"Some people would never be considered, were it not that some excellent adversaries had mentioned them. There is no greater vengeance than oblivion, as it buries such people in the dust of their nothingness.""I have never considered the Situationist International as one of those intellectual errors that only needs to be left to crumble to dust, scattering its corpses. I have always had a horror of those exploiters of other people's discoveries, whose only justification is the synthesis they achieve. I have reason to consider the situationists as sub-marxists from the twentieth zone, full of troglodyte anti-cultural formulations. There is an ex-painter of the Cobra movement, who has principles which have come to nothing (It's me, Asger Jorn, that he's talking about). He only produces abstract lyricism of the fourth zone or fifth order. It was only in 1948, after Bjerke Petersen inspired the formation of Cobra with the support of Richardt Mortensen, Egler Bille and Egill Jacobsen following the war, that he showed himself in a coherent fashion. Even his support in his own country remains without real importance (there are some artists who, if they aren't noticed at the international level, go off and knock out some forged creations in the national framework). I advise him to stick to painting, not because I value his pictures, but because I have read his 'philosophical' works. Abstract art, above all that of a manufacturer prefaced by Jacques Prevert, the Paul Geraldy of surrealism, must be sold well and impassion all the dressmakers. My cultural conception and my creation makes me rigorous in my writings. I already have enough difficulties from being solely responsible for my own writings, whence there are no false phrases or judgements to be retracted." For all the reasons which he so exposes, I understand perfectly that the Lettrist Lemaitre has left it to a scribe to take the trouble to fill 136 pages of his review Poesie Nouvelle No. 13 with closely set little characters in a study on the Situationist International.– D Baltasar Gracian. L'Homme de Cour
The enormous extent of the work is its single excpetional character, which is easily explained. As I think I have shown in my study on value, an endeavour of invention and understanding cannot be paid by the hour, and in consequence cannot objectively be measured with money. The habits of industrial production have clearly penetrated certain strata across the frontier of intellectual life, and for example, journalism is routinely pald by the line. But it is obvious that the interest of these types of workers is to increase the speed and the quantity of production to the detriment of the quality. Above all this can be seen in the poverty of reportage, as this must be got together in time which isn't paid for. And such a way of carrying out work implies an easily overstretched inferior intelligence of the financial backers, who are satisfied with such standards. Lemaitre has been forced to commit such rashness thanks to his stated 'strategic reasons' which however remain obscure. He says, he 'avoided the idea of expounding on the SI' himself. If so, he had better squarely let the matter drop or give the work over to a man of culture. Because Lemaitre as an entrepreneur, is completely responsible for the work of his pieceworkers.
In Internationale Situationiste No.4, I unveiled the system, the ideological grammar of Lemaitre, by clarilying that it was a subjective outiook of positions established in relation to Lemaitre himseilf, rather than an objective system. Lemaitre admits his ignorance and his lack of scientific creativity (p.74). How could he then take my statement as an insult? It is indisputable that my critique of the marxist concept of value is strictly scientific, and it is, moreover, the first complete critique which has been made of it. Lemaitre calls it 'sub-sub- sub-marxism'. And why not? It is nevertheless necessary to note that Lemaitre has recognised and evaluated the scientific characteristics in the experimental work of the S.I., as he has been able to deal with this subject for 136 pages without mentioning a single name of any of the participants of this experiment. This is pure objectivity. Lemaitre has played on the law of large numbers. He attributes many quotes without distinction to someone he calls 'the situationist'. These were taken from the writings of ten of our comrades (the collective declarations of the IS are not an issue here: this figure applies only to those texts which are found to be signed individually by their authors).
Lemaitre has fallen in the trap between the absolute and the measurement system of classical Euclidean geometry, as marxism has done. He pushes it only as far as unintentional jokes, such as wanting to distinguish the graduations of eternity. He pretends (p56) to be capable of ensuring a 'more eternal' victory than anyone else.
Elsewhere, it is very funny to read Lemaitre. The post-marxist character inspired by the organisation of the workers struggling to improve their economic situation is clearly visible as the basis of the erotological practice that Lemaitre has pointed out in many large books. The effort so presented to organise a union of gigolos, systematising their struggle for an increase in their wages and markedly improving their technique in satisfying even the most dramatic passions of their clients, is an honest reformist enterprise, the day to day defence of actual employees within the existing economic framework. Lemaitre has recently admitted that this education would be impotent at the situationist stage of miracle-working, but doesn't know what to condude from this intuition. If he made the effort, man could be naturally seen as the producer, and woman as the consumer in the erotic process as long as their relationship had no consequences. And if the number of boys born dropped considerably in relation to the number of girls, this could open perspectives which would merit economic considerations. But it is impossible to consider youth as being more a producer than a consumer; and completely agalnst the interest of youth to diminish their consumption at the cultural level, by means of the reduction of school leaving age proposed by Lemaitre, by which they would be thrown into production more quickly, even if this would be in the interest of industry. Marx's struggle in this realm will always have a passionate value, and our goal is to confim the right, not merely for youth, but for every individual, to realise themselves according to their free desires in autonomous creation and consumption. The focus of such a development could right away be U.N.E.S.C.O., from the moment when the S.I. takes command of it; new types of popular university, broken away from the passive consumption of the old culture; lastly, utopian educational centres which through the relation of leisure to certain arrangements of social spaces, they must come to be more completely free of the dominant daily life, and at the same time functionmg as bridgeheads for an invasion of this daily life, instead of pretending to be separated from it.
