Academic literature on the topic 'Finite-Memory determinacy'

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using additional structure variables. It is obtained by writing the Helmholtz free energy as the sum of a volumetric energy density (function of the determinant of the deformation gradient det F and the temperature [Formula: see text] like the standard perfect-gas law or Noble–Abel stiffened-gas law) plus a polyconvex strain energy density function of F, [Formula: see text] and of symmetric positive-definite structure tensors that relax at a characteristic time scale. One feature of our model is that it unifies various ideal materials ranging from hyperelastic solids to perfect fluids, encompassing fluids with memory like Maxwell fluids. We establish a strictly convex mathematical entropy to show that the system is symmetric-hyperbolic. Another feature of the proposed model is therefore the short-time existence and uniqueness of smooth solutions, which define genuinely causal viscoelastic flows with waves propagating at finite speed. In heat-conductors, we complement the system by a Maxwell–Cattaneo equation for an energy-flux variable. The system is still symmetric-hyperbolic, and smooth evolutions with finite-speed waves remain well-defined.

We analyse the exact solution of the eigenproblem for the Heisenberg Hamiltonian of magnetic heptagon, i.e. the ring of N = 7 nodes, each with spin 1/2, within the XXX model with nearest neighbour interactions, from the point of view of finite extensions of the field ℚ of rationals. We point out, as the main result, that the associated arithmetic structure of these extensions makes natural an introduction of some Galois qubits. They are two-dimensional subspaces of the Hilbert space of the model, which admit a quantum informatic interpretation as elementary memory units for a (hypothetical) computer, based on their distinctive properties with respect to the action of related Galois group for indecomposable factors of the secular determinant. These Galois qubits are nested on the lattice of subfields which involves several minimal fields for determination of eigenstates (the complex Heisenberg field), spectrum (the real Heisenberg field), and Fourier transforms of magnetic configurations (the cyclotomic field, based on the simple 7th root of unity). The structure of the corresponding lattice of Galois groups is presented in terms of Kummer theory, and its physical interpretation is indicated in terms of appropriate permutations of eigenstates, energies, and density matrices.

We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what kinds of strategies are sufficient or required to play optimally (e.g., randomization or memory requirements)? Our contributions further the understanding of arena-independent finite-memory (AIFM) determinacy, i.e., the study of objectives for which memory is needed, but in a way that only depends on limited parameters of the game graphs. First, we show that objectives for which pure AIFM strategies suffice to play optimally also admit pure AIFM subgame perfect strategies. Second, we show that we can reduce the study of objectives for which pure AIFM strategies suffice in two-player stochastic games to the easier study of one-player stochastic games (i.e., Markov decision processes). Third, we characterize the sufficiency of AIFM strategies through two intuitive properties of objectives. This work extends a line of research started on deterministic games to stochastic ones.

We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of $\omega$-regular objectives, due to its relation to many natural problems in theoretical computer science. We focus on the strategy complexity question: given an objective, how much memory does each player require to play as well as possible? A classical result is that finite-memory strategies suffice for both players when the objective is $\omega$-regular. We show a reciprocal of that statement: when both players can play optimally with a chromatic finite-memory structure (i.e., whose updates can only observe colors) in all infinite game graphs, then the objective must be $\omega$-regular. This provides a game-theoretic characterization of $\omega$-regular objectives, and this characterization can help in obtaining memory bounds. Moreover, a by-product of our characterization is a new one-to-two-player lift: to show that chromatic finite-memory structures suffice to play optimally in two-player games on infinite graphs, it suffices to show it in the simpler case of one-player games on infinite graphs. We illustrate our results with the family of discounted-sum objectives, for which $\omega$-regularity depends on the value of some parameters.

A political minimalism? That would obviously go against the grain of our current political ideology → in fact, we are in an era of political maximalisation (Roland Barthes 200, arrow in original).Barthes’ comment is found in the ‘Annex’ to his 1978 lecture course The Neutral. Despite the three decade difference I don’t things have changed that much, certainly not insofar as academic debate about the cultural and social is concerned. At conferences I regularly hear the demand that the speaker or speakers account for the ‘political intent’, ‘worth’ or ‘utility’ of their work, or observe how speakers attempt to pre-empt and disarm such calls through judicious phrasing and citing. Following his diagnosis Barthes (201-206) proceeds to write under the title ‘To Give Leave’. Here he notes the incessant demand placed upon us, as citizens, as consumers, as representative cultural subjects and as biopolitical entities and, in this context, as academics to have and to communicate our allegiances, views and opinions. Echoing the acts, (or rather the ‘non-acts’), of Melville’s Bartleby, Barthes describes the scandalous nature of suspending the obligation of holding views; the apparent immorality of suspending the obligation of being interested, engaged, opinionated, committed – even if one only ever suspends provisionally, momentarily even. For the length of a five thousand word essay perhaps. In this short, unfortunately telegraphic and quite speculative essay I want pause to consider a few gestures or figures of ‘suspension’, ‘decline’ and ‘remaining aside’. What follows is in three parts. First a comment on the nature of the ‘demand to communicate’ identified by Barthes and its links to longer running moral and practical imperatives within Western understandings of the subject, the social and the political. Second, the most substantial section but still an all too brief account of the apparent ‘passivity’ of the narrator of Imre Kertész’s novel Fatelessness and the ways in which the novel may be read as a reflection on the nature of agency and determination. Third, a very brief conclusion, the question directly; what politics or what apprehension of politics, could a reflection on stillness and its ‘political minimalism’ offer? 