The graded product of real spectral triples

Forming the product of two geometric spaces is one of the most basic operations in geometry, but in the spectral-triple formulation of non-commutative geometry, the standard prescription for taking the product of two real spectral triples is problematic: among other drawbacks, it is non-commutative, non-associative, does not transform properly under unitaries, and often fails to define a proper spectral triple. In this paper, we explain that these various problems result from using the ungraded tensor product; by switching to the graded tensor product, we obtain a new prescription where all of the earlier problems are neatly resolved: in particular, the new product is commutative, associative, transforms correctly under unitaries, and always forms a well defined spectral triple.Comment: 15 pages, no figure

Isolated-line commutator-amplifier

Commutator device combines several individual signal-input lines into single output line. Its desirable characteristics are - low input impedances, high output impedance, very high forward-to-reverse transmission ratios, and minimal gating spike coupling to either the inputs or the output

Writing the Island

The historians may call this a failed expedition. For the first time, we didn’t complete a circumnavigation of Isla Espiritu Santo, an accomplishment that usually entails 50 miles of epic paddling in sea kayaks so loaded with food, water, and gear that it takes eight students to lift one. But in March 2010 it was not to be; El Norte, the bully of the Sea of Cortez, had nearly blown us off the beach, and we’d had to remain on the lee side of the island, roaming the canyons and diving the reefs because we couldn’t safely kayak the windward swells. And yet, these students not only managed to learn a thing or two about Baja’s natural history, they managed to go about the business of learning in such a way that they became the tightest community of any class with which I’ve worked. The reflections below, taken from my field notes, are an attempt to figure out what went right, so very right, during an experience that had all the underpinnings of a pedagogical disaster

Solid-state current transformer

A signal transformation network which is uniquely characterized to exhibit a very low input impedance while maintaining a linear transfer characteristic when driven from a voltage source and when quiescently biased in the low microampere current range is described. In its simplest form, it consists of a tightly coupled two transistor network in which a common emitter input stage is interconnected directly with an emitter follower stage to provide virtually 100 percent negative feedback to the base input of the common emitter stage. Bias to the network is supplied via the common tie point of the common emitter stage collector terminal and the emitter follower base stage terminal by a regulated constant current source, and the output of the circuit is taken from the collector of the emitter follower stage

The Buzz about Sustainability

I wear sweater vests, I never split infinitives, I trim my beard close, and I read a poem at the beginning of every class. More to the point, as a member of the English faculty at a distinguished university, I distrust any word that had not been coined by the time my father—himself formerly a professor at a Jesuit university—completed his undergraduate studies. So what am I doing as the faculty director of a Residential Learning Community (RLC) organized around the theme of “sustainability”? In the past 18 months, the university that employs me hired its first sustainability coordinator, held its first Campus Sustainability Day, inaugurated a sustainability- across-the-curriculum program, has looked at ways in which sustainability might serve as a key theme for upper-division courses in the new Core Curriculum, and approved a Sustainable Living Research Project at the undergraduate level. Even this fine magazine has decided to dedicate this issue to the theme of sustainability

Non-Associative Geometry and the Spectral Action Principle

Chamseddine and Connes have argued that the action for Einstein gravity, coupled to the SU(3)\times SU(2)\times U(1) standard model of particle physics, may be elegantly recast as the "spectral action" on a certain "non-commutative geometry." In this paper, we show how this formalism may be extended to "non-associative geometries," and explain the motivations for doing so. As a guiding illustration, we present the simplest non-associative geometry (based on the octonions) and evaluate its spectral action: it describes Einstein gravity coupled to a G_2 gauge theory, with 8 Dirac fermions (which transform as a singlet and a septuplet under G_2). This is just the simplest example: in a forthcoming paper we show how to construct more realistic models that include Higgs fields, spontaneous symmetry breaking and fermion masses.Comment: 24 pages, no figures, matches JHEP versio