An excellent book could be made out of Lemaitre's economic theory seen as a literary work like a Rabelaisian farce, with the revolt of youth taken as a caricature of the revolutionary and socialist thought of the nineteenth century. But from the moment when Lemaitre shows that he takes it seriously, he is a demagogue. One of the classic gimmicks of demagogues is to mobilise the people agalnst dangers which everyone knows about, and which excite them, but which have become inoffensive. It has been the fashion to shout wrongly about fascism since the war, when new socio-cultural conditions are being prepared, and when the new ideological dangers appear inoffensive; and leading to moral rearmament by all the variants of neo-religious fanaticism. Far from 'misrecognising the power of his method', as Lemaitre says, I have recognised them, I denounce them, and I declare war on them. I prefer a contrary method. And the sole consideration I can give to Lemaitre, to his scribbler, to those who could adhere to their system of thought, or just as likely to take it up and use it without them, it is to quote the phrases to which I am absolutely opposed. In No.13 of Poesie Nouvelle:
"My level of merit based on the works or actions which improve the human condition place in their lower ranks the current provisional practices. I believe that at the daily level the 'non- being' formulated by certain existentialist philosophers is true: we are only a mass of waste material having some possibility of acquired and limited choices. But what distinguishes my system is that, for me, the only liberty, which is minimal, resides in the minuscule invention or discovery of that rare being which is known as the 'innovator', in the wake of whose revelations that the other human beings can only follow, as they have until then followed the 'lesser good', the inferior." (p116)
"Righlty or wrongly, I have always believed afresh in the power to sometimes use the energies of my fellows better than they themselves." (p44)
"'They must trust and follow me, instead of always staying behind." (p29)
"The religious Jews can pretend that no-one has gone further than them, as the Messiah has not arrived. The Christians have reason to state that they have not been outclassed as their fellows have not been saved from their misery, and as they have been helped to the resurrection of the dead... .At this general level, I give reason to these groups, who defend certain essential values and that I hope to honestly supersede by offering them what they want: the Messiah, human safety, the resurrection of the dead, gnosis." (p28)
"The situationists, like the sub-troglodytes that they are, no longer want to conserve anything... they not only reject the future of cultural disciplines, but also the past and the present, in the name of a pseudo-utopian, outdated, spineless, infantile bluff... Finally our ignorant reactionaries will be rejected by and punished by the research of disciplines of knowledge, just as they have rejected and punished others in the past." (p63)
I believe that these extracts from Lemaltre's Mein Kamf suffice to show his main tendency towards 'degenerate art'. As for the threats, those that go so far as to make use of them are not always equipped with the capacity of the most extensive sanctions. And we are not then in any way frightened by constructing this 'provisional' life, because Lemaitre has let us know (p123) that he has "a great horror of his living person". Well, that's his problem! He also said that he preferred Malraux to the situationists (but will this complement be paid back?) Anyway, I would let him get on with Malraux. For nothing.
"I am sad, but in spite of all my efforts, M. Mesens doesn't want to publish PIN. Even when I said to him that we didn't want any money, he laughed and said that if he was to publish it, we would have to give him money, but that he had no intention of doing so. He had read it attentively but he didn't like it. He said that it would have been more topical twenty five years ago, but that now we would not be greeted with comprehension... There is another thing: there are some imitators, for example, the lettrists in Paris who copy the Ursonate that Hausmann and I did, and we weren't even mentioned, we who had done it twenty five years before them, and with better reasons."– Kurt Schwitters. Letter of 29 -3-47 quoted in Courrier Dada.
What weapons does Lemaitre want to use? Here, he falls for the psychiatric theory of a little Swiss man called Karl Jaspers, who from his perspective attains a 'stature' equal to that of Moses and of Plato (p66 & p80). From Lemaitre's perspective, this Jaspers has become enormous, because he is closer to him in time and ideas. The enormity of Jaspers, who has the merit of being considered as one of the most famous imbeciles of our century, is to have postulated with all the authority of a non-scientific psychiatrist, that all individuals who are not an imbecile like him are mentally ill, and by this fact a public danger that society should be able to allow them to be locked up and nursed. Lemaitre has amplified this idea to a world dimension: everyone is mad; an integral therapy would be necessary, and is clearly justified; and according to him the therapy would be, quote: "only to have proposed an integral therapy capable of curing the permanent illness of youth and world history".(p55)
What is this permanent illness of the history of the world? During the phase of youth, each individual or group possesses a fantastic will, in relation to minimum capacities and non-existent consciousness. The adult age possesses a real power stronger than their will, which is subject to the routine of actions. The fatigue of old age is compensated for by experience, the consciousness which dominates power and will. By proposing Gnosis for the salvation of youth, Lemaitre only proposes a process of rapid ageing, he even proposes that the youth should engage their wills as quickly as possible in social power, prisoner, of the existing establishment.
Lemaitre precisely reproaches the situationists for not following the rules of his game: "So many mythic and mystifying formulas, which confound their classification and their integration into the domain of knowledge, also hinder the establishinent of necessary historic relations between the superseded-superseding and the superseding-superseded." In effect, unswervingly convinced of his linear succession, of his little hierarchy etc., blind to everything else, Lemaitre cries that the situationists have not superseded him, and are to be placed much lower down than him. Well then? My friend the Danish Poet Jens August Shade told me one day: "You can fall so low that the fall becomes uplifting." There is nothing mystifying in our behaviour. I have never had any desire to supersede you, Lemaitre and company. We are coming across each other: that's all. And now we are going to continue with the same trajectory that we approached by, without this encounter having had the slightest importance.
The Leninist example of the troglodytes was equally badly chosen. The conflict between Lenin and the Russian futurists is only one example in a general crisis and a subversion of the revolution to which Lenin had contributed with his very compact and superficial attack against leftism considered as 'an infantile disease', rather than as an illness of infancy, of hope. Anyhow, I am old enough to remember the epoch when Lenin himself was considered as a troglodyte by the whole world. One day, I shall probably be used, when I am dead as an anti-troglodyte against someone.
Lemaitre is infatuated with the idea that time could abolish unfashionable cultural references which he has found, or had his specialist scribe pick up in the public libraries. But as anyone knows, like living reality, culture is what is left when all that has been understood has been forgotten. Nothing is worse than stupidity combined with a never failing memory. This is without wanting to discuss the weak quality, the wholes and bluffs in the digest of encyclopedism of Lemaitre's brain trust.
