Unconventional complexity measures for unconventional computers

Unconventional computers—which may, for example, exploit chemical/analogue/quantum phenomena in order to compute, rather than electronically implementing discrete logic gates—are widely studied in both theoretical and practical contexts. One particular motivation behind unconventional computation is the desire efficiently to solve classically difficult problems—we recall chemical-computer attempts at solving NP -complete problems such as the Travelling Salesperson Problem—, with computational complexity theory offering the criteria for judging this efficiency. However, care must be taken here; conventional (Turing-machine-style) complexity analysis is not always appropriate for unconventional computers: new, non-standard computational resources, with correspondingly new complexity measures, are often required. Accordingly, we discuss in the present paper various resources beyond merely time and space (and, indeed, discuss various interpretations of the term ‘resource’ itself), advocating such resources’ consideration when analysing the complexity of unconventional computers. We hope that this acts as a useful starting point for practitioners of unconventional computing and computational complexity.     

The Indefinite Dyad and the Golden Section: Uncovering Plato’s Second Principle

Scott Olsen examines the philosophy of Plato to bring to light the nature of Plato’s Second Principle, known as the Indefinite Dyad, sometimes called the Greater and the Lesser, and its relation to the Golden Section, ϕ . He responds to the challenge posed in 1983 by Kenneth Sayre, and explains how the the Indefinite Dyad can be used to derive the square roots of 2 and 3.     

Palladio’s Villa Emo:The Golden Proportion Hypothesis Defended

At Nexus 2000, Rachel Fletcher argued that Palladio may well have made use of the ‘golden section’, or extreme and mean ratio, in the design of the Villa Emo at Fanzolo. In this issue of Nexus Network Journal, Lionel March argued that the Golden Section is nowhere to be found in the Villa Emo as described in I quattro libri dell’archittetura. In the present paper, Rachel Fletcher defends her original thesis, comparing the Villa Emo as actually built to the project for it that Palladio published in his book.     

Is There a Future for AI Without Representation?

This paper investigates the prospects of Rodney Brooks’ proposal for AI without representation. It turns out that the supposedly characteristic features of “new AI” (embodiment, situatedness, absence of reasoning, and absence of representation) are all present in conventional systems: “New AI” is just like old AI. Brooks proposal boils down to the architectural rejection of central control in intelligent agents—Which, however, turns out to be crucial. Some of more recent cognitive science suggests that we might do well to dispose of the image of intelligent agents as central representation processors. If this paradigm shift is achieved, Brooks’ proposal for cognition without representation appears promising for full-blown intelligent agents—Though not for conscious agents.     

Tangibles for learning: a representational analysis of physical manipulation

Manipulatives—physical learning materials such as cubes or tiles—are prevalent in educational settings across cultures and have generated substantial research into how actions with physical objects may support children’s learning. The ability to integrate digital technology into physical objects—so-called ‘digital manipulatives’—has generated excitement over the potential to create new educational materials. However, without a clear understanding of how actions with physical materials lead to learning, it is difficult to evaluate or inform designs in this area. This paper is intended to contribute to the development of effective tangible technologies for children’s learning by summarising key debates about the representational advantages of manipulatives under two key headings: offloading cognition—where manipulatives may help children by freeing up valuable cognitive resources during problem solving, and conceptual metaphors—where perceptual information or actions with objects have a structural correspondence with more symbolic concepts. The review also indicates possible limitations of physical objects—most importantly that their symbolic significance is only granted by the context in which they are used. These arguments are then discussed in light of tangible designs drawing upon the authors’ current research into tangibles and young children’s understanding of number.     

Witness and presence in the work of Pierre Huyghe

The relation between “presence” and “representation” is an age-old topic in the arts, but it is further complicated in our time of advanced media conditions. Pierre Huyghe is one artist who has consistently addressed questions of presence and representation throughout his artistic oeuvre, including the role of the witness within it. Considering the sophistication of Huyghe’s work with regard to the riddle of presence in the realm of contemporary means of representation, the artist’s work is taken as a case study for a broad range of artists exploring related topics within the arts and the media. This paper argues that art that interrogates the question of presence within the context of contemporary media culture—from Marina Abramović to Stelarc, Jeffrey Shaw to Julia Scher—asks for being interpreted through presence theories developed within the field of media studies in addition to methods of art theory and criticism. Accordingly, Huyghe’s work is productively related to one such theory, namely the YUTPA model by Caroline Nevejan, which theorizes the interrelated concepts of natural, mediated, and witnessed presence.     

