Always One Bit More, Computing and the Experience of Ambiguity

3 Always One Bit More, Computing and the Experience of Ambiguity Matthew Fuller Fun is often understood to be non-conceptual and indeed without rigour, without relation to formal processes of thought, yielding an intense and joyous informality, a release from procedure. Yet, as this book argues, fun may also be found, alongside other kinds of pleasure, in the generation, iteration and imagination of operations and procedures. This chapter aims to develop a means of drawing out an understanding of fun in relation to concepts of experience in the culture of mathematics and in the machinic fun of certain computer games. Mathematical concepts of experience, as something to be effaced, in terms of the grind of churning out calculations, understood as an acme of human knowledge bordering on the mystical or something both prosaic, peculiar and thrillingly abstract have been crucial to the motivation and genesis of computing. Experience may be figured as something innate to the computing person, or that is abstractable and thus mobile, shifting heterogeneously from one context to another, producing strange affinities between scales – residues and likeness among computational forms that can occasionally link the most austere and mundane or cacophonous of aesthetics. Among such, the fine and perplexing fun of paradox and ambiguity arises not simply in the interplay between formalisms and other kinds of life but as formalisms interweave releasing and congealing further dynamics. There are many ways in which mathematics has been linked to culture as a means of ordering, describing, inspiring or explaining ways of being in the world, but it is less often that mathematics thinks about itself as producing figurations of existence, and such moments are useful to turn to in gaining a sense of some of the patternings of computational culture.

92 Fun and Software The experience of number ‘There are no non-experienced truths’. This concise statement of the intuitionist position in mathematics comes from Luitzen Egbertus Jan Brouwer at the opening of his essay ‘Consciousness, Philosophy and Mathematics’.1 To put it the other way around, a truth, in mathematics, cannot be unknown even given a rigorous logical armature for its existence. A truth of such sort would be something like a statement of Pi calculated to an accuracy of one digit more than that which is currently known to the calculator. Brouwer’s argument would be that until that calculation is actually made, or a construction for it is given, Pi is not yet, that number but exists in a state of indetermination beyond that point. A positive way of putting this is that for Brouwer, mathematics is ‘the free activity of the creating subject’ (het scheppende subject),2 a notion rather akin to the slightly less purified notion of fun that we are working with here and having a familial relation to Oblonsky’s assertion in Anna Karenina that ‘Some mathematician has said pleasure lies not in discovering truth but in seeking it’.3 One of the key arguments of Brouwer’s intuitionism was around the principle of the excluded middle. This principle states that for every mathematical statement, either it or its negation is true. As mentioned with the example of Pi above, Brouwer believed that a number only came into existence when it was calculated rather than existing in some state of ideal reality that is simply and imperfectly cited. This meant that for Brouwer, it would be possible to imagine correctly formulated mathematical statements that could be neither true nor false. Indeed, for him, no statement about a mathematical entity such as an infinite set could be known precisely in such terms, they had to be experienced, enumerated.4 The argument is against formalism in one way, and idealism in another, against the idea of universal pre-existing numbers. Brouwer’s position is a kind of constructivism, building a form of inductive reason that is not determined in advance but composed of a rigorous relation to a world of abstraction. My intention is not to propound Intuitionism here, but to use this work as a starting point to think through some of the context in mathematics and logic in which the computer was conceptualized, and then to draw this out in relation to the question of fun, in the broad, passionate, even obsessive sense of the word that Olga Goriunova proposes for this volume. This will lead to asking whether fun needs to be experienced, and by whom or what, or if such experience can also move through, for instance, computers? Further, how does fun circulate, what is