1.For Barthes, (in 1978), one of the factors defining the contemporary intellectual scene was the way in which “politics invades all phenomena, economic, cultural, ethical” coupled with the “radicalization” of “political behaviors” (200), perhaps most notably in the arrogance of political discourse as it assumes the place of a master discourse. Writing in 1991 Bill Readings identified a similar phenomenon. For Readings the category of the political and politically inspired critique were operating by encircling their objects within a presupposed “universal language of political significance into which one might translate everything according to its effectivity”, an approach which has the effect of always making “the political […] the bottom line, the last instance where meaning can be definitively asserted” (quoted in Clark 3) or, we may add, realized. There is, of course, much that could be said here, not least concerning the significant differences in context, (between, for example, the various forms of revolutionary Marxism, Communism and Maoism which seem to preoccupy Barthes and the emancipatory identity and cultural politics which swept through literature departments in the US and beyond in the last two decades of the twentieth century). However it is also possible to suggest that a general grammar and, moreover, a general acceptance of a telos of the political persists.Barthes' (204-206) account of ‘political maximalisation’ is accompanied by a diagnosis of its productivist virility, (be it, in 1978, on the part of the increasingly reduced revolutionary left or the burgeoning neo-liberal right). The antithesis, or, rather, the outside of such an arrangement or frame would not be another political program but rather a certain stammering, a lassitude or dilatoriness. A flaccidness even; “a devirilized image” wherein from the point of view of the (political) actor or critic, “you are demoted to the contemptible mass of the undecided of those who don’t know who to vote for: old, lost ladies whom they brutalize: vote however you want, but vote” (Barthes 204). Hence Barthes is not suggesting a counter-move, a radical refusal, a ‘No’ shouted back to the information saturated market society. What is truly scandalous he suggests, is not opposition or refusal but the ‘non-reply’. What is truly scandalous, roughish even, is the decline or deferral and so the provisional suspension of the choice (and the blackmail) of the ‘yes’ or ‘no’, the ‘this’ or the ‘that’, the ‘with us’ or ‘against us’.In Literature and Evil Georges Bataille concludes his essay on Kafka with a comment on such a decline. According to Bataille, the reason why Kafka remains an ambivalent writer for critics, (and especially for those who would seek to enrol his work to political ends), lays precisely in his constant withdrawal; “There was nothing he [Kafka] could have asserted, or in the name of which he could have spoken. What he was, which was nothing, only existed to the extent in which effective activity condemned him” (167). ‘Effective activity’ refers, contextually, to a certain form of Communism but more broadly to the rationalization or systematization intrinsic to any political program, political programs (or ideologies) as such, be they communist, liberal or libertarian. At least insofar as, as implied above, the political is taken to coincide with a certain metaphysics and morality of action and the consequent linking of freedom to work, (a factor common to communist, fascist and liberal political programs), and so to the labour of the progressive self-realization and achievement of the self, the autos or ipse (see Derrida 6-18). Be it via, for example, Marx’s account of human’s intrinsic ‘capacity for work’ (Arbeitskraft), Heidegger’s account of necessary existential (and ultimately communal) struggle (Kampf), or Weber’s diagnoses of the (Protestant/bourgeois) liberal project to realize human potentiality (see also Agamben Man without Content; François 1-64). Hence what is ‘evil’ in Kafka is not any particular deed but the deferral of deeds; his ambivalence or immorality in the eyes of certain critics being due to the question his writing poses to “the ultimate authority of action” (Bataille 153) and so to the space beyond action onto which it opens. What could this space of ‘worklessness’ or ‘unwork’ look like? This non-virile, anti-heroic space? This would not be a space of ‘inaction’, (a term still too dependent, albeit negatively, on action), but of ‘non-action’; of ‘non-productive’ or non-disclosive action. That is to say, and as a first attempt at definition, ‘action’ or ‘praxis’, if we can still call it that, which does not generate or bring to light any specific positive content. As a way to highlight the difficulties and pitfalls, (at least with certain traditions), which stand in the way of thinking such a space, we may highlight Giorgio Agamben’s comments on the widespread coincidence of a metaphysics of action with the determination of both the subject, its teleology and its orientation in the world:According to current opinion, all of man’s [sic] doing – that of the artist and the craftsman as well as that of the workman and the politician – is praxis – manifestation of a will that produces a concrete effect. When we say that man has a productive status on earth, we mean, that the status of his dwelling on the earth is a practical one […] This productive doing now everywhere determines the status of man on earth – man understood as the living being (animal) that works (laborans), and, in work, produces himself (Man without Content 68; 70-71 original emphasis).Beyond or before practical being then, that is to say before and beyond the determination of the subject as essentially or intrinsically active and engaged, another space, another dwelling. Maybe nocturnal, certainly one with a different light to that of the day; one not gathered in and by the telos of the ipse or the turning of the autos, an interruption of labour, an unravelling. Remaining still, unravelling together (see Harrison In the absence).2.Kertész’s novel Sorstalanság was first published in his native Hungary in 1975. It has been translated into English twice, in 1992 as Fateless and in 2004 as Fatelessness. Fatelessness opens in Budapest on the day before György Köves’ – the novel’s fourteen year old narrator – father has to report for ‘labour service’. It goes on to recount Köves’ own detention and deportation and the year spent in the camps of Auschwitz-Birkenau, Buchenwald and Zeitz. During this period Köves’ health declines, gradually at first and then rapidly to a moment of near death. He survives