Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

A Poetics of Designing

The chapter provides an overview on what it means to be in a world that is uncertain, e.g., how under conditions of limited understanding any activity is an activity that designs and constructs, and how designing objects, spaces, and situations relates to the (designed) meta-world of second-order cybernetics. Designers require a framework that is open, but one that supplies ethical guidance when ‘constructing’ something new. Relating second-order design thinking to insights in philosophy and aesthetics, the chapter argues that second-order cybernetics provides a response to this ethical challenge and essentially it entails a poetics of designing. //// 'A Poetics of Designing' is part of the first book-length collection of texts in Design Cybernetics. It introduces the subject from the point of view of aesthetics. Importantly, the chapter argues that second-order cybernetics circumvents the necessity for a muse inspired artist or genius as a mediator between higher spirits and life, in favour of artists and designers who have true agency. //// Cybernetics is often associated with AI, which is, however, only one of the branches that developed on the basis of the interdisciplinary research begun in the 1940s and entitled cybernetics. I hope the chapter contributes to a better understanding of the second-order cybernetics that has been conceived in close relationship with art and design from the late 60s onwards

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Programming in different languages is like composing pieces in different keys, particularly if you work at the keyboard. If you have learned or written pieces in many keys, each key will have its own special emotional aura. Also, certain kinds of figurations “lie in the hand ” in one key but are awkward in another. So you are channeled by your choice of key. In some ways, even enharmonic keys, such as C-sharp and D-flat, are quite distinct in feeling. This shows how a notational system can play a significant role in shaping the final product