Always One Bit More, Computing and the Experience of Ambiguity 93 its processuality when it also becomes computational and, to go in the opposite direction of tracing the ambit of fun to a wider assemblage, what forms of computing make such experience most palpable? The way that intuitionism focuses mathematical thinking on experience, in the work of Brouwer, (but to some extent also that of Henri Poincaré, a mathematician who always put the experiential and interpretative nature of his subject to the fore)5 allows us to draw out some filiations to the experiential nature of software. Formalist mathematics, of the kind Brouwer was arguing against, presupposed that there were undiscovered truths that could be set out, in advance of their actually being known, by axiomatic reasoning which would implicitly have realized them. That is, the axiom comes before the number and before the calculation. For intuitionists, this makes the whole of classical mathematics a simply syllogistic exercise, and reduces its status as a science. Brouwer proposes four forms of conscious experience: stillness, sensational, mathematical and wisdom, which are arrayed in a linear progression of state each of which builds an understanding of mathematics as primarily epistemological and mystic in that ‘research in the foundation of mathematics is inner enquiry with revealing and liberating consequences’.6 As is well known, one of the key controversies around the programme of formalist mathematics, and especially that of David Hilbert, was that generated by Alan Turing in work that led to the formulation of automatic computing in the famous paper, ‘On Computable Numbers with an Application to the Entscheidungsproblem’.7 If one reads Turing’s work with an eye to that of Brouwer, we can see some interesting correlations. Brouwer’s definition of real numbers is propounded in the second part of Turing’s short Correction published in the following year and which sets out a clarification of what is meant by a computable number.8 While Brouwer opposed the idea of completed infinities as something that precludes experience, he tried to bring together the idea of the discrete and the continuous in a series of numbers, say all those between zero and one. In the act of working these out, the sequence of numbers that you generate is that series, in its state of unfolding in your mind. Charles Petzold notes that ‘In the intuitionist continuum, real numbers are always incomplete – unfinished and never to be finished…’.9 In this sense, numbers are like drives: eternal combustion engines, perpetual commotion machines and, as such, intuitionism situates mathematics in time. (One experiences numbers in relation to others, their ‘two-ity’, in that

94 Fun and Software the number one already implies a movement towards two. Numbers imply a relation to the continuum as an ongoing.) In §9 of ‘Computable Numbers’ Turing argues that a machine carrying out an algorithmically defined task is, at a certain level of abstraction, mathematically equivalent to a human carrying out the same task. If a machine finds the problem unsolvable given the algorithm, then so too would a human. There is a network of such problems that Turing works through at various times in the relationship between computing and intelligence,10 but here Turing’s machine provided a direct link to the work of Brouwer in that a calculation is always a process, occurring over time.11 It is not (in terms of the problem staged in the paper) finely predictable – there is no machine that can decide in advance of the computation of an infinite set what the next number of that set must necessarily be; the work is limited to actually computable numbers, ‘the subset of the real numbers that can actually be calculated’.12 Needless to say, there is also an abrupt difference between their approaches, since Turing’s work is here predicated upon the ability to disengage, or abstract, mathematical capacities. Whether one takes an intuitionist or constructivist approach, computation can be said to have a quality that is to certain a degree participative and processual. For Brouwer, this process was experience. Turing, however, liked to play with the ambiguity between the human and the machine, the slippage of one into the other and their differentiation, indeed the radicality of the Turing Machine, as Alonso Church named it, was its invigoration of mathematical logic with things from outside it.13 At this point one must consider one of the aspects of the discussion of Brouwer developed by Chris Atten whose phenomenological reading suggests that a key difficulty in the promulgation of intuitionism is its lack of reflexivity; the position of the mathematician is fundamentally solipsistic.14 Atten argues that Brouwer’s figuration of mathematical consciousness (understood as four forms of thought) cannot be reflected on because to do so would require a further form of consciousness capable of such reflection and the production of figures of mutual understanding. Because the Turing Machine alienates mathematics from the merely human creative subject, without succumbing to idealism, while still maintaining a relation to an understanding of computation as experience, its form of constructivism offers the possibility of articulating, if not necessarily achieving, such reflexivity. But equally in the movement of experience to computers, circulating among machines, networks, codes, interpreters, interfaces and users, of various kinds, intents, states and arrangements, the simply phenomenological

Always One Bit More, Computing and the Experience of Ambiguity 95 interpretation of the human individual requires supplement. And the way in which such a reflexive understanding of computational experience is constructed is emphasized, or becomes more explicit and tractable, in some kinds of procedures than others. MMORPGs and the demand for experience One way of understanding, via a difference, this experience of slippage crosses over into the cultural understanding of ‘fair-play’ in games, and those that hack them. Here, there is an implicit requirement that computational processes are experienced, as something to be judged and interacted with on the basis of human skill. To experience them otherwise is to ‘cheat’. An example of the persistence of such a requirement is in the rules governing many MMORPGs (massively multi-player online role-playing games) such as World of Warcraft or Runescape. Here, the use of macros, AutoTypers (to repeat messages), AutoClickers (to repeat functions) and other kinds of bots, is generally deemed to be an offence, a violation of the game.15 But such things, particularly bots, can, in turn, be a means of having fun with the rule sets of online gaming, through griefing or more interesting means. On the one hand, the prohibition of bots argues for an assumed level playing field, that real users are playing the game, not sets of competing scripts or mechanical devices tapping keyboards. In turn, the use of gold farmers, or professional players, in MMORPGs is seen as a betrayal of such an experiential requirement, but also as part of the game, when players are increasingly plugged into wider sets of economic systems through games as backchannels.16 The demand for a certain kind of subject as the experiential target of the operation and manipulation of procedures, symbols and interactions that constitute such games suggests that computing is experiential, but experience is itself subject to what might politely be called ‘variation’. Machinic and distributed experience of computing In discussing computing as experience this chapter is not concerned with arguing that computers have or experience fun in the same way that humans do, nor even that the latter classification of entity experience any particular kind of fun, but