and the novel closes with his return to his home town. Köves is, as Kertész has put it in various interviews and as is made clear in the novel, a ‘non-Jewish Jew’; a non-practicing and non-believing Hungarian Jew from a largely assimilated family who neither reads nor speaks Hebrew or Yiddish. While Kertész has insisted that the novel is precisely that, a novel, a work of literature and not an autobiography, we should note that Kertész was himself imprisoned in Buchenwald and Zeitz when fourteen.Not without reservations but for the sake of brevity I shall focus on only one theme in the novel; determination and agency, or what Kertész calls ‘determinacy’. Writing in his journal Galley Boat-Log (Gályanapló) in May 1965 Kertész suggests ‘Novel of Fatelessness’ as a possible title for his work and then reflects on what he means by ‘fate’, the entry is worth quoting at length.The external determinacy, the stigma which constrains our life in a situation, an absurdity, in the given totalitarianism, thwarts us; thus, when we live out the determinacy which is doled out to us as a reality, instead of the necessity which stems from our own (relative) freedom – that is what I call fatelessness.What is essential is that our determinacy should always be in conflict with our natural views and inclinations; that is how fatelessness manifests itself in a chemically pure state. The two possible modes of protection: we transform into our determinacy (Kafka’s centipede), voluntarily so to say, and I that way attempt to assimilate our determinacy to our fate; or else we rebel against it, and so fall victim to our determinacy. Neither of these is a true solution, for in both cases we are obliged to perceive our determinacy […] as reality, whilst the determining force, that absurd power, in a way triumphs over us: it gives us a name and turns us into an object, even though we were born for other things.The dilemma of my ‘Muslim’ [Köves]: How can he construct a fate out of his own determinacy? (Galley Boat-Log 98 original emphasis).The dilemma of determinacy then; how can Köves, who is both determined by and superfluous to the Nazi regime, to wider Hungarian society, to his neighbours and to his family, gain some kind of control over his existence? Throughout Fatelessness people prove repeatedly unable to control their destinies, be it Köves himself, his father, his stepmother, his uncles, his friends from the oil refinery, or even Bandi Citrom, Köves’ mentor in the camps. The case of the ‘Expert’ provides a telescoped example. First appearing when Köves and his friends are arrested the ‘Expert’ is an imposing figure, well dressed, fluent in German and the director of a factory involved in the war effort (Fatelessness 50). Later at the brickworks, where the Jews who have been rounded up are being held prior to deportation, he appears more dishevelled and slightly less confident. Still, he takes the ‘audacious’ step of addressing a German officer directly (and receives some placatory ‘advice’ as his reward) (68-69). By the time the group arrives at the camp Köves has difficulty recognising him and without a word of protest, the ‘Expert’ does not pass the initial selection (88).Köves displays no such initiative with regard to his situation. He is reactive or passive, never active. For Köves events unfold as a series of situations and circumstances which are, he tells himself, essentially reasonable and to which he has to adapt and conform so that he may get on. Nothing more than “given situations with the new givens inherent in them” (259), as he explains near the end of the novel. As Köves' identity papers testify, his life and its continuation are the effect of arbitrary sets of circumstances which he is compelled to live through; “I am not alive on my own account but benefiting the war effort in the manufacturing industry” (29). In his Nobel lecture Kertész described Köves' situation:the hero of my novel does not live his own time in the concentration camps, for neither his time nor his language, not even his own person, is really his. He doesn’t remember; he exists. So he has to languish, poor boy, in the dreary trap of linearity, and cannot shake off the painful details. Instead of a spectacular series of great and tragic moments, he has to live through everything, which is oppressive and offers little variety, like life itself (Heureka! no pagination).Without any wilful or effective action on the part of the narrator and with only ‘the dreary trap of linearity’ where one would expect drama, plot, rationalization or stylization, Fatelessness can read as an arbitrarily punctuated series of waitings. Köves waiting for his father to leave, waiting in the customs shed, waiting at the brick works, waiting in train carriages, waiting on the ramp, waiting at roll call, waiting in the infirmary. Here is the first period of waiting described in the book, it is the day before his father’s departure and he is waiting for his father and stepmother as they go through the accounts at the family shop:I tried to be patient for a bit. Striving to think of Father, and more specifically the fact that he would be going tomorrow and, quite probably, I would not see him for a long time after that; but after a while I grew weary with that notion and then seeing as there was nothing else I could do for my father, I began to be bored. Even having to sit around became a drag, so simply for the sake of a change I stood up to take a drink of water from the tap. They said nothing. Later on, I also made my way to the back, between the planks, in order to pee. On returning I washed my hands at the rusty, tiled sink, then unpacked my morning snack from my school satchel, ate that, and finally took another drink from the tap. They still said nothing. I sat back in my place. After that, I got terribly bored for another absolute age (Fatelessness 9). It is interesting to consider exactly how this passage presages those that will come. Certainly this scene is an effect of the political context, his father and stepmother have to go through the books because of the summons to labour service and because of the racial laws on who may own and profit from a business. However, the specifically familial setting should not be overlooked, particularly when read alongside Kertész’s other novels where, as Madeleine Gustafsson writes, Communist dictatorship is “portrayed almost as an uninterrupted continuation of life in the camp – which in turn [...] is depicted as a continuation of the patriarchal dictatorship of a joyless childhood” (no pagination, see, for example, Kertész Kaddish). Time to turn back to our question; does Fatelessness provide an answer to the ‘dilemma of determinacy’? We should think carefully before answering. As Julia Karolle suggests, the composition of