The Borromean Knot

The Borromean Knot

I have looked at knots in the past because I like the way that they are both physical objects and powerful metaphors, they tie things together, mentally and physically. But now as I'm trying to get to grips with some alternative approaches to thinking about my own mental life, I have discovered a particular mental knot that is used to try to explain subjectivity or some of the key aspects of our mental life from a psychoanalytic point of view. 

In mathematics Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other. They break apart into unknotted and unlinked loops when any one of the three is cut or removed. I. e. the rings are held together only by the presence of all three. If any one of the rings is cut open, the entire structure falls apart. Sometimes this is represented by three overlapping circles, but this takes away the vital three dimensional nature of this idea, it doesn't work in two dimensions, so if you need to draw one you need to give the rings some form of three dimensional indicators, such as the white spaces in the drawing above, that indicate which part of the circle sits on top and which below. 

This construction was historically one of the heraldic symbols of the dukes of Borromeo, which is why it is called what it is. 

Odin's knot

In Norse mythology, triangles are used to express the same idea, (the Valknut) and topographically it makes no difference to the concept. The knot belongs to a tradition of thinking that is centred around the use of fibres to think with. In this case 'seidr', (Old Norse seiðr, 'cord, string, snare') was a form of shamanistic magic concerned with discerning the course of fate and how to effect change, which was done by symbolically weaving new events into being. Odin's knot, like any other form of weaving, is a structure that only makes sense when it is complete, the individual threads or cords are thin and insubstantial, but when brought together as a weaving or in this case an idea, a powerful concept is realised.

However there is another version of Odin's knot, one that fuses together all three triangles as a continuous band, and this represents the fact that differences are an illusion. 

Odin's knot

Borromean Rings also represent the symbol of the Trinity in Christianity, the three interlocking rings signify the divine trinity, which represents the belief that God is of one Being made up of three distinct Persons who exist in co-equal, co-eternal communion as Father, Son and Holy Spirit.  In fact these interlocking rings can be used as symbols for many sets of interlocked triads such as past, present and future.

It is however the Borromean Knot as used by the psychoanalyst Jacques Lacan that I'm going to try and focus on, as it might help me with some sort of structural support when trying to think through the relationship between the world out there and the inner world of embodied mental processes. 

Lacan and the Borromean Knot

The three rings are first of all 'real', in that topology is about solid, three dimensional objects and their surfaces. Therefore when Lacan decides to use it as a symbol, it is a much more solid symbol than a geometric figure, such as a circle or a triangle. 

It is a symbol of an inseparable bond, so that whatever is joined together by this bond is seen as a totality, something that might have three components, but no one component can be free of the other two; if it ever is, it would actually cease to exist in the form it takes. Lacan uses the knot to illustrate his structural theory of three registers or orders of what he thinks of as the psychoanalytic experience or categories of the psyche; the Real, the Symbolic and the Imaginary. However, he chooses the Borromean Knot, not just because of its interlocking nature but because of the fact that its loops have to be 'real' or three dimensional to work, they have to be loops of chain or rope. This he states, means that rather than simply representing this structure, topology is that structure. 

The knot is not just a way of illustrating the interdependence of the three orders, it is also a structure that helps Lacan to think about what the three orders have in common. Each ring represents one of the orders, and certain elements can be located at intersections of the rings. and these can be used to focus on the relations which bind or link the three aspects of the psychoanalytic experience. He argues that if the knot is broken or unravelled in some way it results in some form of psychosis. There is though a further element in his concept, which he calls the 'sinthome', which he thought of as a fourth ring, a ring that was needed to go beyond the symbolic. I can see why he might need this, and its the problem with theory and representational systems. It's ok to have an idea and to set out a theory, but where is the lived experience, at what point can you get totally lost in the activity and in effect become it? The 'sinthome' it seems to me is not just about a need to have a fourth ring to ensure the three rings hold together, but is a reminder that there is a reality beyond symbolic meaning, and that is for myself a very useful thought. I'm often asked about my work, 'What does it mean?' and by that I gather that people want me to describe its symbolic meaning, but I tend to avoid this, as it can be like a trap, in doing so, it can seem to empty the work of meaning, rather than communicate what its trying to say. 

