Seeing Numbers

In 1890 William James listed several “elementary mental categories” that he postulated as having a natural origin. Among them, alongside the ideas of time and space, he also listed the idea of number. A symptomatic feature of Informatics as well as Cognitive Science today is the tendency not to talk so much about ideas as about their representations, either in the computer or in the brain. Taking up somewhat different perspective I will discuss the way natural numbers, viewed as counts of real or imagined objects, may be experienced phenomenally. I put forth even some speculative ideas about mental number processing by numerical savants

Sixty years of cybernetics: cybernetics still alive

summary:This informal essay, written on the occasion of 60th anniversary of Wienerian cybernetics, presents a series of themes and ideas that has emerged during last several decades and which have direct or indirect relationships to the principal concepts of cybernetics. Moreover, they share with original cybernetics the same transdisciplinary character

An NMR Analog of the Quantum Disentanglement Eraser

We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.Comment: Four pages, one figure (RevTeX 2.1), to appear in Physics Review Letter

III.3 CoRoT’s planets: A family portrait

This book is dedicated to all the people interested in the CoRoT mission and the beautiful data that were delivered during its six year duration. Either amateurs, professional, young or senior researchers, they will find treasures not only at the time of this publication but also in the future twenty or thirty years. It presents the data in their final version, explains how they have been obtained, how to handle them, describes the tools necessary to understand them, and where to find them. It also highlights the most striking first results obtained up to now. CoRoT has opened several unexpected directions of research and certainly new ones still to be discovered

Educational change process: A case study of a rural school district\u27s reading reform

Beginning reading instruction is the subject of much debate in educational fields as well as in the political arena. The product of such debates is often a push to reform reading programs and teachers are targeted as the ones to carry out these reforms. If reading educators have been actively involved in a reading change process, what are their concerns about change and the influence of mandated legislation? The purpose of this qualitative research study was to examine how teachers and administrators initiated and implemented a balanced reading innovation. It also investigated how the Concerns-Based Adoption Model identified teachers\u27 concerns during the implementation of the innovation and the impact of “No Child Left Behind” legislation. Leadership also emerged as a key aspect of change in this study. Results of this study will provide insight into educators\u27 responses to reading reform and how that translates into their current instructional decision-making processes and student learning. It also provides insight for change facilitators and the importance of recognizing individual stages of development within a change process

Strict deterministic grammars

A grammatical definition of a family of deterministic context free languages is presented. It is very easy to decide if a context free grammar is strict deterministic. A characterization theorem involving pushdown automata is proved, and it follows that the strict deterministic languages are coextensive with the family of prefix free deterministic languages. It is possible to obtain an infinite hierarchy of strict deterministic languages as defined by their degree

A Note on the correspondence between Qubit Quantum Operations and Special Relativity

We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences.Comment: 6 pages, revtex, v3: revised discussio