the novel and our search for a logic within itreveal the abuses that reason must endure in order to create any story or history about the Holocaust […]. Ultimately Kertész challenges the reader not to make up for the lack of logic in Fatelessness, but rather to consider the nature of its absence (92 original emphasis).Still, with this point in mind, (and despite what has been said above), the novel does contain a scene in which Köves appears to affirm his existence.In many respects the scene is the culmination of the novel. The camps have been liberated and Köves has returned to Budapest. Finding his father and step-mother’s apartment occupied by strangers he calls on his Aunt and Uncle Fleischmann and Uncle Steiner. The discussion which follows would repay a slower reading, however again for the sake of brevity I shall focus on only a few short excerpts. Köves suggests that everyone took their ‘steps’ towards the events which have unfolded and that prediction and retrospection are false perspectives which give the illusion of order and inevitability whereas, in reality, “everything becomes clear only gradually, sequentially over time, step-by-step” (Fatelessness 249): “They [his Uncles] too had taken their own steps. They too […] had said farewell to my father as if we had already buried him, and even later has squabbled about whether I should take the train or the suburban bus to Auschwitz” (260). Fleischmann and Steiner react angrily, claiming that such an understanding makes the ‘victims’ the ‘guilty ones’. Köves responds by saying that they do not understand him and asks they see that:It was impossible, they must try to understand, impossible to take everything away from me, impossible for me to be neither winner nor loser, for me not to be right and not to be mistaken that I was neither the cause nor effect of anything; they should try to see, I almost pleaded, that I could not swallow that idiotic bitterness, that I should merely be innocent (260-261).Karolle (93-94) suggests that Köves' discussion with his uncles marks the moment where he accepts and affirms his existence and, from this point on begins to take control of and responsibility. Hence for Karolle the end of the novel depicts an ‘authentic’ moment of self-affirmation as Köves steps forward and refuses to participate in “the factual historical narrative of Auschwitz, to forget what he knows, and to be unequivocally categorized as a victim of history” (95). In distinction to Karolle, Adrienne Kertzer argues that Köves' moment of self-affirmation is, in fact, one of self-deception. Rather than acknowledging that it was “inexplicable luck” and a “series of random acts” (Kertzer 122) which saved his life or that his near death was due to an accident of birth, Köves asserts his personal freedom. Hence – and following István Deák – Kertzer suggests that we should read Fatelessness as a satire, ‘a modern Candide’. A satire on the hope of finding meaning, be it personal or metaphysical, in such experiences and events, the closing scenes of the novel being an ironic reflection on the “desperate desire to see […] life as meaningful” (Kertzer 122). So, while Köves convinces himself of his logic his uncles say to each other “‘Leave him be! Can’t you see he only wants to talk? Let him talk! Leave him be!’ And talk I did, albeit possibly to no avail and even a little incoherently” (Fatelessness 259). Which are we to choose then? The affirmation of agency (with Karolle) or the diagnosis of determination (with Kertzer)? Karolle and Kertzer give insightful analyses, (and ones which are certainly not limited to the passages quoted above), however it seems to me that they move too quickly to resolve the ‘dilemma’ presented by Köves, if not of Fatelessness as a whole. Still, we have a little time before having to name and decide Köves’ fate. Kertész’s use of the word ‘hero’ to describe Köves above – ‘the hero of my novel…’ – is, perhaps, more than a little ironic. As Kertész asks (in 1966), how can there be a hero, how can one be heroic, when one is one’s ‘determinacies’? What sense does it make to speak of heroic actions if “man [sic] is no more than his situation”? (Galley Boat-Log 99). Köves’ time, his language, his identity, none are his. There is no place, no hidden reservoir of freedom, from which way he set in motion any efficacious action. All resources have already been corrupted. From Kertész’s journal (in 1975): “The masters of thought and ideologies have ruined my thought processes” (Galley Boat-Log 104). As Lawrence Langer has argued, the grammar of heroics, along with the linked terms ‘virtue’, ‘dignity’, ‘resistance’ ‘survival’ and ‘liberation’, (and the wider narrative and moral economies which these terms indicate and activate), do not survive the events being described. Here the ‘dilemma of determinacy’ becomes the dilemma of how to think and value the human outside or after such a grammar. How to think and value the human beyond a grammar of action and so beyond, as Lars Iyer puts it, “the equation of work and freedom that characterizes the great discourses of political modernity” (155). If this is possible. If such a grammar and equation isn’t too all pervasive, if something of the human still remains outside their economy. It may well be that our ability to read Fatelessness depends in large part on what we are prepared to forsake (see Langar 195). How to think the subject and a politics in contretemps, beyond or after the choice between determination or autonomy, passive or active, inaction or action, immoral or virtuous – if only for a moment? Kertész wonders, (in 1966), ”perhaps there is something to be savaged all the same, a tiny foolishness, something ultimately comic and frail that may be a sign of the will to live and still awakens sympathy” (Galley Boat-Log 99). Something, perhaps, which remains to be salvaged from the grammar of humanism, something that would not be reducible to context, to ‘determinacies’, and that, at the same time, does not add up to a (resurrected) agent. ‘A tiny foolishness, something ultimately comic and frail’. The press release announcing that Kertész had been awarded the Nobel prize for literature states that “For Kertész the spiritual dimension of man lies in his inability to adapt to life” (The Swedish Academy no pagination). Despite the difficulties presented by the somewhat over-determined term ‘spiritual’, this line strikes me as remarkably perspicuous. Like Melville’s Bartleby and Bataille’s Kafka before him, Kertész’s Köves’ existence, insofar as he exists, is made up by his non-action. That is to say, his existence is defined not by his actions or his inaction, (both of which are purely reactive and functional), but rather by his irreducibility to either. As commentators and critics have remarked, (and