96 Fun and Software that computation itself can be fun, a form of passionate involvement that in some circumstances can also be said to be machinic and distributed. It is machinic in the sense that it implies multiple elements in states of relation and distributed in the sense that it occurs across such relations, partly in the way in which different materials and their handling of processes conjugate and yield time. As processing is distributed, a computing machine or piece of software might be said to take part, in its own terms, in Brouwer’s sense, of the excluded middle. An example of such machinic and distributed interweaving can be found in the software art project Human Cellular Automata, which proposes that such a condition can be experienced.17 But we can also suggest that, given the constructivist slant of Turing’s work, there may be some other form of experience, or to be more precise, open-ended undergoing, of mathematics that would not be human in the sense that Brouwer argues for, but neither would it be strictly simply axiomatic and deductive. In order to talk about circulating fun as being distributed and processual, it is useful to turn to some of the qualities of such relations, and to start to do so through computing, maintaining a link to computing as experience. Brouwer talked about the experience of the creating mind, and proposed that mathematics was the ultimate exercise in free thought – both in the sense of mathematics as the purest form of thought as the realization of the mind without any intrinsic relation to other aspects of the world, and also, because of that quality, as the most literally unencumbered, unfettered thought. It is useful to maintain this sense of the unencumbered quality of thought as a modality of the powers of abstraction. Here though, such abstraction can also be seen to emphasize, and provide a precondition for, the combinatorial nature of thought in relation to and as part of other forms of experience, and, via Turing, the constituent heterogeneity of computing. In order to get a sense of the nature of such experience it is useful to map some forms of relation that are not quite of the same order as this image of thought, but are also significant in the experience of computation – ambiguity and paradox. Ambiguity and paradox In his book, How Mathematicians Think, William Byers differentiates the formalized, algorithmic means of doing maths from the moment of discovery. This is done in a somewhat different mode to Brouwer, in that Byers aims to

Always One Bit More, Computing and the Experience of Ambiguity 97 produce an alliance, or at least draw out affinities, between the constructivist and idealist or formalist schools through an emphasis on ambiguity, but this idea of ambiguity, one that Byers establishes through accounts and example from many areas and ages of mathematics is one that is also processual and experiential. Ambiguity is a state which admits of more than one interpretation, or, more precisely, to exist in a state in which as Byers puts it two (or more) ‘self-consistent but mutually incompatible frames of reference’18 have to be inhabited. In disciplinary terms we can think of the overlap of two not quite commensurable formalisms such as that between logic and mathematics, or, in the example of geometry and arithmetic, fields which sometimes coincide, but which are not entirely mappable one to the other without causing interesting effects. As an example of such effects, one sees ambiguity on occasions when the idea of a number as a quantity and as a process are linked, for instance in the number ‘one third’ being equal to 0.3 recurring in decimal notation. In the second version, knowing a number also involves calculation but also requires a sense of the unreachable limit.19 For Byers, understanding these two forms of the number requires a creative act, one with a certain affinity to Brouwer’s intuition. Interestingly here, we are also talking about different forms of notation. There is perhaps a case for a media theory of mathematics allied with ethnomathematics.20 One that moves from pen and paper to one dimensional grids, through independent realms of abstract objects and the discourses that sustain them, to minds as putative entities, to other exciting forms of stationary.21 But to move into more fully aesthetic terms, ambiguity emerges from the existence of two or more of these interpretative states. Ambiguity is not simply something requiring the gentle discernment of nuance or the capacity to pleasure in the multifaceted, which it certainly can be. It can also present a being with a torn and bleeding reality in which one scale of a life is incommensurable with, yet bound to, another scale that it cannot avoid. Its painfulness may also combine with another layer, that of the joy of being able to step outside of an overdetermination. Ambiguity manifests too as the double bind or the infernal alternative, experience squeezed into systemic imperatives, as much as the subtle flickering of recognition of multiply nuanced being.22 As a form of experience we can ask of different occurrences of ambiguity: how deeply can or must one inhabit ambiguity, what are its roles and latencies at different conjunctures of experience?