Design frictions

A fusion of architecture and media technology, video-mediated spaces facilitate collaborative practices across spatial extensions. This paper contributes an architectural perspective on presence design, exploring its potential to create architectural extensions that facilitate knowledge sharing and remote presence. With the example of a mediated therapist, taken from the author’s design-led research (Gullstr?m 2010), the paper illustrates spatial design concepts (e.g. mediated gaze, spatial montage, shared mediated space), which, unaddressed, may be said to impose friction and thus impact negatively on the experience of witnessed mediated presence (Nevejan 2007). Mediated presence cannot be ensured by design; however, by acknowledging that certain features are related to spatial design, a presence designer can monitor them and, in effect, seek to reduce the ‘design friction’ that otherwise may inhibit, e.g., trust and knowledge sharing. It concludes that a presence-in-person paradigm prevails in our society, founded on the expectations of trust and knowledge sharing between individuals, and hereby addresses the contribution from presence design to architectural practice—as well as the reciprocal contribution from architecture to presence design—given that mediated spaces currently provide viable alternatives for meetings and interactions, hence with a fundamental impact on all human practices.     

Architecture for Mathematics: The School of Mathematics at Città Universitaria in Rome

One obvious aspect of the relationship between architecture and mathematics is the nature of the actual places designed by architects for the mathematical community. The School of Mathematics of the Città Universitaria was designed by Giò Ponti. Claudio Presta examines Ponti’s design to see how architecture can create an appropriate space for doing mathematics. What is the meaning, if there is one? What are the motives that drove the architect to create a building expressly for the School of Mathematics and not a simple/complex building in which the School could simply be housed? Ponti provides an answer by following the shape of the Greek theater for one part of the building, while the dimensions of the other part tend towards the Golden Section.     

Architecture, Patterns, and Mathematics

Nikos Salingaros posits the importance of architectural pattern in man’s intellectual development, examining how twentieth century architectural attitudes towards decoration and pattern have impoverished man’s experience of both mathematics and the built environment.     

Assessing architectural evolution: a case study

This paper proposes to use a historical perspective on generic laws, principles, and guidelines, like Lehman’s software evolution laws and Martin’s design principles, in order to achieve a multi-faceted process and structural assessment of a system’s architectural evolution. We present a simple structural model with associated historical metrics and visualizations that could form part of an architect’s dashboard. We perform such an assessment for the Eclipse SDK, as a case study of a large, complex, and long-lived system for which sustained effective architectural evolution is paramount. The twofold aim of checking generic principles on a well-know system is, on the one hand, to see whether there are certain lessons that could be learned for best practice of architectural evolution, and on the other hand to get more insights about the applicability of such principles. We find that while the Eclipse SDK does follow several of the laws and principles, there are some deviations, and we discuss areas of architectural improvement and limitations of the assessment approach.     

Evolution of fuzzy logic: from intelligent systems and computation to human mind

Inspired by human’s remarkable capability to perform a wide variety of physical and mental tasks without any measurements and computations and dissatisfied with classical logic as a tool for modeling human reasoning in an imprecise environment, Lotfi A. Zadeh developed the theory and foundation of fuzzy logic with his 1965 paper “Fuzzy sets” (Zadeh in Inf Control 8:378–53, 1965) and extended his work with his 2005 paper “Toward a generalized theory of uncertainty (GTU)—an outline” (Zadeh in Inf Control, 2005). Fuzzy logic has at least two main sources over the past century. The first of these sources was initiated by Peirce in the form what he called a logic of vagueness in 1900s, and the second source is Lotfi’s A. Zadeh work, fuzzy sets and fuzzy Logic in the 1960s and 1970s.     

A new problem for rule following

Wittgenstein saw a problem with the idea that ‘rule following’ is a transparent process. Here I present an additional problem, based on recent ideas about non-Turing computing. I show that even the simplest algorithm—Frege’s successor function, i.e. counting—cannot by itself determine the ‘output’. Specification of a computing machine is also required.     

Rudolph M. Schindler—Space Reference Frame,Modular Coordination and the “Row”

While Rudolph Schindler’s “space reference frame” is becoming better known, its relationship to the “row” has only been recently investigated. The theory of the “row” counters traditional proportional notions, many of which are derived from the principle of geometric similitude a principle which is mostly represented in architectural drawings by regulating lines and triangulation.     