as the quotes given from the text above hopefully illustrate), Köves has an oddly formal and neutral ‘voice’. Köves’ blank, frequently equivocal tone may be read as a sign of his immaturity, his lack of understanding and his naivety. However I would suggest that before such factors, what characterizes Köves’ mode of address is its reticence to assert or disclose. Köves speaks, he speaks endlessly, but he says nothing or almost nothing - ‘to no avail and even a little incoherently’. Hence where Karolle seeks to recover an ‘intoned self-consciousness’ and Kertzer the repressed determining context, we may find Köves' address. Where Karolle’s and Kertzer’s approaches seek in some way to repair Köves words, to supplement them with either an agency to-come or an awareness of a context and, in doing so, pull his words fully into the light, Köves, it seems to me, remains elusive. His existence, insofar as we may speak of it, lies in his ‘inability to adapt to life’. His reserves are not composed of hidden or recoverable sources of agency but in his equivocality, in the way he takes leave of and remains aside from the very terms of the dilemma. It is as if with no resources of his own, he has an echo existence. As if still remaining itself where a tiny foolishness, something ultimately comic and frail.3.Is this it? Is this what we are to be left with in a ‘political minimalism’? It would seem more resignation or failure, turning away or quietism, the conceit of a beautiful soul, than any type of recognisable politics. On one level this is correct, however any such suspension or withdrawal, this moment of stillness where we are, is only ever a moment. However it is a moment which indicates a certain irreducibility and as such is, I believe, of great significance. Great significance, (or better ‘signifyingness’), even though – and precisely because – it is in itself without value. Being outside efficacy, labour or production, being outside economisation as such, it resides only in its inability to be integrated. What purpose does it serve? None. Or, perhaps, none other than demonstrating the irreducibility of a life, of a singular existence, to any discourse, narrative, identity or ideology, insofar as such structures, in their attempt to comprehend (or apprehend) the existent and put it to use always and violently fall short. As Theodor Adorno wrote;It is this passing-on and being unable to linger, this tacit assent to the primacy of the general over the particular, which constitutes not only the deception of idealism in hypostasizing concepts, but also its inhumanity, that has no sooner grasped the particular than it reduces it to a thought-station, and finally comes all too quickly to terms with suffering and death (74 emphasis added).This moment of stillness then, of declining and remaining aside, represents, for me, the anarchical and all but silent condition of possibility for all political strategy as such (see Harrison, Corporeal Remains). A condition of possibility which all political strategy carries within itself, more or less well, more or less consciously, as a memory of the finite and corporeal nature of existence. A memory which may always and eventually come to protest against the strategy itself. Strategy itself as strategy; as command, as a calculated and calculating order. And so, and we should be clear about this, such a remaining still is a demonstration.A demonstration not unlike, for example, that of the general anonymous population in José Saramago’s remarkable novel Seeing, who ‘act’ more forcefully through non-action than any through any ends-directed action. A demonstration of the kind which Agamben writes about after those in Tiananmen Square in 1989:The novelty of the coming politics is that it will no longer be the struggle for control of the state, but a struggle between the State and the non-State (humanity) […] [who] cannot form a societas because they do not poses any identity to vindicate or bond of belonging for which to seek recognition (Coming Community 85-67; original emphasis).A demonstration like that which sounds through Köves when his health fails in the camps and he finds himself being wheeled on a handcart taken for dead;a snatch of speech that I was barely able to make out came to my attention, and in that hoarse whispering I recognized even less readily the voice that has once – I could not help recollecting – been so strident: ‘I p … pro … test,’ it muttered” (Fatelessness 187 ellipses in original).The inmate pushing the cart stops and pulls him up by the shoulders, asking with astonishment “Was? Du willst noch leben? [What? You still want to live?] […] and right then I found it odd, since it could not have been warranted and, on the whole, was fairly irrational (187).AcknowledgmentsMy sincere thanks to the editors of this special issue, David Bissell and Gillian Fuller, for their interest, encouragement and patience. Thanks also to Sadie, especially for her comments on the final section. ReferencesAdorno, Theodor. Minima Moralia: Reflections on a Damaged Life. London: Verso, 1974.Agamben, Giorgio. The Coming Community. Minneapolis: U of Minnesota P, 1990.———. The Man without Content. Stanford: Stanford U P, 1999.Barthes, Roland. The Neutral. New York: Columbia U P, 2005.Bataille, Georges. Literature and Evil. London: Marion Boyars, 1985.Clarke, Timothy. The Poetics of Singularity: The Counter-Culturalist Turn in Heidegger, Derrida, Blanchot and the Late Gadamer. Edinburgh: Edinburgh U P, 2005.Deák, István. "Stranger in Hell." New York Review of Books 23 Sep. 2003: 65-68.Derrida, Jacques. Rogues. 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‘We are faced today with an entire system of communication technology which is the perfect medium to host and transfer the very programs designed to destroy the functionality of the system.’ (IBM Researcher: Sarah Gordon, 1995) Despite renewed interest in open source code, the openness of the information space is nothing new in terms of the free flow of information. The transitive and nonlinear configuration of data flow has ceaselessly facilitated the sharing of code. The openness of the info-space encourages a free distribution model, which has become central to numerous developments through the abundant supply of freeware, shareware and source code. Key moments in open source history include the release in 1998 of Netscape’s Communicator source code, a clear attempt to stimulate browser development. More recently in February 2004 the ‘partial leaking’ of Microsoft Windows 2000 and NT 4.0 source code demonstrated the often-hostile disposition of open culture and the potential threat it poses to existing corporate business models. However, the leading exponents of the open source ethic predate these events by more than a decade. As an extension of the hacker, the virus writer has managed, since the 1980s, to bend the shape of info-space beyond recognition. By freely spreading viruses, worms and hacker programs across the globe, virus writers have provided researchers with a remarkable set of digital footprints to follow. The virus has, as IBM researcher Sarah Gordon points out, exposed the info-space as a ‘perfect medium’ rife for malicious viral infection. This paper argues that viral technologies can hold info-space hostage to the uncertain undercurrents of information itself. As such, despite mercantile efforts to capture the spirit of openness, the info-space finds itself frequently in a state far-from-equilibrium. It is open to often-unmanageable viral fluctuations, which produce levels of spontaneity, uncertainty and emergent order. So while corporations look to capture the perpetual, flexible and friction-free income streams from centralised information flows, viral code acts as an anarchic, acentred Deleuzian rhizome. It thrives on the openness of info-space, producing a paradoxical counterpoint to a corporatised information society and its attempt to steer the info-machine. The Virus in the Open System Fred Cohen’s 1984 doctoral thesis on the computer virus locates three key features of openness that makes viral propagation possible (see Louw and Duffy, 1992 pp. 13-14) and predicts a condition common to everyday user experience of info-space. Firstly, the virus flourishes because of the computer’s capacity for information sharing_; transitive flows of code between nodes via discs, connected media, network links, user input and software use. In the process of information transfer the ‘witting and unwitting’ cooperation of users and computers is a necessary determinant of viral infection. Secondly, information flow must be _interpreted._ Before execution computers interpret incoming information as a series of instructions (strings of bits). However, before execution, there is no fundamental distinction between information received, and as such, information has no _meaning until it has been executed. Thus, the interpretation of information does not differentiate between a program and a virus. Thirdly, the alterability or manipulability of the information process allows the virus to modify information. For example, advanced polymorphic viruses avoid detection by using non-significant, or redundant code, to randomly encrypt and decrypt themselves. Cohen concludes that the only defence available to combat viral spread is the ‘limited transitivity of information flow’. However, a reduction in flow is contrary to the needs of the system and leads ultimately to the unacceptable limitation of sharing (Cohen, 1991). As Cohen states ‘To be perfectly secure against viral attacks, a system must protect against incoming information flow, while to be secure against leakage of information a system must protect against outgoing information flow. In order for systems to allow sharing, there must be some information flow. It is therefore the major conclusion of this paper that the goals of sharing in a general purpose multilevel security system may be in such direct opposition to the goals of viral security as to make their reconciliation and coexistence impossible.’ Cohen’s research does not simply end with the eradication of the virus via the limitation of openness, but instead leads to a contentious idea concerning the benevolent properties of viral computing and the potential legitimacy of ‘friendly contagion’. Cohen looks beyond the malevolent enemy of the open network to a benevolent solution. The viral ecosystem is an alternative to Turing-von Neumann capability. Key to this system is a benevolent virus,_ which epitomise the ethic of open culture. Drawing upon a biological analogy, benevolent viral computing _reproduces in order to accomplish its goals; the computing environment evolving_ rather than being ‘designed every step of the way’ (see Zetter, 2000). The _viral ecosystem_ demonstrates how the spread of viruses can purposely _evolve through the computational space using the shared processing power of all host machines. Information enters the host machine via infection and a translator program alerts the user. The benevolent virus_ passes through the host machine with any additional modifications made by the _infected_ _user. The End of Empirical Virus Research? Cohen claims that his research into ‘friendly contagion’ has been thwarted by network administrators and policy makers (See Levy, 1992 in Spiller, 2002) whose ‘apparent fear reaction’ to early experiments resulted in trying to solve technical problems with policy solutions. However, following a significant increase in malicious viral attacks, with estimated costs to the IT industry of $13 billion in 2001 (Pipkin, 2003 p. 41), research into legitimate viruses has not surprisingly shifted from the centre to the fringes of the computer science community (see Dibbell, 1995)._ _Current reputable and subsequently funded research tends to focus on efforts by the anti-virus community to develop computer hygiene. Nevertheless, malevolent or benevolent viral technology provides researchers with a valuable recourse. The virus draws analysis towards specific questions concerning the nature of information and the culture of openness. What follows is a delineation of a range of approaches, which endeavour to provide some answers. Virus as a Cultural Metaphor Sean Cubitt (in Dovey, 1996 pp. 31-58) positions the virus as a contradictory cultural element, lodged between the effective management of info-space and the potential for spontaneous transformation. However, distinct from Cohen’s aspectual analogy, Cubitt’s often-frivolous viral metaphor overflows with political meaning. He replaces the concept of information with a space of representation, which elevates the virus from empirical experience to a linguistic construct of reality. The invasive and contagious properties of the biological parasite are metaphorically transferred to viral technology; the computer virus is thus imbued with an alien otherness. Cubitt’s cultural discourse typically reflects humanist fears of being subjected to increasing levels of technological autonomy. The openness of info-space is determined by a managed society aiming to ‘provide the grounds for mutation’ (p. 46) necessary for profitable production. Yet the virus, as a possible consequence of that desire, becomes a potential opposition to ‘ideological formations’. Like Cohen, Cubitt concludes that the virus will always exist if the paths of sharing remain open to information flow. ‘Somehow’, Cubitt argues, ‘the net must be managed in such a way as to be both open and closed. Therefore, openness is obligatory and although, from the point of view of the