The minimal perimeter enclosing N planar regions, each being simply connected and of the same area, is an open problem, solved only for a few values of N . The problems of how to construct the configuration with the smallest possible perimeter E and how to estimate the value of E are considered. Defect-free configurations are classified and we start with the naïve approximation that the configuration is close to a circular portion of a honeycomb lattice. Numerical simulations and analysis (...) that show excellent agreement to within one free parameter are presented; this significantly extends the range of values of N for which good candidates for the minimal perimeter have been found. We provide some intuitive insight into this problem in the hope that it will help the improvement in future numerical simulations and the derivation of exact results. (shrink)

Upon doing something generous for someone with whom you are close, some kind of reciprocity may be appropriate. But it often seems wrong to actually request reciprocity. This chapter explores the wrongness in making these requests, and why they can nevertheless appear appropriate. After considering several explanations for the wrongness at issue (involving, e.g. distinguishing oughts from obligation, the suberogatory, imperfect duties, and gift-giving norms), a novel proposal is advanced. The requests are disrespectful; they express that their agent insufficiently trusts (...) the hearer to recognize their own reasons to reciprocate, and the close relationship between them morally requires this kind of trust. This proposal is articulated and situated in the recent discussion of the normativity of requests. The chapter concludes by explaining how these requests may appear appropriate. Agents in these relationships often have standing to make requests, though the standing is lacking in these particular cases. (shrink)

It is hypothesized that iron from biological tissues, liberated during decay, may have played a role in inhibiting loss of anatomical information during fossilization of extinct organisms. Most tissues in the animal kingdom contain iron in different forms. A widely distributed iron‐bearing molecule is ferritin, a globular protein that contains iron crystallites in the form of ferrihydrite minerals. Iron concentrations in ferritin are high and ferrihydrites are extremely reactive. When ancient animals are decaying on the sea floor under anoxic environmental (...) conditions, ferrihydrites may initialize the selective replication of some tissues in pyrite FeS2. This model explains why some labile tissues are preserved, while other more resistant structures decay and are absent in many fossils. A major implication of this hypothesis is that structures described as brains in Cambrian arthropods are not fossilization artifacts, but are instead a source of information on anatomical evolution at the dawn of complex animal life. (shrink)

On concept of Jīva in Hindu philosophy and Vedic literature.

Works of Tran Duc Thao, a Vietnamese philosopher.

Scientific view of Buddhist ethical teachings.