The Golden Section

To Renaissance mathematician Luca Pacioli, it was the Divine Proportion. To German astronomer Johannes Kepler, it was a precious jewel. The only proportion to increase simultaneously by geometric progression and by simple addition, the Golden Section achieves unity among diverse elements in remarkably efficient ways. We explore the Golden Ratio 1: ϕ , also known as the Golden Mean, and its appearance in the regular pentagon and other geometric constructions.     

Optimum design of lattice-columns for buckling

This paper is about the problem of optimization of bracing columns—height of the parallel chords, cross-sectional areas of the chord and bracing and area moments of inertia of the chord and bracing. Optimization parameters have been determined by Lagrange’s multipliers method—inequality constraint functions. Total mass of the construction has been selected as the objective function. Criterions of buckling (general buckling of the bracing column, local buckling of the chord and local buckling of the bracing diagonal) and criterion of deformation are used as the constraint functions. Numerical examples are performed by usage of the obtained theoretical solutions.     

A Justified Plan Graph Analysis of the Early Houses (1975-1982) of Glenn Murcutt

The Justified Plan Graph (JPG) technique was developed in the late 1970s and refined in the following two decades as a means of undertaking qualitative and quantitative research into the spatial structure or permeability of buildings. Famously used by Space Syntax researchers to uncover the social logic of architectural types, the technique remains an important, if not widely understood, approach to the analysis of the built environment. This paper uses the JPG method to undertake a three-stage analysis of the early houses of Pritzker Prize winning architect Glenn Murcutt; the stages are visual analysis, mathematical analysis and theoretical analysis. Through this process the paper offers a rare application of the JPG method to multiple works by the same architect and demonstrates the construction of a series of “inequality genotypes”, a partial “statistical genotype” and a partial “statistical archetype” for these houses. Instead of seeking to uncover the social structure of Murcutt’s housing, the paper analyses the architect’s distinctive approach to ordering space within otherwise simple volumes or forms. The ultimate purpose of this analysis is to offer an alternative space-based, rather than form-based, insight into this architect’s work.     

Physical Limits on Self-Replication Processes

Using few very general axioms which should be satisfied by any reasonable theory consistent with the Second Law of Thermodynamics we argue that: a) “no-cloning theorem” is meaningful for a very general theoretical scheme including both quantum and classical models, b) in order to describe self-replication, Wigner’s “cloning” process should be replaced by a more general “broadcasting”, c) “separation of species” is possible only in a non-homogeneous environment, d) “parent” and “offspring” must be strongly correlated. Motivated by the existing results on broadcasting which show that only classical information can self-replicate perfectly we discuss briefly a classical toy model with “quantum features” — overlapping pure states and “entangled states” for composite systems.     

Reinvention of interorganizational systems: A case analysis of the diffusion of a bio-terror surveillance system

Innovation diffusion theory proposed that adopters—whether individuals or organizations—sometimes reinvent an innovation as they gain experience using it. Reinvention can enhance (or impede) the likelihood of an IS innovation’s acceptance and further diffusion. This paper reports on a case study of BioSense, an interorganizational system that was designed as an early detection tool for bio-terror attacks and subsequently modified to better serve this need as well as to operate as a public health system for pinpointing geographic clusters of dangerous/acute disease outbreaks. By examining the interplay among the political and organizational dynamics and technical properties of the BioSense system, we shed light on processes affecting reinvention in an interorganizational context. We discuss our findings in light of theories of the diffusion and reinvention of innovations. We use Rogers’ (1995) list of factors supporting reinvention to structure the discussion of the fidelity and uniformity of the innovation within the processes it supports in adopting health services organizations.     

Basic principles of mechanical theorem proving in elementary geometries

At the end of 1976 and the beginning of 1977, the author discovered a mechanical method for proving theorems in elementary geometries. This method can be applied to various unordered elementary geometries satisfying the Pascalian Axiom, or to theorems not involving the concept of ‘order’ (e.g., thatc is ‘between’a andb) in various elementary geometries. In Section 4 we give the detailed proofs of the basic principles underlying this method. In Sections 2 and 3 we present the theory of well-ordering of polynomials and a constructive theory of algebraic varieties. Our method is based on these theories, both of which are based on the work of J. F. Ritt. In Section 5 we use Morley's theorem and the Pascal-conic theorem discovered by the author to illustrate the computer implementation of the method.