That geometry should be relevant to physics is no surprise — after all, space is the arena in which physics happens. What is surprising, though, is the extent to which the geometry of space actually determines physics and just how exotic the geometric structure of our Universe appears to be. Plus met up with mathematician Shing-Tung Yau to find out more.
This article is based on a talk I gave at the recent John Cage exhibition in the Kettles Yard gallery in Cambridge. Cage is perhaps best known for his avant-garde music, particularly his silent 1952 composition 4′33″ but also for his use of randomness in aleatory music. But Cage also used randomness in his art.
Florence Nightingale died a hundred years ago, in August 1910. She survives in our imaginations as an inspired nurse, who cared passionately for injured and dying soldiers during the Crimean war, and then radically reformed professional nursing as a result of the horrors she witnessed. But the "lady with the lamp" was also a pioneering and passionate statistician. She understood the influential role of statistics and used them to support her convictions. So to commemorate her on the centenary of her death, we'll have a look at her life and work as a statistician.
Mr and Mrs Magnus are a happy gnome couple. Unfortunately, foreseeing that they will be unable to keep up with their rising mortgage repayments, they've been forced to move into my back garden, where they've acquired a plot to build a house on. Gnome by-laws state that the total number of bricks used in any construction project must be 177 or planning permission will not be granted. How can they manage to stick to the rules?
When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.
What happens when magnetic fields get tangled up in knots? This does happen in the Sun's atmosphere and mathematical models predict that once the magnetic field becomes tangled, it must retain some vestige of this complexity for a long time. This enables the storage of vast quantities of energy. In this article I will outline how the notion of magnetic topology helps us to understand the physical situation and draw such conclusions.