Edwin J. Beggs

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Following a methodology we have proposed for analysing the nature of experimental computation, we prove that there is a 3-dimensional Newtonian machine which given any point x ∈ [0, 1] can generate an infinite sequence [pn, qn], for n = 1, 2, . . ., of rational number interval approximations that converges to x as n → ∞. The machine is a system for(More)
Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2-dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be designed to operate under (a) Newtonian mechanics or (b)(More)
We discuss combining physical experiments with machine computations and introduce a form of analogue-digital Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of analogue-digital machine are studied, in which physical parameters can be set(More)
First, we reflect on computing sets and functions using measurements from experiments with a class of physical systems. We call this experimental computation. We outline a programme to analyse theoretically experimental computation in which a central problem is: Given a physical theory T , explore and classify the computational models that can be embedded(More)
We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra H associated to the factorization of a finite group into two subgroups. The representations of the quantum double are described by a notion of bicrossed bimodules, generalising the cross modules of Whitehead. We also show that(More)
We introduce the notion of ‘bar category’ by which we mean a monoidal category equipped with additional structure induced by complex conjugation. Examples of our theory include bimodules over a ∗-algebra, modules over a conventional Hopf ∗-algebra and modules over a more general object which call a ‘quasi-∗-Hopf algebra’ and for which examples include the(More)
In the theoretical analysis of the physical basis of computation there is a great deal of confusion and controversy (e.g., on the existence of hyper-computers). First, we present a methodology for making a theoretical analysis of computation by physical systems. We focus on the construction and analysis of simple examples that are models of simple(More)
If we measure the position of a point particle, then we will come up with an interval [an, bn] into which the point falls. We make use of a Gedankenexperiment to find better and better values of an and bn, by reducing their separation, in a succession of intervals [a1, b1] ⊃ [a2, b2] ⊃ . . . ⊃ [an, bn] that contain the point. We then use such a point as an(More)