James Gleick (1998) Chaos: The Amazing Science of the Unpredictable, London: Vintage. The book Chaos is very much an introduction to these issues. 'Where chaos begins, classical science stops' (1998: 3) claims James Gleick, responding to the challenge of understanding disorder, irregularities and discontinuities in nature. The study of chaos managed to draw together previously separated scientific disciplines suggesting universal patterns of behaviours of complex phenomenon, leading to new insights. The analysis of 'dynamical systems' appeared to demonstrate a underlying structure of order. In addition to relativity (on an understanding of absolute space and time) and quantum theory (on an understanding of controlled measurement), the importance of chaos is a further assault on Newtonian Physics and its 'fantasy of deterministic predictability' (Gleick, 1998: 6). As a result Physics, in seeking to be a 'theory of everything,' became required to engage in the ways in which order appears to arise spontaneously from disorder. Whereas previously physicists would look for complex causes to account for complex effects, or to add randomness to an experiment to elicit random results, it became evident that very simple and small differences in input could have overwhelming consequences in terms of output - what became known as 'sensitive dependence on initial conditions' or the 'butterfly effect' in popular culture (describing changes in weather conditions: the movement of the wings of a butterfly in one part of the world stirs the air and thus might transform to storm conditions in another part of the world; from the 1979 essay 'Predicability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?'). Plainly, the study of complex system builds upon systems theory itself. It was John Von Neumann, working in the 1950s, who realised that a complex dynamical systems contained points of stability. In turn, in the 1960s, and also influenced by the economist Benoit Mandelbrot, Edward Lorenz based on understanding the unpredictability of weather, claimed that predictability can lead to randomness (the butterfly effect if you like), but furthermore, understood randomness to contain a delicate geometrical structure (not to be random at all in fact). Such an understanding is crucial to the nature of things and the ways in which they change and might be changed within complex systems. Unstable systems, like the weather but also nature in general, almost repeat themselves but not quite. Lorenz saw this as a link between this 'aperiodicity' and unpredictability (contained in his 1963 paper 'Deterministic Nonperiodic Flow'; for my purposes, superficially like Benjamin's understanding of historical process in 'Theses on the Philosophy of History'). This was difficult to model on the computer at first - a rather determinist mechanism that could repeat accurately - but eventually algorithms were developed that could reproduce these processes (this is the kind of artificial intelligence commonly known as artificial life). In Lorenz's work, the complexities of unpredictability were modelled initially by the simple deterministic system of twelve equations and later by three 'nonlinear' equations (Gleick, 1998: 23; note: nonlinear is applied to the expression of relationships that are 'not strictly proportional'). This is also explained and visualised in the 'strange attractor,' that coincidentally looks like the wings of a butterfly, in which the fine structure can be seen within a disorderly stream of data. To show the changing relationships among three variables in a diagram of order and disorder: 'At any instant in time, the three variables fix the location of a point in three-dimensional space; as the system changes, the motion of the point represents the continuously changing variables. Because the system never exactly repeats itself, the trajectory never intersects itself. Instead it loops around and around forever.' (Gleick, 1998: 29; in a note describing the first strange attractor: the 'Lorenz Attractor' of 1963). The loops and spirals never quite meet or intersect, and reveal a 'fractal structure' of stability. Rather like the 'Cantor Effect' in which lines are seen to contain errors and not be continuous, HŽnon's attractor reveals that what appears to be lines, on magnification, are pairs, and then pairs of pairs. However, whether any two successive points appear nearby or not is unpredictable. The attractor is like a Russian doll but more extreme in that it demonstrates infinite regress, an inexhaustible sequence of folding and stretching a line (Gleick, 1998: 150-1). Strange attractors held a fascination, held a strage attraction. In unwittingly Hegelian terms, the physicist David Ruelle commented that : 'A realm lies there of forms to explore, and harmonies to discover' (Gleick, 1998: 153). With