Nietzsche’s Epistemic Perspectivism

Nietzsche offers a positive epistemology, and those who interpret him as a skeptic or a mere pragmatist are mistaken. Instead he supports what he calls per- spectivism. This is a familiar take on Nietzsche, as perspectivism has been analyzed by many previous interpreters. The present paper presents a sketch of the textually best supported and logically most consistent treatment of perspectivism as a first- order epistemic theory. What’s original in the present paper is an argument that Nietzsche also offers a second-order methodological perspectivism aimed at enhancing understanding, an epistemic state distinct from knowledge. Just as Descartes considers and rejects radical skepticism while at the same time adopting methodological skepticism, one could consistently reject perspectivism as a theory of knowledge while accepting it as contributing to our understanding. It is argued that Nietzsche’s perspectivism is in fact two-tiered: knowledge is perspectival because truth itself is, and in addition there is a methodological perspectivism in which distinct ways of knowing are utilized to produce understanding. A review of the manner in which understanding is conceptualized in contemporary epistemology and philosophy of science serves to illuminate how Nietzsche was tackling these ideas

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Reflection from a free carrier front via an intraband indirect photonic transition

The reflection of light from moving boundaries is of interest both fundamentally and for applications in frequency conversion, but typically requires high pump power. By using a dispersion-engineered silicon photonic crystal waveguide, we are able to achieve a propagating free carrier front with only a moderate on-chip peak power of 6 W in a 6 ps-long pump pulse. We employ an intraband indirect photonic transition of a co-propagating probe, whereby the probe practically escapes from the front in the forward direction. This forward reflection has up to 35% efficiency and it is accompanied by a strong frequency upshift, which significantly exceeds that expected from the refractive index change and which is a function of group velocity, waveguide dispersion and pump power. Pump, probe and shifted probe all are around 1.5 μm wavelength which opens new possibilities for "on-chip" frequency manipulation and all-optical switching in optical telecommunications