Lemaitre seems to disdain the experimental value that we have recognised in the lettrist movement around 1950, in two or three sectors of culture. He says that the experimental aspect of lettrism had been real but negligible in comparison to its essential value: a system of creation. Thus he impudently spits on his only asset, because we consider, as history will consider with us, that all that he calls his 'creation' is absolutely empty and has no future. Because Lemaitre believes that it is his solipsistic dream of creation which must be recognised as the sole historic value, he is astonished that, for example, we don't recognise the importance of lettrist poetry. This poetry has no importance as an artistic creation, even as a function of the 'creative', arbitrary and untransferable systemisation of Lemaitre. As much as the whole of the lettrist movement has for a time played a role in the real avant-garde of a given epoch, onomatopoeic Poetry, which was its first manifestation, came twenty five years atter Schwitters, and clearly was in no way experimental.
In other respects there was nothing unique about the lettrists except in Paris. However, Lemaitre is so geographically bound that, without smiling, he measures the comparative influences of the S.I.. and groupuscles which appeared for six months on the Left Bank, and which are still only known about by him; he judges them according to artides whose dedication has generally been solicitated by the groups themselves or "posters plastered all round Paris in their name" (p41). This Lemaitre allows concessions to everyone for making known the discoveries which, as has been seen, all the mystifiers, Christian or not, have on sale. He pretends that he had plenty of time to understand, and does not ask about the reason for this total incomprehension, for this refusal of the whole world in relation to his wonderful creations. It is fifteen years since lettrism arose, it has chosen no enemies, but wants to convert the whole world. And without slackening, it has presented the (sub-Cartesian) demonstration of its dogmas throughout twenty books. However it has remained very poorly known about. And, to take his examples, Lemaitre doesn't want it recognised that fifteen years after their appearance, surrealism or symbolism had already been largely imposed on culture. In a much less greedy epochs than our own, these movements appeared, a novelty in all domains, and then the cultural ideologies, much less decomposed than those of today, fought them in the name of the conservation of the order of the past. Hence Max Bense, the German equivalent of this anecdote of systematic, paradialectic, and deadly boring 'lettrist thought'. They are equally typical of this epoch. What do you want? They are of great use as classifiers of values. But of values without actuality. In terms of Americanised culture, these are the gadgets of the Ideal home exhibition of the spirit.
"It takes less time to create a material which is deficient, much longer to form a personality. And if a single error has been made in the production of the material, it can be repaired, if necessary, by destroying the useless machine and so going through profits and losses. A man, once formed, is not destroyed; for forty years he is ready to perform the activity for which he has been trained".– Alfred Sauvy. De Malthus a Mao Tse-Toung
Chinese perspective is not Chinese culture. But it is a valuable and important outlook. At any one moment, real living humanity covers a little less than two centuries. The oldest are about a hundred years old, and some among the new born will be destined to live as long in the future. There is a perpetual tension between these two temporal extremes of humanity. The cycle of this wheel of life, this eternal return is a permanent revolution upon which thousands of reflections have been made since the Summerians, the Buddhists, Plato, Schopenhauer, Nietzsche and so on. Zoroastrianism is the outcome of this train of thought, with the idea of a single oriented rotation of history from a unique beginning up to a definitive and irreversible end. This dualist outlook and unilateral orientation was transmitted to Judaism, Christianity and Islam; at the same time it passed into Mithraism, manicheeism and gnosticism. Following Lemaitre's Gnostic confession, it is clear that he is not capable of understanding the dialectic dynamism of Buddhism, but that he follows dualism; and that his appeal to youth is simply the classical and traditional subversion of minors. Regretfully, I believe that I have detected the possibility of an unpublished system which is relatively creative in the sense that the application of Chinese perspective to the dimension of time in the west would produce results which could not be predicted. This makes Lemaitre's system even simpler. It is no more than neo-Sorelianism. I have looked all over the place. Through the frequent use of Lenin as a witness to his arguments, and the loan of the origin of these perspectives from Fichte, instead of acknowledging Sorel as the inventor of them, it is shown that Lemaitre has drawn deeply from Sorel – elsewhere he admits to having read him – but with no intention of publicly acknowledging this. The Chinese perspective of Lemaitre is just as impoverished as Sorelian ideology, whose fate is well known.
Sorel's artfulness lay in having studied the formula of ascendant Christianity, and having transported the belief in the zero point of the future (the end of the world and the opening towards an unknown paradise) to a purely technical system. Thus the Christian end of the world can be replaced by anything: the general strike, the socialist revolution, or to be more up-to-date, the man who presses the button on atomic missiles. All those who don't fit in with this perspective are equally assured of punishinent, by using the key formula of all the historic events of our century: the accusation of treachery (to what? the system). In La Roue De La Fortune, I set myself against the mythological exactitude's of Benjaniin Peret, who is shown so high in Lemaitre's estimation. This was because for me all art is an infinite multitude of mythic creations, and because I oppose free creativity to a return to the belief in a single imposed myth, or system of myths. Here, I oppose the idea of multiple paradises to that cherished by Lemaitre: a unique paradise, and ideological carcass once more exhumed. I don't think that Peret's attitude on this subject has ever approached such stupidity as that of Lemaitre, but I saw the peril to come: and Peret can no longer protest when Lemaitre, who stupidly insulted him in 1952 for 'lack of creation', now depends on him.
In any case, no-one can pay a greater compliment to the situationist movement than this confirmation by Lemaitre: "I don't know anyone who believes in the 'situationist group'. The situationists themselves are not situationists as they have written many times To speak of a whole which doesn't exist is to invite the accusation of having invented it". But our sole goal is precisely to invent it. We have invented everything so far, and there is still nearly everything left for us to invent: our terrain is so rich that it scarcely exists.