administrator, it is a recipe for ‘anarchy, for chaos, for breakdown, for abjection’, the ‘closure’ of the network, despite eradicating the virus, ‘means that no benefits can accrue’ (p.55). Virus as a Bodily Extension From a virus writing perspective it is, arguably, the potential for free movement in the openness of info-space that that motivates the spread of viruses. As one writer infamously stated it is ‘the idea of making a program that would travel on its own, and go to places its creator could never go’ that inspires the spreading of viruses (see Gordon, 1993). In a defiant stand against the physical limitations of bodily movement from Eastern Europe to the US, the Bulgarian virus writer, the Dark Avenger, contended that ‘the American government can stop me from going to the US, but they can’t stop my virus’. This McLuhanesque conception of the virus, as a bodily extension (see McLuhan, 1964), is picked up on by Baudrillard in Cool Memories_ _(1990). He considers the computer virus as an ‘ultra-modern form of communication which does not distinguish, according to McLuhan, between the information itself and its carrier.’ To Baudrillard the prosperous proliferation of the virus is the result of its ability to be both the medium and the message. As such the virus is a pure form of information. The Virus as Information Like Cohen, Claude Shannon looks to the biological analogy, but argues that we have the potential to learn more about information transmission in artificial and natural systems by looking at difference rather than resemblance (see Campbell, 1982). One of the key aspects of this approach is the concept of redundancy. The theory of information argues that the patterns produced by the transmission of information are likely to travel in an entropic mode, from the unmixed to the mixed – from information to noise. Shannon’s concept of redundancy ensures that noise is diminished in a system of communication. Redundancy encodes information so that the receiver can successfully decode the message, holding back the entropic tide. Shannon considers the transmission of messages in the brain as highly redundant since it manages to obtain ‘overall reliability using unreliable components’ (in Campbell, 1982 p. 191). While computing uses redundancy to encode messages, compared to transmissions of biological information, it is fairly primitive. Unlike the brain, Turing-von-Neumann computation is inflexible and literal minded. In the brain information transmission relies not only on deterministic external input, but also self-directed spontaneity and uncertain electro-chemical pulses. Nevertheless, while Shannon’s binary code is constrained to a finite set of syntactic rules, it can produce an infinite number of possibilities. Indeed, the virus makes good use of redundancy to ensure its successful propagation. The polymorphic virus is not simply a chaotic, delinquent noise, but a decidedly redundant form of communication, which uses non-significant code to randomly flip itself over to avoid detection. Viral code thrives on the infinite potential of algorithmic computing; the open, flexible and undecidable grammar of the algorithm allows the virus to spread, infect and evolve. The polymorphic virus can encrypt and decrypt itself so as to avoid anti-viral scanners checking for known viral signatures from the phylum of code known to anti-virus researchers. As such, it is a raw form of Artificial Intelligence, relying on redundant inflexible_ _code programmed to act randomly, ignore or even forget information. Towards a Concept of Rhizomatic Viral Computation Using the concept of the rhizome Deleuze and Guattari (1987 p. 79) challenge the relation between noise and pattern established in information theory. They suggest that redundancy is not merely a ‘limitative condition’, but is key to the transmission of the message itself. Measuring up the efficiency of a highly redundant viral transmission against the ‘splendour’ of the short-term memory of a rhizomatic message, it is possible to draw some conclusions from their intervention. On the surface, the entropic tendency appears to be towards the mixed and the running down of the system’s energy. However, entropy is not the answer since information is not energy; it cannot be conserved, it can be created and destroyed. By definition information is something new, something that adds to existing information (see Campbell, 1982 p. 231), yet efficient information transmission creates invariance in a variant environment. In this sense, the pseudo-randomness of viral code, which pre-programs elements of uncertainty and free action into its propagation, challenges the efforts to make information centralised, structured and ordered. It does this by placing redundant noise within its message pattern. The virus readily ruptures the patterned symmetry of info-space and in terms of information produces something new. Viral transmission is pure information as its objective is to replicate itself throughout info-space; it mutates the space as well as itself. In a rhizomatic mode the anarchic virus is without a central agency; it is a profound rejection of all Generals and power centres. Viral infection, like the rhizomatic network, is made up of ‘finite networks of automata in which communication runs from any neighbour to any other’. Viral spread flows along non-pre-existent ‘channels of communication’ (1987 p. 17). Furthermore, while efforts are made to striate the virus using anti-viral techniques, there is growing evidence that viral information not only wants to be free, but is free to do as it likes. About the Author Tony Sampson is a Senior Lecturer and Course Tutor in Multimedia & Digital Culture, School of Cultural and Innovation Studies at the University of East London, UK Email: t.d.sampson@uel.ac.uk Citation reference for this article MLA Style Sampson, Tony. "A Virus in Info-Space" M/C: A Journal of Media and Culture <http://www.media-culture.org.au/0406/07_Sampson.php>. APA Style Sampson, T. (2004, Jul1). A Virus in Info-Space. M/C: A Journal of Media and Culture, 7, <http://www.media-culture.org.au/0406/07_Sampson.php>

