Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Co-ordinated management of intelligent pervasive spaces

The content of this paper is a snapshot of a current project looking at producing a real-time sensor-based building assessment tool, and a system that personalises work-spaces using multi-agent technology. Both systems derive physical environment information from a wireless sensor network that allows clients to subscribe to real-time sensed data. The principal ideologies behind this project are energy efficiency and well-being of occupants; in the context of leveraging the current state-of-the-art in agent technology, wireless sensor networks and building assessment systems to enable the optimisation and assessment of buildings. Participants of this project are from both industry (construction and research) and academia.

Transatlantic spaces: production, location and style in 1960s-1970s action-adventure TV series

This paper argues that transatlantic hybridity connects space, visual style and ideological point of view in British television action-adventure fiction of the 1960s–1970s. It analyses the relationship between the physical location of TV series production at Elstree Studios, UK, the representation of place in programmes, and the international trade in television fiction between the UK and USA. The TV series made at Elstree by the ITC and ABC companies and their affiliates linked Britishness with an international modernity associated with the USA, while also promoting national specificity. To do this, they drew on film production techniques that were already common for TV series production in Hollywood. The British series made at Elstree adapted versions of US industrial organization and television formats, and made programmes expected to be saleable to US networks, on the basis of British experiences in TV co-production with US companies and of the international cinema and TV market.

Compact cosmic ray detector for unattended atmospheric ionisation monitoring

Two vertical cosmic ray telescopes for atmospheric cosmic ray ionization event detection are compared. Counter A, designed for low power remote use, was deployed in the Welsh mountains; its event rate increased with altitude as expected from atmospheric cosmic ray absorption. Independently, Counter B’s event rate was found to vary with incoming particle acceptance angle. Simultaneous colocated comparison of both telescopes exposed to atmospheric ionization showed a linear relationship between their event rates.

Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Marks, spaces and boundaries

Dictionary compilers and designers use punctuation to structure and clarify entries and to encode information. Dictionaries with a relatively simple structure can have simple typography, and simple punctuation; as dictionaries grew more complex, and encountered the space constraints of the printed page, complex encoding systems were developed, using punctuation and symbols. Two recent trends have emerged in dictionary design: to eliminate punctuation, and sometimes to use a larger number of fonts, so that the boundaries between elements are indicated by font change, not punctuation.

Community strategies in England: reshaping spaces of governance?

The preparation of Community Strategies (CS) has been required of LSPs and Local Authorities in England since the passing of the Local Government Act 2000. This paper examines the process and content of two Community Strategies in southern England as part of an ongoing project to understand their impact and explore ways that CSs may be carried through in a meaningful and effective manner. The paper concludes that the two CSs studied illustrate the challenge faced by LSPs in producing Strategies that are meaningful, inclusive and which follow the spirit of the government CS guidance. LAs and LSPs are also posed with a difficult challenge of seeing through an implicitly required transition from a traditional representative democratic structure/process with a more fluid participatory model. Thus we detect that at least two forms of conflict may arise – firstly with elected councillors threatened by a loss of power and secondly between communities and the LAs who are encouraged to problematise local policy and service delivery in the context of limited resource availability.