What we are going to invent is situationist activity itself. And also its definition. Having awkwardly let slip a number of propositions, proposals and appeals in his pamphlet on perfectly unreal footing, Lemaitre pretends:"the situationists and my group could perhaps reach a spiritual understanding on the terrain of the 'situation', however much my critics adhere to my ethical conception of the Creator of elements – superior to the productive constructor of moments of life – and to the vision of integral cultural situations, the outcome of the Creatic – and not simply ludic." I have already shown that we have goals completely opposed to his. All of Lemaitre's options are rejected.
In a note (p.80) where he points out to us the importance of Einstein, Lemaitre has the audacity to add that "time is a notion intrinsic to the situation". We, however, to the extent that we have advanced in the study of given situationists, we find that the question is posed of inventing a situlogy, a situgraphy and perhaps even a situmetry beyond existing topological knowledge.
Lemaitre is amaeed that there is a Scandinavian culture distinct from the dassical wesL Scandinavian culture is ahove all the culture of the forgotten, the forgotten culture and without history, uninterrupted since the stone age, older and more immobile even than Chinese culture. With such a weighty heritage of oblivion, what could I cite from my ancestors.
I am a man without merit. At the same time, I am wicked enough. Journalists and other professional droogs at the service of the existing order call us a 'beat generation'. They are astonished to discover that their knockbacks, their distrust, their absolute refusal to allow us even the chance to eat as badly as an unemployed unskilled worker, that all this has hardened us to the point that we refuse to give these bruisers big kisses the moment when they find us interesting. I remember the time of the Cobra movement, when C.O.Gotz stated that our German comrades had to live on a tenth the keep of any prisoner of the Federal Republic. I know the more than shameful conditions in which the lettrists had to live in order to realise the remarkable works of their creative period. And so it continues. A German artist, whose country will not hesitate to claim the highest glory, has for two years had no other home than the empty railway cars at the station. When I discovered the systematic structures of the situationist tendency, I myself had understood that here was a method which exploited in secret by us could give us a great direct social power, and which would allow us the luxury of truly avenging the insults. I did not hesitate to explain this view to Guy Debord, who completely refused to take it into consideration, which obliged me to make my remarks public. He then told me that it was necessary to leave such methods to people like Pauwels and Bergier, and the mystical old women who are enraptured by minor occult insights. Everyone dreams of marketing its echoes, as Gurdijieff did to his well-to-do disciples. After some reflection, I knew that I would arrive at exactly the same attitude, which is the same vein as all my behaviour up till now; anyway it is the reason for our collaboration in the Sl.
But, "my hesitation could be conceived as the idea of surrendering the secret of secrets, the creation of creation, to the incoherent mob" Lemaitre writes (p.7), which all the more defends his right to the secret, that his 'creatic' nothingness is a matter of a secret of organisation. He justifies himself by the examples of atomic and other secrets. In fact, secret methods transform art into craftsmanship, by the exclusive techniques to reproduce to standards which come later on. Lemaitre is a conscious partisan of this survival of the artisan confraternity. One is accepted by producing an acceptable master-piece. Thus Lemaitre retains a weakness for Debord's first film, simply because he has not understood it. He simply places it icily "amongst the ten best works in the history of cinema". This is his emphasis (p.25).
Lemaitre also reproaches me for having declared that he is finished. He claims that he is alive. That's true; and I didn't say he was dead. I said that he was in the coma (of his system). Which will probably only last as long as he does. The patient appropriation of the secrets of the master – particularly when dealing with a mastership arbitrarily decreed by an individual – clearly guarantees that a very particular commodity can be produced to these standards. But there is no guarantee that this production will be valorised by some desire.
Like Lemaitre, I think that Vassili Kandinsky is a man "who has adduced and defined the abstract" (pl1l). But I don't agree with him that he was an "artistic innovator", nor that I am an abstract painter. I have never made any but anti-abstract paintings following the current of Hans Arp and Max Ernst, followed by Mondrian and Marcel Duchamp. Kandinsky, in Von Punkt Uber Linie Zur Fleche, had aligned modern art according to the perspective of Euclidean geometry, whereas the innovators mentioned above moved towards an inverse geometry, aiming towards a polydimensional cosmos at the surface, just as at the line and the point. The technique of dripping painting showed the absurdity of Kandinsky's attitude. If you work very close to the canvas, the flow of colours makes surfaces, blotches. But if you arrange things once again at a distance, the colour is divided into little splashes, which only make points. This is exactly like elements in perspective. They start as masses and disappear over the horizon as points. Kandinsky started at the horizon, in the abstract to arrive where? Me, I started in the immediate present, to arrive where?
"The thoughts and observations about it are entirely new; the citations have not been made before; the subject is of extreme importance and has been treated with infinite arrangement and clarity. It has cost me a great deal of time, and I pray that you will accept it and consider it as the greatest effort of my genius."– Jonathan Swift: Irrefutable Essay On The Faculties of the Soul
If, as Lemaitre says, time was an extraneous notion to the situation, situlogy will be as much a study of the unique of the identical form, as morphology. But it could rightly be said that situlogy is a morphology of time, since everyone is agreed that topology is defined as the study of continuity which is the non-division in extension (space) and the non-interruption in duration. The morphological side of situlogy is included in this definition: that which concerns the intrinsic properties of figures without any relation to their environment.
The exclusion of singularities and interruptions, the constancy of intensity and the unique feeling of the propagation of the processes, which defines a situation, also excludes the division in several times, which Lemaitre pretends are possible. But the confusion of ideas by an unlettered person like Lemaitre is much more pardonable than that which prevails amongst professional topologists; and which obliges us to distance ourselves from the purely topological terrain to invent a more elementary situlogy. This confusion is introduced precisely in the formula of orientability which, in reality, is only adaptation to the dimension of time. E.M. Patterson explalns that "the idea of orientablity derives from the physical idea that a surface could have one or two sides. Let us suppose that around each point of a surface – with the exception of the points at the edge (boundary), if there are any – a little closed curve is drawn in a defined sense, whether in the sense of rotation of the hands of a watch or in the contrary sense, having been attached to this point. At this moment, the surface is called orientable if it is possible to choose the sense of the curves, of the manner to which it would be the same for all the points sufficiently close to each other. If not the surface is called non-orientable. All surfaces with only one side are non-orientable."
