Number and Numbers

0.1. A paradox: we live in the era of the despotism of number, thought is submitted to the law of denumerable multiplicities, and yet (or rather precisely in so far as this default, this failure, is nothing but the obscure obverse of a submission without concept) we have at our disposal no recent, active idea of what number is. The question has been the subject of immense intellectual effort, but for the most part the significant achievements of this labour belong to the beginning of the twentieth century: they are those of Dedekind, Frege, Cantor, and Peano. The factual impact of number brings with it only a silence of the concept. How can we understand today Dedekind’s question, posed in his 1888 treatise, Was sind und was sollen die Zahlen [“The Nature and Meaning of Numbers”]? What purpose numbers serve, we know very well: they serve, strictly speaking, for everything, they provide the norm for everything. But what they are we don’t know, or we repeat what the great thinkers of the end of the nineteenth century – no doubt anticipating the extent of their future domain – said they were.

0.2. That number reigns, that the imperative must be: "count!" – who doubts this today?

0.3. Firstly, number rules our political conceptions, with the currency (consensual, even if all politics of the thinkable is enfeebled) of suffrage, of opinion polls, of the majority. Every "political" assembly, general or local, municipal or international, voting-booth or public meeting, is settled with a count. And every opinion is measured by the standard of an incessant enumeration of its advocates (even if such an enumeration makes of every fidelity an infidelity). What counts – in the sense of what is valued – is that which is counted. Inversely, everything that deals with numbers must be valued. "Political Science" finesses numbers within numbers, cross- references series of numbers, its only object being shifts in voting patterns – that is, changes – usually infinitesimal – in the tabulation of numbers. So political "thought" is a numerical exegesis.

0.4. Number rules over the quasi-totality of the "human sciences" (even if this ciphered alibi can scarcely hide the fact when we speak here of "science", what we have is a technical assemblage whose pragmatic basis is governmental). It is overrun by the statistical data of the entire domain of its disciplines. The bureaucratisation of knowledge is firstly an infinite excrescence of numbering.

0.5. Number governs cultural representation. Certainly, there is television, viewing figures, advertising. But that is not the most important thing. It is in its very essence that the cultural fabric is woven by number alone. A "cultural fact" is a numerical fact. And inversely, whatever produces number can be assigned a cultural place; that which has no number will not have a name either. Art, which has to do with number only insofar as there is a thinking of number, is a culturally unpronounceable word.

0.6. Obviously, number governs the economy, and it is there without doubt that we find what Louis Althusser called the "determination in the last instance" of its supremacy. The ideology of modern parliamentary societies, if they have one, is not humanism, the rights of the subject. It is number, the countable, countability. Every citizen is today expected to be cognizant of foreign trade figures, of the flexibility of the exchange rate, of the developments of the stock market. These figures are presented as the real through which other figures are processed: governmental figures, votes and opinion polls. What is called "the situation" is the intersection of economic numericality and the numericality of opinion.

0.7. Number informs our souls. What is it to exist, if not to assert oneself through a favourable account? In America, one starts by saying how much one earns, an identification that has the merit of honesty.

0.8. Marx: "the icy water of egoistic calculation". And how! To the point where the Ego of egoism is but a numerical web, so that the "egoistic calculation" becomes the cipher of a cipher.

0.9. But we don’t know what a number is, so we don’t know what we are.

0.10. Must we stick with Frege, Dedekind, Cantor or Peano? Hasn’t anything happened in the thinking of number? Is there only the exorbitant extent of its social and subjective reign? To what extent does their idea of number prefigure this anarchic reign? Did they think number, or the future of generalised numericality? Isn’t another idea of number necessary, in order for us to turn thought back against the despotism of number, in order to subtract the Subject from it? And has mathematics assisted only silently in the comprehensive socialisation of number, of which latter it had previously held a monopoly? This is what I wish to examine.