98 Fun and Software Given such an understanding of ambiguity, we can say that a paradox is a recursively nested ambiguity. That is, ambiguity is a statement or condition that contains the implication or fully stated condition of incompatibility with itself. Paradox is largely logical and semantic. Both are essential to software. Both paradox and ambiguity draw out the experiential and the temporal. Paradox breaks with the immediate time typical of statements made in first-order logic by forming a loop back to the condition of the formation of such thought, the decision to think, or the accident of thought. Both ambiguity and paradox are aesthetic modes that find particular forms in computation. Fun becomes systemic If computing is experiential, something that can be said to have roots in its mathematical underpinnings, how does such experience become fun? And then there is the question of aesthetics. Fun is often presented as wholesome enjoyment, a state of amusement in which the cares of the world are rinsed from us. In the entrepreneurial cast of the term, fun may also be an exhilarating intellectual and emotional overinvestment in a thing that leads to a technical and, perhaps, financial yield. But fun is itself ambiguous, being, in many cases, also perverse. In an epigraph to his Cent mille milliards de poèmes Raymond Queneau cites Alan Turing as saying that ‘[o]nly a computer can appreciate a sonnet written by another computer’.23 In order to enjoy such a poem, Queneau suggests, one would have to be something other than a straightforward literary reader. There is a funny set of unpackings here, the proposition of computer intelligence, one that would not correspond to that of humans, or things of other kinds, thus also implying a queer sympathy among a kind, but there is also a sense in which recognizing computing as cultural is somehow preposterous, and at the same time delightful, and indeed Turing, in the article, ‘Computing Machinery and Intelligence’24 is intrigued by mis-identification and guessing, a playfulness at the root of computing. There is a relay between computers set up by this proposal, that is not one of strict computation in the sense of an immediate realization of first-order propositions manifest at the level of flows in circuits, but recognition and appreciation as yielding, revealing and hiding, enjoying something over time. Turing’s understanding of experience in this article is quite different to that established by Brouwer. Turing’s is so concretely

Always One Bit More, Computing and the Experience of Ambiguity 99 formulated in abstract terms that it can pass from one or more modes of realization to another, the human computer to the abstract machine. Brouwer’s is so interwoven in the experience of the abstract that it singularizes experience, is unutterable in words, but they are both coupled with a relation to knowledge, to a subject and to a kind of existence.25 And, in the circulation of experience through time, we can say that is something that, as Turing exemplifies, in both his paper on the entscheidungsproblem and the epigraph used by Queneau, experience is also something that moves around, beyond people into devices, networks, arrays, processes. But in doing so, experience or undergoing itself undergoes changes in kind. Thus we can reframe the suggestion that, in the conditions of computational and networked digital media, in software cultures, ambiguity and paradox become machinic and distributed. Such process may not be fluid and smooth, but perhaps halting, lame, encountering boredom. We can say that some of this is echoed in the repetitive language and constrained behaviours worked through by Beckett, in Quad,26 or other cases of his more procedural writings and scripts. As Deleuze asks, ‘Must one be exhausted to give oneself over to the combinatorial, or is it the combinatorial that exhausts us, that leads us to exhaustion – or even the two together, the combinatorial and exhaustion?’27 Complementary to this image, we can propose fun as a tendentially more joyous involvement in the combinatorial, one that does not necessarily run counter to the exhausted, but places finitude in undecided relation to the continuum, as for instance in phasing in music (exemplified in Steve Reich’s ‘Drumming’28 or the polyrhythmicality of breakbeats) but also to escape and to the powers of invention in relation to constraint, indeed, to find the two as mutually, ambiguously entangled. Machinic funs For Guattari, ‘The machine, every species of machine, is always at the junction of the finite and infinite, at this point of negotiation between complexity and chaos’.29 Here, in machinic terms, are means by which the combinatorial may connect with exhaustion, but also, recursively, with other forms of combinatorial, generating paradoxes, ambivalence multivalence. The machinic is part of a larger set that Guattari compares to Kleinian part objects, entities that rely for their

