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)
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)