Higher Dimensions
Riemann's idea was to introduce a collection of numbers at every point in space (i.e., a tensor) which would describe how much it was bent or curved. Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe the properties of a manifold, no matter how distorted it is. This is the famous construction central to his geometry, known now as a Riemannian metric.
Read more about this topic: Bernhard Riemann
Famous quotes containing the words higher and/or dimensions:
“When a person hasn’t in him that which is higher and stronger than all external influences, it is enough for him to catch a good cold in order to lose his equilibrium and begin to see an owl in every bird, to hear a dog’s bark in every sound.”
—Anton Pavlovich Chekhov (1860–1904)
“The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.”
—Thomas Jefferson (1743–1826)