This mixture of geometry and physics is quite out of order. It is easy to prove that a sphere only has one surface, and likewise a ring. That a cone possesses two surfaces and a cylinder three, etc. but logically a surface can only have one side. Anyway, a surface with two sides is not topological, because there is a rupture in continuity. But the reason for which we are put on the false scent of the double surface with two sides is clear: it's because that's what allows the linkage of topology with the general tendency of geometry: the search for equalities, or equivalencies. Two figures are explained as being topologically equivalent, or homeomorphs, if each can be transformed into the other by a continuous deformation. This is to say that there is a single figure in transformation: situlogy is the transformative morphology of the unique.
The gravest error which was introduced by adapting the classic perspective of geometry to topology, is the adaptation to classic distinctions of geometry following the number of coordinates in linear topology, the topology of surfaces and the topology of volumes. This is impossible and ridiculous if elementaries of situlogy are understood, because in topology there is a precise equivalence between a point, a line, a surface and a volume whereas in geometry there is an absolute distinction. This confusion is clearly reflected in the Moebius strip, which is said to possess "two surfaces without homeomorphy" or to represent "surfaces with a single side" without a back or front, without an inside or outside. This phenomenon can even lead people to imagine that the Moebius strip only possesses a single dimension, which is completely absurd, because a Moebius strip cannot be made with a piece of string, even less with a line. What is most interesting about the Moebius strip is exactly the relationship between the two lines of the parallel edges.
It is possible to study geometric equivalencies, congruences and likenesses of a Moebius strip, if a particular fact is taken into account: the length of a Moebius strip could be infinite compared to its width, but cannot be shorter than a particular calculable proportion compared to this width. It's up to the mathematicians to construct and calculate the Moebius strip at its minimal limit Once constructed, it would be found that we are dealing with an object where the line which marks the width of the strip at a point taken by chance, makes a perfect right-angle with same line drawn on the opposite part of the strip, however these two same lines are parallel, if the strip is smoothed into a cylinder. The same line which at one point represents the horizontal at another point represents a vertical. There are thus three spatial dimensions, apart from the space if the strip is not flattened. Hence the strangeness of the Moebius strip. Two Moebius strips of this type can thus always be put into likeness, and with the same width of strip, put into congruence.
It seems that no-one has yet marked on the strange behaviour of all the topological forms and figures in their relationship with the system of spatial co-ordinates (vertical, horizontal, depth) in which they play, making them be born and disappear, and transforming one into the other. For Euclidean geometry, the system of coordinates is a given basis. For situlogy, no, as it creates and disposes of the coordinates at will. Thus Euclidean geometry has a duty to go beyond all situlogical considerations to take as a point of reference the system of coordinates at right angles which is the schema of the law of least effort. Rene Huygues shows, in his work Art and Man, that it is with the development of metallurgy, after the agrarian epoch, that the division is produced between the two styles of Hallstadt and La Tene, which is none other than the division between geometric and situlogic thought. Through the Dorians geometric thought was implanted in Greece, giving birth to rationalist thought. The contrary tendency wound up in Ireland and Scandinavia. Walter Lietzman notes, in his book Anschauliche Topology: "In art, for example in the age of the Vikings, knotwork was used as ornamentation with pleasure. I have before me a photo of the knot gardens of Shakespeare at Stratford, in which the arrangement of flowers in the form of knots is shown... What does Shakespeare see in these knots? I'm not able to say. Perhaps its a matter of some error or more a deliberate confusion with the theme of the labyrinth. The question is raised twice with him: In Midsummer Night's Dream (Act II, scene 1), and in The Tempest (Act III, scene 3)."
There is no possible mistake. James Joyce in Finnegans Wake, by pronouncing the absurd phrase "No sturm, no drang", had overcome the ancient conflict between classicism and romanticism and opened a ski-slope towards the reconciliation of passion and logic. What is needed today is a thought, a philosophy and an art which conforms to what is projected by topology, but this is only realisable on condition that this branch of modern science is returned to its original course: that of "the situ analysis" or situlogy. Hans Findeisen, in his Shamanentum, indicated that the origins of shamanism, which still survives amongst the Lapps, are to be found in the cave paintings of the ice age, and it is enough that the ornamentation which characterises the Lapp presence is simple knotwork. The knowledge of secret topologies has always been indicated by the presence of signs of knots, strings, knotwork, mazes etc. And in a curious way since antiquity the weavers have transmitted a revolutionary teaching in forms which are more or less bizarre, mystifying and subverted. A history too well known to have been studied seriously. The perversion in that should be noticed rather than the reverse.
The relation that the writings of Max Brod established between Kafka and the Danish astronomer Tycho Brahe is as profound as the relationship between Shakespeare and Hamlet: and their presence at Prague which, since the time of La Tene radiated topological thought, is as natural as the astonishing results that Kepler could extract from the calculations of Brahe, by adapting them to the methods of geometry and classical mathematics, which was impossible for Tycho Brahe himself. This shows once more that topology remains the source of geometry, and that the contrary process is impossibe. This indicates the impossibility of explaining the philosophy of Kierkegaard as a consequence of the philosophy of Hegel. The influence of Scandinavian thought in European culture is incoherent and without permanent results, like a true thought of the absurd. That there has always been a Scandinavian philosophical tradition, which structures the tendency of Ole Roemer, H.C. Oersted, Carl von Linne etc., completely distinct from English pragmatism, German idealism and French rationalism is a fact which can only be astonishing in that it has always been kept secret. With the Scandinavians themselves ignoring the base logic of this profound and hidden coherence, it is as much ignored by others. I have the greatest mistrust of all the ideas on the benefits of learning. However in the actual situation in Europe it seems to me that an ignorance of this subject presents a danger. Thus I consider that the fact that Swedenhorg and Novalis had been mine-engineers is more important than the chance postulates of such as Jaspers which allowed the label of mad schizophrenics to be stuck on their backs. This is not because this is a fact which could be established in a scientific manner, but because it is a basic skill of topological thought, like that of weavers, and this fact could lead us to the precious observations for the founding of situlogy.
