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:
“Sitting in that dusky wilderness, under that dark mountain, by the bright river which was full of reflected light, still I heard the wood thrush sing, as if no higher civilization could be attained. By this time the night was upon us.”
—Henry David Thoreau (1817–1862)
“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)