I wrote down the transcript of the last half-hour of Dean's lecture Exploratory Diagrams and Abstract Machines, which I did to aid my research for my research paper...
Dean kenning exploratory diagrams and abstract machines lecture 0:55:41 (theory part)
Gonna look at:
C.S Pierce, Very interesting philosopher and developed this theory of semiotics in early twentieth century/late nineteenth century, did a lot of diagramming himself
Chatalet, french mathematician/philosopher,
Deleuze, deleuze and guttari but especially deleuze
What pierce said is that “a diagram is mainly an icon, and an Icon of intelligible relations,”
In a nutshell what an icon is something which looks, bares a resemblance, physical resemblance to the thing that’s been represented. It’s not abstract.
And we’re used to these icons now, the little smiley faces, you know, we live in a kind of technical world of the Icon. often replacing texts, you know, words, which are not icons but are symbols. I’ll go into that a bit more. But a diagram is an icon. In other words, it relates in terms of similarity, to its object.
He also says - he says a lot of things about diagrams, but he also says “experiments upon diagrams are questions put to the Nature of the relations concerned,” so you see this term ‘relations’ come up. The diagram is fundamentally about relations, the relations of a thing. That’s what a diagram does, it can represent or depict the relations of a thing. He very much sees them, he was actually like a chemist, a scientist, before he became a philosopher, and he sees diagrams like experiments, as things, almost like replacements, for experimenting upon the actual object, you could construct the diagram and experiment upon the diagram. So they’re very kind of functional objects, and they really hold a kind of inner truth, a kind of essence, of the thing that’s being looked at.
These are a couple of Pierce’s ? venn diagrams, he? Someone who drew, he did diagrams and doodles and so on, very interesting one, not published on the left, on the minotaur (C.S Pierce, Labyrinth) in a maze, little abcd figures in various places. And one of his existential graphs developed this whole system of diagrammatically representing, kind of logical statements, and i won’t go into those, but that’s just to give an indication.
/Okay, so let’s look a bit more at semiotics and signs. Might be more familiar with sausurre’s system, a lot of you, of signifier-signified. For Saussure, the sign is made up of the signifier and the signified or the sound-image, that’s the sound of the word that we say, whether we say it out loud or we say it in our heads, or read something or write something. And the signified which is the concept of the thing that we are signifying. Now, notice that there is nothing outside of this, there’s no object. And this was seen as a bit of a breakthrough and really led to all kinds of innovations within structural semiotics.
But Pierce’s sign does move out to the object, you have what he calls the representamen, which is actually the sign, as such, the kind of, signifier really. But you also have the object itself, and you also have the interpretant, that’s the person who is interpreting the sign that’s being produced. So it’s a different kind of notion, the interpretation and reality of the actual object.
/Now, “any Representamen is either an Icon, an Index, or a Symbol,” so for pierce, everything is in threes. Everything in the entire cosmic philosophy comes in threes.
So an icon, “partake[es] in the characters of the object.”(SIMILARITY) In other words, it’s related to the object in terms of similarity, which i said already.
The index “really and in its individual existence connect[s] with the individual object” (REAL CONNECTION) there’s a real connection. A shadow is an index of the object that’s casting the shadow. A medical symptom is the index that there’s a sign that there’s something wrong at some level and so on.
The symbol “denot[es] the object, in consequence of a habit” (CONVENTION) so what this means is that there is a conventional sign system which we all agree upon, and hopefully when I’m speaking you will understand the words I’m using, because I’m expecting that the way I’m using the words will have a meaning for me as it will for you. So there’s a kind of habit involved in the symbol. It’s a conventional language, such as writing words, or mathematical notation is another conventional symbolic language.
/Now, icons themselves, which are the first of these Representamens, or signifiers, the icon itself is split into three. So Pierce writes, “[Icons] which partake the simple qualities… are images; those which represent the relations… of the parts of one thing by analogous relations in their own parts, are diagrams; those which represent the representative character of a representamen by representing a parallelism in something else, are metaphors.”
I’ve just put some examples here. These are all icons, right? They’re all icons in the sense that they’re all images, but they’re also all icons in the sense that they are relating to the object in case the brain in terms of similarity, or analogy. The image does it based on qualities, there’s something in this pencil drawing qualitatively similar to an actual brain. The diagram does it through an analogy of relations of parts. So the parts of an actual brain are here, analogous to the parts I described in the diagram, and they’re all labelled as such. Metaphor, such as, a brain is like a computer, or like a computer chip or circuit or something, is similar through something parallel that it holds with the thing that is the sign. So in this case it might be the idea that we are processing information. The brain is a kind of system for processing information, so we use this metaphor.
There’s not really pure diagrams, or pure images, the image itself is a bit diagrammatic, you know, it’s schematic, it’s not exactly like a brain, of course. The diagram is of course, an image, in the sense that it does look somewhat like a brain, as well as being a diagram, also has symbols, all the words, these are symbols, conventional language. So there’s no purity but they are distinct conceptually.