increased computer processing power, complexity was seen to be evident in the simplest of bifurcation systems. The mathematician Frank Hoppensteadt fed a simple 'logistic nonlinear equation through his Control Data 6600 hundreds of millions of times,' taking images of the computer's display at each of a thousand different values of the parameter, a thousand different tunings'. The bifircations appeared, then chaos, 'and then, within the chaos, little spikes of order, ephemeral in their instability.' (Gleick, 1998: 77) Using bifurcation diagrams too in analysing population changes, and drawing together genetics, economics and fluid dynamics, Robert May saw these simple equations as metaphor, as they were only a representation of reality not reality itself (Gleick, 1998: 77-8). Here complex behaviour might be seen to be 'machinic' (in the sense of Deleuze and Guattari describe, in excess of organic and technical) suggesting new collective and complex subjectivities. The point, here, is that simple deterministic models could produce what looked like disorder, but in fact held a delicate structure of order. May went on to apply these ideas to biological systems and in particular to the study of disease - evoking the plague and sick body or 'desiring machine' in Artaud's work. In keeping with the alleged 'universality of chaos,' this indicates something of its potential for 'intra-disciplinary' work - using Guattari's term to avoid the accusation of universality. Even the most disorderly data reveals a kind of order. That there is 'order in chaos' is a clichŽ but what is the nature of this order and how universal (where different systems are seen to behave in the same way) or indeed how totalitarian (in which they are made to)? Unpredictability leads to universality according to Mitchell Feigenbaum's theory - universality at both a structural and metrical level, not just in patterns but numbers (Gleick, 1998: 180). In biology, Darwin established a teleological theory of causality (evolution), driven by 'natural selection' not God. But this was too reductionist in another direction. The naturalist D'Arcy Thompson draws upon an understanding of dynamical systems to describe life in more complex terms of motion and responding to rhythms - not just material forms but their dynamic structure (Gleick, 1998: 202; 'Evolution is chaos with feedback' according to Joseph Ford, in Gleick, 1998: 314) - in a description that sounds uncannily like dialectical materialism (at least to a dialectical materialist it does). To stretch the connection, it is said that antagonistic balance emerges from feedback (in SolŽ & Goodwin, 2000: 100). In chaos theory, a closed nonlinear system presents inner rhythms of order and disorder - universal elements of motion (cue Engels). Complex systems, such as the human body, are places of motion and oscillation (getting poetic, Gleick says that pattern is born amid formlessless; 'Life sucks order from a sea of disorder' 1998: 299). A living organism, according to Erwin Schršdinger, has the 'astonishing gift of concentrating a 'stream of order' on itself and thus escaping the decay into atomic chaos' (in Gleick, 1998: 299; evoking DNA as life's building block). Is it partly a question of recognising this not as deterministic but as a sense of inherent agency? Clearly nonlinear aspects are a key issue in the inner workings and unpredictability of complex systems involving human organisms. Despite the lack of determinism (no particular change in mind but change all the same), this has positive potential for human agency as metaphor and in terms of real effect even if the nature of the change was unpredictable - small stirrings might lead to stormy conditions that might eventually lead to a new calm (note: in the social field, this is at least in keeping with Negri's work as a not-deterministic model of revolution). If this sounds like a description of revolution, Gleick argues this is the case in terms of scientific method at least. He describes the work of Thomas Kuhn in disputing that science necessarily progresses by the teleological accretion of knowledge and as a rational enterprise of finding solutions to identified problems (1998: 36). Instead, he argues that 'revolutions' or 'paradigm shifts' occur when scientists question fundamental assumptions, when they question orthodoxies. This may be true, but there is a sense in which he is presenting an avant-garde of science here. Surely the point is that change emerges in unpredictable ways too and from small inputs - Gleick appears to contradict himself here in perpetuating a top-down model of expertise and maverick experimentation. In parallel, Ernst Mandel's model of economic change could be seen to be similarly deterministic ultimately (discussed elsewhere). However, Mandel's model does not reject the past as it