Topoi/Graphein: Mapping the Middle in Spatial Thought

Topoi/Graphein: Mapping the Middle in Spatial Thought


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In Topoi/Graphein Christian Abrahamsson maps the paradoxical limit of the in-between to reveal that to be human is to know how to live with the difference between the known and the unknown. Using filmic case studies, including Code Inconnu, Lord of the Flies, and Apocalypse Now, and focusing on key concerns developed in the works of the philosophers Deleuze, Olsson, and Wittgenstein, Abrahamsson starts within the notion of fixed spatiality, in which human thought and action are anchored in the given of identity. He then moves through a social world in which spatiotemporal transformations are neither fixed nor taken for granted. Finally he edges into the pure temporality that lies beyond the maps of fixed points and social relations.

Each chapter is organized into two subjects: topoi, or excerpts from the films, and graphein, the author’s interpretation of presented theories to mirror the displacements, transpositions, juxtapositions, fluctuations, and transformations between delimited categories. A landmark work in the study of human geography, Abrahamsson’s book proposes that academic and intellectual attention should focus on the spatialization between meaning and its materialization in everyday life.

Product Details

ISBN-13: 9781496205773
Publisher: UNP - Nebraska
Publication date: 05/01/2018
Series: Cultural Geographies + Rewriting the Earth Series
Pages: 192
Product dimensions: 6.00(w) x 9.00(h) x (d)

About the Author

Christian Abrahamsson is an independent scholar in Sweden. He is the coeditor of GO: On the Geographies of Gunnar Olsson. Gunnar Olsson is a professor emeritus at the Uppsala University in Sweden. He is the author of Birds in Egg/Eggs in Bird, Lines of Power/Limits of Language, and Abysmal: A Critique of Cartographic Reason

Read an Excerpt



It all begins with a close-up of a group of deaf children playing charades.


Jean — Anne!

Anne — Jean? Hi ... What are you doing here?

Jean — Where's Georges?

Anne — Away. Went three weeks ago.

Jean — Where to?

Anne — Kosovo. Why? Has something happened? What's your problem? What's going on? What's wrong?

Jean — I'm not going back.

Anne — Why, if you don't mind me asking? Look, I'm in a hurry. Tell me what's wrong as we walk.

Jean — When's Georges back?

Anne — No idea. You know what your brother's like. Is it so urgent? How did you get to Paris?

Jean — On the first train. I've been here an hour.

Anne — What?

Jean — Your fucking door code's changed!

Anne — Why didn't you call me?

Jean — I got the answer-phone.

Anne — Sorry.

Jean — I need a place.

Anne — Sorry?

Jean — Here in Paris.

Anne — How come?

Jean — I fucked off.

Anne — You did?

Jean — I can't stand him.

Anne — Is that all?

Jean — He's doing up the old barn.

Anne — So? Hold on, you must be hungry, too.


Anne — In the bath, I can't hear the phone.

Jean — What?

Anne — Forget it. Aren't you hungry? Now where were we? Oh yes, what's your dad up to?

Jean — He's renovating the barn.

Anne — So?

Jean — To live in when I take over.

Anne — So?

Jean — So, I'm not staying.

Anne — Really? Why not? Wasn't your dream to run the farm?

Jean — No, never. That was his dream.

Anne — Okay. This isn't really the time or place. I'll get Georges to call, okay?

Jean — I'm not going back.

Anne — You should know by now you must do what your father says. Later, you can make your own mind up.

Jean — I already have.

Anne — We'll talk it through later, now is not the time. The show opened last night, I got to bed at 4:30, I just have time to glance at our press, and in precisely 48 minutes, I have an important meeting. Go easy now on my poor little soul. Here, take the keys. The code is 48B13. If you're tired you can stretch out on the couch. I'll be back by 12. Let's be clear: you've seen my place, there's not room for three. Got that? Remember the code? See you later. If anyone calls, let the answer-phone get it.

[A street corner: a woman is begging, Jean passes her by and tosses a dirty napkin in her bowl. A young man sees this and chases after Jean demanding an explanation.]

