstseing and the ego, perhaps because i is imaginary. This value gives to the product which equals -1 an historical retardation, so that, significantly speaking, -t2 seems symmetric and the power of retarded flow is invested in i. [(-1) x t2 = -t2 , or, (future - past) = (past - future) or, symmetry. In another sense, by multiplying advanced time by a negative whole, we get retarded time, or psychological, real, time. But, it was an imaginary that produced the negative whole in the first place.] This seemingly magical power of the imaginary to produce psychological time has no ground in the structure, and when retardation is properly invested in -t2 as contingent, then √-1 and I 2 can be read structurally again. The repression of signifiers’ freedom, in the sense of their objectivity or of a lack of signification, gives us the ordinary sense of narrative flow in that, psychically t2 is subjected to -t2 . However the collapse does not give classical meaning because it is i that was used to create proper flow and hence, repression (because i, the square root of negative one, cannot be made subject to the order of law as symbolised – it resists symbolisation absolutely).

What we call ‘real time’ is actually a pseudo-time (not the same as imaginary time), which collapses meaning and closes off signification by order of the law. It is the essentially structural task of analysis to smear meaning out again by re-associating and re-differentiating the signifiers. The important theoretical implication for analysis here, is that as unconscious ‘expressions’, what are read as causes in dreams may just as well be, no, should also be read as effects. Dreams, as structural, not psychological ‘texts’, should be read ‘backwards’ as well as ‘forwards’. (Indeed, postclassical particle physics tells us that we may do this in real life also, but it is not so necessary as indeterminacy is always cancelled out by the dominant consensus of classical meaning, ie, a chair is a chair because we ‘measure’ it as a chair and thus its uncertainty is cancelled out.) Dreams, as desiring to subvert the order of the real world, with different functions and reasons are much more prone to uncertainty – hence their ‘weirdness’ and lack of reason when the observer ‘collapses’ their function according to classical, asymmetric rules.

Finally, are there any clues in Freud’s own writings that such symmetrical analysis may be of use to psychoanalysis? Indeed there is. When commenting on the causal relation (as distinct from the logical relation) between thoughts in dreams Freud noted that, “A causal relation between two thoughts is either left unrepresented or is replaced by a sequence of two pieces of dream of different lengths. Here the representation is often reversed, the beginning of the dream standing for the consequence and its conclusion for the premise. An immediate transformation of one thing into another seems to represent the relation of cause and effect.? (see endnote 7)

And what of the idea of simple wish-fulfilment and of the representation of erotic dreams? Once again, we have, at least, a clue: while all other dreams are “traced back by analysis to erotic wishes [,] this assertion is not aimed at dreams with an undisguised sexual content, which are no doubt familiar to all dreamers from their own experience and are as a rule the only ones to be described as ’sexual dreams’.” (endnote 8) This would at least appear to support my statement that there is no proper bar or resistance between the symbolic and the imaginary in a sexual dream, I have taken Lacan’s formulation of desire then to suggest that, nonetheless, sexual dreams do yet represent something other, more original than the symbolised erotic wish.

List of references: Sigmund Freud, ‘On Dreams’ in, The Freud Reader, ed. Peter Gray, (Vintage, London, 1995), p. 165.

When writing of reality here and below, it is not exactly the Real which ‘resists symbolisation absolutely’ that is being signified. More closely, I mean the production of the real by the symbolic: “Through that which becomes embodied only by being the trace of a nothingness whose support cannot thereafter be impaired, the concept, saving the duration of what passes by, engenders the thing… It is the world of words that creates the world of things… Man speaks, then, but it is because the symbol has made him man.” (Lacan, ‘The function and field of speech and language in psychoanalysis’ in, op. cit., p. 65.)

Jacques Lacan, ‘Subversion of the subject and dialectic of desire’ in, Ecrits: A Selection (WW Norton & Co, New York, 1977), p. 307.

ibid, p. 317.

John Gribbins, Schr?dinger’s Kittens (Phoenix, London, 1996), p. 210.

ibid, p. 211.

Freud, op. cit., p. 158.

Freud, op. cit., p. 169.