Les jeux sur graphes à deux joueurs et à somme nulle constituent un modèle central en informatique théorique. De tels jeux modélisent une interaction potentiellement infinie entre un système dit réactif et son environnement. Le système est considéré comme un joueur et souhaite garantir une spécification (traduite en un objectif de jeu). Son environnement est considéré comme un joueur antagoniste. Le but est de synthétiser automatiquement un contrôleur pour le système qui garantit la spécification peu importe le comportement de l'environnement, ce qui correspond à construire une stratégie gagnante dans le jeu dérivé.Une question cruciale dans cette problématique de synthèse est celle de la complexité des stratégies : si des stratégies gagnantes existent, à quel point peuvent-elles être simples et à quel point doivent-elles être complexes ? Une mesure standard de complexité des stratégies est la quantité de mémoire nécessaire pour implémenter des stratégies gagnantes pour un objectif donné. En d'autres termes, quelle quantité d'information faut-il retenir au sujet du passé pour prendre des décisions optimales concernant le futur ? Des preuves de l'existence de bornes sur les besoins en mémoire ont historiquement eu un impact important. Par exemple, de telles bornes ont mené à des preuves de décidabilité de théories monadiques du second ordre, et sont au cœur de nombreux algorithmes efficaces pour la synthèse. Les objectifs déterminés à mémoire finie (c'est-à-dire ceux qui admettent des stratégies gagnantes se limitant à une mémoire finie) sont particulièrement pertinents, car ils mènent à l'existence de contrôleurs pouvant être implémentés en pratique. Dans cette thèse, nous cherchons à améliorer la compréhension de la détermination à mémoire finie. Nous distinguons deux axes dans nos contributions.Premièrement, nous introduisons le concept de détermination à mémoire finie indépendante de l'arène, qui décrit les objectifs pour lesquels une unique structure automatique de mémoire suffit pour implémenter des stratégies gagnantes dans tous les jeux. Nous caractérisons cette propriété via des propriétés algébriques et de langages dans différents contextes (jeux joués sur des graphes finis ou infinis). Nous montrons en particulier que la compréhension des besoins en mémoire dans les jeux à un joueur (c'est-à-dire les jeux plus simples dans lesquels le même joueur contrôle toutes les actions) mène généralement à des bornes sur les besoins en mémoire dans les jeux à deux joueurs et à somme nulle. Nous montrons également que si l'on considère les jeux joués sur des graphes infinis, les objectifs déterminés à mémoire finie indépendante de l'arène sont exactement les objectifs oméga-réguliers, ce qui fournit une réciproque au célèbre théorème de détermination à mémoire finie de ces objectifs. Ces résultats généralisent des travaux précédents au sujet des objectifs pour lesquels aucune mémoire n'est nécessaire pour les stratégies gagnantes.Deuxièmement, nous identifions des classes naturelles d'objectifs pour lesquels les besoins en mémoire ne sont pas complètement établis. Nous introduisons les objectifs réguliers (une sous-classe des oméga-réguliers), qui sont des objectifs dérivés de langages réguliers. Nous donnons une caractérisation effective des besoins en mémoire de ces objectifs pour chacun des joueurs, et nous étudions la complexité de décider de l'existence d'une petite structure de mémoire. Nous considérons ensuite des objectifs plus complexes définissables avec des automates de Büchi déterministes. Nous caractérisons ceux pour lesquels le premier joueur n'a besoin d'aucune mémoire pour implémenter des stratégies gagnantes (une propriété appelée semi-positionnalité). Grâce à cette caractérisation, nous montrons que la semi-positionnalité est décidable en temps polynomial pour ces objectifs. Ces résultats complètent des travaux fondateurs sur les besoins en mémoire des objectifs oméga-réguliers
We study two-player zero-sum turn-based games on graphs, a framework of choice in theoretical computer science. Such games model the possibly infinite interaction between a computer system (often called reactive) and its environment. The system, seen as a player, wants to guarantee a specification (translated to a game objective) based on the interaction; its environment is seen as an antagonistic opponent. The aim is to automatically synthesize a controller for the system that guarantees the specification no matter what happens in the environment, that is, a winning strategy in the derived game.A crucial question in this synthesis quest is the complexity of strategies: when winning strategies exist for a game objective, how simple can they be, and how complex must they be? A standard measure of strategy complexity is the amount of memory needed to implement winning strategies for a given game objective. In other words, how much information should be remembered about the past to make optimal decisions about the future? Proving the existence of bounds on memory requirements has historically had a significant impact. Such bounds were, for instance, used to show the decidability of monadic second-order theories, and they are at the core of state-of-the-art synthesis algorithms. Particularly relevant are the finite-memory-determined objectives (for which winning strategies can be implemented with finite memory), as they allow for implementable controllers. In this thesis, we seek to further the understanding of finite-memory determinacy. We divide our contributions into two axes.First, we introduce arena-independent finite-memory determinacy, describing the objectives for which a single automatic memory structure suffices to implement winning strategies in all games. We characterize this property through language-theoretic and algebraic properties of objectives in multiple contexts (games played on finite or infinite graphs). We show in particular that understanding the memory requirements in one-player game graphs (i.e., the simpler situation of games where the same player controls all the actions) usually leads to bounds on memory requirements in two-player zero-sum games. We also show that if we consider games played on infinite game graphs, the arena-independent-finite-memory-determined objectives are exactly the omega-regular objectives, providing a converse to the landmark result on finite-memory determinacy of omega-regular objectives. These results generalize previous works about the class of objectives requiring no memory to implement winning strategies.Second, we identify natural classes of objectives for which precise memory requirements are surprisingly not fully understood. We introduce regular objectives (a subclass of the omega-regular objectives), which are simple objectives derived from regular languages. We effectively characterize their memory requirements for each player, and we study the computational complexity of deciding the existence of a small memory structure. We then move a step up in the complexity of the objectives and consider objectives definable with deterministic Büchi automata. We characterize the ones for which the first player needs no memory to implement winning strategies (a property called half-positionality). Thanks to this characterization, we show that half-positionality is decidable in polynomial time for this class of objectives. These results complement seminal results about memory requirements of classes of omega-regular objectives