A tossed paper bag is the spark that brings them together. A seemingly insignificant and thoughtless act ties them to each other. The argument between Jean and Amadou is further inflamed when more people arrive at the scene. The police arrive and Amadou is arrested, Maria taken into custody, and Jean set free. A tossed bag changes the lives of three people. The remainder of the film is nothing but a variation of the same scene; the objects and situations that bind together and hold apart may shift while the limit remains the same.

Amadou — What's with you? Was that a good thing to do?

Jean — What?

Amadou — Do you feel that was right?

Jean — Fuck you. You stupid or what?

Amadou — You're going to say sorry to the lady.

Jean — Fuck you. Let go of me! Who the hell are you? Let go!

Amadou — Now, say sorry. Didn't you hear me? Say sorry!

Jean — Let go, fuck you!

Shop owner — It's beyond belief! What's going on? Clear off out of here! Hooligans! Unbelievable!

Amadou — Hold on, I can explain. Don't go. [to Maria] This young man humiliated the lady.

Jean — Just let go of me!

Anne — Let go of him! Are you mad? Why are you picking on him?

Amadou — Is it your problem? Who asked your opinion? Do you know what he did at least? Ask before you leap in.

Anne — What's going on?

Jean — He hit me.

Shop owner — Typical ...

Amadou — What?

Jean — He hit me!

Amadou — Maybe you could tell her why?

Anne — Do you mind telling me what's going on?

Amadou — I don't see why I should. ... But everyone seems interested, so I'll tell you. The lady ... Wait there, please. And you stay here! [to Jean] Don't go sneaking off.

Jean — Get the fuck out of my way!

Anne — Let him go, for God's sake! Stop ... Calm down, Jean!

Police 1 — Break it up!

Police 2 — What's going on here? What's he done? [points to Jean] Shop owner — They put on quite a show.

Amadou — Wait, I can explain.

Police 2 — That's a smart idea.

Amadou — Ok. I'll tell you if you give me the chance. This boy, this young man, humiliated a woman begging outside the bakery ...

Police 2 — What woman?

Shop-owner — The one with the yellow bag.

Police 2 [to his colleague] — Victor ...

Amadou — He threw a scrunched- up bag ...

Police 1 — Come here [to Maria]

Shop owner — ... sitting there, putting off customers. We're not inhumane, but ...

Police 2 — Thank you [hands Anne her ID papers]

Anne — Can we go?

Police 2 [to shop owner] — You can come and make a statement if you wish.

Shop owner — Who'll look after ...

Amadou [to the police] — Can I have my ID?

Police 2 [to Maria] — ID!

Amadou [to the police] — Can I have my ID back, too?

Police 2 — I doubt it. What do you think? Come along to the station first. Understand? Understand?

Amadou — Yes.

Police 2 — Good. ... Take his details [pointing to the shop owner]

Police 1 — Please, this way. [to Maria]

Amadou — I've done nothing wrong. I'm coming of my own free will.

Police 2 — Don't make trouble.

Amadou — You don't need to touch me. I'll come, no problem.

Police 2 — If you don't comply I'll put the cuffs on. Okay? Come on.


The geometric point is an invisible thing. Therefore, it must be defined as an incorporeal thing. Considered in terms of substance, it equals zero.

Hidden in this zero, however, are various attributes which are "human" in nature. We think of this zero — the geometric point — in relation to the greatest possible brevity, i.e., to the highest degree of restraint which, nevertheless, speaks.

Thus we must look upon the geometric point as the ultimate and most singular union of silence and speech.

— Wassily Kandinsky, Point and Line to Plane

A crossroad: the point where two roads intersect. One could formulate the problematic that Haneke's film wrestles with, to steal Simmel's question, How is society possible? Or, more precisely, how are communication and community possible? Is the unknown code yours or is it mine? What is the difference between you and me? When my understanding of you is always an understanding of you through myself? Whose code is unknown, and what are the implications that follow from this dilemma?

