I have decided to try to get through Roger Penrose's 1000 page epic The Road To Reality at a few pages a day over the next year. I have been reading about non-Euclidean geometry. Euclid was a Greek genius who wrote down the rules for shapes drawn on a flat page. You'll be familiar with the idea that the angles in a triangle add up to 180 degrees. This Christmas I made a pomander decoration. It involves shoving cloves into an orange. They were used centuries ago when it was believed that bad smells caused disease. They thought the nice smell of the cloves would keep them from catching contagious diseases. Doh! But look at the triangle below. The two yellow ribbons cross at 90 degrees at the top. Each yellow ribbon crosses the central red ribbon at 90 degrees. So the triangle has three angles adding up to 270 degrees. The normal rules don't apply on a curved surface like a sphere. This is important when studying the Universe because Einstein showed that space-time is a surface that is curved by the gravity.
