What is Radical Recursion?

Recursion or self-reference is a key feature of contemporary research and writing in semiotics. The paper begins by focusing on the role of recursion in poststructuralism. It is suggested that much of what passes for recursion in this field is in fact not recursive all the way down. After the paradoxical meaning of radical recursion is adumbrated, topology is employed to provide some examples. The properties of the Moebius strip prove helpful in bringing out the dialectical nature of radical recursion. The Moebius is employed to explore the recursive interplay of terms that are classically regarded as binary opposites: identity and difference, object and subject, continuity and discontinuity, etc. To realize radical recursion in an even more concrete manner, a higher-dimensional counterpart of the Moebius strip is utilized, namely, the Klein bottle. The presentation concludes by enlisting phenomenological philosopher Maurice Merleau-Ponty’s concept of depth to interpret the Klein bottle’s extra dimension

The Generalised Liar Paradox: A Quantum Model and Interpretation

The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth-falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m)^m dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous 'time' dynamics is possible: typical truth and falsehood value oscillations are described by Schrodinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of 'truth-value by inference' projectors, (iv) time invariance of unmeasured state.Comment: 13 pages, to be published in Foundations of Scienc

Speed of light on rotating platforms

It is often taken for granted that on board a rotating disk it is possible to operate a \QTR{it}{global}3+1 splitting of space-time, such that both lengths and time intervals are \QTR{it}{uniquely} defined in terms of measurements performed by real rods and real clocks at rest on the platform. This paper shows that this assumption, although widespread and apparently trivial, leads to an anisotropy of the velocity of two light beams travelling in opposite directions along the rim of the disk; which in turn implies some recently pointed out paradoxical consequences undermining the self-consistency of the Special Theory of Relativity (SRT). A correct application of the SRT solves the problem and recovers complete internal consistency for the theory. As an immediate consequence, it is shown that the Sagnac effect only depends on the non homogeneity of time on the platform and has nothing to do with any anisotropy of the speed of light along the rim of the disk, contrary to an incorrect but widely supported idea.Comment: Latex, 2 figure

Poor Philanthropist II: New approaches to sustainable development

The second title in the Poor Philanthropist Series, this monograph represents the culmination of a six-year journey; a journey characterised in the first three years by in-depth qualitative research which resulted in an understanding of philanthropic traditions among people who are poor in southern Africa and gave rise to new and innovative concepts which formed the focus of the research monograph The Poor Philanthropist: How and Why the Poor Help Each Other, published by the Southern Africa-United States Centre for Leadership and Public Values in 2005

Causal Loops in Time Travel

About the possibility of time traveling based on several specialized works, including those of Nicholas J. J. Smith ("Time Travel"), William Grey (”Troubles with Time Travel”), Ulrich Meyer (”Explaining causal loops”), Simon Keller and Michael Nelson (”Presentists should believe in time-travel”), Frank Arntzenius and Tim Maudlin ("Time Travel and Modern Physics"), and David Lewis (“The Paradoxes of Time Travel”). The article begins with an Introduction in which I make a short presentation of the time travel, and continues with a History of the concept of time travel, main physical aspects of time travel, including backward time travel in the past in general relativity and quantum physics, and time travel in the future, then a presentation of the Grandfather paradox that is approached in almost all specialized works, followed by a section dedicated to the Philosophy of time travel, and a section in which I analyze Causal loops for time travel. I finish my work with Conclusions, in which I sustain my personal opinions on the time travel, and the Bibliography on which the work is based

Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length. The classical and quantum dynamics of a particle propagating in kappa-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the Lorentz transformations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which Planck's constant is zero but the Planck length is non-vanishing. This may be relevant for phenomenology such as observations by FERMI, because at leading order there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.Comment: LaTeX, 28 pages, no figures, substantially revise

The Classroom as a Potential Space-teaching Negotiation through Paradox

In this article, we describe and analyze a way of teaching negotiation which recognizes and accepts paradoxes, such as caring and frustrating the students at the same time and helping them being more autonomous while manipulating them. In this analysis, the classroom is considered tantamount to a transitional space (Winnicott). This way of teaching is not the easiest one for the professor and for the students, as it is shown. But it helps the students to really listen to others, to sincerely try to understand the rational of others, and finally be more creative in the options they propose, all skills and capacities necessary to better negotiate.Creativity; Negotiation; Paradox; Teaching; Transitional Space; Winnicott