The film's second scene perfectly captures the question that Haneke grapples with. In one sense this scene is a fragment of the film in its totality, a fragment that when placed under the microscope allows us to reformulate Simmel's question, How is society possible? The nature of urban life is enacted in this short scene, captured in the actions of the individuals, in the shifting thresholds that connect them to each other. Thus the scene offers us an opening into the movements that fixate the fixed point of individuality, an opening that lets us trace the miniscule fluctuations of the fixed points before they settle into seemingly indivisible identities. To approach these fixating fixed points is to approach the limit of the taken for granted, a limit in which identity reveals itself for what it actually is, an attempt to block the movements of an ever-changing world, an attempt at making the world graspable through fixations and limitations, to inoculate the multitude of variations with consistency and predictability; in short, to order the world.

That the main part of the book begins with this chapter is no mere coincidence. A mapping of the in-between cannot take its point of departure anywhere else than in the fixed point, in identity, in the fixed and the fixating. It is in this cartography that we, as semiotic animals, feel at home. It is here and nowhere else that we think we know with certainty and trust that we are on firm ground. As semiotic animals we traverse the world aided by fixed points and creative triangulations, a strange and perpetual dance in which the semiotic and the geographical merge; which is not to say that we are the sum of these fixed points and identities. The compass with which we traverse this landscape is the copula is.

Axiom: the point is indivisible; it lacks spatial extension


Does the Fixed point Move? Is Identity Indivisible?

The questions return once again: how do we find our way in an ever-changing world? And is it even conceivable to encounter the new on its own terms, without folding it back into the logic of recognition and presupposition? The questions bear on the geometry of the fixed point and the origin of identity. The reader should not be confused by the fact that this chapter departs from axiomatic formulations. The maps that we traverse are primarily not those of mathematics, they are the maps of the social sciences and the humanities; more precisely, they are the maps of a habitual and lingering anthropocentrism. There are, however, deep affinities between these maps and the maps of mathematics, as these maps are dependent on, and conditioned by, an abstract Euclidian space, a space regulated by a metrical and pointillistic logic, a logic that determines the configuration of the fixed point and identity.

The primary focus of this chapter is the relation between the two numbers 1 and 2, a relation that can be described with the sign =. The equal sign becomes the sign through which we can grasp the transformations and movements that take place in Code inconnu, since it is along the = that communication takes place, and hence the movements that simultaneously anchor and distort the unknown codes of Code inconnu. For if identity can be conceived as a point it is always a point dependent on another point for its definition and proper localization. Every surveyor knows that without knowing the position of another point it is impossible to decide one's own position. It is always a question of triangulation. It is at this juncture that Haneke's concrete illustrations intersect with my abstract map. In his world it is a question of individual solitude. In my words it is a problematic deeply related to the solipsistic fixed point of identity.

a, a=a, a=b

Let us rehearse the aim of the book: to map the limits of the in-between. In this chapter, and in Haneke's film, the in- between is conceived as an unknown code, another name for the translations that take place in the limit that both separates and unites us. The question is whether the code is unknown in the relation between two points. Or, more precisely: how do points communicate? Expressed differently: what transpires in the equal sign? It becomes a question of the rhetoric and logic that govern the translation and communication between fixed points. The associations and expressions that illustrate these translations are infinite; thus, through necessity the mapping techniques at our disposal need to be minimalistic. How could we otherwise map the limits and relations of the fixed point without getting lost?


a cannot be given a proper name nor a definite description. For already in the naming of a, a foundational violence is committed. When I am forced to speak as I, to define myself in relation to preestablished categories, I commit violence against myself. I know that I am a. But for you to know who I am, I am forced to lie and describe myself as a=a, or as a=b, an impossible and unsolvable dilemma, since I can never describe myself as that I know myself to be, that is, as a. To be able to communicate I am forced to give myself a name or accept a name given to me by another. How then are we connected and held apart? Is it three different a's we encounter in the film's second scene? Is it as naked a's they meet? Or is it as a=a, or a=b? Through the equal sign we approach the indiscernible limit that circumscribes and regulates the being together of the social: in the case of Abu Ghraib, expressed in the leash that chains together incommensurable identities in a perverse instance of togetherness, a horrific illustration of the degree zero of that social decree that, at any cost, forces us to communicate with each other. Through these translations we understand that the equal sign first presented itself as an "is," but in reality is an "as if." For when we say that this is a man, woman, barbarian, human, alien, we are actually saying that it is as if it were a man, woman, barbarian, human, alien.


