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Camillo Sitte’s blueprint for making beautiful cities seized the imagination of the world before falling into obscurity in the twentieth century. Here is his forgotten formula.
The French mathematician Nicolas de Condorcet was a passionate believer in democracy, but he also discovered a frustrating paradox within it: A majority can sometimes vote itself into a logical loop. Mathematicians have now found that this “logical loop” maps onto a strange topological shape: the Klein bottle, a surface with no distinct inside or outside. On this episode of The Quanta Podcast, host Samir Patel speaks with writer Alex Stone about this new connection between this centuries-old voting paradox and the Klein bottle — and how it illustrates just how difficult it is to translate a group of individual preferences into a single choice. This topic was covered in a recent story for Quanta Magazine. Each week on The Quanta Podcast, Quanta Magazine editor-in-chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.
In the UK, many waders nest on farmed grassland, with species such as Lapwing (alongside) and Oystercatcher enjoying the security of an all-round view, often on a flat field. By the time that chicks are a few days old, the grass will have grown and it’s probably time to either cut the field for silage … Continue reading Giving waders time to nest