(Alain Badiou, Number and Numbers)

The communist hypothesis remains the good one

From "Censorship Today: Violence, or Ecology, a New Opium for the Masses"

by Slavoj Žižek

So what is the problem here? It is easy to make fun of Fukuyama's notion of the End of History, but the majority today is "Fukuyamaian": liberal-democratic capitalism is accepted as the finally-found formula of the best possible society, all one can do is to render it more just, tolerant, etc. The only true question today is: do we endorse this "naturalization" of capitalism, or does today's global capitalism contain strong enough antagonisms which will prevent its indefinite reproduction? There are three (or, rather, four) such antagonisms:

1. Ecology:
In spite of the infinite adaptability of capitalism which, in the case of an acute ecological catastrophe or crisis, can easily turn ecology into a new field of capitalist investment and competition, the very nature of the risk involved fundamentally precludes a market solution - why? Capitalism only works in precise social conditions: it implies the trust into the objectivized/"reified" mechanism of the market's "invisible hand" which, as a kind of Cunning of Reason, guarantees that the competition of individual egotisms works for the common good. However, we are in the midst of a radical change. Till now, historical Substance played its role as the medium and foundation of all subjective interventions: whatever social and political subjects did, it was mediated and ultimately dominated, overdetermined, by the historical Substance. What looms on the horizon today is the unheard-of possibility that a subjective intervention will intervene directly into the historical Substance, catastrophically disturbing its run by way of triggering an ecological catastrophe, a fateful biogenetic mutation, a nuclear or similar military-social catastrophe, etc. No longer can we rely on the safeguarding role of the limited scope of our acts: it no longer holds that, whatever we do, history will go on. For the first time in human history, the act of a single socio-political agent effectively can alter and even interrupt the global historical process, so that, ironically, it is only today that we can say that the historical process should effectively be conceived "not only as Substance, but also as Subject." This is why, when confronted with singular catastrophic prospects (say, a political group which intends to attack its enemy with nuclear or biological weapons), we no longer can rely on the standard logic of the "Cunning of Reason" which, precisely, presupposes the primacy of the historical Substance over acting subjects: we no longer can adopt the stance of "let the enemy who threatens us deploy its potentials and thereby self-destruct himself" - the price for letting the historical Reason do its work is too high since, in the meantime, we may all perish together with the enemy. Recall a frightening detail from the Cuban missile crisis: only later did we learn how close to nuclear war we were during a naval skirmish between an American destroyer and a Soviet B-59 submarine off Cuba on October 27 1962. The destroyer dropped depth charges near the submarine to try to force it to surface, not knowing it had a nuclear-tipped torpedo. Vadim Orlov, a member of the submarine crew, told the conference in Havana that the submarine was authorized to fire it if three officers agreed. The officers began a fierce, shouting debate over whether to sink the ship. Two of them said yes and the other said no. "A guy named Arkhipov saved the world," was a bitter comment of a historian on this accident.

2. Private Property:
The inappropriateness of private property for the so-called "intellectual property." The key antagonism of the so-called new (digital) industries is thus: how to maintain the form of (private) property, within which only the logic of profit can be maintained (see also the Napster problem, the free circulation of music)? And do the legal complications in biogenetics not point in the same direction? Phenomena are emerging here which bring the notion of property to weird paradoxes: in India, local communities can suddenly discover that medical practices and materials they are using for centuries are now owned by American companies, so they should be bought from them; with the biogenetic companies patentizing genes, we are all discovering that parts of ourselves, our genetic components, are already copyrighted, owned by others...

The crucial date in the history of cyberspace is February 3 1976, the day when Bill Gates published his (in)famous "Open Letter to Hobbysts," the assertion of private property in the software domain: "As the majority of hobbysts must be aware, most of you steal your software. /.../ Most directly, the thing you do is theft." Bill Gates has built his entire empire and reputation on his extreme views about knowledge being treated as if it were tangible property. This was a decisive signal which triggered the battle for the "enclosure" of the common domain of software.

3. New Techno-Scientific Developments:
The socio-ethical implications of new techno-scientific developments (especially in bio-genetics) - Fukuyama himself was compelled to admit that the biogenetic interventions into human nature are the most serious threat to his vision of the End of History.

With the latest biogenetic developments, we are entering a new phase in which it is simply nature itself which melts into air: the main consequence of the scientific breakthroughs in biogenetics is the end of nature. Once we know the rules of its construction, natural organisms are transformed into objects amenable to manipulation. Nature, human and inhuman, is thus "desubstantialized," deprived of its impenetrable density, of what Heidegger called "earth." This compels us to give a new twist to Freud's title Unbehagen in der Kultur - discontent, uneasiness, in culture. With the latest developments, the discontent shifts from culture to nature itself: nature is no longer "natural," the reliable "dense" background of our lives; it now appears as a fragile mechanism which, at any point, can explode in a catastrophic direction.

