Ian Stewart Quotes That Will Inspire You to Live Your Best Life

1. If our brains were simple enough for us to understand them, we'd be so simple that we couldn't. The Collapse of Chaos: Discovering Simplicity in a Complex World

2. On the other hand, these events show real science in action, warts and all. If no one is allowed to get things wrong, no progress will ever be made. It also illustrates scientists’ willingness to change their minds when new evidence comes along or old evidence is shown to be misleading. Calculating the Cosmos: How Mathematics Unveils the Universe

3. The American mathematician Jeffrey Weeks analysed the statistics of these fluctuations for manifolds with a variety of topologies. One possibility fitted the data very closely, leading the media to announce that the universe is shaped like a football (US: soccer ball). This was an inevitable metaphor for a shape that goes back to Poincaré: the dodecahedral space. In the early twenty-first century footballs were made by sewing or gluing together 12 pentagons and 20 hexagons to make what mathematicians call a truncated icosahedron – an icosahedron with the corners cut off. An icosahedron is a regular solid with 20 triangular faces, arranged five to a corner. The dodecahedron, which has 12 pentagonal faces, gets into the act because the centres of the faces of an icosahedron form a dodecahedron, so both solids have the same symmetries. ‘Football’ is more media-friendly, albeit technically imprecise. Calculating the Cosmos: How Mathematics Unveils the Universe

4. This is Lorenz’s famous (and widely misunderstood) butterfly effect: a flap of a butterfly’s wing can cause a hurricane a month later, halfway round the world.If you think that sounds implausible, I don’t blame you. It’s true, but only in a very special sense. The main potential source of misunderstanding is the word ‘cause’. It’s hard to see how the tiny amount of energy in the flap of a wing can create the huge energy in a hurricane. The answer is, it doesn’t. The energy in the hurricane doesn’t come from the flap: it’s redistributed from elsewhere, when the flap interacts with the rest of the otherwise unchanged weather system.After the flap, we don’t get exactly the same weather as before except for an extra hurricane. Instead, the entire pattern of weather changes, worldwide. At first the change is small, but it grows – not in energy, but in difference from what it would otherwise have been. And that difference rapidly becomes large and unpredictable. If the butterfly had flapped its wings two seconds later, it might have ‘caused’ a tornado in the Philippines instead, compensated for by snowstorms over Siberia. Or a month of settled weather in the Sahara, for that matter. Calculating the Cosmos: How Mathematics Unveils the Universe