100 Fun and Software actuation on kinds of coupling, tripling and connection, and which in such connection create being. The search for such coupling or tripling, their state of two-ity, results in sets of projective-introspective relations, generating subjectivities.30 Such connectiveness in Klein is ambivalent, ‘bad’ as well as good and exploratory; a generator of phantasy, nourishment and its denial; despisement, copious muddling and ravages of yearning. One paradoxical example of a machinic fun, which resonates with the concern for an ethnomathematical analysis of notation, arises from a use of numbers that is not mathematical but literary yet still combinatorial. Claude Klosky’s text ‘The First Thousand Numbers in Alphabetical Order’31 is a subtle and in a certain sense systematically hilarious work. Its simple procedure is to list the alphabetically written versions of the numbers from one to one thousand in alphabetic rather than numerical order. One could say that this is a kind of formalistic triumph, with an ‘irrelevant’ set of ordering principles that is axiomatically described by the work’s title, yet here we are drawn to learn that not all formalisms are of the same order and that in the shifting logic of this procedure there is the possibility of eliciting something new in the ‘proper matter’ of one by the application of another. The specific quality of the work is manifestly only recognizable through experience, that of actually working through at least some of the text. To read the whole one must be solemn, or raptured, a chatbot or somehow else unlike a reader of text, to take on, in Craig Dworkins’ terms, the role of a parser,32 and to do so invites the mind to tingle with a kind of procedural pleasure that is somehow always syncopating the many itchy transitions between boredom and surprise. A formalism as such is itself always ambiguous, itself partial as it yields to, merges with or elides the suctions and trickiness of the different generative capacities of matter: alphabetism and number; the ego and the creative subject; computing and the ambiguities of fun. Minecraft ALU and CPU by theinternetftw A recent encounter that brought about such a pleasure was that with screencapture documentation of the construction of two of the three basic components of a computer in the MMORPG Minecraft by a hacker named theinternetftw. Minecraft is a slightly clunky but very endearing looking game, still in Beta at the time of theinternetftw’s project, but one that has sophisticated sandbox

Always One Bit More, Computing and the Experience of Ambiguity 101 gameplay untrammelled by set plots or points-systems and with a growing and avid user-base. Minecraft is somewhat like an enormous constructor set, in that everything is composed out of cubes, but one with monsters that attack you, wandering wildlife known as mobs or ‘mobiles’, a well-developed game physics of different natural materials (such as wood, iron, diamond, soil) that are to be sourced, worked and assembled and, in posing the highly manipulable components of the world, essentially form the core of the game. Minecraft is also cool because, as the name suggests, players go under the surface of the game, into the ground. Users make elaborate traps, laggily rendered rollercoasters, volcanos spewing bitmapped lava, underwater glass tunnels with which to view pulsating rectilinear squid, meat factories (which mobs are lured into and elaborately slaughtered and processed) and explore undocumented features and glitches. In turn, Minecraft takes the sandbox principle as a core recursive form. Users create enormous amounts of media around the game, and thousands of playergenerated maps where games and scenarios developed within the game are circulated online as additional files allowing for different rule sets and genres to be adopted and played with on top of the Minecraft engine. Importantly, for this project and many others, one of the elements of the game, a type of material called Redstone, allows you to create basic logic circuits.33 The fundamental elements of a computer include an arithmetic logic unit, a central processing unit and a program counter. The first of these was made in Minecraft by theinternetftw in Autumn of 2010, the second a few weeks later.34 Invented by John von Neumann, an arithmetic logic unit performs addition and subtraction.35 More sophisticated ALU also do multiplication and division (as an extension of addition and subtraction) and include the Boolean logic of AND, OR, XOR (to return to Brouwer, the Exclusive Or being a way of framing numbers that generates the excluded middle). To make an ALU out of basic components such as TTL chips is a familiar rite of passage for electronic engineering students but it is the particular way in which this has been done which raises theinternetftw’s work above the level of such an exercise. Part of what is contradictorily fun about constructing a computer in this way is that working in Minecraft is pretty laborious. The scale of the circuit compared to that of the view of the player dramatically reverses the ratio that we are used to in viewing circuits – each byte of memory here corresponding to a block of space. The system is enormous and each block has to be put in place, one by one, mouse-click by mouse-click. It’s also not an environment that is easily scripted, and this is a clunky process. It is therefore a relatively