4. New Forms of Apartheid:
Last but not least, new forms of apartheid, new Walls and slums. On September 11th, 2001, the Twin Towers were hit; twelve years earlier, on November 9th, 1989, the Berlin Wall fell. November 9th announced the "happy '90s," the Francis Fukuyama dream of the "end of history," the belief that liberal democracy had, in principle, won, that the search is over, that the advent of a global, liberal world community lurks just around the corner, that the obstacles to this ultra-Hollywood happy ending are merely empirical and contingent (local pockets of resistance where the leaders did not yet grasp that their time is over). In contrast to it, 9/11 is the main symbol of the forthcoming era in which new walls are emerging everywhere, between Israel and the West Bank, around the European Union, on the U.S.-Mexico border.

So what if the new proletarian position is that of the inhabitants of slums in the new megalopolises? The explosive growth of slums in the last decades, especially in the Third World megalopolises from Mexico City and other Latin American capitals through Africa (Lagos, Chad) to India, China, Philippines and Indonesia, is perhaps the crucial geopolitical event of our times. It is effectively surprising how many features of slum dwellers fit the good old Marxist determination of the proletarian revolutionary subject: they are "free" in the double meaning of the word even more than the classic proletariat ("freed" from all substantial ties; dwelling in a free space, outside the police regulations of the state); they are a large collective, forcibly thrown together, "thrown" into a situation where they have to invent some mode of being-together, and simultaneously deprived of any support in traditional ways of life, in inherited religious or ethnic life-forms.

While today's society is often characterized as the society of total control, slums are the territories within a state boundaries from which the state (partially, at least) withdrew its control, territories which function as white spots, blanks, in the official map of a state territory. Although they are de facto included into a state by the links of black economy, organized crime, religious groups, etc., the state control is nonetheless suspended there, they are domains outside the rule of law. In the map of Berlin from the times of the now defunct GDR, the are of West Berlin was left blank, a weird hole in the detailed structure of the big city; when Christa Wolf, the well-known East German half-dissident writer, took her small daughter to the East Berlin's high TV tower, from which one had a nice view over the prohibited West Berlin, the small girl shouted gladly: "Look, mother, it is not white over there, there are houses with people like here!" - as if discovering a prohibited slum Zone...

This is why the "de-structured" masses, poor and deprived of everything, situated in a non-proletarized urban environment, constitute one of the principal horizons of the politics to come. If the principal task of the emancipatory politics of the XIXth century was to break the monopoly of the bourgeois liberals by way of politicizing the working class, and if the task of the XXth century was to politically awaken the immense rural population of Asia and Africa, the principal task of the XXIth century is to politicize - organize and discipline - the "de-structured masses" of slum-dwellers. Hugo Chavez's biggest achievement is the politicization (inclusion into the political life, social mobilization) of slum dwellers; in other countries, they mostly persist in apolitical inertia. It was this political mobilization of the slum dwellers which saved him against the US-sponsored coup: to the surprise of everyone, Chavez included, slum dwellers massively descended to the affluent city center, tipping the balance of power to his advantage.

How do these four antagonisms relate to each other? There is a qualitative difference between the gap that separates the Excluded from the Included and the other three antagonisms, which designate three domains of what Hardt and Negri call "commons," the shared substance of our social being whose privatization is a violent act which should also be resisted with violent means, if necessary: the commons of culture, the immediately socialized forms of "cognitive" capital, primarily language, our means of communication and education (if Bill Gates were to be allowed monopoly, we would have reached the absurd situation in which a private individual would have literally owned the software texture our basic network of communication), but also the shared infrastructure of public transport, electricity, post, etc.; the commons of external nature threatened by pollution and exploitation (from oil to forests and natural habitat itself); the commons of internal nature (the biogenetic inheritance of humanity). What all these struggles share is the awareness of the destructive potentials, up to the self-annihilation of humanity itself, if the capitalist logic of enclosing these commons is allowed a free run. It is this reference to "commons" which justifies the resuscitation of the notion of Communism - or, to quote Alain Badiou:

The communist hypothesis remains the good one, I do not see any other. If we have to abandon this hypothesis, then it is no longer worth doing anything at all in the field of collective action. Without the horizon of communism, without this Idea, there is nothing in the historical and political becoming of any interest to a philosopher. Let everyone bother about his own affairs, and let us stop talking about it. In this case, the rat-man is right, as is, by the way, the case with some ex-communists who are either avid of their rents or who lost courage. However, to hold on to the Idea, to the existence of this hypothesis, does not mean that we should retain its first form of presentation which was centered on property and State. In fact, what is imposed on us as a task, even as a philosophical obligation, is to help a new mode of existence of the hypothesis to deploy itself.