/ so i’m gonna move on now to the second, the second figure, (Gilles) Chatalet, who like a said was a mathematician, who wrote this amazing book called Figuring Space, which is about the interconnection of signs, mathematics, and philosophy, in terms of gestures and diagrams, how scientists work out, breakthrough, conceive of new spaces, configure new spaces. Through a hands-on, imaginative, refiguring, which happens through thought experiments, experiments with objects, and diagramming techniques. And what’s interesting about Chatalet is that he very much unlike the diagrams in the beginning, the isotype diagrams, he’s very much against rationalism. And he sees diagramming as something more like magic, something more occult. So he writes:
“There remains, however, a confused desire to take up again in the flesh of what is perceived as a whole that has been mutilated by technical disbursement, a genuine nostalgia for magical power, exasperated by the incapacity of classical rationalism to get to grips with all these sleights of hands, all these “recipes”, all these thought experiments, these figures and diagrams, all these dynasties of problems seemingly capable of the “miracle” of reactivation. This reactivation is “informative” [giving shape] in the proper sense and cannot be reduced to the conveying of a pre-conceived form from one transmitter to another receiver,”
Okay, so this is clearly, along the lines, that I’m explaining, exploratory diagrams, this is not about transmitting pre-conceived information, it’s about forming new shapes, forming new senses, through these figures, thought experiments, and diagrams. So he goes on,
“A diagram can transfix a gesture, bring it to rest, long before it curls up into a sign, which is why modern geometers and cosmologers like diagrams with their peremptory [insisting on immediate attention] power of evocation. They capture gestures mid-flight; for those capable of attention, they are the moments where being is glimpsed smiling,”
/So very kind of poetic metaphor but I’ll give a couple of examples from his (book), and this is from his final chapter where he talks about geo-electric, kind of electro-magnetic geometry. At the top we have a diagram from the perspective of a rationalist _perspective where we get a distance from the object that’s being seen. In this case, the way that the electricity is moving in a circle around this magnet. In the bottom diagram, which relates to the earlier, the ___ which I’ll describe, the scientist, diagrammer kind of leaps into this space, this round circular motion, in order to carve out this new geometrical electromagnetic space, you cannot do from a distance, it’s really about not watching these movement of these things in a circle, but the way that electromagnetic field is formulated by going through and turning through this circular motion.this is not the kind of diagram in science books which explain how electromagnetism works, it can become that but that’s not what he’s interested in. what he’s interested in is this moment when these scientists and mathematicians are trying to figure it out, trying to come to terms with it, and they can only do that in an embodied sensual way, through these thought experiments, that are enabled by our hand gestures that take place when one draws a diagram. So you’re bringing about something new through these techniques, not something that is pre-existing knowledge.
/so my final example is (Gilles) Deleuze, Deleuze is probably the toughest really, the hardest, the most difficult, because his diagram is really very unlike anything we understand to be a diagram. He also calls the diagram an abstract machine, and he describes it as, this is when he’s writing with Guttari in A Thousand Plateaus, he says
“The abstract machine is pure Matter-Function - a diagram independent of the forms of substances, expressions, and contents it will distribute.”
What he means by that is very complicated, but he is talking about Matter-Function in the sense that, whether the matter is language, or whether the matter is subatomic particles, or whether the matter is cells or genetic material, a diagram functions to distribute this matter in various ways so that something can come about. It’s nothing to do with the substances themselves, the diagram is not seen in the thing that comes about, it’s nothing to do with the expressions and content, it’s nothing to do with semiotics, in the way that Saussure or Pierce would talk about it. It’s to do with something that exists on a virtual level, springs something into being, but the diagram itself remains virtual, it remains completely abstract. Deleuze does draw diagrams actually, but he probably wouldn’t describe them as [laughs] diagrams, the diagrams would remain virtual but he does these quite nice little hand drawings in various places,
/this is in Foucault, in 1986, and he initially gets the idea, the concept of the diagram from Foucault, Foucault writes this book Discipline and Punish, with a very famous section on the Panopticon. The Panopticon is this prison devised by Jeremy Bentham, it doesn’t have to be a prison, it could be a school, it could be a workplace, where the prisoner or the pupil or the worker is always cognitive of the fact that he could be being watched at any point. Whether or not he’s being watched, he might be being watched. So there’s this tower in the middle, and there’s these cells all around the edge, in this kind of circular architecture. And the person in the tower is like the prison guard who at any point can look into these cells, which you can look through, and you can see, this prison on the right is apparently saying his prayers, being a very good prisoner, and obviously reforming and being a decent citizen when he comes out and all that stuff. So this is applicable to the areas but what Foucault says,
“But the Panopticon must not be understood as a dream building: it is the diagram of a mechanism of power reduced to its ideal form…”
In other words it’s not a diagram as in a blueprint of the architectural structure, which is another type of diagram, it’s a diagram of a mechanism of power, which can be applied in all kinds of material forms the way that matter can be distributed, to function in a particular way, in this case, of surveillance. So the actual panopticon is also the diagram of surveillance TV, CC TV, it’s also the diagram, you could argue, of the way we are monitored on our phones, on our computers, all these things. So the diagram exists as an ideal form of power and operation.
