This paper is an expansion of my lecture for David Epstein’s birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3– manifolds. This “logical progression” makes a good story but distorts history a bit: the ultimate aims of the characters in the story were often far from 3–manifold theory. We start in sectio...

In two eye-tracking experiments the role of contrastive pitch accents during the on-line determination of referents was examined. In both experiments, German listeners looked earlier at the picture of a referent belonging to a contrast pair (red scissors, given purple scissors) when instructions to click on it carried a contrastive accent on the color adjective (L + H*) than when the adjective ...

In the children's game of rock-scissors-paper, players each choose one of three strategies. A rock beats a pair of scissors, scissors beat a sheet of paper and paper beats a rock, so the strategies form a competitive cycle. Although cycles in competitive ability appear to be reasonably rare among terrestrial plants, they are common among marine sessile organisms and have been reported in other ...

Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populati...

Upon changing the oxidation state, a reversible open-close motion of chiral molecular scissors, composed of a redox-active ferrocene pivot and an isomerizable azobenzene strap, can be realized only by UV light.