But all this is only presented as a possible technique subordinated to the work of the S.I, the allies and enemies of which can easily be seen. The situationists reject with the greatest of hostility the proposal arising in Bergier and Pauwels' book, The Dawn Of Magic, which asks for help in setting up a proposed institute to research occult techniques; and the formation of controlling secret society reserved for those today who are in a position to manipulate the various conditions of their contemporaries. We would not in any case collaborate with such a project, and we have no desire to help it financially.
"From all evidence, equality is the basis of geometric measurement" as Gaston Bachelard said in Le Nouvel Esprit Scientifique. And he informs us: "When Poincare had shown the logical equivalence of various geometries, he stated that the geometry of Euclid would always be the most useful, and that in case of conflict between this geometry and physical experience, it was always preferable to change physical theory than change the elementary geometry. Thus Gauss had pretended to experiment astronomically with a theorem of non-Euclidean geometry: He wondered if a triangle located in the stars, and hence of enormous surface, would show the shrinking of surface indicated by the geometry of Lobatchowski. Poincare did not recognise the crucial character of such an experience."
The point of departure of situgraphy, or of plastic geometry, must be Situ analysis developed by Poincare, and pushed in an egalitarian direction under the name topology. But all talk of equalities is openly excluded, if there aren't at least two elements to equalise. Thus the equivalence teaches us nothing about the unique or the polyvalence of the unique, which is in reality the essential domain of situ analysis, or topology. Our goal is to set a plastic and elementary geometry against egalitarian and Euclidean geometry, and with the help of both to go towards a geometry of variables, playful and differential geometry. The first situationist contact with this problem is seen in Galton's apparatus that experimentally produced Gauss's curve (see the figure in the first issue of Internationale Situationiste). And even if my intuitive fashion of dealing with geometry is completely anti-orthodox, I believe that a road has been opened, a bridge thrown across the abyss which separates Poincare and Gauss as far as the possibility of combining geometry with physics without renouncing the autonomy of the one from the other.
All the axioms are cut offs against the non-desired possibilities, and by this fact contains a voluntary illogical decision. The illogic which interests us at the base of Euclidean Geometry is played between the following axes: – things which are superimposed upon each other are equal; – the sum is greater than the part. This absurdity is seen, for example, the moment that we start to apply the definition of a line as length without breadth.
If two lines are superimposed, one equals the other. This must result in either two parallel lines (which shows that the equality is not perfect and absolute, or that the superimposition is neither) or the union of the lines in a single line. But if this line is longer than a single line, or if it has acquired width, the lines would not be equal. But if the lines are absolutely equal, the whole is not bigger than the part. This is an indisputable logic, but if it is true, we are in an absurdity because geometric measurement is precisely based on the axiom that the whole is greater than the part. The idea that two equal lengths are identical is found in geometric measurement. But two things can never be identical, because then we would say they were the same thing. If a murderer must be identified to a judge, it isn't enough that this is an individual who looks exactly like the person who committed the crime. The identical twin will not do in these circumstances. It is certain that there are no equalities, no repetitions, as in the case of the Konigsberg bridges. In Geometry, an identity of length and position excludes all quantitative consideration. But how is it possible through superimposition to reduce the infinite number of lines of equal length to one line, which is no bigger than any single line of these; in such a case where it is unthinkable to divide a line in two, are both equal to the divided line?
If a line is moved from its position, at the same time it remains in its position, a surface has been created rather than two lines. The superimposition, which shows that the two lines are equal, cannot be practised without the duality disappearing: otherwise they could not be equalised. A single line is equal to nothinig. This proves that there is no reality in the absolute idealism of Euclid's formula that a line has no thickness. The proof by superimposition is impossible, even if the process is modernised by employing the formula of congruence, or an identity of form, but still excepting spatial position.
We can reduce a thousand points to a single point by superimposition, and this point is equal to one of the thousand points. But a point cannot be multiplied and left at the same place, and displaced at the same time. This would be a line. As for volume, these can only be superimposed in the imagination. It could only be achieved with two phantom volumes without real volumes. The abstract character is at once the strength and weakness of Euclidean Geometry. The slightest abstraction in topology is only a weakness.
A thousand times zero is only zero, and nothing can be abstracted from zero. Euclidean Geometry is used in this irreversible and unilateral sense: it's oriented. And all the Geometries, apart from situgraphy, are the same as it. Orientation is a linear concept, and a vector is also called a half-vector, because it also signifies the distance covered, and the sense in which this has been chosen, is calied its positive sense. The zero point, chosen at some point on the line is fixed as a point of commencement. An oriented straight line is thus not a line in itself, but the combination of a line and a point. An oriented plane is a plane in which is chosen a sense of rotation called direction, and this plain is also linked to a point, the centre of rotation, which could allow the establishment of an axe of rotation at right-angles to the plane of rotation.
Space is oriented as there is a sense of rotation associated around each axis of space, called the direct sense of space. This Installation allows everything that can be called measurement. But of what does measure consist? This is the most curious thing about this business. All the measures of equal units whether of length, of size, height, mass, time or whatever unit derived from these basic notions, consists of their indications by, on a half-line, a spatial demi-dimension divided into equal intervals oriented from a point of origin towards to infinity. This half-line does not need to be straight, but could be inscribed on the circumference of a circle. If the extension makes several revolutions these become the distances of a greater linear or circular extension. Here is the principle to which all possible measure arrives in the final analysis. Any measure cannot explain whatever may be outside of this limit of a development along a demi-line.