/so this is what Deleuze kind of picks up on. This virtual function. again , Deleuze and Guttari in A Thousand Plateaus:
“Diagrams must be distinguished from indexes, which are territorial signs, but also from icons, which pertain to reterritorialization, and from symbols, which pertain to relative or negative deterritorialization. Defined diagrammatically in this way, an abstract machine is neither an infrastructure that is determining in the last instance nor a transcendental idea that is determining in the supreme instance. Rather, it plays a piloting role. The diagrammatic or abstract machine does not function to represent, even something real, but rather constructs a real that is yet to come, a new type of reality,”
(he’s using terms of Pierce quite directly here) (Deleuze and Guttari want to go full deterritorialisation, let’s say, so they want to escape all three all these types of signs)
So this is a kind of radical, exploratory notion, in the sense that Deleuze and Guttari are against representation of any type. The diagram is autonomous, in the sense that it plays a piloting role, it’s purely creative. It constructs something that doesn’t exist at all. Later, they further explain what it is not. It’s not axiomatics, it’s not an axium. It’s not schematic.
“Axiomatics [...] possesses a deliberate will to halt or stabilise the diagram, to take its place by lodging itself on a level of coagulated abstraction too large for the concrete but too small for the real,”
I think this is quite a nice way of understanding what Deleuze and Guttari mean by the diagram. When you get a kind of simplified - so we began this lecture about how the diagram simplifies, when you get a simplified schema, of something, an abstraction, for Deleuze and Guttari this is not abstract enough, right, it’s too large for the concrete, it misses too much, it simplifies too much, it schematises too much, but at the same time it’s too small for the real, so it’s not abstract enough, it doesn’t go far enough to this point beyond signification and representation.
/Now I think the point where Deleuze’s conception of the diagram gets a little bit more concrete, a bit easier to understand is this book called Francis Bacon(Logic of Sensation), it’s this book all about painting. And Deleuze thinks that the diagram operates in painting. This is the quote from Francis Bacon. There he is in his studio, wonderfully messy, entropic studio. And true bohemian this guy. He, in his interviews with__, he describes the process of painting or beginning to paint, or trying to paint, he says that
“[involuntary marks are made] and you survey the thing like you would a sort of graph [diagramme]. And you see within this graph the possibilities of all types of fact being planted,”
“[I]f you think of a portrait, you maybe have to put the mouth somewhere, but you suddenly see through this graph that the mouth could go right across the face [...] you would love to be able to make a Sahara of the appearance,” Bacon, quoted in Deleuze
So what’s Bacon talking about here, he’s talking about the process of beginning to paint, he doesn’t wanna pick up all the clichés and conventions, he can never start it right, anyone who’s a painter knows it’s very hard to get going, so he kind of begins, and then he does some random marks, and then he steps back, he looks at it, as if it’s a diagram. And then he suddenly sees things. He sees the way that this man could be stretched, like it’s really really big, like the Sahara Desert. He sees the way that the skin could become something else, rhinoceros skin, something. And that’s the point where something new is able to be created.
So that for Deleuze is the diagram. The diagram is this point where something is surveyed, you’re in this moment of chaos, and something comes out of it, a fact can be planted.
/Deleuze writes, “It is as if, in the midst of the figurative and probabilistic givens, a catastrophe overcame the canvas,”
And this catastrophe is the diagram. So if we look at this painting, triptych by Bacon (Three Studes of Figures on Beds, 1972), the diagram is not these little circular diagrams and so on, which look very diagrammatic, the diagram is the thing that allowed this painting to occur. Which is now hidden, within the painting itself. But it’s the catastrophe that happened before something new could be produced.
/This is the final slide. He gives an example from Van gogh.(slide image: Wheat Field with Cypresses, 1889) He writes that
“The diagram is the operative set of traits and colour-patches, of lines and zones. Van Gogh’s diagram, for example, is the set of straight and curved hatch marks that raise and lower the ground, twist the trees, make the sky palpitate,”
So that’s a beautiful description of what Van gogh’s doing to these painterly marks, and these colour patches, these are the basic tools of a painter. You look at this van gogh painting, and you don’t see a diagram, doesn’t look remotely diagrammatic. But Deleuze would say Van Gogh has a diagram. Van Gogh’s diagram is not the way that the trees relate to the sky or the perspective or the lack of perspective, the diagram is in the way that he forms these marks, that allow this matter to function in a particular way, be distributed, to go back to the quote.
So it’s a very abstract notion of the diagram, but I do think the book on Bacon is very very good for painters, and it does allow us to get a better understanding of Deleuze’s diagram, of this virtual diagram. He actually goes on to describe it in terms of modulation, and he gives an example of an analogue synth, forms a sensory analogy, which is not like the visual analogy that Pierce is interested in when talking about the diagram, and that’s a kind of further elaboration. But it’s very much about connecting immediately about the central nervous system, rather than with a kind of distance, objective distance of a typical diagrammatic representation.