Models, Ideas, Eras.
Use of Models.
Models are very useful things, allowing us to visualise larger structures in miniature. Of course it's very important to choose an appropriate model and be exact about it's conditions of use and acknowledge it's limits; any model chosen carries with it both the bias of the modeller and that of the user.I would even go so far as to say that the history of philosophy and thought could be modelled through a model of models... Really exciting models, or at least those in my eyes, are those which acknowledge their own limits, but also sit on the edges of falling apart. De Landa is interesting because each of the models he provides transforms into another, it doesn't lose usefulness, but fails to make the phase shift, and is so always stranded in it's own domain, it's own basin of attraction. It's the bit in between the domains of models that holds charge.
Warning! This could be a distracting deviation...Too late to be included in the body of this work, I started reading another models book `Mind Tools, the five different levels of Mathematical Reality'. Just for the hell of it, I will summarise it very briefly. His modelling is less useful for this current essay because it is about Math and not Machine paradigms, but since the two are somewhat connected, I thought it would make an interesting diversion...
Rucker defines the `five levels of mathematical reality' as...
1. Number. This corresponds to dealing with points on a line, the line being that of real numbers. An examination of the archetypes of small numbers and Phythagorian principles, as well as numerology, shows how common and ancient this way of dealing with the world is. Number is Digital is `How Many?' is discrete.
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2. Space. The description of space is, initially, the study of geometry, then increasingly complex systems - quadratics, conics, polynomials,et al. Space is the study of the smooth: Space is analog is `How much?' is continuous.
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3. Logic. The first order of thought that links number and space. By letting a symbol stand in for a complex reality, logic allows the use of new languages like algebra, and the elaborate assemblage of mathematical theories. Logic is digital is synthetic.
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4. Infinity. Also connects number and space by breaking space into infinitely many distinct points; ie between 0 and 1 is an infinite number of possible fractions. The language of infinity is calculus; differentiation and integration provide ways of thinking of a curve as an infinite staircase of points. While infinity is complementary to logic, it also passes beyond it. Godel proved that no finite logical system can provide all the facts about an infinite set of natural numbers. Infinity is analog is analytical.
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5. Information. Because this is a current phase shift concept, information is harder to define. An number of information theories exist, the earliest being Information Theory, realised by Shannon at Bell labs in the 1940's. He was the formulator of the idea data `bits'. Moving beyond this we get theories like Cybernetics, AI, neural networks. In general information rests in three concepts; information length (and the study of how much information can be represented by less information; ie compression), complexity and understanding. Information can integrate all the four modes above, and communicate between them openly. Viewed in this way information is comprehensive is translation, is communication.
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With these understandings, Rucker goes on to give his progression of mathematical models and their eras:
1. Middle Ages. Written language provides the means to label things, and scholarship concentrates on accumulating lists and cases. Simple numbers were used as a part of the process of labelling, and corresponds to the belief that the world was a `stack' of principles and orders.
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2. Renaissance. With the rise of perspective, space becomes manipulable by math. World view changes to become a set of objects in space, rather than names in God's mind. Things came to be viewed as spatially oriented; Galileo asserts that the space that planets are in in fundementally the same space that people occupy. The distribution of printed books also has subtle effects; the act of reading induces people into using an enriched imaginary space.
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3. Industrial Revolution. The advent of the machine sees things viewed as logical processes. Newtons `Principia' is a logical system, a search to provide a set of universal laws to describe the world's machinic nature. Economics follows a model of the society as a large machine. Boole defines a symbolic logic. (This is where De Landa starts, with the clockwork mechanism, a predetermined logical series giving rise to a certain effect).
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4. Modernity. Limits are seen to press in around people. A generalised alienation occurs, arising from a realisation of the worlds' unaffectable infinity. There is a profound questioning of the rational, and, with evidence from the study of infinity structures, it is realised that logic has a limit. Set theory arises as the study of the infinite, while confusions at the sub-atomic level of science undermines absolutism. Einsteins theory of the changing nature of energy, mass and speed is appropriately called `The Theory of Relativity'. In essence, it becomes realised that no complete description of the world can be made, and this is borne out in Godels work.
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5. Postmodernity. Encouraged by the growth of computers, individuals tend to see themselves as a finite system that processes information rather than an immortal soul. The generalised ideas of Chaos become prevalent, and physical systems begin to be seen as informational processors. The notion of information as an absolute good (`information wants to be free') leads to a growing pluralism and to an extent offsets the alienation of modernity.
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Clearly there are parallels between Ruckers ideas and those of De Landa. It's beyond the scope of this essay to look further into this, but both views share a paradigmatic construct. The bulk of this essay looks at something beyond Ruckers Math-centric analysis, however, and pushes into the combination of an informatics with identity.