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:
“For the most part we think that there are few degrees of sublimity, and that the highest is but little higher than that which we now behold; but we are always deceived. Sublimer visions appear, and the former pale and fade away.”
—Henry David Thoreau (1817–1862)
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)