What Frege asked Alex the Parrot: Inferentialism, Number Concepts, and Animal Cognition

While there has been significant philosophical debate on whether nonlinguistic animals can possess conceptual capabilities, less time has been devoted to considering 'talking' animals, such as parrots. When they are discussed, their capabilities are often downplayed as mere mimicry. The most explicit philosophical example of this can be seen in Brandom's frequent comparisons of parrots and thermostats. Brandom argues that because parrots (like thermostats) cannot grasp the implicit inferential connections between concepts, their vocal articulations do not actually have any conceptual content. In contrast, I argue that Pepperberg's work with Alex (and other African grey parrots) provides evidence that the vocal articulations of at least some parrots have conceptual content. Using Frege's insight that numbers assert something about a concept, I argue that Alex's ability to answer the question "How many?" depended upon a prior grasp of conceptual content. Developing this claim, I argue that Alex's arithmetical abilities show that he was capable of using numbers as both concepts and objects. Frege's theoretical insight and Pepperberg's empirical work provide reason to reconsider the capabilities of parrots, as well as what sorts of tasks provide evidence for conceptual content

Spectral analysis of boundary layers in Rayleigh-Benard convection

A combined experimental and numerical study of the boundary layer in a 4:1 aspect-ratio Rayleigh-B\'{e}nard cell over a four-decade range of Rayleigh numbers has been undertaken aimed at gaining a better insight into the character of the boundary layers. The experiments involved the simultaneous Laser Doppler Anemometry (LDA) measurements of fluid velocity at two locations, i.e. in the boundary layer and far away from it in the bulk, for Rayleigh numbers varying between $1.6 \times 10^7$ and $2.4 \times 10^9$. In parallel, direct numerical simulations (DNS) have been performed for the same configuration for Rayleigh numbers between $7.0 \times 10^4$ and $7.7 \times 10^7$. The temperature and velocity probability density functions and the power spectra of the horizontal velocity fluctuations measured in the boundary layer and in the bulk flow are found to be practically identical. Except for the smallest Rayleigh numbers, the spectra in the boundary layer and in the bulk central region are continuous and have a wide range of active scales. This indicates that both the bulk and the boundary layers are turbulent in the $\textrm{Ra}$ number range considered. However, molecular effects can still be observed and the boundary layer does not behave like a classical shear-driven turbulent boundary layer.Comment: 10 pages, 6 figures, Accepted for publication in Phys. Rev.

Wound-up phase turbulence in the Complex Ginzburg-Landau equation

We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to states within a range of allowed winding numbers. The analogy with the Eckhaus instability for non-turbulent waves is stressed. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of allowed winding numbers vanishes. We explain the states reached at long times in terms of three basic states, namely quasiperiodic states, frozen turbulence states, and riding turbulence states. Justification and some insight into them is obtained from an analysis of a phase equation for nonzero winding number: rigidly moving solutions of this equation, which correspond to quasiperiodic and frozen turbulence states, are understood in terms of periodic and chaotic solutions of an associated system of ordinary differential equations. A short report of some of our results has been published in [Montagne et al., Phys. Rev. Lett. 77, 267 (1996)].Comment: 22 pages, 15 figures included. Uses subfigure.sty (included) and epsf.tex (not included). Related research in http://www.imedea.uib.es/Nonlinea

Making Progress Through California Multiple Pathways: Findings from the ConnectEd Network of Schools Evaluation, 2007-2008

High school students participating in 16 California multiple pathways programs generally graduated at higher rates, met university requirements in greater numbers, performed better on high school exit exams and were more engaged in school and learning. This report summarizes a 2007-2008 study of the ConnectEd Network of Schools, capturing positive results as well as challenges. Results are not considered conclusive, but provide encouragement and insight as Irvine launches a larger-scale demonstration: the California Multiple Pathways District Initiative. The report is also intended to offer insights to funders, policymakers and practitioners who, like Irvine, see great potential in California multiple pathways to help students build a strong foundation for success in college and career -- and life. The study was conducted by MPR Associates, Inc., a leading education research and consulting firm

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, spectra given by conformal field theory. The probability of the different configurations in the stationary states of the three models are not only related but have interesting combinatorial properties. We show that by extending Pascal's triangle (which gives solutions to linear relations in terms of integer numbers), to an hexagon, one obtains integer solutions of bilinear relations. These solutions give not only the weights of the various configurations in the three models but also give an insight to the connections between the probability distributions in the stationary states of the three models. Interestingly enough, Pascal's hexagon also gives solutions to a Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few references are adde