Euclidean and analytical Geometry were developed within its classical discourse, itself following the orientation of a demi-line. Starting with a point without spatial dimension, this is moved forward and so traces a line. The line is moved forward in a direction perpendicular to its extension to produce a surface, with which the same process is used to create a volume. But this oriented movement, which from a point produces a line, a surface, a volume, this movement in itself does not enter into geometric considerations in its relations with spatial dimension. The inconsistency is evident. The act of superimposition is also impossible without movement, but from the moment when all the necesary movements to establish classical geometry are put on trial, purely spatial phenomena can no longer be spoken of, and nevertheless movement is there from the beginning. We can wonder whether time has only a single dimension, or whether in the future we might not be obliged to apply to time at least three dimensions to be able to arrive at more homogenous explanations of what has happened. That remains to be seen. But one thing is certain: time cannot be reduced to a demi-dimension or to an oriented length with a measuring instrument. We thus also reach another question as to whether what we know as 'time' in its scientitic definition, as a measure of duration, and the form under which time enters relativity theory, isn't simply the notion of orientation or the demi-line.
Oriented geometry can, thanks to its orientation, ignore the notions of time inherent to its system. But, in order to take consciousness of the role of time and of its real role in relation to the three spatial dimensions, we are obliged to abandon the path of orientation by the demi-line, and to found a unitary homeomorphism.
When we want to use the expression dimension, we are immediately faced with the problem of its exact interpretation and definition. A dimension can be defined in a logical fashion as an extension without beginning or end, neither sense nor orientation, an infinity, and it's just the same with the infinity in the dimension of time. This is eternity. The extension of one of the three spatial dimensions represents a surface, an extension without beginning or end. If the system of linear measurement can only measure the demi-line, the system of measurement from two coordinates at right angles can only give a measure of space for figures drawn in a quarter of a surface, and the information of 3D measurements are even poorer as they are drawn within an eighth of a sphere from the angle of measure of 90 degrees of three oriented co-ordinates in the same direction. To avoid this perpetual reduction of knowledge, we shall proceed in the inverse sense.
For the witness of a crime, identification is to define the suspect as the possible unique. But homeomorphism poses us various problems. It could easily be viewed as follows: now it is no longer a matter of identifying the assassin, but the poor victim that the brute has voluntarily ridden over several times with their motor car. They have an aspect which differs in a tragic way from the fellow that was known during their life. Everything is there, but crudely rearranged. They are not the same, yet it is still them. Even in their decomposition they can be identified. Without doubt. It is the field of homeomorphism, the variability within unity.
Here the field of situlogical experience is divided into two opposed tendencies, the ludic tendency and the analytical tendency. The tendency of art, spinn and the game, and that of science and its techniques. The creation of variabilities within a unity, and the search for unity amongst the variations. It can be clearly seen that our assassin has chosen the first way, and that the identifiers must take up the second, which Iimits the domain to the analysis of sites, or topology. Situlogy, in its development, gives a decisive push to the two tendencies. For example, take the network represented by Galton's apparatus. As a pinball table, it can be found in most of the Paris bistros; and as the possibility of calculated variability, it is the model of all the telephone networks.
But this is the creative side, which precedes the analytical side in general and elementary situlogy: the situationists are the crushers of all existent conditions. Thus we are going to start our demonstration by returning to the method of our criminal. But to avoid making this affair a bloody drama, we shall dive head long into a perfectly imaginary and abstract world, like Euclid.
We start by lending an object a perfect homeomorphism, an absolute and practically inexistent quality, like the absence of spatial extension that Euclid gives to his point. We give absolute plasticity to a perfectly spherical ball with a precise diameter. It can be deformed in any way without being broken or punctured. Our goal is clear before this object of perfect three dimensional symmetry. We are going to completely flatten it to transform it into a surface with two dimensions and to find the key to their homeomorphic equivalence. We are going to reduce the height of this sphere down to zero in ten equal stages, and calculate the level of increase of the two corresponding dimensions at the registered reductions of the third progressively as the ball is transformed more and more into a surface. The last number can be deduced from the preceding nine. It is evident that we don't end up at infinity, as the same process with a ball five times as large must give a surface at least five times as big, and two infinities with a difference of measurable dimensions is beyond logic (except for Lemaitre when he speaks of eternity). The practical work of calculation linked to this experiment, we shall leave to the mathematicians – if they have nothing better to do.
We haven't finished. We choose a diagonal in this immense pancake without thickness, and start to lengthen the surface in exactly the same way as in the previous experiment, to end up with a line without thickness, making the calculations in a similar fashion. Thus we have the homeomorphic equivalence expressed as numbers between an object in three, two and one dimension, and the whole world can start to protest. The most intelligent will be patient, saying that Euclid staried with a point. How is this immense line reduced to a single point? I can only return to the sphere. If the situlogy was a uniquely spatial and positional phenomena this will be true.
Einstein has explained that if a line can reach the speed of light, it will contract until it disappears completely as regards the length along the direction of the trip. However a clock would stop all together at that speed. This is what we are going to do. The whole matter is settled in this way. The only minor inconvenience of this spectacular process is invisible: I cannot regain possession of my point which flies off across the universe. If I could transform this movement across space into rotation in place, I would have more or less mastered my point.
Einstein declared the "space and time conceived separately have become empty shadows, and only the combination of both expresses reality". It is from this observation that I'm going to clarify the Euclidean point, which possesses no dimensions and, as it is within space, before however representing any other dimension, at least represents the dimension of time introduced into space. And it is all the more impossible to fix a point without duration in space. Without duration there is no position.
But in order that this point can possess the quality of time, it must possess the quality of movement, and as the geometric point cannot be displaced in space without making a line, this movement must be rotational, or spinning around itself. Although this movement must be continued, it does not however have an axis nor spatial direction; and what's more vortex cannot occupy the least space. If this definition of the point is richer and more positive than that of Euclid, it does not seem to be less abstract. But since I have learnt that there is a Greek geometer, Heron, who inspired Gauss with a definition of the straight line as a line which turns around itself as an axis without the displacement of any of the point(s) which compose(s) it; and that plenty of people agree that this is the only positive thing which has ever been said on the subject of the straight line, I feel I'm on the right track.