102 Fun and Software non-obvious situation in which to make such a machine – especially given that the Redstones need recharging every 15 blocks, so that workarounds have to be made to cope with this. Examining this device moves us away from the idea of computation as something increasingly fast, increasingly small, into something that you can walk around, need to fiddle about with, fine-tune and observe happening. As in many domains of application, computation moves out of the box into more and more aspects of space36 this is a project that generates a complementary dynamic, establishing computation in a way that is only legible as a spatial experience. Such work also draws on the tradition of emulation hacks in which say, to exaggerate slightly, a Cray supercomputer would be used to emulate a Sinclair Spectrum, running a Cray emulation. A computer becomes its own bug, but that bug is another machine, running itself. Formalisms mesh with, irritate, propitiate and explore each other, producing luminous declivities, skittering patterns, banqueting halls of mirrors, slag heaps of unprocessed symbols, states and efflorescences cross-pollinating at a myriad of uneven rates and via an entire zoology of third parties. In this regard, there’s also something fascinating about using such a relatively graphically naff system to draw out what is now such a well understood piece of engineering, rendering an iconic structure into something like a megalithic airport terminal, but one in 128-bit colour, with rectilinear sheep, pigs or chickens wandering around, and one that at night runs the risk of being infested with zombies.37 Megalithic chuckles So how does the Minecraft computer inflect the notion of machinic and distributed fun? There is a version of the excluded third in Philip Agre’s description of technical knowledge in which a computer model ‘either works or does not work’38 but also a recognition of its insistence on empiricism in that ‘[c]omputer people believe only what they can build, and this policy imposes a strong intellectual conservatism on the field’.39 The process and nature of computation is excluded in the first, but is taken as a source of truth in the second, and here mathematics enters into its various kinds of relation to and distance from engineering, a discipline whose realism may often make it inventively as well as demonically otherworldly. Here though a totemic piece of computer architecture, when translated into another domain of realization, that

Always One Bit More, Computing and the Experience of Ambiguity 103 of Minecraft with all the curiosities and interest of its gameplay, logic and visual and physical quirks, becomes something else, something fascinating, magnificently ridiculous, and is done in a way which allows it to be explored. Computing becomes about its experience as such, the machine is, in this instantiation, slower than many of the first electronic computers. Fun in software here lines up with a hackerly processual passion at a meeting point between complex orderings of many kinds but also enrols the jointly incremental and transversal nature of invention which produces, through ambiguity, the capacity not only to see things in different lights, but also to draw hitherto unworked capacities out of them. Akin to Turing’s symphony written for another computer, it is a computer made, paradoxically, within a computer. One can say, triumphantly, ‘Look, I’m computing with the computer on my computer!’ But it is an experience that also circulates via other means, drawing us into the monumental excitement of being able to add two to three via an enormous stone mechanism composed of pixels. In such a paradox, and in a state of multiple ambiguities, computing finds itself reformulating the machinic compulsion to connect, refigure and experience the partial object. There is indeed a deep ambiguous fun in computing, in achieving such a microcosmic achievement on an epic scale. Notes 1 2 3 4 Brouwer, Luitzen Egbertus Jan, ‘Consciousness, Philosophy and Mathematics’, Proceedings of the Tenth International Congress of Philosophy (Amsterdam, 11–18, August 1948; Amsterdam: North-Holland, 1949), 1235–49. See for the context of this debate Gray, Jeremy, Plato’s Ghost, The Modernist Transformation of Mathematics (Princeton, NJ: Princeton University Press, 2008). Brouwer, Luitzen Egbertus Jan, ‘Volition, Knowledge, Language’ (1933), in W. van Stigt, Brouwer’s Intuitionism (Amsterdam: North-Holland, 1990), 418–31. (The original title, Willen, Weten, Spreken, implies that, rather than abstract categories, these are things that are experienced as willing, knowing and speaking.) See also, for a discussion, Mark van Atten, On Brouwer (Singapore: Thomson Wadsworth, 2004), 64. Tolstoy, Leo, Anna Karenina, trans. Louise and Aylmer Maude (London: Vintage, 2010), 192. For an approach which translates between formalism and intuitionism, see Kolmogorov, Andrei Nikolaevich, ‘On the Principle of the Excluded Middle’