is dialectical and based on the nonlinear principles of historical materialism. Can we think about scientific discoveries in a similar way? The importance for social theory and indeed socially-engaged arts practice, is that disorderly behaviour of simple systems act as a creative process: 'It generated complexity: richly organized patterns, sometime stable and sometimes unstable, sometimes finite and sometimes infinite, but always with the fascination of living things.' (1998: 43) -- notes Bourbaki: Taking the name of a French General of Greek origin, a group of mathematicians used the pseudonym Nicolas Bourbaki to credit their work. The group stressed the primacy of mathematics insisting on a detachment from other disciplines. Rejecting the use of pictures too, they demanded that mathematics should be formal and pure - not subject to the ordure of other disciplines and the outside world (a parallel to Clement Greenberg perhaps). The computer somewhat reinforced the power of images to supply mathematical insight and led to demise of Bourbaki values (precepts, style and notation) that took such a hold on the French academy. Somewhat ironically, this remains an open source name in the mathematics world (alongside other open source names in new media such as Karen Eliot or Luther Blissett). Dust (add to notes on measurement and fractal geometry): ___________________________ _________ _________ ___ ___ ___ ___ _ _ _ _ _ _ _ _ [and so on] 'The Cantor Dust', named after the nineteenth-century mathematician Georg Cantor, describes a process: 'Begin with a line; remove the middle third; then remove the middle third of the remaining segments; and so on. The Cantor set is the dust of points that remain. They are infinitely many, but their total length is 0. The paradoxical qualities of such constructions disturbed nineteenth-century mathematicians, but Mandelbrot saw the Cantor set as a model for the occurrence of errors in an electronic transmission line.' (Gleick, 1998: 92-3) The description was useful for scientists trying to understand the nature of errors and the cause of noise. At every level of scale, Mandelbrot discovered that the relationship of errors to clean transmissions remained constant. Following this line of thinking that encourages Mandelbrot to famously ask: 'How long is the coast of Britain?' The answer is infinitely long or that it depends on the length of your ruler. Mandelbrot surmises that as the length of the measurement becomes smaller, the coastline gets longer - to the point where it is being measured at an atomic scale, when it become infinite. In addition, the measurer affected the measurement. Euclidean geometry is thus seen to be full of errors, as are other measures perhaps - value for example. When measurement is attempted in three dimensions, traditional methods become even more nefarious and fractal dimensions are required (although at a fractal level, they are simple of course). To Scholz, this is the 'humpty-dumpty effect' of never being in position to fully join two broken pieces back together again (Gleick, 1998: 106). The parts will, forever, remain incomplete. Information: It was Claude Shannon who introduced the term 'information' in the 1940s to describe the units carried over communication lines and transmissions (Gleick, 1998: 255). This information was clearly not simply words or numbers, or ideas or concepts but something more generic and abstract. Information was stored in binary on-off switches that were known as bits, and information theory became the means to measure this and to assess its errors or noise. In Shannon's information theory, ordinary language consisted of 'redundancy' - noise that is 'redundant' in terms of conveying meaning, suggesting a shorthand version and predictive messaging (sms txt msgs cm 2 mnd), as well as economical ways of compressing data. Entropy: 'Entropy' is derived from thermodynamics (and non-equilibrium thermodynamics is closely associated with complexity theory through the work of Ilya Prigogine) but also has relevance to information theory (through the work of Claude Shannon for instance). It is the term given to describe the inexorable tendency of the universe and other isolated systems to slide towards a state of increasing disorder. It is a measure of disorder in a physical system. Strange attractors, that conflate order and disorder, also increase entropy, and in a sense produce information. Information and chaos are linked: 'As a system becomes chaotic, however, strictly by virtue of its unpredictability, it generates a steady stream of information.' (Gleick, 1998: 260). Evidently, orderly disorder could be generated by simple processes, and demonstrate that chaos pulls the data into patterns (Gleick, 1998: 267) - somewhat disputing the idea of entropy and presenting an optimistic turn for praxis.