But Lacan's Borromean Knot has letters and the word 'meaning' inscribed into the various overlapping sections and these are where the detail in terms of his thinking is held. 

Lacan's Borromean Knot

There is a very neat chess metaphor used by Žižek to explain the differences between Lacan's three orders. Žižek explains them like so:

'For Lacan, the reality of human beings is constituted by three intertangled levels: the Symbolic, the Imaginary, and the Real. This triad can be nicely illustrated by the game of chess. The rules one has to follow in order to play it are its symbolic dimension: from the purely formal symbolic standpoint, ‘knight’ is defined only by the moves this figure can make. This level is clearly different from the imaginary one, namely the way in which different pieces are shaped and characterised by their names (king, queen, knight), and it is easy to envision a game with the same rules, but with a different imaginary, in which this figure would be called ‘messenger’ or ‘runner’ or whatever. Finally, real is the entire complex set of contingent circumstances that affect the course of the game: the intelligence of the players, the unpredictable intrusions that may disconcert one player or directly cut the game short.'

(Žižek: How to Read Lacan, pp. 8–9)

Žižek returns to this issue in his book, 'Event: Philosophy in Transit' and if you put the two descriptions together you get a reasonable idea of Lacan's three registers.

'For Lacan, the Imaginary, the Symbolic and the Real are the three fundamental dimensions in which a human being dwells. The Imaginary dimension is our direct lived experience of reality, but also of our dreams and nightmares — it is the domain of appearing, of how things appear to us. The Symbolic dimension is what Lacan calls the ‘Big Other,’ the invisible order that structures our experience of reality, the complex network of rules and meanings which makes us see what we see the way we see it (and what we don’t see the way we don’t see it). The Real, however, is not simply external reality; it is rather, as Lacan put it, ‘impossible’: something which can neither be directly experienced nor symbolised — like a traumatic encounter of extreme violence which destabilises our entire universe of meaning. As such, the Real can only be discerned in its traces, effects or aftershocks.'

(Žižek 'Event: Philosophy in transit' pp. 119–20)

My personal interest is in this case the fact that for Lacan, direct lived experience of reality is fixed into the 'imaginary' register. 

Right in the centre of Lacan's annotated diagram is the letter 'a'. Small case, and standing as an abbreviation for 'autre', or in English, 'other'. Or is it what Lacan had called 'The Fragile Absolute'

Lacan states that there is a price we all must pay in order to gain access to the social world of other humans. We must undergo a process of finding limits to our natural 'jouissance'. 

'Jouissance' as used by Lacan, has been described as: 'The lost plentitude of one's material bodily drives given up by the subject in order to enter the symbolic order and access the symbolic power of the phallus, something that occurs upon the adoption of language and acceptance of the rules of the name-of-the-father'. 

I.e. There are laws to follow, the first ones of which you learn from your parents. Lacan for some reason called this process 'symbolic castration'. Which sort of makes me have a mental shiver.  You are supposed to have sacrificed an 'enjoyment' that in fact you never really had on the alter of the Symbolic (Law). You sort of 'remember' the prohibition of that enjoyment and resent your Symbolic castration for having had an intuition of something that may not even exist. As far as I can see, this works as a story, a fabrication of the mind, such as the classical Freudian tale of Oedipus, who fulfilled a prophecy that he would end up killing his father and marrying his mother, thereby bringing disaster to his city and family.. The “lost” enjoyment concentrated in the 'objet a' is an impossible enjoyment, hence it is a 'Fragile Absolute'. 

