It turns out that hyperbolic structures are very common in nature, and the place where lots of people encounter them is coral reefs. Sea slugs, and a lot of other organisms with frilly forms, are biological manifestations of hyperbolic geometry, which is also found in the structure of lettuce leaves and kales, and some species of cactus.
Margaret WertheimOne of the great sources of employment for people with Ph.D.s in geometry is the animation industry.
Margaret WertheimI have an abiding interest in how ordinary people produce knowledge, and what it means for individuals to know the world. I thought I'd be a theoretical physicist because I love physicists' views of the world - I find general relativity and quantum theory thrilling - but I have always felt uneasy with the idea of an Ultimate Truth. One of the functions of science is to help us instrumentally; it helps us to build things like microchips and GPS satellites. But another function of science in the modern world is to help us feel "at home in the universe".
Margaret WertheimSeeing and playing with physical objects can enable access to symbolic ideas. When I studied physics and math at university it was all done through equations and textbooks whereas artists go to art school and start making stuff; they fling paint at the walls, they dance and bash things together with giant bits of metal. Our society has come to think of science as being a very abstractified thing, and art as being a materialized thing.
Margaret WertheimAlmost all major scientific projects today are huge collaborations, yet we still have this public obsession with the idea of the individual scientific genius. One of my goals as a science communicator is to celebrate the collaborative dimensions of science, which I think will be critical for facing the ecological and resource challenges ahead. In a sense, we are all corals now.
Margaret WertheimOne way to think about a pure hyperbolic surface is that it's the geometric opposite of a sphere. If you look at a sphere, the curvature is the same everywhere, as opposed to, say, an egg, which clearly does not curve the same everywhere. This is what makes spheres geometrically important. Mathematically speaking, a sphere has positive curvature and a hyperbolic surface has negative curvature, but both have constant curvature everywhere.
Margaret WertheimScience is not just for an elite few. Science's vision of the universe is becoming increasingly inaccessible. That doesn't mean it's wrong. On some levels, general relativity is right, because we have to take its calculations into account to produce accurate GPS systems. Instrumentally, it's correct to something like twenty decimal places. But epistemologically and psychologically, it is not available to most of our population.
Margaret Wertheim