104 5 6 7 8 9 10 11 12 13 14 15 16 17 Fun and Software (1925), in From Frege to Goedel, a Sourcebook in Mathematical Logic 1879–1931, ed. Jean van Heijenoort (Cambridge, MA: Harvard University Press, 1967), 414–37. See, for example, the chapter, ‘On the Nature of Mathematical Reasoning’, in Poincaré, Henri, Science and Hypothesis (New York: Dover, 1952). Brouwer, Luitzen Egbertus Jan, ‘Consciousness, Philosophy and Mathematics’. Turing, Alan, ‘On Computable Numbers, with an Application to the Entscheidungsproblem’ (1936), in The Essential Turing, ed. B. Jack Copeland (Oxford: Clarendon Press, 2004), 58–90. The problem consists of finding the limits to computability, problems that are too hard for an ‘effective procedure’ (a step-by-step method of working) to solve due to the nature of the number to be calculated. Turing, Alan, ‘On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction’ (1937), in The Essential Turing, 94–6. In this note, among other things, Turing specifies an intuitive definition of the term ‘computable number’. Without specific mention of Turing, an excellent exploration of the philosophical consequences of the intuitionist concept of number can be found in Evans, Aden, ‘The Surd’, in Virtual Mathematics, The Logic of Difference, ed. Simon Duffy (Bolton: Clinamen Press, 2006), 209–34. Petzold, Charles, The Annotated Turing (Indianapolis, IN: Wiley, 2008), 317. See, e.g. Turing, Alan, ‘Computing Machinery and Intelligence’, in The Essential Turing, ed. B. Jack Copeland (Oxford: Clarendon Press, 2004), 433–64. Petzold, The Annotated Turing, 307. Ibid. See, Hodges, Andrew, ‘Alan Turing and the Turing Machine’, in The Universal Turing Machine, A Half-Century Survey, ed. Herken, Rolf (Vienna: Springer, 1995), 3–14. van Atten, Markus S. P. R, Phenomenology of Choice Sequences (Utrecht: Zeno Institute of Philosophy, 1999), 73. There are other reasons for this prohibition as such programs are also occasionally Trojan Horses. See, e.g., Doctorow, Cory, For the Win (London: Harper Voyager, 2010). Castronova, Edward, Synthetic Worlds (Chicago: University of Chicago Press), 2005. This project, first performed at the Software Summer School in London in 2000, and subsequently elsewhere, consists of a crowd of people arranging themselves into a grid formation and carrying out a set of instructions inspired by James Conway’s ‘Game of Life’. See, http://www.spc.org/fuller/projects/the-humancellular-automata/ (accessed 12.12.2013).

Always One Bit More, Computing and the Experience of Ambiguity 105 18 Byers, William, How Mathematicians Think, Using Ambiguity, Contradiction and Paradox to Create Mathematics (Princeton, NJ: Princeton University Press, 2007), 28. 19 Ibid, 40–1. 20 Brouwer, who thought of language simply as a shed residue of, or impediment to, mathematics, on the one hand, or an exact technique for memorizing mathematical constructions, on the other (see his Cambridge Lectures on Intuitionism (1951), (Cambridge: Cambridge University Press, 1981), would probably be appalled at the idea. Edsger Dijkstra, on the other hand, always alert to the medial conditions of thought, suggests, in EWD 1000, that ‘No future history of science can ignore the change the advent of the copying machine has made’. 21 Of signal relevance here is the approach exemplified by Bernhard Siegert in ‘Cacophony or Communication? Cultural Techniques in German Media Studies’, trans. Geoffrey Winthrop-Young, Grey Room, 29 (2008): 26–47. 22 For the double bind, see, Bateson, Gregory, Jackson, Don D., Haley, Jay and Weakland, John H. (1956), ‘Towards a Theory of Schizophrenia’, in Towards an Ecology of Mind (Chicago: University of Chicago Press, 2000), 201–27. The ‘infernal alternative’ is posed by Isabelle Stengers and Phillipe Pignarre in Capitalist Sorcery, Breaking the Spell, trans. Andrew Goffey (London: Palgrave Macmillan, 2011). 23 Turing in Queneau, Raymond, Cent mille milliards de poèmes (Paris: Gallimard, 1961). 24 Turing, ‘Computing Machinery and Intelligence’. 25 Here we can develop a relation to Foucault’s understanding of experience. Looking back he reformulates, to some extent, a thematic running through from his earlier to his later work – experience. That is to say that ‘forms of knowledge, matrixes of forms of behaviour, and the constitution of subjects and modes of being’ are experiential, rather than static. Foucault, Michel, The Government of Self and Others (Michel Foucault: Lectures at the Collège de France 1982–3), trans. Graham Burchell (London: Palgrave Macmillan, 2010), 5. 26 Beckett, Samuel, ‘Quad’, in Collected Shorter Plays (London: Faber and Faber, 1984), 289–94. 27 Deleuze, Gilles, Essays Critical and Clinical, trans. Daniel W. Smith and Michael A. Greco (London: Verso, 1998), 154. See also, Beckett, Samuel, Quad et autre pièces pour la television suivi de L’épuisé par Gilles Deleuze (Paris: Éditions de Minuit, 1999). 28 Reich, Steve, ‘Drumming’ (1970–191). 29 Guattari, Félix, Chaosmosis, an Ethico-Aesthetic Paradigm, trans. Paul Bains