But, and this is where Lacan constructs another tale for us to think about, the lost 'jouissance', that primal something that was lost as you become subject to society and its laws, is the thing around which you construct the subjective story of yourself. This is why we are always wondering what we are and why we are. This awareness of some sort of loss, is what makes us into the desiring subjects we are. the 'a' at the centre, is the lost 'other' that causes us to desire in the first place and this is why Lacan also called it the 'object-cause of desire'. It is the only thing that belongs to all three aspects of the psychoanalytic experience. 

If we then turn to 'JA' which seems to be translated as 'autre jouissance', this it seems is a sort of pure 'jouissance' of the Real beyond any symbolic contamination. This 'escape' is somewhat problematic though as it seems to rely on a very male centred phallocentric idea, in which for some reason, this other is associated with the feminine, therefore this 'jouissance', I would argue, lies outside the ring of the Symbolic, and as far as I can understand his logic, it would then appear that not being male is a form of psychosis.  At another point he mentions a “pure difference” and a “fermenting” Nature, things that stand outside of the sacrificial lack. The important issue in terms of the diagram, is that JA sits outside of the symbolic. Here we can see the problem with words again. When naming things, nouns are either so or not so, they create binary divisions, whilst events are closer to the truth as they are open ended and they evolve. 

The section that is made by the overlap of the real and the symbolic is labelled 'Jφ' φ is the lowercase version of the Greek letter phi Φ.  In Lacan's terminology Jφ stands for 'phallic jouissance'. This means that this concept stands outside of the 'imaginary', it is outside of the domain concerning how things appear to us. Lacan at one point plays with the similar sounds in French of le nom du père (the name of the father), le non du père (the no of the father), to emphasise the legislative and prohibitive functions of the father, and this lies central to why this is a 'phallic jouissance'. The symbolic world that the father introduces the child into is a construct that we have to come to terms with, even if we resent it. Because it is not a part of the imaginary experience it is a 'castrated' enjoyment. 

Meaning is set between the symbolic and the imaginary and sits outside of the real, which is, according to Lacan, inaccessible to psychoanalysis itself. Because of the overlaps between rings, there can be various combinations between the elements. Thus, for example, there can be a symbolic or imaginary hole in the real, for instance a nightmare may leave you with a deeply traumatic aftereffect, a real object may become an icon within the symbolic. Likewise, there can be a consistence or hard core of 'meaning' within the symbolic, or a hole in the imaginary, whereby direct experience is seen as an illusion. The sliding between categories does seem to me to be more akin to how I experience being and when I try to sense my own psyche, its illusiveness and slippery nature is part of its essence, it is something you can't nail down. 

I can intuitively grasp what Lacan is saying, but I think he would have been better at setting it down as a form of poetry or a personal fable rather than as a psychoanalytic conundrum. My own day to day anxiety is I'm sure rooted in my relationship with my father, his harsh rule still impinging on my own ability to trust my instincts, as I still feel myself inwardly seeking his approval before I do anything. Something that I have battled with all my life, and that has at times seemed 'mythic', a something to externalise in order to overcome its hold.

If I had to choose my own geometric figure to represent that movement between the outer and inner worlds that I seem to inhabit it would however be the triquetra.  The triquetra is a triangular figure composed of three interlaced arcs and as you follow them round you realise they are all part of the same figure. Lacan's struggle to unpick the reality that sits outside of perception, from the world of symbols that humans use to give order to their world, is at the end of the day, as far as I can see, a failure, but an interesting one. I am constantly trying myself to find visual structures that give some sort of meaning to my experiences and I do find that those meanings are very illusive and that they have something to do with my inner psyche and my bumping into a something out there, together with the need to resolve the experience of both. 

The triquetra

The representation of three curved forms as a continuous band represents, like Odin's knot, the fact that differences are an illusion. 

Sometimes when I'm awake I think I'm asleep and sometimes when I dream I think I am awake. The topology of dreams is perhaps the next thing to explore. 

See also:

Knots

Lacan and drawing as an external self

Patterning, ties, entanglements and knots

The weaving of grids

The triangle