But an axis can only have a rotation in a sense. It is necessary to stop it to spin it in the contrary sense. However a point in rotation, by a continuous change of its axis of rotation, could be led to a rotation in a contrary sense, whatever the sense. In this way the straight line can be explained thus: if two points rotating at random are connected, they are obliged to spin in the same sense and with the same speed, the faster being braked and the slower accelerated.
All the points of a line acquire a presence in the spatial dimension equivalent to their loss of freedom of movement, which has become oriented in space.
If we want to stay with this oriented and positive definition of the line on our backs, a plastic definition is needed. To understand this, it is necessary to remind ourselves that plastic geometry does not place the accent on the infinite character of dimensions, but on their character of a presence in general space and time, which could be finite or infinite, but which are primarily in relation with all the objects whose extension is wanted to be studied. Each volume, each surface, each segment of line or piece of time makes a part, or is extracted from the general mass of universal space and time. In the analysis, for example, of a linear segment in the egalitarian geometry of Euclid, abstractions of an 'infinite' character are made of the line. A piece is cut away by forgetting the rest. In unitary geometry, this is not possible. A line is not an uninterrupted series of points, because the points have lost something in order to be able to establish a line. In a segment of a line, there are only two points which could be observed, the two points at each end of the line. But how is it explained that on a line segment there are two rather than a single zero point? The only possible explanation is that a line segment with two zero points is composed of two demi-lines superimposed, with the zero points crossed, going in opposite directions. A line segment is thus a line to double distances, there and back, and of a length double the distance between the two polarised ends or in counterpoint. This is a basis for plastic or dialectical geometry. From this outlook, each determined volume is a volume within general volume, or universal space, fragmented by a surface: just as each surface is a fragment of the universal surface distinguished by some lines; and each linear section is a linear segment determined by some points; and each point a moment within time, detetmined by its duration.
The specific surface which determines a volume, the voluminous surface is termed the vessel, form etc. And as a function of separation between two volumes it possesses the character of an opposition between the inside and outside; similarly the separation of a surface by a line opposes before and after, and so also the point on a line distinguishes the positive and negative sense of a distance. These signs thus only make sense as the relation between two dimensional systems, in the same combination of co-ordinates. The problem becomes more complex when we start to play with several co-ordinate systems in relation with each other such that it could be termed projective geometry, of which the best known example is central perspective.
In order to better understand not only the system of projections, but also the system of objectification in general it is necessary to see how the co-ordinate systems unfold and which is the initial primary system. The primary system of all observation is the system of co-ordinates inherent to the observers themselves, their subjective co-ordinates. Ordinarily this elementary requisite for observation is ignored. The co-ordinates of the individnal are known as front, behind, above, below, left and right; and play an enormous role for orientation, not only in science, but of a primordial way in ethics, the social orientation where the individual is drawn to the left and then the right, toppling forwards, always forward thanks to progress, pushed from behind and pressed towards the ascent and the higher pathways, to finally be carried underground. The direction to the right is the direction of least resistance, of the right line, the direction said to be just or rational; and opposed to it, the left is by nature the anarchic direction of the game, of the spinn or of the greatest effort. But each time that the political left becomes the direction of a development of justice, following the path of least resistance, this opposition lacks tension. The trajectory of descent is delineated by the path of least resistance So,from our outlook of oppositions, the left direction of the left, that of games, must represnt the ascent. This is what I have tried to prove with the reversal of dialectics. In the Scandinavian languages the word droite (German recht, English right) means ascension (hogre) towards the heights, which symbolises the left elsewhere. The confusion in social orientation in Europe and in its vocabulary gains from being so rich and contradictory in this respect. These are purely objective observations, without any pragmatic consequence, but which have had an influence even on the most elementary religious conceptions (heaven – fire).
In reality the metric graduations of a co-ordinate system allow the establishinent of a network of parallel lines of co-ordination at equal intervals. The zero point and the positive directions can be chosen and changed in the system as is desired thanks to this squaring up. It is the same thing for the line and for the system of three co-ordinates.
When the system of co-ordinates of an observed object is displaced in relation to the basic system of co-ordination for observation and measure, this sometimes necessitates projection. The projective geometry thus shows the rules of the relations between two or several systems of co-ordination, as if there were two or several spaces. In this way, the same space can be multiplied into several by projection. But this is only justified through the time dimension.
However, positive geometry, which works with the demi-line, the quarter surface and the eighth of volume, allows another purely spatial game. The right angle formed by the two negative demi-lines of a co-ordination in two dimensions can be displaced and put in opposition to the positive angle, thus establishing, for example a square. This operation explains how the square could find its explanation in the relationship between the circumference and the diagonal of a circle, even though the circle cannot be defined as a derivative of the square. This definition of the square by juxtaposition joins our dialectic definition of the line, and shows how situlogy is more immediate than geometry which always runs into the problem of squaring the circle.
Here we have roughly sketched out some consequences of the disorder which situlogy could introduce to geometric thought, but it is evident to those who know this material, that the consequences will not be any the less as regards our physical and mechanical conceptions. It has already been understood by Einstein's definition that the notion we have of light doesn't lend itself to any spatial dimension. However it would be wrong to consider light as being immaterial. Even the old mystical notion of the four elements could be reconsidered. We know that they don't exist as absolute phenomena, but it is however strange that modern science has refused to consider a distinction of matter as pronounced as that between solid, liquid, gaseous objects and light. When an ice cube suddenly melts and stretches on the surface of a table, it can he concluded that the liquid state represents the loss of one of the spatial dimensions, replaced by a liberation of discharge; that the liquid is a matter of two spatial dimensions. And the constant of tensions of surface tension seems to be as important in physics as the constant of the speed of light. The logical condusion this gives rise to, is that gases have only one dimension, compensated for by the play of their movement. And for an example of something which has even less dimensions, think of Maurice Lemaitre and his friends.