106 30 31 32 33 34 35 36 Fun and Software and Julian Pefanis (Sydney: Power Institute, 1995), 111. See, for further discussion of such an approach, Guattari, Félix, The Anti-Oedipus Papers (Los Angeles: Semiotext(e), 2006) and the riddling of reality with such machines in Anti-Oedipus: Deleuze, Gilles and Guattari, Félix, Anti-Oedipus, Capitalism and Schizophrenia, trans. Robert Hurley, Mark Seem and Helen R. Lane (London: Athlone, 1984). The term, part of a general discussion in Object Relations theory, runs through much of Klein’s work. See, e.g., Mélanie Klein, ‘Some Theoretical Conclusions Regarding the Emotional Life of the Infant’, in Envy and Gratitude and Other Works 1946–1963 (London: Hogarth Press and the Institute of Psycho-Analysis, 1975). Klosky, Claude, ‘The First Thousand Numbers in Alphabetical Order’, in Against Expression, an Anthology of Conceptual Writingi, (eds) Craig Dworkin and Kenneth Goldsmith (Chicago: Northwestern University Press, 2011), 148–60. It is notable that this piece of work would change each time it is translated into another language as the alphabetical ordering of the letters would differ, rendering the formalism that generates the work, as given in its title, fundamentally playful. Dworkin, Craig, Parse (Berkeley, CA: Atelos, 2008). For a description of the use of Redstone to create circuits, see: http://www. minecraftwiki.net/wiki/ (accessed 12.12.2013). For video of the first ALU, see: http://www.youtube.com/watch?v=LGkkyKZVzug; for initial documentation of the CPU, see: http://www.youtube.com/ watch?v=sybOqi_dgX0&feature=related. The program counter and a revised ALU (of 11 October 2010) is shown at: http://www.youtube.com/watch?v=sybOqi_ dgX0&feature=related (all accessed 12.12.2013). The cheerful and laconically enthusiastic tone of the commentary by theinternetftw make these a pleasure to watch. The full computer seems not to have been built, however a number of others have since developed Minecraft computers of various sorts, including, in June 2011, a dual core CPU by anomalouscobra and jomeister15, see: http://www. youtube.com/watch?v=EaWo68CWWGM&feature=related/, and in September 2011 a full gaming computer Redgame by laurensweyn, a video of which is at: http://www.youtube.com/watch?v=lB684ym3QY4&feature=related (all accessed 12.12.2013). von Neumann, John, First Draft of a Report on the EDVAC, Contract No.W-670-ORD-4926, between the US Army Ordnance Department and the University of Pennsylvania (University of Pennsylvania, Moore School of Electrical Engineering, 30 June 1945). See Kitchin, Rob and Martin Dodge, Code/Space, Software and Everyday Life (Cambridge: MIT Press, 2011).

Always One Bit More, Computing and the Experience of Ambiguity 37 The slight naffness of Minecraft, its clunky aesthetics, the laboriousness of the construction work within it, alongside the exuberance of imagination involved and expended in it by millions of players is a subtext of the hugely popular Yogcast series of comedic, lackadaisical commentary on Minecraft, posted on YouTube. In the last few years, since Minecraft has come out of beta, a highly active scene of ‘Let’s Play’ video makers has emerged with their own channels. 38 Agre, Philip, Computing and Human Experience (Cambridge: Cambridge University Press, 1997), xi. 39 Ibid., 13. 107