The equal sign is a translation machine, a machine through which reality is fixed in preestablished fixed points and discrete categories. In its presence we find ourselves in an eternal Platonic landscape, a landscape of continuously shifting shadows and dazzling lights. Through the copula is the I is fixed in an abstract point "as if" it were I. The copula is shows its true nature, as the prison house of language.

And yet, like every prison, even the "is" has its weak points, its subterranean fault lines, rusty bars, and hidden crevices, weaknesses that any skilled escapologist will know how to take advantage of, for as every escapologist is certain to know, the prison house of is was built long ago. Thus the prison walls of the is will always predate the singular I of any given convict, an asymmetric temporality marked by aporias and paradoxes that will always preclude the taking place of a perfect symmetry. No translation is ever perfect. And no prison house is ever escape proof.

To Anchor the World in Points

In one of human history's most remarkable mapping expeditions the French mathematician and philosopher René Descartes set out to find a point of absolute certitude. His aim was to find a fixed point so eternally fixed that it could provide the terra firma on which the knowledge of the world could be raised. Like Wassily Kandinsky, the French mathematician well knew that the geometric fixed point is void of substance and that it lacks expression. In terms of extension, it signifies the degree zero of contingency. Like Archimedes before him, Descartes discovered the point in which certainty is anchored, the point from which the world is properly surveyed. What an amazing invention! A perfect osmosis between Euclidean geometry and epistemological certainty, the cogitato of human cogito merged with the invisible and indivisible fixed point of Euclidean geometry. When Descartes anchored thought in a point he also anchored the I and the self- knowledge of self in a fixed point. For him, this point did not have a spatial extension because it is separated from the body, a material entity that through its spatial extension is part of the ever-changing world. The point does, however, possess the quality of universality.

Thus the Cartesian method is actually a map, a map outlining the precarious translations between uncertainty and certainty. In order for Descartes to fix thought he had to anchor it in an unmovable fixed point. But this unmovable point is simply a lever for thought, an image of thought that renders possible the fixation of human faculties, faculties that are nevertheless conditioned by and dependent on a movable time-space. Viewed from this understanding of the point — as a transcendental fixation of thought — Descartes's map becomes, above all, a map surveying the representational logic expressed in the copula is or =. Through these fixations the world is transformed into a series of points or transcendental categories that are connected by lines, lines that, in turn, are always anchored in points.

The World Is a Map

This map always preexists any given territory, a territory ruled by the representational logic of Euclidean geometry. Every encounter — in which something new can emerge — is thus folded back into that which already is, into the topography of the a priori and designated fixed points of reason and certainty. Viewed from this perspective, the present map can be understood as an investigation of the limit between that which can be represented and that which cannot, between that which can be fixed and that which cannot.


Excerpted from "Topoi/Graphein"
by .
Copyright © 2018 Board of Regents of the University of Nebraska.
Excerpted by permission of UNIVERSITY OF NEBRASKA PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents

List of Illustrations    
Foreword: Born Again, by Gunnar Olsson    
Introduction: Angle of Power    
Part 1. Code inconnu/Crossroads
Chapter 1. Encounter/Point    
Chapter 2. Wall/Stone    
Chapter 3. Code inconnu/When Above    
Chapter 4. Limits/Oedipus    
Chapter 5. Stranger/Terra Firma    
Part 2. Lord of the Flies/Passages
Chapter 6. Desert/Line    
Chapter 7. Thing/Swerve    
Chapter 8. Lord of the Flies/Through    
Chapter 9. Division/Hermes    
Chapter 10. Fire/Terra Nullius    
Part 3. Apocalypse Now/The Event
Chapter 11. Dream/Plane    
Chapter 12. River/Cloud    
Chapter 13. Apocalypse Now/In-Between    
Chapter 14. Darkness/Janus    
Chapter 15. Abyss/Horror Vacui    
Part 4. Geographein

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